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T HE
C 0 L L E G I A N
St. John's College
May, 1963
�On the Ornamental Cosmos
Charles Antell of the Ritz is walking along the avenue
with his golden hairs glistening and
his fingernails glistening -and
his eyeballs glisfening because he polishes them with a soft cloth
every eveni~g ori.e -~huri.d-red times. --What are you looking
·'a.t,
Charles Antell durley locks?
My eyes my eyes my delicate eyeballs
are mirrors.
The appearance of each new poet is
indicated by a sea1.
The poets are
listed at the end of the volume.
I•m looking at the back of a reflection
(the world sees the world in my eyes)
)eyes my in world the sees
1
�Image
Time, a tart pn tilted stilts
trips boldly through the courtyard.
Her dresses move about her form
Tehee1
she shouts and shakes her hips
at me, _ the drooling watcher.
yes, we fly through the air'
-a pattern of black birds,
crossing and recrossing
f
floating with the ease o - our wings
;
..
upon the cold sky
beautiful alone
beautiful in our changing pattern
2
3
�On a Poet
who is this fuzzy mouthed egotist who thinks he
In this nighttime there is a never ending repetition of rain
and a stirring of small winds across the surface of my cheeks.
I will sit here by the window waiting for your face at the
door, ~
your hand on the handle, and I will remember you.
can own five_ sparrows? .
the period king, word scrambler, jester, peste:r-,
persistent procrastinator, redundancy's minister
. : _:."
~
It was once, passing through a door, that I raised my head
and was awash in yoµr eyes,
that I was swept back into the room from which I had just come
come)
t
um
b
1
to feel the startled muscles of my mouth leaping,
i
and the short moment's blue ocean engulf me.
n
g (i.n
dow
The light comes and goes,
a succession of landscapes and photographs, laughing faces,
waving hands, and two men clasping each other by the shoulderse
A
small child sings as she stumbles,
and you pause to watch her.
nf ·
the st
eps -the night's up
(nig~t
mare
horses leaping)
and singing voices in a
2.!;ce I would come home very cold from school and fall asleep on my bed
wrapped in a red and blue quilt,
hearing the rain outside my window.
Will you come down the hill to the river now?
The dry rain falls upon grey leaves, curling in the grass.
Will you come to this place where I am neither myself nor anyone:
The leaves cover the sidewalk like snow and the rain falls onto paper.
room
faces in the
dark (eyes
fall feet
falling head
falling face
closing
.door .
opening
baby baby
fall
i
Stop motionless against the sky, come quietly.
You will touch me before I can reach my hand to your face.
4
5
.
�Do
± Detec~
a Sudden Change of Fancy?
o squeeze your sausage fingers
your short thick glossy hands with their dry packed fingers
People's faces pop shut
moving within th~ms'e~ ve' . as over hot coals.
s
the top
and witness me squirming in my chair.
Pepsi Cola, say the passionless red letters
my stomach is liquid, the heat within my throat boils over:
goe~
on the bottle
which span the surface (this and something more
~are
warm fluid flowing beneath the still skin.
which I
not repeat to myself):
I see your fingers touch that book,
the advertisement ignores the contents
the brown hair on the backs of your hands,
concea1ment by the congealed exterior.
Oh America --
the strand of grey hair stuck to the; armpit of your jacket,
the selfish small mouth refused tome,
You don your dust colored glasses,
and know the low slow sucking tide of my blood
you trample as you turn away.
as I touch you with my eyes.
If I could pull a chartreuse or purple
mustach from out of my nose
and wave it under your eyes until those same
eyes widened in amazement,
believe me, I would
until you could once again know that I am of
I have never seen your hands,
yet dream of them in deference to your eyes which touch too harshly;
for I am not strong enough to return this clasp of eyes.
Bring your hand to me, one quick touch becoming
substance.
the air is rather thick in this corner, dearie,
you can•t, I tell you, see through it.
the touch of bodies,
the easy blending of flesh before the moment spills away.
6
7
�·..
A Good Case for
- -~,. ..
·
B~~!ity
o I would taste the words, roll them in my wet mouth
slowly tease them with the tongue,
The chandelier's great light
notice the juices, the salty flavor, and remember:
illuminated the programs
do they dissolve quickly, sliding easily down the throat,
that the decorated women
soon forgotten,
and penguin men
or do they remain, pungent aftertaste, memory of delight?
wera :reading (as they sometimes do)
and now as the cutglass chandelier
dimmed
the renowned pianist
Rubinov Stanowsky
slowly walked on stage
quite penguined also
and bowed ever so politely
to the awed audience
flicking back his tail (as he always does)
he sat at the piano
waited for complete silence
raised his right hand
and with one finger
sounded a most
magnif~cent
A
Arose
bowed
and left
for that was all he had to say.
·. . f '
8
9
�The Constant Variable
I
making little shadows of gray
gray and white and brown filled my room
stores stood as fortresses armed with irate .owners
I had white curtains
a paint-peeled door and two brown-streaked windows composed a shelter
and on my bureau was a mirror
doorways were clothed with men trying to escape the hungry cold
I
could see brown boxes against gray
unshaven
I
could see a desk and two white bedspreads
dirty
sometimes I liked to lie on my bed among my furniture
they outlined their building counterparts
and sometimes I lay in the comfortable warmth
and sometimes in the cold
I
- II
had a rug on my floor
it was gray
some winter nights my room was warm when all the rest of the house
dark hurts the eyes
was cold
for one tries to see
it is impossible · to · see in the· ·dark
but then some winter nights my room was cold when all the rest of
the house was warm
I
my walls were gray
:_ · - .....
quiet library gray
can't
:
but then I don't try
. ..:,;
restricted prison gray
. · -,.;·
even gray
red's a little too bright
void of shadow
I want something more subdued
when light came through my window
perhaps something with simpler lines
it settled on my floor and never touched my gray walls
no
in my room I had a chair and a table
that won't do at all
a bureau and a bookcase
that's a nice blue
all of dark brown wood
blue won't do
their square shapes blocked the wall
a room with furniture so square and cornered had gray walls
it's snowing
my room had two beds of dark brown wood
I'll have to wear my galoshes
I hate beautiful sndW :' ~ .
· '·
each had dull white bedspreads
and I liked to run my fingers around the designs that were raised
from my bedspreads
10
soft snow
purring snow
11
..... .
�no
blue won't do
blue won't do
I won't even try it because I know that I won't like it
snow's gray and white
now if it were red
a~d
blue
- . ·~
snow's never red
children should be quiet when it snows
except underneath a sunset
their noise is irreverent
bright red lights
I
think that my bedspread's very nice
paris is red
you can walk down the streets when it's cold and glmv like a
the yellow brings out gray
steel ingot
and gray brings out orange
and the cold wind will sift your hair like flour
and orange brings out green
paris is music
and green brings out red
you can walk down a damp paris street
I like red
I wonder whether red brings out blue
I like those designs too
doesn't anything bring out white and bla9k
red paris
at three in the morning and hear a symphony of silence
complete silence
complacent quiet
you can't start a fresh bottle until you 1 ve finished the old one
a quiet of satisfaction
then you sit and try to stomach stale milk
a room with furniture so square and cornered had gray walls
like stale coffee
or stale wine
I
or stale cigarettes
or stale cheese only that's better stale
hate beautiful snow
soft snow
purring snoviT
blue's stale like milk
but I think it's .s topp.e d
only it's blue
skim milk's blue
the tight cold turns everything to gray
blue won't do
the naked trees and the hard ground
are all gray
snow
winter-beach-sand to run fingers through and make designs
the gray clouds contain the sun
and the sun
like on yellow bedspreads
pushes
and fails
12
13
�but never stops pushing until ~'# finally wins
until bright colors bloom
and down
in some paradises .
stomp
the gray is covered with the white of snow
in the cold
blue snow
with parchment skins cracking
no
and bells
blue won't do
always bells
high bells
III
bells that never went dong
that radio's much too loud
just ding
a little consideration for your neighbors
ding
please
ding
until you leave in the cracking cold
turn it down
and you're claw.pad into the jaws of the· ·roaring subway lion
pass the stuffing
then home to four rooms
no thank you
and a bath in hot cloudy water
I couldn't take another bite
soft white underwear
but it was delicious
smooth
and a stiff white shirt
it's still too loud
with atarch please
make it lower
that should have been soft
inconsiderate neighbors
french cuffs
or button cuffs
french are dressier
yes
your tree
~s
khaki colored suit
quite nice
so brown tie·
the whole street too
just shining with bright
light~
twice around
over
the parade was fun
twice around
the marching
over
with the feet
then through
up
pull it straight
14
and :tight
15
...
�·~~
•
J •
• •
IV
like a noose
he continued
or was it once around
thro~~h
the city
h.er maze.walled by steel
over
ringing steel
and through
whistling in the sky
cold wet steel '
then you take her arm
knifing the wind
and you go dancing
damp shadowed steel
and you drink
silently erect
sip
more dancing
he drifted past the masses of squatting concrete.
and sitting
past t he cracked streets
sip
on which the claws of grinding car motors sent dark
rubber ·wheels ·-humming
and tc:tll:dng
and then everyone stands and waits
and you wonder whether
you are trying to forget the last year
or don't want to see the next one
past the talking lights
laughing
in the rows of mirrors
swallow
v
no more sips
swallow
all so alike ·
and then it's ended
and it's begun
and instead of air there's paper
bits of colored paper
long spiralled bits of colored paper
and the sound of an old tinny band
and ancient songs
16
17
:;
:
.
�Pu12_.e;rty Explored
you see there was this girl
who was beautiful
and built
but her parents were rather prudish
like midvictorian
and they got this chastity belt
..
with heavy l·ea- her straps
t
and they put it on her
and kept it locked
and guess who had the key
mom
so this girl goes around to lawn parties
in the summer
in her lowcut evening gown
with this leather strap showing
it was around her waist
to her shoulder
to her hips
and below
and ±t must have been six inches wide and
two inches thick
which is pretty goddam thick
and she wasn• t particularly infatuated wi.th the thing
so one night
comes this lawn party
and
everyone was on the lawn
and so was she
when this real handsome guy jumps her
but is somewhat deterred by the belt
so she reaches between her breasts
and pulls out this knife
and gives it to the guy
who cuts it off in one stroke
Lord
she says
it's good to get rid of this thing
Notice
·if you will
the shape of her neck (sucli
.
p~~fection)
.
and her bone structure
(truly magnificent)
the nose
(formed with classic lines)
yes, pleci.Se observe
the teeth. ·
aS they smile
(in perfect alignment) .
of course this is a rather poor
photograph
but I .' m sure that you notice
the chin
(bow delicate)
and her lips
(such perfect curves)
is it any wonder
that I love her?
19
�Just One More Amendment Please
Thursday:
Friday:
Monday:
Today my decision was made.
After four years of weighing
both sides carefully, I have decided against it.
Shall write first
draft of letter tomorrow.
Tuesday:
Composed three drafts of letter.
First draft took ten
minutes; second, four hours; third, four hours.
draft as best.
Wednesday:
Decided on first
Shall mail it tomorrow.
Sent letter to Democratic National Committee telling
them I had definitely decided not to seek the Presidential nomination for 1964.
Thursday:
Mailed it air-mail special delivery at 8:10 p.m.
Still no word from Democratic headquarters.
No mention
of letter on radio, television, or in New York Times.
Friday:
Should I have sent letter by registered mail'?
mention of letter.
Still no
Daily. News had an article . on the next to last
page saying that the Democratic headquarters has been deluged with
mail this year.
Was my letter in the .deluge'?
Have others also
sent in letters declining to seek the nomination?
Saturday:
Sent a registered letter to Democratic National head-
quarters saying that under no circumstances would I seek the
Vice-Presidential nomination~ ·: . Mailed at 5:10 a.m.
Sunday: As President I should have inptituted the practice of
mail delivery on Sunday.
Monday: Harper's came out today.
No mention of my letter in it.
Went to news stand and purchased Time, Newsweek and
All had stories on Kennedy and
Tuesday:
u. s.
Rock~f eller,
Reporter.
nothing on me.
Received my subscribed copies of Time, Newsweek and
Reporter.
Still no mention of my letter in them.
subscriptions to Harper's, Time, Newsweek, and
Wednesday:
u. s.
u. s.
Cancelled
Reporter.
Changing only the address and the word 'Democratic' a
few times, I sent letter stating that I should be unable to accept
the Presidential nomination to Republican National Headquarters.
Still no word from Republicans or opposing party.
Sent letter to New York Times asking the question 11 3
the common man in the United States powerless today?•
quotations from Locke, Rousseau, -and Gasset.
Used
Mailed air-mail
special delivery at 5:05 a.m.
Saturday:
Had a funny dream last night; went to read Bible, and,
when I opened it, all the pages were blank.
When I awakened, my
hands were covered with blood.
Weird.
Sunday:
Today I found solace in religion:
Am getting too upset.
what a party ticket, Moses and Christ.
Monday:
Received two letters tod·ay.
Charming thank you note
from Democratic National headquarters suggesting that I try
Republicans.
Also thank you note frdm Republic arts on ··engraved
gilt-edged stationery suggesting that I try Democrates who seem
to be in need of a few declens1ons to seek the nomination.
two letters, one to Republicans, one to Democrats.
to recall exactly what it was that I wrote.
and Republicans received 11:45 a.m.
Tuesday:
Sent
Can't seem
Letters from Democrats
Replies mailed 11:49 a.m.
Sent telegram stating that I would be unable to seek the
Presidential or Vice-Presidential nominations to Liberal Party
headquarters at 4:18 a.m.
· · .,
Wednesday:
Received telegram from Li b-eral Party headqifarters
saying that they were sorry, but they had· already reached their
quota of declensions to seek the nominations.
But suggested that
I try the Democrats or Republicans, or if not, I was certainly
welcome to try to decline in 1968.
Friday:
Sent letter to Liberal Party headquarters asking the
question, •Is this America, Land of the Free?•
Also told them
that it was my privilege to decline to seek the nomination on any
party ticket that I wished.
Though I really had no intention of
declining on their ticket, I told them, because actually I was a
Communist.
I enclosed genuine parchment copies of the Constitution
and the Declaration of Independence with certain pertinent passages
20
underlined several times in red ink.
Miss Rheingold election is fixed.
21
Christ, I'll bet even the
�Somewhere in the Rain
Swing Happy
.
It.. is raining outside now, very softly, and if I stand on
the p()°~ch ~ u,pstairs I can see the ocean and the beach.
I lik_ to swing .
e
around a crowded smoke-filled room
- I .
to the glowing music
1 Why do you ask?
Oh, I suppose it is becauae. 7ou see that
my left foot is still three inches above the grouud. 'Well, do
not worry for ~ have not yet finished getting into i t . In just
a few minutes I shall have my left foot down to the ground.'
to move
an4 glide._
and feel the deep
~sp_ring
st~~-~gs
-~
of
hasfl..
'That is very interesting. 1
inside me
and send me beating
and take a girl
~c~9ss
. w~th
t~e
dark hair
•Yes, indeed it is.
made t·c»o -·s man.:.'
moving room
flQwin~
behind her
1 0r
swinging with me
then spin.. h~r past the
But it's not my fault that the suit was ·
you too big.'
•Young man,do you mind if I use your shoulder to push against?•
tab~es
•Will it take very much longer, for I must be off.'
at which couples huddle over dark green bottles
and see her eyes _ filling with .a
and her white
•Excuse me, Madam, but how did you get into that ' bathing
suit? 1 ..., ..
tee~h ~mj.ling
~parkling
•Yes. But it . will take me only a few more minutes.
only another inch and a half to go.•
light
at the sepsation of moving barefoot
' ". -
_unaware of all that surrounds her
but the muted trumpet
have
•Then go ahead, but ·please hurry.•
happily
so freely .
I
'I may not loo·k 'very desirable with all of me flapping over
my suit, but you should see me when I 1 m all in.'
•You must be quite out.•
·~Vhen?
•
•When you're all in. 1
and the vibrating bass
'Oh, yes.'
tossing her head back
•And I saw the negro boys with t4eir large hands wrapped
around the watermelons, their large black hands wrapped around
their red watermelons.'
like a wild pony
•Pardon me?•
1 Real.ly nothing.
Just a little social significance.
farther have you to go?'
•About an inch.
How much
Just hold still.'
•Do you have this problem often?'
•Every summer.
There, now my left leg is resting on the ground.'
•Can you walk?'
'I'm not sure. I've never tried • . I ~ jv..pt lean until I fall on
the beach and just stay in that position and smile at the men who pass.•
•Do they ever stop?'
No. But they often slow down. They are quite amazed, but, you
see, it's really nothing. What laps on the outside, I overlap on the
inside. Do you see?'
1
. 22
23
�. 'Yes ·, I . think so• · Shall- I help
~you
fall to the beach? 1
'That would be very kind of you. I'll just start tilting,
and then .you catch me. That's very good. You seem quite
experienced in these things.•
'Really? Well, I must admit that I don't get to do this
very of ten, though I sometimes hold the bottom of ladders for
my friends who are climbing them. 1
who is just like her mother
but in tenth gra.de.
Everybody says
the daughter
is just as disgusting as the mother
•Well, how do ybu like what you see, '.'h one:Y,?''
You bought it at Macy's. 1
•It's a very nice suit.
•Why yes, I did.
You're qui t e an observant young man.'
'Oh, not at all. I merely read the label.
on inside out. Shall I help you get up?'
Your suit is
but the boys still
take her out
for just one night.
She gives them what they want
and parts with
The House With the Drawn Shades
o~e
The
sh~des
are always drawn
with . professional discretion.
. Many different cars
park in the driveway
ironic kiss.
No boy's sincere
or cares
to compliment
her brand new
overgrown with grass
dress.
while their drivers enter the house
stay for an hour or so
One day she came to school
late in the afternoon with
scrapes on her freshly bruised neck
and pay her
as they happily leave
acquired from her temperamental
to return again
ma.
She said .they didn't hurt
for more.
Everybody knows of her
and about her and
shows no resp ect for her
but they know
she cried in bed all morning
behind shades drawn
or her daughter
as in death.
24
25
�Unresolved
I Make No Footprints
i •• :
Childhood
In the north sea howl I call
but it has
•Iceberg' .·
has :faded no~
gorie
for· it calls ·to me
but no one hears.
and I follow its becko'riing .finger
Leda with her s·oft fur wrap
with wistful· backward , gla11~:es
draws
a small child's hand.
Adulthood is not here
The passing look, never twice.
yet it lures me forward
Hunchbacks
with hints of future fame
draw second looks.
'When I was a child, I spoke. • •
' •• became
a man, I put • • •
My youth wept of the passion.
and
;
. .
:
implic_a~io.P.s
of hid,den knowledge
and promises of a great love
. -~ .
So I stand an unnamed being
at the fulcrum of the lever
Why
can't I weep now?
I stop to watch myself fill , up.
afraid to step forward or baokward
for I know if I do
the journey to the end
Strange
stopping with no
I did not choose
will be impossible
coffin near.
to ascend
26
27
�Cuba
The day was such
that the wind blew running through the grass
Uncaptured and Unclaimed
and the water lapped at ·the a:o;ck like an angry feline
a cat is soft
the sky was black
and silky
with all the anger of nature
·and ' vain
against man,
its walk flowing
her bastard son.
and graceful
and smooth
the eyes of a cat
are penetrating
or incinerating
the cat is free
Everything could have been so smooth
and chooses only
like a silver thread leading to the moon
to visit man
unbroken by the limits of finitude
But instead
and so does woman
I cut it
deliberately
not with my nails in anger
but with a single thought
28
29
�Riding a white horse,
Wearing a sword,
Singing the song.
Come you travelling fellows.
Come see your father
In the straw.
I am the rational· animal, .
And yet, rationality cannot
'
com~e nsate.
..
The lack is obvious, . . ..
And yet, I kno w not· what it - is.
'·
'
desi,re is there and . cent~_rs itself;
And yet I know' ho.t what- on •. ,
Th~
'· '
Relieve yourself, give in . to. t:W-1.
:(.ee.li~g.
Disassociat~ me . an~ ~ rational~
Do this and I will'- ·believe _
;
Do this and perhaps I will $now
..
Whether the intellect- trav::e.ls. where I go,
The Idiot
Or if the emotion strong;
Is the real me.
Red is Red,
hat am I, a thing which feels,
W
Black is Black.
And in feeling knows the lacking,
But, my good sir!
you must remember the
And in the feeling knows not whether
cause of the integral facets of the colloidal
This is a real lack.
suspension.
1 1 11 find out soon,
The reason for the purple hue, the dew,
For give in I must,
The vapor, the lighting and angle
Though satisfaction, I am sure,
And a million a nd one p e rtinent f a cts
W
ill not be the result.
And bits of extraneous information.
I save me?
I must be wrong!
30
. -~ ·....
31
�Passing the Time
It's a very nice day outside.
I
am in the house.
Carefree
The sun rises, stretches in the laughing sky and sets _
Scattering its purse of summer gold
Friends are all over the world.
While setting fire to the dewy meadows
They are inside also.
It shares the day with the lark's love caress.
_The big city is nearby,
But everyone in it is going someplace.
I h.ave nothing . to do,
And I am much like everyone.
The whole world is . going so. eplace,
m
But it leaves everyone alone.
Perhaps we are all inside the house
With nothing to do but watch,
As everyone goes.
There is the blue of morning: . awakening bruised
Do we really know that they also
In the solitary dawn.
Have nothing to do.
There is the blue of noontime:
blank monotone
Riding high behind a brassy sun.
There is the blue of dusk:
crouching thief
Everywhere and always feasting upon the empty heart.
There is the blue of evening:
frozen
Into dark dreams by hopeless wishing -Pas tel searchers wandering
Starless, moondrugged and alone.
32
33
�.:;.'•
·, ~::
Changeless Night
•. -.
-:.
,,._
....
...~ ~":"- . ·
A · Son:g' by<tf::ii u:}- --~·~; _;;f
.:
(Early Surig Poet-2.;. 936"."97¢1 >·:
· Thou wert black-nippled night
L~..;.t-~-
When ·Will-.. the
On whom the famished dawn doth feed.
..,•:
···:
. fiP'~~~~; '··or-· spri'.ng··.:- ~hd -' the ~oon .tfr..__ ~µ~.µmn
,
~~"i~~~ii:~~!~i:~1~~~~i:·:;~~%~:e~;m:::~e~;
High-.crested night
Unq· ~~/:~'¥1e; -o~~ght:{ m~-ph.,
Whose arched neck bears proud the emblem of eternity.
-~---
Ji~·
.[
Whose song is a whirring whisper of sacred truth.
And night, now you are quiet, busy streets
to ·iook
'c. •--~.- . . -·.'" _
. .
b~ck.~ at
--=··:>
_
Ra;Li~C~gs ~·t, eX'q_~s'.si-tely
Frozen-lipped night
cann~t .- bea:r
I
cl:fase .to be?
my . fo r me r
ki:r.igdqm:·
carved wood and
J.:a t tic es
o ( I in.i:t..Y cu t j a de
Shoulc;l still be there. ·'
._
....
But they · are· . ~<?. longe_ mizie.
r
-
:.__._
,
·\, ... ·.
:'...'.
· ·:
.
'Yo·~- · sir, · how .._~~ch g~ief do ; ou have?' .
y
On which a wayfarer of universal wondering still stops
', '. -·
'·
~;t
·<· .
i$ as a torr_
ent rushing eastward i~·-,the SJJ~_:Lng~'
1 My':_ rief
···g
.
,:i:;.·'
- .
'
·.......
\
! ·-- ~ ·~.:.........
To doubt but then believe because
. .-
·::~- '~:~:. ·.: . :-.. t~· .. .
You must remain our goddess of. relief, · despai.r ·and sleep.
.
·.:~~' \
___
- ..
~,;
;
'.,--:,..:__'.
··. --.
· --·""-·i• .
<61
.
. ,.
,. •.;r-;.:,:--;
I
:';
:-: ·
......
./
-~
. '
-
'..;.{
_;· ·
..
,. ·.
.
,
...
··...
34
,~
..
35
'
~·
.
. -.
~
�..-~·
The Snake-Swift Building of the Years
/
the snake-swift building of _
the years
to crystal clarity
outgrows the tears of youth
to claim the sky -of love
on childhood's wings • .
time's pinions ride the
clo~ds
locked · in siTence bright beneath the· -sun
and more still than the stillness
of the quiet "corr-i·dors . of
memory.
ii
-
~- ···: . ..
a girl's voice echoes
through the hall,
cascading over empty chairs
I people with my eyes into an
audience of love,
and pours from dusty corners
to return to that lone shado w
~,,..~
~ ·=
-
~-
and her song.
the yell?wed light drops gently
to her shining eyes
caresses fleetin gly her hair
and having seen her fades again
to dark .
the song is over
·
and my people smile -- and vanish.
37
__
. _ ______
-,.
........
..... .....
_.
~-~,
�iii
the spring grows green
with memories of .. our lost
loves,
the pale mag:r;tolias. bloom_.
with breasts of thqse .
who slumber in their
winding-sheets of snow.
all we have lost returns to us' ·
but still we mourn.
My uncle, out to impress me,
Took me to the little town'.s chief bar
And introduced me to a friend,
An old Jewish comic
Who had just been playing burlesque
In Miami ..
,They talked for a while together:
My uncle about his depressions and diabetes,
The comic about audiences and crooks.
I
think the old fellow knew
we stand tran$fixed beneath
Why I was there,
the circles of the stars
For he kept his eye on me,
and in their ever-shifting
patterns
we rejoice.
And when he got up to do his routine, he said:
"Before I start tonight folks,
I ant to mention a friend who has
Honored
Us this evening with his presence;. • •"
Politely, the audience clapped at my uncle's name.
My uncle reddened and smiled all aver his face.
Driving home, he asked me:
"Well, what do you think of your old uncle now?",
And whether I liked his friend.
I told him the truth, of course:
I had been impressed that evening with them both.
39
�Not to Notice is God's Great Mercy
The young nurse·
On a Happy Occasion
With the golden hair
By Gad, I hated you standing . there pregnant,
And the remarkable breasts
flaunting your belly, caressing· his .arm;
Moves quietly across the private room :
your glance, by its absence, said plainly _
you'd seen me,
To fetch a diaper for the old woman
as did your sweet smile, and excessive
cha~m.
Who grins senselessly
• •
Upon the bed.
(but at least you st·tt11 cared enough not to.
~orgive
fbr my love remaining when your love was gone.)
me
The old woman we.ts herself, now,
She even fails to recognize them,
The children
The grandchildren
The great-granchild
Who gaze at her from pictures on the wall.
Orsino Observed
The great, full years, invisible to most,
Now even hide from her.
He holds his scret to him,
Of beast and raging river:
, .· Tum}>ling down
See those shrunken breasts,
Young woman,
See that wrinkled crease
Beneath the crown
Which once received sharp pleasure
Falls lordliness, the giver
Of all his virtues to
And delivered splendid sons.
hi~.
But the young nurse
He holds him
self ap a rt,
W
ith the golden hair
To display secret .. sadness:
Hardly seems to notice.
Minor key
Reaching f'or the diaper,
Melody
Her mind is busy elsewhere,
Hints to some his madness,
Planning dinner
But hides the thundering, stricken heart.
For her husband and their son.
Nor need she. notice now. •
Nor should she see. • •
40
41
•
�In his memory.
· .: ·. ·.
But he got old, and
No Final Request
then an artery broke and tpe warm love of the sun
tempered, and
Into the North,
made taut by an
the vital land,
:
neat-set in the hills and built with teeming cities,
Alien climate poured out, and
he came, a long time past,
:
.
•:"":
·.
_:
.; ;
-·
':'.
~
.
1·
.
1• • .:.
•
• •
• • .,t
with it him -- as if
striving, he and the warm love, to find their way back
From the soft, caressing
to the
land of his fathers -his birth-land, flat with its cotton and tobacco ·a nd beans
and peanuts and red clay,
flat and the clay both loved.
In the cemetery,
in the family plot,
Where the thick pine woods
are dense and sweet
and hot in the haze of dust from the roads and feet
of the pickers, and the river lazes east•
there are three azaleas, ariff a .honey-and-bee-heavy
. .
;
wisteria
climbing on a cream-dotted magnolia.
Quiet, haze, heat,
North he came,
heavy scent, rest;
and strode through
that alien, far-from-his-life land, and like so man of his
kind
and so many of his kind there, in the coolness to know
only
1I
dreamed and did, and all his
·'-
am home. '
·
He'll dream about that
Life was sweat and pain.
when he looks out
But he said
it was good, and he had learned of men and ways
wise in
all this,
'
- .--l. -'
from his mountain-cold grave North
: . ~ .. ~
.
;;:
oh~
: _·'·:i:t·.-. ..
and in his quietness.
. .·..
military
.:.
..
And like so many
of his kind, there was
1
down home• always,
b~loved
artd imaged like old satin
glowing fro m age and love.
An alien in an alien place ·
foreign to all he ever knew or loved·
t
forever no more 'down home.•
~
42
- ·; ··
he had a fine
�Summer Days
River Song
That summer was lifted limb by limb
Up in to the. -~r~e
'Bright, splashed-greens whirled-blues
o~ tside
Up into the leaves,
my window,
And from each hight, .
always living,
Over dandelion distanc·es .
clear and clean-tumbling
Completed in a breath by bees,
sparkling sun~reflecting unhindered onflow.
. ,. -
+ :.
In spring tearing-up, clearing', '·
.
swe~ping befor~
.
~
.~ .
Each day was . lifted into morning •
-
My mother .gav·e he.r:
it;
gro~ery
list,
in winter, stillness and lace-lovely
And the birds thr,ew parties in the air,
ice-loving frosted
Yelling their names across in note.s
young water roaring.
To new and old a9quaintances.
And then at noon a string of ants,
Down, soft slow-lengthened
Strung into families of feet,
passage of ·still-deep
Went somewhere .up or down the tree,
noon haat darkening wavering
One step - and brother at a time.
tree-weeping
The wind in_the le_iyes aboye my window
c
moss-bedded fern quilted,
Set shadows moving over the grass,
probably holy -swim holey cow-lapping boyhooded ·'i·i ver,
Over the green leaves on my cup.
-
.
.
..
To
Benny,
our gardener, who drank,
backfloating, or raft drifting
And drove a beautiful red bike
love-counched, soaking up sun.
With blue strea,mers on the handlebars,
Shadows were a bother, like the lawn;
Bend making, and slow-turning
chocolate, crow flow'h . a~d . cat swum,
He turned the sprinklers on both of them,
foam edged
Under our house, and in the air,
The water ringing in the _pipes
·haze heavy tide pushed backwater· ~· · ·
Until my mother told him, Wait,
log-moving swallowing storm spawning
You come back and water when they're gone • • •
fertile ·· replenisher;
but most of all mud loaded, new-earth former,
They struck the passing cars, struck -fire
beloved
Instantly, .and feel in the evening.
untimed and untiming.
I hid my face and cried, afraid,
Until the lion of our company
Slapped me, and kissed me bravely,
44
Lifting me up from the deep grass.
45
�On Sundays, Listening to the Little
On Sundays, listening to' the little
..
Wind shakes
~he
spider's thread,
three-foot singing sensation
The sunlight slips a Ld breaks.
of the National Baptist Convention•:
Then sunlight out of broken sunl:ight breaks,
WindspedQ
;
the all-weathered owner of unnumbered
... ...
~·
..
~
.
•
street-corners, cravats and fiends
and, here and there, himself,
Harry walks out of theY (questioning
fair d·aylight singing) down
steps almost in time, his fingers patted
from one equally through ten, to break
Two Parts Invented
today hopefully yesterday's fall,
and a squat Ever-U!Y!brella Lady
ahoy, ·conducting your car's path away,
goes up in feathers as you go by,
Mister Aftermath, ··who comes and goes
My mind moves on to beauty,
and beauty taken, moves on
and on to ever, ever
moving and overtaken
by waving everywhere:
•Come aboard
suddenly, for always there's song abroad
on certain Sundays, and for sure
Pigeons
1
are we who don't dirt ever,
from stone to stone stepping
in a stream, from ever to ever
in a silence singing, on
and on -- it moves a r:ay.
2
we will scream forever at red light s,
and refreshed by Caution, be thrown
I wonder, by listening,
to wings and blessed by green lights
what am I singing myself,
on Sundays, such
as you ask me, then at once
three-foot ~
singing sensations·
of sweet marjoram and sunrise.•
explain, seeing my confusion,
how my hand seems moving in time
to you, it seems so.
I say,
No w you are seeing things, now
and we sing on together.
46
~.
' ·,: ..
47
• .J
• • ~ - :
�We the Honoured of a Green Land
•and, behold, there was a swarm of bees
and honey in the carcass of the lion.•
·
·Jud~es, Chap. 14,8
'At sea there is nothing to be seen close by • • •'
Sarah Orne Jewett, The Country of the Pointed Firs
There was nothing to be seen close by,
We the honoured of a green land attend this Birth.
the distances were pointless blue,
We who were fed with the cracked bones of birds
until the captain took to drinking
Have this report from a people of the desert,
imagina~ion,
A flowing of spears in the angles of a river.
and as he sailed beyond himself,
And the lion murdered this evening with joy
described the islands and the fish,
Swells like a river in rain of great sweetness,
until his ship encircled him.
like a fool;
The spears in our hands are trembling yet with bees.
And the women paint their
thi~hs
a thousand times,
And yet the captain sailed beyond,
Maddening breathless men with the smell of eagles.
if not beyond where he had been,
Unclosed sores are comforted with seamless cloth,
nor travelling in terms of wind,
A land of green stones is washed.with the spit of
yet beyond knowing where he was;
children.
We the living and the dead attend this Birth.
he could not say how this was so,
except to say he was at sea,
with nothing to be seen close by.
48
�-
--
---
- 4 - -- - - - - -
----
--
...
· Library Rea.:ding Room
minds at work.
the s _
tones of ·~ Jaranes ~
of sand spacing the distanc~s
~
--------...-..
distant WOrldG of th6'ught.
they, we all sit.
e high, echoing room where
turn us all to flurried 'biras.
_,f -
c;;__ . . . . . . . . . . . . . . . . . . .~ _____ _
___
·--
- ------...
�Road Cha~t:
1956
thunder, thunder, thunder, thunder;
run with tar, melts you under,
thumbs to the moon, hearts to the sky,
Fields, fields, many hundreds of green fields,
rounded fields, . caught in ·tfre storm,
and one farmer riding a mule to home.
soul always saying, why, why, why,
and answer the soul with your quiet foot cry,
say that without it your eyes would soon die
Kansas and Arkansas, blackbirds and corn,
everything moves one ' way, the other way,
the stalks in a body, side to side like mourners.
hobogregorians chanting their chant,
Noon and rain, the day like night,
singing their song,
rattling shutters and something forgot in the barn,
screaming along,
wind skips a basket, bouri~i~g fr~~ down the ~lope, towards the
run, run, run, run,
shed.
this is for fighting
this is for fun
search till you find
that holy town
where holier gods
come tumbling down
and grant you forever
the golden crown.
52
53
�The Poem Called Dusk
Dust of horses. Women and dying men. The stones on
the clubs soak red moist into their cold pits, blood
melting into the palmed granite.
The wagon rumbling on,
creaking up the slope.
Then the songa . and the feasts and the dancing and
sleep.)
No baby cries within the new-wood box,
cushioned with used diapers,
Watching the shadows of those years,
squashed against the aged pine-board,
he is dead as his grandaughter,
iron-hinged wagon sidings.
the baby, Betty Shoots-Alone,
her chest wheezing that afternoon,
The small grave over Charbonneau Creek,
swept in grass like the wispy,
sucking and rasping, and racked.
Her death song a muted chortle.
white hair of Grant Iron Lightning
when he stands so still,
The western skies split apart,
watching the spring dances.
and rain flushes gullies in the thin grained dirt.
And his eyes crease like the puckered pouch,
beaded, hanging at his belt.
Lightning sears, a white sheen,
like fear in the hearts of children.
The rings within his trunk have dried
Against the hill, the bearers
tight as rawhide round the rock. • •
outlined like charred trees,
(ornamented with tassels of trader's yarn, bought
for a squaw, five minutes against a deer-greased
thigh, along the slippery, shaded bank of the Platte.
Buffalo glue also, from the hoof, keeps the yarn in
place. And porcupine guard hair dyed vermillion and
the rawhide-covered stick handle, once parchment yellow,
now oiled black with sweat.
The sweat of much fear, solitary, and overcome by
clenching the sweat club tight in the fist, while
galloping at breakneck speed toward the camp of Crows.
The dawn holds her breath. They plunge in silent attack.
or statues aged in coal.
The storm is blunted by their silence.
'What's that bunch of injuns doin' in this mess,' says a surveyor,
peering through the staccato-t8pping rain
on his split-shingled roof.
The man running naked from his teepee.
The beginning
of screams. Sun just flooding up. The heart. The
beating of hooves. Coming upon him -- bewilderment in
a glance -- beside him -- lean over the whipping mane --,
and the contorted spine of a man shrinking from a blow
with upraised arms -- too late -- and past the falling
victim who behind crumples.
The camp now alive with:
The screams and noises.
54
55
�Early Fall at
~~as D'O~,
Nova Scotia
The Home all shut
Dawn; and the swimmer on top the tall piling,-
to night.
Eye dancing with lake. spread· sun, ·
And _
-windows
like lanterns and the wind
Body clothed in a swooning chill.
in the garden.
The deep citadel, · his consciousness-, drawh far within.
Slowly Joaquin pacas,
It lies hot
be neath t he dim portraits.
As a smouldering castle
Outside is coming, is rumbling,
In a moat of ice.
the wind from the shore,
There is only the blindness;
the wind in the garden. -
The wind tearing, deep gulping, ear racking
All night these slight sounds
Blindness, the breath,
~n
inhale~
and shiveririg wrench.
You, morning lake; you, diat:1ond w
·ater.
like guitars.
56
...
his breast
break into the house
from · the garden,
_··.
·57
�Murray~-~
Tambourine
Into the waves at Les Saintes Maries
Mother, you were walking home.
the gypsies and their children
One late afternoon I saw you from my window.
carry the
Beneath
And half down the block that reeling fall day,
stat~es.
~~e
soaring of a tern,
A dust devil, whirlwind, leaf-wheel,
the gold and leaf encrusted figurines
caught you with the packages in yoµr arms.
disappear before the foam.
And on you, swirling up in leaves,
A child stoops
a spiraling_ ramp spun round.
the chanters
throng. past -- and,
· piclti.ng . ~p
the empty shell of
You cringed, slit your eyes,
and half enjoyed the honor, center;
this sudden excitement.
a hermit crab, sees the beautiful · sky,
the Span.ish cliffs,
The swallowing caramel sun
the sleeping hulls of beached boats,
had gulped all the street, the parked cars,
the painted saints,
and the dying grass.
and the long white splash of each wave.
wind had gone mad 9 carrying
There, too, the
(frightened stallions across the sky)
clouds moving in throned splendor
toward the east,
clouds shifting colors by the minute,
luminous, holding their hues like carved thunder.
Mother, you looked so fresh.
Your cheeks were blushing with wind.
In the warmth of the house,
now with us,
your ha:;1py eyes.
You were smiling,
and we all put the packages away.
58
59
�Anabasis:
Pra"\rer ..
Night streets in the Old City,
Passage me to. these,·
grass-stoned,
Voices in the gardens softened by lilacs
tree~leaved.
Lord, passage me ·to·.:these ~·
··
And the heavy quiet:
among · waves of fall~ fields.•
Soon I will say I've forgotten her name
Now, yes, hold me in ·theci, -
Or the way it was for us and Athens,
tigh t, ·unwavering, · Lord"
Held secure thbse days
Between the mountains and the sea.
It was after all only spring and the islands
Barren hills, some fig trees and lemons,
Wild poppies bleeding in the rock shado ws
Terraces of wind and barley
Mounting up from cobalt se a.
She moved at my side dark,
'
.
-
Hair braided color of the nights,
Moved silent and knew the path.
W carried almonds and oranges from Piraeus
e
And wine from Rhodes.
There were not many gulls.
For a while we rested on a high place
Watching a boat pass lost in distance
Then spoke softly in her language
Descending to the sea.
In the water
sh~
laughed at Yiannis' warning,
Gave me lemons and garlands of the waves.
Together we took on form and context
From the singing rocks above.
That night passing the place where we had bathed,
From the boat watching the cove recede,
Dark in dark she turned from me
. 60
61
�(continued)
IvTine ·
For something had passed between us
And now was gone.
These things I
Altered chords of Chopin, early
Spring is over here.
Wisteria
r~placed
Concerto and late Ballade,
by roses.
The flower is ripening fruit.
Brilliant peacocks molting in· .the park
Send victorious.
consider mine.
~hildren
laughing with · plumes
Through the chalk streets.
Summer heat begins.
Berceuse and Barcarolle.
Courbet's self-portraits and the spot
Of cadmium orange in almost any Corot.
That corner of a park
Where paths cut angles beyond the bench
Now the
islan~s , ~E? ..
behind me
In the south -- Mykonos, Aigina, Seriphos;
Now the Canal and Corinth _Gulf again
To last days at
Ithac~
and Corfu,
Bound for Brindisi and the West.
Roll the names
o~
the tongue.once more • • •
Of desolation, and the lamp
Casts artificial light on unnamed trees,
All amateur theatrical.
A small hotel in Amsterdam, a town
In western Denmark, askew amalgam
Of marzipan and fears of the North
Sea.
The language is forgotten.
The season has passed. ·
A billiard room in Sweden
Where I entered feeling thin and sweetly
Foreign.
I
let a Swedish sailor
Photograph my fierce portrait of someone else.
Perhaps the things that I consider
Mine are least mine.
62
63
�Percussion
Learni,ng .
This is the recipe
For etude and elegy
I made my ·f irst right turn
Wit and melody
On a corner of · upp_er Broadway.
Wood agai1iSt metal
Hammers the harmony
F~lt is the feeling
I was ?- . learner
And asked my teacher
\ivho 1Has ready to reach
For the duplicate brake
Whether the pedestrians
Hush and sonority
Were volunteers.
Are kinds of percussion
Fearless,
The movement of muscle
Those pedestrians,
Is merely mechanical
Packaged, beparcelled, peram.bulat_ed,
All well-know legatos
Didn't, I dare say, know from which eighty
Entirely illusive
To which eighty they ambled.
And the teacher, his ears
Oh factual physicist
Attuned to wheels within wheels,
Author of overtones
Ignored my joke about the volunteers.
Harken to history
Rush to redecible
Etude and ele gy
Sweet sostenuto
The sounds of my century
Steinway and Bechstein
Are boxes of mystery
64
65
�Overhe a rd
Do you, Barry, remember that escapade in Harrisburg?
Do you (0 News from Nowhere, the smiles) Barry
Remember (puzzles and peartrees) that amazing escapade
In Harrisburg?
Remember the escapade here in the City
Sixteen Eighteen
Far from the bus station and the Susquehanha
Coastal and incandescent
'Why do these gentlemen wish to throw me out
Alert in the chorus of college-boys
Of the window?' asked an obscure Bohemian secretary
Who catch Dinah or Martha on that underrehearsed rebound
Before he was unexpectedly exfenestrated and miraculously saved
Between the bars
By a pile of castleyard rubbish or an angel of God.
Thus to be flung into History, and by one's Fall
Where culture is bound in new rows·
Introduce three decades of winter, delusion and war?
Linked and in a line
Or merely as one for good measure, to show
Like the uncut Strindb erg on half the shelves of Stockholm.
That the ignorant often are accidentally in castles?
Go ahead, Harry,
Mis-spell the Mickey Mouse song
But whisper the words, whippoorwill:
Some children should be
epice~e
and not overheard.
O Barry, or Harry, there's a puerile nastiness of tongue
The language of lady philosophers
And of the uncertain momentum of Show Business.
Keep talking, canary,
In Metropol itself
There's Nowhere like Harrisburg.
66
67
�Pygmal~on:
A Sapphic
Concerning
Pr~,v".1:~.l
Here you stand, a promise and a shadow,
Consecrated formerly, born once,
Standing nakedly
Just begun in heat of conception,
Your beauty flies from you.
alon.~,
Now consummated.
Standing nakedly alone,
Limbs entwined began, in a moment,
Place and Time.
-Th~
chisel and mallet
Laid aside, the ivory, breathless,
Lacked gracious movement.
And seeing nakedness
Peering flatly at you from your mirror,
Your image and your body mingle incestuously,
And thus beget the idiot monsters
Of that too-reflective loveliness.
Place and Time:
how.dark, lacking motion,
Lacking form; an echo entwined in
Mists, until the light.of· desire,
Standing nakedly with me,
Your beauty flies from you to me.
Chaos informing-,
Standing nakedly with me,
Shapes anew the · forms ·;of.-the artists
Loving father, most gracious mother.
Join your love, and be consummated,
Daughter and sister.
And seeing me conceive and comfort you,
I recount you to yourself;
And thus your nakedness, through me,
Begets our union's singularity
Your true nakedness.
68
69
�I
I
A May Morning
Five A. M._
_
On the Edge
Randall Court
Annapolis, Maryland
The purple fabric of Richard Strauss
---
Swathes the room with Don Juan •
.
Dark; but darkness somehow luminous
We've finished the cigars and wine,
As whispers of fog enfold the town.
So filtered cigarettes and beer
Abet our musings as we stare
Damp; but dampness warm as a caress
Wavers --
almo~t
Through the smoke at our game of chess.
sea-spray, almost rain.
We sit on thj, edge of something strange
Night; but night has never been like this ,
And shift the men with a beery lunge.
So palpably flesh, a courtesan
The shortening cigarettes glow orange.
The smoke swirls, and there's a swell
Breathing on the face-a phantom kiss,
And ebb in the music.
Soft, as softly come the sounds of dawn .
But somehow nothing seems to change.
Ashes fall,
Here is the lamp that lights the game
And defines our own positions.
Far
Beyond this coza nimbus, space
Recedes into the dark and time
Drops into an infinite square
Of smoke and music, chess and beer.
70
71
�Deep within the woods,
half-sleeping in a glade
and I was left al.o ne•
I heard a sudden nois€
Running to the place
and saw her being led .
where they had di.s appeared,
by two men through the trees.
I -only saw the tracks
She hadn't any clothes;
left by something hooved.
her hair was wildly down
There was nothing there,
and swung below her waist.
no traces · of the three.
Their skin was golden-brown,
I searched the woods awhile
their hair was curly, dark,
and never found a thing,
and from wliere I sat,
but still I se• .:m to hear
it 1ooked as if they wore
their ' laughter echoing.
baggy pants of fur.
It shakes the very ground
The laughter of the three
and thunders in my ear;
was not forgettable.
the madness of that sound
Completely frightening,
is more than I can bear.
it was not a sound
that I had ever heard.
Theirs was urgent, low,
hers hysterical,
somehow wanton, eager,
somehow filled with terror.
They held her by the arms
and hurried her along,
and all the forest sounds
crescendoes as they passed.
I struggled to my feet
and called out after them,
but they were quickly gone.
The woods again were still
72
73
�Behold the dolphin standing on its tail
ALBANY, GA.; BIRMINGHAM, ALA.; GREENWOOD, MISS.; ETC • • • 1963
Accepting a piece of herring and the applause
Of the sun-suited crowd for whom it has
I will stop saying 'Yes sir' tomorrow,
Jumped hurdles, juggled ten-pins, tossed a ball.
And when I stop they all will understand.
He and his brothers once killed sharks for sport
I know that there is more hate in the land
In the green Pacific far from any port•
Than my new bravery will undergo
Without new walls of fear, but I will show
Behold the dazzling white peacock.
It struts
Myself before their pallor and withstand
With boundless, unfathomable pride,
The leaping heat from the flames that I have fanned,
Spreads and rattles the great white fan,
And crush these walls of fear by shouting:
And stalks its mate behind the bars,
I will walk where I damn well please, and sing
Amid the tinfoil, candy wrappers, old cigars.
My song even to white men in the street
Can it live in there?
Who curse as I pass.
It can, it can.
I don't fear abuse;
Scream, call the cops, you can do anything
Behold the sarcophagus.
It looms immense
In the dusty room, amid the bones,
But change my mind -- my song is :!..!!][_ sweet:
No compromise, no deal, NO, I refuse.
Amphoras, weapons, and rubble of ancient stones.
Far from Egypt, the Sphinx, the sand, the Nile,
The weight of the pyramids; the ageless smile
Smiles on regardless of time and circumstance.
A museum piece:
the ancient awe of death;
And now we threaten life itself -- the earth.
Behold the bomb.
Must everything be sacrificed
To mankind's ugly needs?
He already uses
Nature's most elegant constructions as he chooses.
But it is clear that this does not suffice.
And mankind -- foolish, clever, brave and vain
Will treat himself no better in the end.
74
75
No!
�To .. the Night
Darkness,
Night, night
Soft wings of shadows· ·
Beat, beat;
Upon the earth, the shadows fall
Across the greying fields of grain, of wheat,
And barley and oats;
Across the cities and the towns and the villages,
Lights are going out, . ··
Men are going to sleep.
Darkness
Night, night
Soft wings of darkness
Beat, beat.
As on a greying cloud, the last rays of sunlight
Shine down on human endeavor;
People are coming home; nightwatchmen are going to work
along with scrub women, and janitors who like ancient
farmers across the . dirty floors throw sawdust like seed
and reap the harvest of the dirt and grime and soot of the
city by the day: which is cleansed by the night; commuters
travel on
bus,~
on train, on car towards home and wife and
children and supper . and evening papers and sleep,
And sleep and love. and rest until,
Until the morning and the day.
77
�W
idm:1' s Lament
Communion at the Mass of Midnight
0 Lord, I am full of unsaid things,
I remember racing clouds
I love the beauty of thy house,
I looked up and saw the sun.
But as for me, I walk in innocence,
With
Thy will be done.
In my soul, I had no care.
Chanting I mount thy altar:
But now he's dead, 0 God, he's dead,
Glory to God
And now, what shall I do?
Glory to God
We knew each other that first night
Glory to God,
We loved and were one without the light,
I will go to the altar of God,
I looked up and saw darkness
To God, the gladness of my youth
But was not alone.
Singing yea,
But now he's dead, 0 God, he's dead,
I love Thee;
And now, what shall I do?
0 Lord not my will but Thine,
Th~re
With mouth open
A ball beneath my navel.
Singing
I felt it there with probing hand
My Lord and my God
.
,•
- -
f~esh-thrown
rice in my hair,
was a lump beneath my chest,
And in the . night lay still;
My Lord and my God
And silent and mysterious
My Lord and my God,
A knowing smile crossed my lips;
And the wine is mixed ·with water.,
I hoped it would be a son.
And God becomes . a C.hild. ·
But now he's dead, 0 God, he's dead,
Existence contains. a Child which contains existence
And now what shal.l I do?
Which contains a Child which contains. • •
'l)he ringi.n g of·· the bell;
It was mid-December, the second year,
Chanting at the _altar of my youth:
But then, 0 God, my man was there;
Sed tantum die verba
My map was waiting at the foot of the stair.
Sed tantum die verbo
But now he's dead, 0 God, he's dead,
Sed tantum die verbo,
And now, what shall I do?
I must go and cover my face
The baby grew strong and passed a year,
The
cry~ngbaby
filled my ear.
Lest I drown in unsaid things.
79
�And we were married four.
And now, what shall I . do?
But on this day he forgot to say,
•Wom·an we•ve been married four
It was ten and two years,
And we had three, and I expecting a fourth,
And four to this same day.•
When he came home so soon and early;
cried
- And -cried' some more,
I
I smelt the liquor on his breath;
•I•ve lost my job, woman' he- said to me,
And locked him out the bedroom -door.
•And you with a fourth and having three•;
But nbw he•s dead, O God, he's dead,
O God, why won't you let me be?
· And now, what shall I do?
But now he's dead, O God, he's dead,
But then next day, he ·came walking in,
A tinkling in his hand
And now, what shall I do?
But things worked out, and they stayed four:
A twinkling in his eye
And then I cried and cried some more,
Three boys and a girl.
And how that man, he loved that girl
And hung the music box above our door~
But now hel°s dead, o ·God, he's dead,
The girl and the three.
And with these four the Lord, he let them be.
And now, what sha11 -· r do?
But now he's dead, 0 God, he's dead,
And sometimes-yet, \vhen I'm upset,
I reach and turn the- key
..
'
And now what shall I do?
I told him once, I told him again,
And listen
And then I told him once more,
And li:sten
Until it sets me free.
But now he's dead , · 0 Gotl , he's , dead ,
•Don't work so hard, you're not that young;
And ·now, what shall I -do'?
He· wasn't as good as I would have had,
And he wasn't as bad as: I would have taken,
But he was good to the children
And kind to me;
And being that, I let · him be.
. But now he's dead; -0 ·Gad; he's dead,
80
Pay heed the cough that racks your lung.•
He laughed a t m
e,
A woman.
But now he's dead, 0 God, he's dead,
And now, what shall I do?
The nights they grow this season cold
And I feel for where he should be.
But warmth there is not,
81
�Burial of a King
And love there is not,
And neither is there he.
But the bed grows cold
As I grow old,
With my memory.
But now he's dead, 0 God, he's dead,
.And now, what shall I do?
'And Uzziah slept: with his fathers, and they buried him with
his fathers in the field of the burial which belonged to the
kings; for they said, He is a leper: and Jotham his son
reigned in his stead.'
Chronicles 26:23
Uzziah' s dead.
Upon the hill they buried him
Amid the field of millet.
The valley of the kings,
For thus the king should lie,
Buried with his ancestors.
Jotham twenty-five
In the time of Isaiah,
Lions of Judea,
Jotham twenty-five,
Only twenty-five
Cried,
For a leper died.
And the wind blew cold and steady as they left.
82
85
�Song o-f ' the Bride.groom
· How shall I build the house of our love
H~:Vl. shall . I. l.ay o·µr · bi:>y{~r? .
With
flow~rs
thrown fresh and marybud· dew,
There I will pluck the flower.
With drifts of sunlight and honeysuckled dew,
Image in Color .
don't call it love, for
the grass is wet with
tears or dew
(but green as green)
and the sky is pink-tinged
There we shall spend the ·hour.
How shall I say of our loVe my love
How shall I sing of our yo"uth? ·
With lilacs and lilie~s- and lavender rue
With melodied singing of small birds above 1
There I will sing of my love unto you
like carnival candy
and bitter with remembrance,
for the water's tossing back from
self to self,
(forced acceptance)
and the lost clouds are pulled driftlessly
There we will sing of our love.
by,
my tongue is purple when I finish the
grapes
that grew these summers,
(and I am tempered
with the endless hurt)
.. _.! !_. -.
# ..
.;
· · . --.
but don't call it love.
86 ·.
�After Reading Descartes
On Reading J aizies •J Qyce_:-.
a moo cow came out of
.. -·
;. I ; '
r, ..
The world is fathoms and fathoms dark
and lonesomely empty
thin blue air ·
as a mind on a fire-bleached
(gauzey, effervescent
as red apple glass
stained against the tongue)
moo cows just don't suddenly come from the
into inevitable deception
artists don't have friends
they're free, and happy?
. the meaning of time
the color of tears
the edge of the ·. sky
(my daddy is an artist
and I can ' t come out to play
my daddy is an artist
so you'll have to go away)
create
order from chaos
pres~qt
bumbling their way
ask me another:
searching for rationality
stand still and straight and (lo! a second coming )
but where did he come from?
historical
mountain-top,
The world is fathoms and fathoms deep
and incandescent as red wine bottles
burning dully in
fitful dreams that
do not end with the midnight
who goes in the night?
hark:
be still
and listen:
order is a beautiful quiet
The world is fathoms and fathoms dense
and tangled as braids
that are slept on,
we have no choice -and there are not enough mountains left
88
89
�Dialogue
My sister is dying and nobody cares
nobody cares
at
is very
something like a pigeon's neck
.he said
all
My sister is dying, but nobody's crying
(though she
---Iti~
small)
My sister is dying, but nobody knows
it's hidden with a terrible lie
Nobody knows it, so nobody shows it
and no one will even try
My sister is dying, I know this well
And it is all too true:
nobody knows it, so nobody shows it
and there 1 s nothing I can do
My sister is dying and nobody cares
all colors of the wheel . to catch
the sun this morning
(a formidable magician)
---somehow like a medallion my grandmother
· had
(long before she died)
making her cheeks
smooth and rose-color soft
---The very young and very old he said
full of worn phrases of love
and despair
kissing me slowly
nobody cares at all
My sister is dying, but nobody's crying
(though she is very small)
---my grandmother died and
her medallion
(won for an unknown honor,
bought for fifty cents,
ages ago)
was buried with her
90
91
�Symposium
---The sun he said does not touch the
dull gray of graves, not
the mind makes the judgments:
lambs, going off to
their bloodless slaughter, follow
in winter
merry
nor spring
the plastic piper whistles
nor summer
and the tears of joy
nor fall
er tears of sorrow
just pigeon's necks he said
kissing me
dried by wind dreams
(there is no language of the mind,
you know)
the mind .tak.espossession:
pretension, late at night
and early day
watching moons crawl pearly
to consequence
and lone
(there is a sadness of the mind,
you know)
the mind can destroy what
the mind possesses:
and you are there
before me,
in dusty armour
and tarnished silver,
away from the war:
undestroyed
(you must not be mine)
92
93
�Poseidon
I
We live on the strand of a wild dream
The fish we eat are haunted with the dead god
.·.
The old tyrants are rubbed into the coins
And moonbeams work magic into our soil.
We live in the filthy ear of Poseidon
His sea washes music and seaweed in my soul.
Time has poured the
-~~icky
Stories in our brains
· •.
Death runs with an oily pulse iri our blood
And this sadness is our
~~ace
and plague
The foresight of a poor man is limited and unhappy.
II
Never wander lonely into Poseidon's marble· shado·w .
Make this distance a ·ditch and abyss
Build these rocks into a . thorny garden, ·a heartless fire
Never drive into your deepest wall a silence.
Silence is a thin noise
A gold cover is the sound of moving silence
We will be a naked unadornment
It is a strange story that makes it so
But home is best an empty place
Quiet nothing the only god
A raindrop and a glance will make us warm
95
�v
Never mention any death the stars suffer
Forget the green that stays buried in the sea
Will you hear me?
These sun myths must cease.
Must I scare and shout now?
.III
Must I lose you for awhile in the explicit?
Say once that moon means fixed beam
The orb a shiny rock
If you tell a friend that your husband is a child,
Say that tides wander, a little lost
If you whistle distractedly, if you demand an endless excitement • • •
Say that waves follow a twisted circle:
nothing more.
Someday what an ugly man means will infect you
But never, tell that moon and water dance together:
Only God kno·ws his joy
And his Word hang limp somewhere
Forget the evil of white flesh in another room
Then,you will visit the cracked temple that serves Poseidon.
There is no watered world gone, drunk by fish
VI
No Atlantis in any realm
A~l
But .
things exist and all things are true
~e are not poets
In that ruined hall the daylight your eyes carry will go out
Your mind will steam and darken
And your love drain away into a shadow
We cannot' believe all things
Leave them in their pity
Please, cover them, ·f or they . are naked and crying
At last, the rich gloom his gauntness casts will become a person
Your torn mind, in their dark land, will lose itself.
He will give you many pictures
IV
Connect only what keeps your life
He will teach you his eyes and his tongue
His lips Hnd his swollen neck
They are all beautiful truths
Sing nonsense to make children dream easier
I warn you most, you are my One
You stand a stone placed ,there:
Our time has its mouth
All the broken hills, every departure,
And you are too sad on its edge already.
Every song that rips its hair will stand with you.
Ask him all questions, present him each unhealed wound
Say quietly that colors bother and pain
And like a clean rose that dies a stink
His godly fury will pound your silence into a sea.
96
97
�~-
I Am A War Poet
Dark moon, mother love -Without breadth or number.
The cold candles are melted and bent,
I remember
With huge thumbs of wax pressing down on the velvet.
Similar evenings, alive
_·- ,
11-
.
Some went out this morning and will be replaced
When she was, would give
By dowagers of this town who will nurse them
Herself to her
(Candles are dear now) through their first urges to die.
lover~
The Sun, my father.
Mother love alive:
The candles are a sort of memorial to those who died
Captured in mirrors live,
From this town -- I do not presume to call it mine.
Open to the eyes
Of the sea.S
One can almost name the candles -- some are hunched
Whose surfaces break into plates that shine.
Under a shield of their own wax created by the draft.•
In some the wick is long and the . flam~ steady. · ,.
At times I cannot stifle the laugh
That ;r~sh:E;'s' · thr~~gh my. .tee_th as these candles parody
Their namesakes, and comment tellingly on those who rush to replace
A certain candle, keeping one lit from the other in a sterile
generation.
The rest of the church is simple -- a few old men
With half an eye on the icon in front, above the shuddering lights,
And half an eye on their loose hands which they gather in their laps.
That figure on the cross has annoyed me.
I wonder,
Would the men whose skin hangs in loose folds robe-like
Respect that icon if the face were twisted as it would be in the
present war'?
Would they admire a gilded figure with a tube up his ass
Being given an enema of acid, stripping the pride of pain?
It is easier to worship the pride than just the pain.
98
99
�The Skin Diver
; :
:_ ·-
... ..:- ~:...
- __ _:~· .:,___
-
.
Outside, here in the soft spring rain, ,
~he _wate~ .~p~ats_- .
Perhaps he sat on sand
Off the end of the slates of the church
Onto a brown cold cement which is like
The cement is
slowly _ chip~ing
away
One night, and
di~ease-roughened
skin.
now~
Watched this colored whore
Roll her dark breasts .and wear
Lace ribbons bubbling over stones
And as I walk down the street, I am thinlti-ng, remembering •• •
Remembering how
~he
rain then tittered
And the dust faded into itself.
o~ ~he _
tin plates
He saw her where
The walking yard emptied.
The food bolted, the cigarettes crushed quickly.
It was a sham, that picnic,
attempt at
t~at
even .- ~
And let them ride
was taken,
Went back to the tediu.m of .betting . _ .
pools on J..iberation
. . ·.
. .
.
·
.
wh~n
I didn't fight; I only went
Stands in it, sawdust and crowd noise.
dru_nk, I would show.
~o
see them die.
I remember one, his huge gol,de_ head in my la~, smiling slowly_
n
,
Sleepily.
Under the power of her big blues voice
With the brassy jazz of one-night
,
D-day or some day when the pool:s would be over• _ ...
I even have scars which,
She played wf th side men
Who would always be side men,
~rass.
And I and the others, I who could not fight,
That combed her hair. ·
His armor clashed as he rolled; his sh1eid falling
away.
Or maybe it was
A tinny, up-tempo chorus
Where she rolled her eyes
And laughed outrageous
A few screams from the horses cou1d . be. ·.hea;r.d.,. _
.,,. -
Loud.
And then I was taken away, pulled rp~g;rly, :u~_,__ my ..lap .
On a beach one night,
.
.
.
~
From under his head, my outr,~ge ' v~o-~~!1-t :.· ..' .-:
Until I was smacked with the f .lat o f .a broadsword
.
.
-.
.
And laughed at.
:
'
~
.
(They eve.µ 'ilvinked .at
~
e~c_h ot~er.)
That was some years . ag<;:>. :· I , s_ ppoe_:J . had _missed my chance.
u
e
Maybe he stood
A beach on a point of land,
And saw her dark legs spread
Around him.
His palms began to sweat
When he saw this brazen
Black whore stretch
It sticks in my . craw to weep. . syllablet;;_~ ;. -:, : .-·
- .
. ...... .
.
. - ..
Over a bar of sand
But come now, 0 Muse, tell me • • • t
:
And hum -- no blush
~
.
;
~
As if she didn't see him.
See she sung for him,
100
.
101
But he could
�And wanted him to come
But those huge stone
To see if he was man enough for her.
Lips, wrinkled, almost puckered, swung
Shut and crushed his spear gun.
It took lead around his waist
He looked around then
And a clumsy spear gun
And saw she had flung away
And artificial lungs
Her street-corner smile and played
To match her song
every note for keeps.
Once she was up and really _
wailing.
enough
She rolled around his boat, moaning
He was man
Soft, teasing his haste
He scrambled into his boat and saw her
As he began to make the dive,
Moaning, still rolling around him.
The dive to seek her ·loye,
He swore at her and cried,
To find and take her love.
There live
to try one night.
And threw at her the lead belt.
There giant clams unknown
To him; he was new
But in · 'th~ water it was a feather falling:
To giant clams.
Lower, - i6wer, slower still, ·
He was down to bottom slopes
To blacked-out deeps
Where water hissed in his ears-
Where it too wouid roll and sway
And strangled light to cold. green bars.
· ' Whe!f= A~bius, king of jazz
The kelp in tempo swayed --
Comes to blow this brazen hussy
Ev en he was pushed and returned,
Up, to make her big blues voice
Back and f o r th a bov e. the giant cl am •
Sin g his tune, his tempo. Rave notice.
He was
Too close,
Maybe even bumped it; he was
Too excited and far too
~eep.
The clam itself is sort of soft
102
103
�Voyage of the Killarney
December, 1959
I
Syruping the brain
The palate itched to madness
By the sour-lemon, pupil-cutting mast.
The sea is a fearful place of dreams
The sun stood high, mercury-speared
Backing into the rivers of life
Melted the siren-wax and day-long gold we heard·
The caustic salts of bottomless
~oundings
And whales weave together with perches
Barnacles noiselessly swallowing tP.e sea-scream.
Our faces squinting toward the cool fishes
Swimming the ocean-lymph like shadows of diamonds,
Nibbling at our mossy skull.
Day burst past the silly sail-cloth tourniquet we set and
The sea-lungs breathe and pinch the pleural cavity of thought
Bled the dark 1 ning cloud-stuffed sky.
And visions of shark slash by
Tom talked the stars into existence
Ripping into the lonely nuclear sinuses of time.
Metaphored the sleep-stabbed giant's eye to gleam.
The tackle whistled in the wind-night.
Squid and octopi, startled, move away then
We slept dreaming of crystal porpoises.
From the chartless corners of the brain-wash
Arching their backs against the gargoyle.d weight-wet of thought
III
Working their knuckles on the unhourglasse_d sand-_gri ts.: of the mind,
At dawn we rubbed the seagulls from our ears
The ear listens then and in the sea shell _o_f. . the skull.
Our lashes rocked the boat- scraping at fog
It hears the algae munching on the sea-feast
The dampness clinging like larded elbows;
Salivating on the rocks the crisping foam of endless appetites
We drove it out with whips of coffee
For long creations still undreamed.
Filled the sails with bacon gusts
II
Charring those mists to forgetfulness.
That sloop knew the stir and smell of humans
And we went sailing on that shrewd sea
Thirty feet of tight-caulked pride
Noses pressed against the glassy air
Bright work sanded to . the soul.
Gulping the wind-scuff
It found the sun at eight breeding over the foredeck
Like infant birds mother-beak.
Bright as the dream-bite.of sharks
Sails snapped and down the furrow of the tongue
Curing, curing the weary, water-logged sea.
That teaked thing cruised,
104
105
�Southeast to the Trades we went
The Woodcarver
Jib hammocking the eye-long breezes
Mains'l, sea-berry full, webbing the handstretch up that fat sky
When I was a boy there was an old man
The day a timeless sun-journey into dark.
And dark,
shadow-panthe~,
Who taught me chess; he had been my grandfather's friend:
came on
A craftsman in wood: he carved his own chess men;
We saw him drop soft-pawed to the deck
And once he had made a sweet-toned violin
Devour our eyes and eat his way
Which he played for us sometimes, in the evening.
To the sea-murmur in our brain.
IV
He was born in the Black Forest; his name was Grimm:
And then Nassau!
A lovable man; but his art had no sale.
That dream poised in a sky-riot
It was factory stuff people brought him to mend.
Rose in the ripe eye
He went on at his musing and his lathe,
Like a whale-burst sea!
Turning out bowls and curios, unpaid.
God-like we nodded.
And then went in
My hand vein-ruin on the tiller
Tops were the only sellouts of his trade:
Shapely spinners of hard yellow wood,
Felt my sea-youth gasp and suffocate
Slim as a hornet and spiked with steel;
On the brittle land-air.
They would split a dimestore top at a fall,
And, Jonah-sucked, we headed in!
As a fighting cock might spur a barnyard fowl.
And I saw Time relearn the creases in our eyes
Jonah-sucked, we headed in!
I have not his white beard or his wrinkled skin,
But I like the notion of that old man.
I like that honest way of the neglected crafts .
I am told surrealism is the door
To make a man modern like Rene Char.
I say I have bowls to make, or a violin;
I will even turn out tops now and then,
l
Small things for child-hearts to spin.
If such they please, of such we have heard:
'Forbid them not, for the kingdom is theirs.•
106
107
�Suppose I have kingdoms they do not share;
They are closer at least than the smart fellows are.
Why should I sing in the falsetto choir?
I will go back to the dark shop where I went as a boy,
Among strange treasures:
ostrich eggs, a crocodile,
Carved clocks and pipes and puppets; there let me stand
By the white-haired companion of one for whom I was named,
Watch him choose from seasoned wood something with a tough grain,
And turn it slowly to a polished form,
As he leans in the cave of light by his whirring lathe.
I have been thinking of a collection of poems, of which
the title-number would be"The W
oodcarver", and the sections
of the book suggested by phrases from that poem.
samples.
C.G.B.
109
Here are
�•Little Tops'
M Apple
ay
Queen of Night
.
.
All night I have kept you waking
In the slow unrest of love;
May_.~pple is your flower 1
Cre~am-wh-ite, .wit.h.d:rawing ·~ ·
Hardly noticed under its leaves,
We have seen the gray moon streaking
The
hills of home,
war~
The long moonlight probing
The fringed lake and the grove.
Now the day
... . . ..
And the
i~
breaking
~ay
birds are shrill;
Reason comes creating
Until we bend down
And
see the green tent
Fi1r~a :with glowing,
. .Ana·· our .sense reels
Under a smell like
The .ripe odor of fruit.
In the blind depths of the will;
And to the world of making
I must follow the day's spell.
•
But you, my love, will shade you
Deep in the sepia grove.
Sleep, my soul's soft shadow!
I would not have you move,
Till the moon and I shall wake you
To the slow unrest of love.
'•
110
111
·.
. : ..J
�'Something with a Tough Grain'.
Renegade
Gilbert, Swamp . and Blackbird
Having flown to Newark after two weeks of Mississippi,
The thunder came and we paddled into the tooth of it --
And running with all bags across the road for a city bus,
Waves, wind and rain, prognostications out of Lycidas:
The cheapest transportation,
1
That fatal and perfidious bark'
~-
I sit down in a Number Four full of smoke and .laughter;
a canoe built
By the wife's father for himself alone, sunk to the gunnels
A mechanic haranguing the driver about nuts and bolts,
And wobbly as quicksilver -- What should I care?
Then off to his grape arbor and how he makes wine;
Having with me again the master painter, neglected Don
Voices, scrambled, converging from all sides:
Quixote of the brush.
'Well fer cryin 1 out loud, ya can't do it that way. • •
. .
Mopping water from the bottom,
My shirt for a sponge, we came, as the rain cleared,
•I must have fleas.
To the overgrown creek's end:
Begins to scratch I feel things crawlin' on file •• •'
beneath a rock-oak slope
Soon as the double-crossin' cur
And flanked with pine, a blue-green swamp of reeds, the tide-
'Didn't rain hard?
Flat surface hatched with allizarine dead stems.
•Christ, did she think she could break it up and not pay?'
Across
Are ya kiddin'? · rt flooded the place.'
From the crabbers' shacks and long sleek boats, by a bridge
At my side a Negro w~man, . having every right
A quirk of decay has turned to an heirloom from a Chinese
To be there, and damned well knowing it --
Pen (where a redwing blackbird flies from the swamp nest,
And not a drawling plante! or wif e-and-sla~e-holding
Creaks like a hinge, that opens to music, rupture of gold
Caucasian toting his coon gun
And vermeil from black flight and the sunlit spill of the
It was home, down there, I stayed at, thought I enjoyed it.
trill),
We reach the wooded shore.
The painter squints for a focus;
Now I heave the rib cage and gulp air,
Snuff up the Northern city;
I withdrawn to a hummock of moss, lean to a pine
Surprise myself, mouthing:
•By God!
And write -- nothing to celebrate but the fact of sharing
It's good to be in a free country again!m
Again the thunder-and-sky-reflecting tide-swamp world
That is ours, and the rusty creaking of a coal-black bird
That flying breaks in wings of flame and -- yes -- song.
112 ·
113
�'Polished Bowls'
The Fire
Barn Swallow
A swallow skims low over the field,
Turning and darting as insects rise.
I see the blue back, orange breast, forked tail,
Pursue the motions, the bank, the dive,
The swerve in flight, a snatch at swerving flies.
He sees me also, bends his course
To skirt my presence, flutters, cries.
The fire was slow. kindling; it was damp wood,
Old, and moistened by the earth and rain.
Two times I rose to mend it from your side,
Stirred the wet sticks and blew the smoldering ends.
Then in the clear cold night and clearing of the wood,
We two, under the_ stars, hearts not young,
_
And wet with time's worse rains, forgot the fire -Until suddenly it was there, each kindled point
I find him beautiful; I only guess
At what he finds, beyond that prey.
I am not one to take the world on trust
Probabilities remain, and this is probable:
The flight of his outwardness, the stance of mine,
Harbor like visitants, some angel I,
Enforcing another, to take us by surprise,
A brightness huge and fierce, a living flame,
That sent up sparks to coil across the dark,
Earth's poor matter assaulting the night sky,
A trembling moment of immortality
Such was the constellation of our love.
Banking in timelessness, intrinsic, free.
We lay afterward a long time
On the plain ground, earth, where we are bred,
And watched the lattice of transfigured wood
Slough films of gray ash and renew its glowing;
And in the cleared space o+ the dew-cold forest,
Saw now and then how a few last sparks would rise
To that brief ecstasy among the stars.
115
114
�'Strange Treasures'
Baby Blue · Ey.es
Ripe as a fruit. and globed with youth
Gulfs of living water, down and down,
And paired with eyes as luminous <as blue,
Once we have gone far enough
That break in glances like ·a changeful sea,
Into the element, that fish
Stands before me the most vocative girl
With jaws and teeth, called picua,
Of twenty years of teachfng; ·J..ips inquiring;·
Does not repel, but beckons;
May she write her theme
·o i love, on which she is
;-.
knowledgeable.
We pursue, she withdraws
Into the deeper water. • •
My eyes swim with blue,
•No doubt,• I tell her," 'that will be satisfactory.
Or if I close them, wave on wave
Relate it, if you · can, ·to Penelope and Calypso. 1
Revives the swinging pools,
How peerlessly her stirring leaves the room
Where fire corals show
And leaves my silence stirred with crazy jazz:
Blood crimson in the blue ·. ·
•Jeepers creepers, where'd you get them peepers;
(I am one who has downed
(Loosers weepers) where'd you get them eyes?•
A philtre of such love
There is no return to the land.)
Earth 'reels in the sun, ·
But all around it cool,
Laps .the luminous blue.
Where the blown
Cres~s
wave ripples
of white, and the sea
Glints with purple, th~re the reef,
Down swaying fans unfolds
The summons of its caves.
ll6
117
�•To be Played in the Evening'
Strar·~ er
The smile on her._
The
A
e~ghty-year
old woman
stranger in the house
~ip_s. \_.
_·--·
_. She calls into the darkness
(Further than ·consciousness, the wind-blown candle):
She has lived in half her life,
And which now she has to leave,
•Here Kitty,
Kitty, Kitty;
Taken to another room
Come Kitty, Kitty;
For the children to pack her things,
Come Ki tty.
•
Stumbles . among cases, files,
Relics of extinguished hope~ • •
A towering darkness on the Delta,
Lightning, thunder,
Great oaks
whi~ped
in the wind.
The lights go off together.
She understands a moment,
Then forgets.
Gropes from lamp to lamp
Trying to flick them on.
Bewildered,
Calls the cat.
..
(To bring the years' lost kittens from the storm.)
A door slams in the wind,
Trees brush the window.
Rain in sheets goes solid on the screen.
She trips and stands smiling,
Lost, but not worried.
(It is we who draw back in fear.)
118
119
�The
School of the Seed
Mock~_21 gbird_
If the school of the ant teaches there's no laboring
That plain gray bird with the blur of white on the wings,
Call him an artist in the modern sense:
In the winter, better go to school of the seed,
A mountebank, a charlatan, a mimic,
Like the hierophants for whom grain was central
The most quarrelsome bird,
(Except a grain of wheat fall to the earth and die)
Fighting all day with the robins;
An oval door into the saving kingdom,
Well, he makes amends.
The halls of Demeter, the season's dying.
It is spring now; the nights are warm,
Surely you can read the signs of the seasons?
Full of blossoming.
A snake also in the stars, the largest constellation,
Outside the window, roses
There is
Distill themselves, contending with the honeysuckle.
Coiled almost encircling the pole, and he holds
On the black tree magnolias are white in the moon.
In his folds the round kernel of the world.
I wake as the leaf-fringed hollow,
If the wandering soul must go into those caverns,
Already filled with fragrance, overflows with songo
Let it go, like Orpheus, singing.
I·
In the dim solitude I give him leave.
Water shines in the sun; low sun .on the waves
Let him be as cursed all day as he pleases,
Sows the whole surface with light ._.
If only the midnight reaches of the soul
Pale winter light down the leafless trees, cold
He quicken with this water,
On the leaf-brown floo:r. where death - is ., working.
The well that flowed in the garden
Close your eyes and turn your back to the sun;
From the rock, under the tree of life.
Dark requires your presence in his caves.
121
�Sold
Where
Where I wandered
The timid thrush was safe
In the snow
And pushed aside ·
To sing sure silver notes at dusk
And orioles built their swinging nests
Wet dark leaves
To find arbutus
Long before the spring. • •
Where I looked for
Jacks-in-the~pulpit
In still dark privacy. • •
Where I gathered
Sumac's candelblooms
With bittersweet
To last me all the winter through --
White violets Where I wandered
Wild geraniums
Watched
When earth was soft with birth
And growing green smelled sweet .
Listened
Felt
The turning of each season
W
here I reached and cut
Is no more;
Armsful of dogwood
Birds will never sing again
To grace a room
With ivory-white bouquets
Through these acres
And there will never be a newly green
And where I heard
Or flowers.
The peepers j ingling tune
Then later listened
To the plunking of fat frogs
Gargantuan machines have slashed
Across the woods
And rawed all growth
In love --
To painful roots
And man has built
An air-conditioned structure
With ample parking space.
122
123
�The First Poem Written
The waves march in like a regimented army,
each line precise and unwavering,
and they send themselves against their foe,
falling lifelessly back among their ranks.
And in time they conquer.
·:a..
125
�There, through the
Poem
doorw~y,
sitting _in dust alive with sun,
There is a crate of lemons
washed ashoi-a · ~ •· > :· ,.. ·
is an old man.
How sad he seems
in the
haze
of the late day
where the waves
with his eyes closed.
break into foam
And little children from the past
and I may go and spend an afternoon
taunt him with laughter
throwing them
sung by rote.
back at the sea
He smiles,
hunched by the door,
. ··
silent in the noises of the street.
127
126
..
�Back Country Poem
An Orange Cockroach
burning the insistent
sile~~e.
of gothic love:
The wooden owl
st6o~
in the _yard
scummed and eaten
by weather:
equipment
jerking
jesterlike
in lunar . perambulat;i.ons;
an old bird
ico~
of the folk
who put it there
waging brittle fury
in fernmoist rooms of love:
out back of a house
on a mountain road
miming pyrrhic war.
underneath the trees.
128
.1 29
�The Sea is a
Did you ever sit
port of Cat
and wait for the moon
to turn into a globe
that sallies forth continuously
from a slice?
in all of its parts:
a jade bandit
and master of cat-shy turbulence
I believe that
the man who lives there
an old cat
calls it
•self-realization.'
but still
with uncomfortable eyes.
130
131
�Five Haiku
Spring Love Poem
a beetle crawls
toward the stem of a lilac;
rain begins
to
Only
fail.
one evening ·
in the late leaving
fish entangled in
hours of sun
a net -- no more the subtle
I knew a girl
motion of the tide.
on a bridge
(and the water
the echo of a
so far below
falling leaf penetrates the
as we leaned in wind
stone on which it lands.
to watch the boats
returning
going away;
a black and white moth
and we speculated on them
on a weed by an old well;
laughing
water reflections.
as strangers laugh
when they.wish to love)
a broken bottle
and I took her hand
lying in the sand:
her eyes
the sea is angry today.
were heavy orange
were other
snowflakes disappear
little
on the surface of a pool
suns.
instant memories.
Finally, she turned and walked away
calling back goodbye.
a fly's wing falls
in the morning;
the earth's awakening noise is great.
132
1
133
�It Was at a Certain End of Being
and we were sitting on an iron stairway
watching the evening disappear
willow leaves dropped in the heat children called cats meowed
playing _
q_l;1ilc1-ren 1 s · game_s _
suddenly stopping to sense in the manner of cats
performing the critical ritual of spiders
and these not order but
there were cosmic questions being asked
fantastic explosions
and the sun was leaving them unanswered
WE WERE TRUE REVOLUTIONARIES'!.;
leaving the night
we waited
and made jokes but our eyes contradicted us
we watched a spider a good omen we said
the cats and the children are our spokesmen we said
and all of a sudden
we had methods all at once we were eager for night
we assumed greater identities
especially that of the spider \Vi th the acuity of eight eyes
especially that of the candor of childre·n
especially that of the prophetic code of the cat
we became fanatic decipherers of the cosmos
we ran down t he s t airway we ran down the street
questing
off to ask <lirect'io- from those who knew -:·the -night
ns
defying all systems of order
opening up reality
we were giants and voracious beastminds running against the
deadline of the sun
134
135
�A Poem Whose Origins are in Queen Mary's Garden, Regents Park, London
To Hear the Wind Blow in Furthest Summer
The circling gulls
swing up and interchange
when the butterfly bush
is like a last old clown
in endless rhythm
low above the pool in the park
in a lavender wig
occasionally skimming the water
and the crickets cry
in monotony. • •
whose surface
is woodcut by sun ·
giving back
fragments· ~ :·
of white motion
insouciant
as the child with bread
beside the pool
whose smile
is sign of knowledge ··
of complicity
whose hand
by casting crumbs
interrupts the dallied glide
excites the raucous laradine cry
explodes the tinted print of sun
controls
the very nature of the circumstance
sharing dominion of the park with
only those who
sit and.watch.
136
137
�Summer
Song
Out in a sun fo r est
Some Untitled Thoughts about the Supject in General
(A Minor Manifesto)
with a black cat
:
and a bunch of oranges
tramping until .1 . -re:ached
a great-_qutcropping of rock
by a stream.
I sat down
the cat drank
I ate the oranges
and smelled the woods
a toad jumped into the water
·. ·:
The way
the words
run
down
the
page
not so . much their Pi?CUliar meanings
but
what
is done with them
and through them -and
not the visual effect
' but the.
: 4:- ~.
FORM
or capacity to express the development
toad
sun
not the meaning:
my cat
all in the forest
by the rock •.
who knows what
'mice in a flowerpot'
means
or
'in a city a child sits in an
with an umbrella'
all~y .
..
the.se .
and all the rest
are too private I ·don 1 t · care how one has tried
(what about that word 'one' you say
well maybe that's me and you and both of us together
and all the rest of the world
and what the ~ell
it's still a mystery so just look at the poem
don't scratch at it
·· ·
.let it stay there caught on the paper)
think about all of it at once
don't be so God damned condescending
138
139
�The Approaches
there are migrations and interchanges
I.
of the brittly shaken branches
:From
the · wo~king · of the wings of birds
~g9: .. thE?.: f~r.away 1J~r<:].s
_
that work upon themselves much as they work upon the mi nd
above country snow
the sun is untangled from various myths
the noise of the ice-covered branches
and is not abstracted but transmogrified
of trees in the wind
as are the functions of energy
as is the mind
each by the other in conjunctions of cause
the sun
below the birds
IV.
behind the trees
I am as the blackwind and as the sun
I
or essential altering of the structure of contact
I
am the extender:
in which the object is stripped of intrinsic action
I
compose through expansion the final form
and used as a final -axiom
of my sensibilities --
and is not an experience at all
And that which I do is done to me
but a basis
II.
am all the movements of the universe
(the origins are no longer present
(and a certain transcending of vision
or assuption of noumenal discipline)
their implications are sustained as extensions of will
III.
come the circularities:
V.
it is that if I am there
What is · 1eft is. the .future of the mind .
and made critical by the syndrome
and the field
the participation begins
and the seasons
an awareness
Notes:
of performance:
implications
alluviate ·
who shall say in what manner
or why
but do not ask it
..t..
140
l
The action of the birds seems to represent the possibilities
of liberation, or the mind's own venturing. The icy
branches make noises of what is perhaps the poetic basin
or deep thicket of the mind's unformed call to create.
The country is large and black and white and silent. The
sun is a force; the orange of the setting sun is an unexplained beckoning or obscession. The winter is sharpnesss,
is acuity stripped of previous construction. Black wind
is also a force, an antipo dy of the sun in the catalogue
of the circularities. All of these things make up a real
scene. To get the feeling of the poem it is perhaps
necessary to have experienced the scene. And one must
ask -- is one mind ano t her~z
141
�Spontaneous Riding Poem
In Delusions I Can Pull Down the Sun and Hold it Rusting:
Alrno st night ·
suffusion of orange/chinese blue
I am the devisor
driving hard on streets
and I cry
at my own formulations ·.
maneuvering:_
I exploit myself
I
the mind down
am reassured only
by the necessity of my arrangements
to the shifting gears
again and against themselves shifted
jokingly
:·refer to myself
as a sort of carpetbagging tragedian
I
11
am worried', some would say.
I
say
I
am sick with fear
that I may tar and feather myself
eye
double functioning:
that
is
navigates
also sees
partakes intrudes
and drive myf3~lf away
in wealth of
charred by the very ·sun with which I deceived myself
in my plot against the world
every sharp edge in city made of edges
Only action blurred
people
in continuous going away from a point
running dance step negotiation
intervention
i am racing through them
the operator
feet feet
car gears car machinations combinations
Then city cemetery hill:
narcotic everywhere smell
of honeysuckle.
142
�The Grey of the Afternoon is not Grief
A Mournful Poem Because it is
Required/.]2~ecessary
but the rejection of circumstance
which claims even birds swifting in . the sky
The weirs
and leaves the trees isolate i~ their silence
have been up since
earliest morning
vines clutch gathered stones
garden chairs remain arrang.ed with leaves
and some men have
the gathering crickets' chant begins
built a fire/it burns
against the sky
and soon
there is the fragile dance of butterflies
a smaj.l fire and they
as night reveals itself
aren't even singing
in blue film
dissolving the trees
(oh the stakes are driven firm
leaving only the sibilance of wind
against the water
which is a fountain
spraying in a sortilege of surprise.
144
145
�Come Forth as Life by Outburst
small bells should be rung randomly
--plainsongs/let there be no
What is the measure of
allelujahs or shouting
the mind invaded
this is a time for
by love
clarity
that is:
--back country road by waster orchard viney stone wall:
a celebration
child after rain walking and stopping;
congregations of butterflies the rusty fields the puddles
the child's stick
,
of the mind's opening
which
··=
a divining or in some way mysterious
cause:
overwhelms
shouting later
loudly say:
REFLECTIONS OF THE SUN'S CORTEGE:
the words progressions on lines in
a dwelling among/a radix
patterns determined by feeling
or grace
as though a pentecost
logic a barrier not
the mind implodes/explodes
so consideration and turning inward
assumes the spectacle
PROLEPSIS
this VISION as artifice of love a
forecast/the mind answers with a
music a beat a dancing:
and then
THE OPENING THROUGH LOVE WHICH IS FINALITY
(1.
must be done it is insufficient
2.
IT IS THE UNIVERSE BUT I
the poem is the mind's music it
the mind is
by
m~de
aware
love nothing else)
cannot comprehend it
(perceptual inaccuracies
the limited range of my being
historically)
146
I answer after performing this:
the mind is measureless
�Poet's
Song
Taking as I please
I
give again
I
give
the great orange sun
a tree in wind
a child
Giving gladly
I assign my soul
to any other soul
who stands with love
and seems
alone
.148
�Song of the Goatherd
An oil puddle is black
Sing I, the drunken goatherd, sing
(like love)
Sing I of things high and low;
Reflecting the sky.
Wander among the hills
Sing I drowned drunken with wine sleep
A kite against the sky
Wet noses of goats on my face.
is a snake writhing deep in
J.M.
an unknown pool.
never
To every part of its face
to pass away
the smile stretched,
in smoke.
From ear to ear to ear.
B.H.
At Two
Title Unknown
I just ran
Learning near an open window in that
barefoot
Empty shadowed room,
in a breeze
He watches minute sparks of dust and earth. • •
Swirling with the sun.
Then turns away and would avoid their fall:
To clean white paper.
through the soft night grass.
It made me think
of ice cubes floating in lemonade
a red dripping watermelon
fireflies
and a string of Japanese lanterns
dimly swaying between two summer trees.
J.L.
The young girl turns her head toward me.
Her eyes are closed.
How sad her large mouth.
S.R.
�0 skies, who have made so few turnings,
Why should my heart not melt with your snows?
The branches of the pine trees
Begin high above where we stood together.
In this night of snow
They are shaken by the wind
0 they are singing proudly in the forces of the wind.
I cannot tell whether
They remember or have forgotten.
If no one
Should love me again in the sky's few turnings,
I shall not be the first.
0 it is morning now
Why should my heart not melt with your snows?
151
�You have. spoken to me of the rhythm of life.
The storm would not be chaos,
But that . I do not want his boat to go ~pon. these seas •
.·:· .. ,;:· .· .
Ah! There is the devil -- confusion.
Ah mother, I knew him better than the skies.
They bore bitter fruits
Who froze in the old seasons. ..
High on a white horse he rides clothed in red;
;~ .
Mother, I have seen such beauty.· ·' ·.-":" '. :.
Fine is the Tien, but he is not yet so intense.
Jealous I am, jealous for his youth.
How long will he be gladly smaller than the skies?
For the sake of falling blossoms, seek no words.
.. ~
The warrior will not listen if you tell him of them.
Put his armour away gently, and smile at his sons.
Blossoms fall silently, how can I tell you?
But my warrior is a rough man.
Put his armour away gently, and smile at his sons.
152
153
.
.; . : ~
�...
Poets
Page
Susan Roberts
II
1
Jeremy Leven
I
9
John Meixner
Maxine Marshall
26
Susan Kennedy
Y. c. Tsein (translation)
27
30
33
35
Richard Bond
37
Richard Freis
Francis c. Brooke, III
Kenneth Butler
39
Eric Lutker
III
Peter Naboko'ff
Elliott Zuckerman
Richard Carter
ARTISTS
. 42
Sanford Fisher
8, 94, 149
36, 108
60
152
50-51
Robert Fields
76
Sam Larcombe
124
Brett Fields
James Mensch
Judy Millspaugh
Mary Louise Biggar
45
The art worlc for this issue was done in conjunction
51
63
68
with the Visual Arts Committee.
70
IV
Noel Meriam
James Mensch
87
V
Nancy Linn
David Londow
Editors
95
John F. White
John Cantwell Kiley
VI
VII
ViII
IX
98
104
Charles G. Bell
107
Marian Sherman Borsodi
122
Sam Larcombe
Janet Huber, Sheryl Benton,
Barbara Hockman, Sam Larcombe,
125
Jeremy Leven, James Mensch,
Susan Roberts
X Mary Louise Biggar
Richard Freis
David Lachterman
David Castillejo
77
149
151
Typed by:
Audrey A. Kempton
Mimeographed by: James McClintock
Seals printed by: Katja Vasiljevich and other members
of St. John's College
Woodblocks printed by:
Paul Whitmore, Whitmore Press,
Annapolis
��
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The Collegian
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The Collegian began as a student newspaper; became a college community literary publication in 1952 and continued until 1969; became a student newspaper again in 1969; discontinued publication from 1980 until 1989 when it again became a student literary publication.<br /><br />Click on <a title="The Collegian" href="http://digitalarchives.sjc.edu/items/browse?collection=26">Items in The Collegian Collection</a> to view and sort all items in the collection.
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Annapolis, MD
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St. John's College Greenfield Library
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155 pages
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text
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paper
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Freis, Richard (Editor)
Lachterman, David (Editor)
Castillejo, David (Editor)
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The Collegian, May 1963
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1963-05
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·"'" ....
T HE
C 0 L L E GI A N
St• John °s CoJ 1. oge
June,
_ .I
1963
.
��_J~
2£. Contents
The Epistemological Elements of the
Special Theory of Relativity.
Confirmations of the Theory ••••••••• John Cantwell Kiley •••••• l
Portfolio:
Four Nudes •••••••••••••• Judy Millspaugh
Ted Stinchecum
Brett Fields
Richard West ••••••••• after 18
Charles G. Bell's
The Married Land:
A'"Review •••• ::-:-:7••••.••••••••..•••• Eyvind Ronquist •••••••••• 19
Innocence and War
First Prize Sophomore Essay, 1962 ••• Mary Louise Biggar ••••••• 27
The Final Statement: Poem ••••••••••• J.M.E. Michele ••••••• Inside
Back Cover
Faculty Advisor: Eva Brann
Editors: Richard Freis
David Lachterman
��The Epistemological Elements of the
Special Theory of Relativity.
Confirmations of tne Theory
~r. Kiley has permitted us to print such excerpts
of his doctoral dissertation entitled The Metaphysical Foundations of the Epistemology of Albert
Einstein as would be appropriate for the Collegian.
We have chosen Chapter I, Section D, which seemed
to be both fundamental to his argument and generally accessible. We would like to point out that
this selection represents a small preliminary
part of a thesis built up over four detailed
chapters, namely, "that there is no main Einsteinian epistemological doctrine which does not receive, in a completely natural and undistorted
manner •.••••• support by way of an essential explanation within the relevant metaphysical and
psycl1ological position of St. Thomas Aquinas".
E. B.
']
The Special Theory of Relativity appeared for the first
time as a mono5raph by Albert Einstein in Annalen der
Physik 17 in 1905 and was entitled, "On the Electrodynamics of Moving Bodies".
Considering the Newtonian-
type revolution it would produce in man's view of his
universe, it is remarkably brief, running to no more than
t ~irty
small pa3es.
115
In the opening paragraph Einstein reviews a fact of nature
regarding the behavior of magnets and their conducting
coils.
He briefly describes the fact as follows:
If the magnet is in motion and the conductor ~t
rest, there arises in the neighborhood of the magnet
an ·electric field with a certain definite energy,
producing a current at the places where parts of
the conductor are situated. But if the illagnet is
stationery and the conductor in motion, no electric
field arises in tha neighborhood of the magnet.
In the conductor, however, we find an electromotive force, to which in itself there is no corresponding energy, but which gives rise - assuming
equality of relative motion in the two cases discussed - to electric currents of the same path
and intensity as t 1
1ose pro due ed by the electric
forces in the former case.
116
�-2-
He then goes on to say · that "examples of this sort
suggest" ••••
(certain principles of physical nature
117
to him ) which escape . the *'customary view"•iiB In the case
of the relationship of magnets to a coil he says "the
observable· phenomenon here depends only on the .relative
motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two
cases in which either the one or the other of these
bodies is in motion 11 •
119
Now, this above-noted fact (together with its subjective interpretation) is an example of the sort of thing,
says Einstein, wnich when taken "together with the unsuccessful attempts to discover any motion of the earth
relatively to the light medium, suggest that the phenomena of electro-dynamics as well as ·of mechanics possess no properties corresponding to the idea of absolute
rest.
They
SUP-~0est
rather that, as has already been
shown to the first order of small quantities, the same
laws of electro-dynamics and optics will be valid for
all frames of reference for which the equations of
mechanics hold good 11 •
120
Here attention must be given to
stein, viz., "suggest".
thi~
word
~sed
by Ein-
There bas been seen in the
previous sections Einstein's epistemologic insistence that
(a) the scientist must · start with experimental facts and
that (b) these facts do not function as deductive but
rather as suggestible material.
Writing much later in his
caree~,
Einstein is to reem-
phasize this beginning of Relativity theory in empirical
fact.
Thus:
The general theory of relativity owes its existence
in the first place to the empirical fact of the
numerical equality of the inertial and gravitat-
�-3ional mass of bodies, for which fundamental fact
classical mechanics provided no interpretation 11 •
121
These "facts" as Einstein calls them, must be scrutinized for their meaning, however.
According to ordinary
usage the ·fact that a magnet induces electric current in
a closed coil, when the former is moved is what is commonly called a "fact".
A typical "fact" is one which
has the power by itself to overthrow a theory.
Newton's fundamental principles were so satisfactory from the logical point of view that the
impetus to overhaul them could only spring from
the imperious demands of empirical fact. Before
I go into this I must insist that Newton himself
was better aware of the weakness inherent in his
intellectual edifice than the generations of scientists which followed him. This fact has always
aroused my respectful admiration, and I should
like therefore to dwell on it for a moment.
I. In spite of the fact that Newton's ambition
to repres ent his system as necessarily conditioned
by experience and to introduce the smallest possible
number of concepts not directly referable to empirical objects is everywhere evident, he sets
up the concept of absolute space and absolute time,
for which he has often been criticized in recent
years. But in this point Newton is particularly
consistent. He had realized that observable geometrical magnitudes (distances of material points
from one another) and their course in time do not
completely characterize motion in its physical
aspects. He proved this in the f~ious experiment
with the rotating vessel of water. Therefore, in
addition to masses and temporally variable distances,
there must be something else that determines motion.
That "something" he takes to be relation to "absolute space". He is aware that space .must possess
a kind of physical reality if his laws of motion
are to have any meaning, a reality of the same sort
as material point and the intervals between them.
II. The introduction of forces acting directly
and instantaneously at a distance into the representation of the effects of gravity is not in
keeping with the character of most of the processes
familiar to us from everyday life. Newton meets
this objection by pointing to the fact that his
law of reciprocal Jravitation is not supposed to
�-4be a final ex~lanation but -a rule derived by
induction .from experience.
III. Newton's teaching provided no explanation
for the highly remarkable fact that the weight
and the inertia of a body are determined by the
same quantity (its mass). The remarkableness of
this fact struck Newton hims~lf.
None of these three points can rank as a logical
objection to the theory. In a sense they merely
represent unsatisfied de Gires of the scientific
spirit in its strug~le for a complete and unitary
penetration of natural events by thought. This
short account is enough to show how .the elements
of Newtonian theory passed over into the general
theory of relativity, whereby the three defects
above mentioned were overcome.
122
Einstein now tells us what the postulates of
h~s
special
relativity theory are and gives a description of the
first of them.
The special theory of relativity is based on the
following postulate, which is also satisfied by the
mechanics · of Galileo and Newton.
If a system of co-ordinates K is chosen so that,
in relation to it, physical laws nold good in their
simplest form, the same laws also hold good in
relation to any other system of co-ordinates K
moving in uniform translation relatively to K.
This postulate we call the "special principle of
relativity". The word "special" is meant to
intimate that the principle is restricted to the
case when K has a motion of uniform translation
relatively· to K, but that the equivalence of K
and K doesnot extend to the case of non-uniform
motion of K relatively to K.
123
At the same time he proposes a joint postulate that of
the constant definite velocity of light completely
independent of motion.
The special theory will need
only these two postulates, furthermore, as the basis of
a satisfactory electro-dynamic theory using Maxwell's
theory for fixed bodies as a point of departure.
In
addition, the postulates will assume nothing at all about
a luminiferous ether since the theory will attempt to
�-5-
overcome the need for an absolute immobile space which he,
of course, referred to as an empirically defective "fact"
cited in the previous quotatiori under heading one.
We will raise this conjecture {the purport of
which will herea:t:te~ be called the "Principle of
Relativity") to the· status of a postulate, and
also introduce amother postulate, which is only
apparently irreconcilable with the former, namely,
that light is always propagated in empty spac~
with a ciefinite velocity which is independent of
the state of motion of the emitting body. These
two postulates suffice f6r the attainment of a
simple and consistent theory of the electrodynamics of moving bodies based on Maxwell's
theory for stationary bodies. The in.troduction
of a "luminiferou·s ether" will prove to be superfluous inasmuch as the view here to be developed
will not req uire an "absolutely stationery space"
provided with special properties, nor assign a
velocity-vector to a point of the empty space in
which electro-magnetic processes take place.
124
Einstein uses the word"conjecture"in referring to his
first postulate.
He is not yet dignifying it with the
name of a theory:
something arrived at by sufficient
consideration of the arbitrarily chosen objects of
"rigid bodies, clocks and electro-magnetic processes"
and in an atmosphere of novel and unprecedented reflection
(fr ee associat ion).
The theory to b~ developed is bas~d - like all
electro-dynamics - on the kinematics of the rigid
body, since· the assertions of any such theory
have to do with the relationships between rigid
bodies (system of co-ordinates), clocks, and
electro-magnetic process es• Insufficient consideration of this circumstance lies at the root of
the difficulties which the electro-dynamics of
moving bodies at present encounter.
125
Einstein, in the opening -sentence of his original paper
on Special Relativity referred to these difficulties
knuwn to be inherent in the application of Maxwell's
�... ,-·.....
\
equation to moving bodies:
It is known that Maxwell ' - electro-dynamics s
as usually understood at the present time when applied to moving bodies, leads to asymmetries
wnich do not appear to be inherent in the phenomena.126
The facts, then, have suxgested the problem:
the inter-
pretations are made and postulated, the postulation is
then completed and now the definitions need to be supplied
before the deductive process can begin.
Since the whole deductive process is going to be based
on two postulates viz. on the principle of relativity
and on the constancy of the speed of light, Einstein
immediately supplies the definitions for them:
For the Principle of Relativity:
1.
The laws by which this state of physical
system undergo change are not affected, whether
the chan ~ e of state be referred to the one or
the other of two systems of coordinates in
uniform transitory motion.
For the Principle of Light-Speed Constancy:
2.
Any ray of light moves in the"stationary"
system of coordinates with the determined
- .velocii;y c, whether the ray be emitted by a
stationary or by a moving body. Hence:
velocity , = light path time of interval
where time interval is to be taken in the
sense of the definition in part 1.
127
We are now ready to begin the logical deductive process.
The important fact to remember about the significance
of this deductive process is that from this point on
it is a purely logical one and as a result of tnis fact,
the conclusions or theorems of the Special Theory of
Relativity will merely reveal what. have been assumed
�-7-
in the postulates even though the gain to us (viewed
psychologically) may be immense.
Thus, as Carl Hempel
of Yale writes:
It is typical of any purely logical deduction
that the conclusion to which it leads simply reasserts (a proper or improper) part of what has
already been stated in the premises. Thus, to
illustrate this point by a very elementary example,
from the premise, "this figure is a right triangle,"
we can deduce the conclusion "this figure is a
triangle"; but this conclusion clearly reiterates
part of the information already contained in the
premise. Again, from the premises, "All primes
different from 2 are odd" and "n is a prime different from 2," we can infer logically that n is
odd; but this consequence merely repeats part
(indeed a relatively small part) of the information
contained in the premises. The same situation
prevails in all other cases of logical deduction;
and we may, therefore, say that logical deduction which is the on~ and only method of mathematical
proof - is a techniqu~ of conceptual analysis;
it discloses what assertions are concealed in a
given set of premises, and it makes us realize to
what we committed ourselves in accepting those
premises; but none of the results obtained by this
technique ever goes by one iota beyond the information already contained in the initial assumptions.
Since all mathematical proofs rest exclusively
on logical deductions from certain postulates, it
follows that a mathematical theorem, such as the
Pythagorean theorem in geometry, asserts nothing
that is objectively or theoretically new as compared
with the postulates from which it is derived,
although its content may well be psychologically
new in the sense that we were not aware of its
being implicitly contained in the postulates.
128
Einstein demonstrates this character of the logical
deductive process of revealing what is implicit in the
postulates to give us. a "new" truth, in the following way.
He first presents an imaginary experiment involving two
systems, a stationary one and one moving uniformly to
it in a parallel translation.
Thus:
�-8-
Let there be given a stationary rigid rod; and let
its length be 1 as measured by a measuring rod
which is also stationary. W now imagine the
e
axis of the rod lying along the axis of x of the
stationary system of co-ordinates, and tt1at a
uniform motion of parallel translation with velocity
v along the axis of x in the direction of increasing
x is then imparted to the rod.
129
Einstein tells us we must now determine the ·length of
the moving rod.
Since this is _ an
imag~na~y
experiment
we must ascertain this length by two imaginary operations.
Thus:
We now inquire as to the length of the· moving rod,
and imagine its length to ·be ascertained by · the
f6llowing two o~erations: ·
(a} The observer moves together -with the given
measuring rod and the rod to be measured, and
~
measures the length of the rod directly by superposing the measuring rod, in just the same way
as if all three were at rest.
(b) By means of stationary clocks set up in the
stationary system and synchronizing in accordance
with 1, the observer ascertains at what points of
the stationary system the two ends of the rod to
be measured are located at a definite time • . The
distance between these two points, measured by the
measuring rod already employed, which in this
case is at rest, is also a length which may be
designated "the length of the rod" •.
130
The measuring operation involves (a) the process of
superimposing the measuring rod on the rod to be measured
by the observer in the typical way it is done and (b)
the measuring of the length of the stationary rod and the
conptitation of the time it took to measure it.
Now Einstein says:
In accordance with the principle of relativity
the length to be discovered by the operation.
(a}..-we will call it"the' le.n gth of the rod in the
moving system" - must be ·equal to the· length. 1
of the stationary rod.
·'
........ ..... .
·.,
.:....... ·. -·
�-9-
The length to be discovered by the operation (b)
we will call "the length of the (moving) rod in
the stationary system". This we shall determine
on the basis of our two principles, and we shall
find that it differs from 1.
131
In other words,
t ~ i.e
measurement of the length of the rod
in the moving system ascertained by imaginary operation
(a) since it does not involve the second postulate,
viz. that of the constancy of light must be equal to the
length of the stationary rod.
However this cannot be
true of operation (b) because the second postulate is
also involved.
Einstein tells us that the mistake is in assuming the
lengths of (b) operation to be equal:
Current kinematics tacitly assumes that the lengths
determined by these two operations are precisely
equal, or in other words, that a moving rigid body
at the epoch ! may in geometrical respects be
perfectly represented by the same body at rest
in a definite position.
We imagine further that at the two ends A and B
of the rod, clocks are placed wnich synchronize
with the clocks of the st--.< tionary system, that is
:
to say that their indications cprrespond at any
instant to the "time of the stationary system"
at the places where they happen to be. These
clocks are therefore "synchronous in the stationary
system". We imagine further that for each clock
there is a moving observer, and that these observers apply to both clocks the criterion established
in lf-1 for the synchronization of two clocks.
132
In other words, the tendency is to think that the clocks
of the stationary and of the moving system are synchronous
and since the measurement of length requires the calculation of the lapse of time that, since synchronization
between the clocks is assumed that the lengths will be
the same (following the relativity principle of classical
mechanics).
�.:..10-
This, however, Einstein says is a fallacy for the followin. reasons
1
(a ,:s ~n m~i:ug
use of an imaginary
experiment): .
Let a ray of light depart from A at the time ta, let
it be reflected at B at the time of tB and reach
A again at the tiwe t'a taking into consideration
the principles of the constancy of the velocity
of light we find that Tb-\°' :::.~o.V\~ T'a...-T~=~
c-V
c:_TV
Where "-.0-'o denotes the
length of the moving rod meac ured in the s tationary
system. Observers moving with the moving ~od
would thus find ·that the two clocks were not
synchronous, while observers in the stationary
system would declare the clocks to be synchronous.
133
In other words, according to Llathematical calculations
ba, ed on the light speed-constancy postulate, from the ·
s
vantage point of tne stationary system, the clocks
give the same time while from the moving ·s 1 stem they do
not.
There can be only one conclusion, based on such
deduction, a conclusion
i m~, i ri t
postulate when they are
j o _; _ :. 1 ·:~ .J.
as was said in the
t rige ther.
And it is
the one that Einstein i m
med:i.a tely makes, viz., that
of the relativity of simultaneity:
So we see that we cannot attach any absolute
signification to the concept of simultaneity,
but that tivo events which, viewed from a system
of coordinates, are simultaneous, can no longer
be looked upon as simultaneous events when envisaged
from a system ~hich is in motion relatively to
that system.
134
It is not within the purposes of this thesis to
present.in any detail how the ideas of Einstein led
to the development of his whole mathematical structure. .
within either the Special or Generql theories of
Rela~ivity.
Suffice it for our present purpose, -
to show the actual workings of the epistemology of
Einstein in order to expose the elements of empirical
�-11-
suggestion, free invention of the postulate and a
small part of the dedQctive analytical process (only
a part of which, it should be noticed was mathematical
reasoning as distinct from non-mathematical or ordinary)
as it occurred historically in the presentation of the
special theory of relativity by Einstein in 1905 and
which all led up to the confirmation of its theorems.
Regarding observational tests, de Broglie has the
following to say about the Special Theory of Relativity:
As soon as Albert Einstein had laid the foundation
of the special theory of relativity, innumerable
consequences of great interest flowed from these
unusual ideas. Some of the chief consequences
were the Lorentz-Fitzgeralci contraction, the
apparent retardation of moving clocks, the variation
of mass with velocity among high-speed particles,
new formulas containing second-order terms
(termes supplementaires) for aberration and the
Doppler effect, and new formulas for the compounding
of velocities, yielding as a simple consequence
of relativity kinematics the celebrated formula
of Fresnel, verified by Fizeau, specifying the
light-wave-trains (l'entrainement des ondes
lumineuses) of refracting bodies in motion. And
these are not merely theoretical notions: one
can not insist sufficiently upon the fact that the
special theory of relativity today rests upon
innumerable experiwental verifications, for we
can regularly obtain particles of velocities
approaching that of liGht in vac uum, particles
in regard to which it is necessary to take account
of corrections introduced by the special theory
of relativity.. To cite only two examples among
many, let us recall that the variation of mass
with velocity deduced by Einstein from relativistic
dynamics, after havin0 been firmly established by
the experiments of Guye anci Lavanchy, is verified
daily by observation of the motion of the highspeed particles of which nuclear physics currently
makes such extensive use; let us recall that some
of the beautiful experiments of Mr. Ives have made
possible verification of the relativistic formulas
of the Doppler effect, and thus, indirect verification of t~e exist~nte~bf fhe ~ ~~tard~tion of
clocks of which they are a consequence.
135
�-12-
. Ivlinkowski ref erred of course, to a conclusion of
1
. .
..
. .
~pecial ~elativity
~
.
.._
..
wlii6li he
se;n by Einstein himself ,
. ... -·
.::.
. ~
·!-: :
__
1-
t~ll~ u~ ~~~
n6t
1
......\ A
~t
·'
•· . • _
first
136 and which at a later date
provoked the formulation of the General Theory of
Relativity.
One important concern of General
R~lativity
was to demonstrate the physical validity of Minkowski's
prediction about the fading away of "space-in-itself
and time-in-itself in favor of a spci.ce-time unity".
The modification to which the special theory of
relativity has subjedted the theory of space and
time is indeed far-reaching, but one important
point has remained. unaffected. We shall soon see
that the general theory of reldtivity cannot
adhere to (its) simple physical interpretation
of · space and time.
·
137
Instead, the physical interpretation of space and time
as having their own separate physical meaning must ge
abandoned, Einstein says.
In classical mechanics there
was a physical separation of space and time ob·tained
by physical measurements involving the use of fixed
rods and standard clocks.
In classical mechanics, as well as in the special
theory of relativity, the co-ordinates of space and
time have a direct physical meaning. To say that
a point-event has the Xl co-ordinate xl means that
the projections of the point-event on the axis
of Xl determined by rigid rods and in accordance with
the rules of Euclidean geometry, is obtained by
measuring off a given rod (the unit of length)
xl times from the origin of co-ordinates along
the axis of Xl. To say that a point-event has
the X4 co-ordinate x4 = t, msans that a standard
clock made to measure time in a d~finite unit
period., and which is st:· tionary relatively to the
system of co-ordinates arid practically coincident
in space with the point-event, will have measured
off x4 = t periods at the occurrence _ the event.
of
138
These unconscious habitual tendencies of physicists and
�-13people in general, must be put aside in favor of the
postulate of : S'eneral re la ti vi ty which cannot be carried
through otherwise:
This view of space and time has always been in the
minds of physicists, even if, as a rule, they have
been unconscious of it. This is clear from the part
which these concepts play in physical measurements;
it must also have underlain the reader's reflexions
on the preceding paragraph . (2) for him to connect
any meaning with what he there read. But we shall
now show that we must put it aside ana re-~ lace it
by a more general view, in order to be able to
carry through the postulate of general relativity,
if the special theory of reiativity applies to the
special case of the absence of a ~ ravitational
field.
139
At this point, we see the operation of the rule of
simplicity for Einstein, for it is this very rule which
demands this chang e in our view of nature's physical
structure since there is no other way to achieve a
simple formulation of t ue laws of nature except by
abandoning the _
attempt to directly and individually
-measure
s r~ atial
and temporal coordinates by ordinary
rods and standard clocks.
We therefore reach this result: In the general
theory of relativity, s pace and time cannot be
defined in such a way that differences of the
s patial co-ordinates can be dir€ctly measured by
the unit measuring-rod, or differences in the time
co-ordinate by a standard clock.
The method hitherto employed for laying coorJinates into the S}ace-time continuum in a definite
manner thus breaks down, and there seems to be no
other way which would allo\J us to adapt systems of
co-ordinat : s to the four-dimensional universe so
that we might exJ ect from their application a
particularly simple formulation of the laws of
nature. So there is nothing for it but to regard
all imaginable systems of co-ordinates, on principle,
as equally suitable for the description of nature.
140
Thus we are led to the postulate of the General Theory
�- 14..
which requires that:
The general laws of nature are to be expre~~ ~ ~ bv
equations which hold good for all systems of
co-ordinates, that is, _
are co-variant with respet
to any substitutions whatever (generally co-variant).
This postulate Einstein calls the "requirement of
general co-variance (invariance?" and it is this which
takes away from space and time the last remnant of
.
. .
.
physical obJect1v1ty.
ll~l
For Einstein, as has been seen, a point of criticism
for certain physical theories is that they have not been
"natural"; that they have not accounted for the facts
"in a natural way" etc ••••
In fact, it was the very
unnaturalness of Newton's t .heory of action at a distance
142
which ga ve the "impetus to overhaul it 11 •
Simiiarly,
in his early part of the exposition of the General Theoryt
Einstein showed his pre-occupation with "naturalness"
as an aim in the development of his theory.
It is not my purpose in this discussion to represent
the general theory of relativity as a system that
is as simple and logical as possible, and with
the minimum number of axioms; _but my main object is
to develop t his theory in such a way that the reader
will feel that the path ·we h:.ve entered upon is
p~ychologi~ally the natural one, and that the
underlying assumptions will seem to have the
highest possible degree of security.
143
This statement of purpose had just followed a rather
lengthy
argu~ent
for the "naturalness" of the principle
of general co-variance involving
th~
reduction of events
to the motions of material points whose meetings alone
are observable in terms of coincidences, such as between
the hands of a ~lock and points on the dial.
Now the
systems of references are just devices for facilitating
the description of these coincidences.
Thus he says:
�-15As all our ~bysieal ~ experience can be ultimately
rdduced to such coincidence, there is no immediate
reason for prefering certairi sys tems of co~ordinates
to others; that is to say, we arrive at the
requirement of general co-variance.
144
In summary, the epistemology of Albert Einstein then
breaks down into four main tenets:
of inductive beginnings;
concepts;
3.
2.
L
The requirement
tne invention of the primary
the deductive process with its governing
rules of naturalness and simplicity and finally;
the confirmation of the theorems.
4.
The detailed features
pertaining to each of t hese tenets have been traced
through both the properly epistemological as well as the
mathematico-physical writings of Einstein.
An essential
point that must be reemphasized, in summary, is the fact
that Einstein, uniquely among scientists, took the trouble
to develop a
full-fled ~ ed
epistemological doctrine which
became a powerful investigative method in his scientific
work.
And it is clear that the insights he was to
achieve into the nature of physical re&lity were the
result of attention to both science and philosophy.
Indeed, perhaps it was precisely because Einstein had
seen the problem of space and time as something more
than a merely ex:0erimental one, that he was able to
break out of the futile search for an ether and approach
it in a new way.
In any case, he had the wisdom to see
that more adequate epistemological methods would have
to be fashioned.
It is necessary now to undertake an
investi .~ ation
of
the Einsteinian view of reality, a view which must
bear
he~vily
on and even determine the kind of approach
that would be made in Einstein's investigations into
the material universe.
John Cantwell Kiley
�-16FOO·:rN uT'BS
113a.
On this point, see the relevant remarks on
scientific as opposed to "historical.!' causa.iity
by Ernst CAbbIRt;R in his Substance and Function
. and Einstein's Theory on Rela t ivity, New York,
Dover, 1953, P• 220 n~ ff.
114.
A. EINSTEIN, "Autob-iographical Notes 1',
· AEPS, p. 13.
115. ·
"The views of space and time which I wish to
lay before you have sprung from the soil of
experimental physics, and therein lies their
strength. They are radical. Henceforth,
space by itself, and time by itself, are doomed
to fall away into mere shadows, .and only a kind
of union of the two will preserve a independent reality." Opening remarks o'f H.
MINKOWSKI, addressing 80th Assembly of German
Natural Scientists a·n d Physicians at Cologne,
September 21, 1908, in Principles of Relativity,
New York, Dover (no date), p • . 75.
116.
The Principles of Relativity, New York, Dover, p.
117.
Ibid.
118.
Ibid.
119.
Ibid.
120.
A. EINSTEIN, Op. cit. PP• 37-38.
121.
A. EINSTEIN,"On the Theory of Relativity",
pp. 50-51.
122.
A.EINSTEIN, "Mechanics of Newton", pp. 34-35 .
123.
A.EINS rEIN, "The Foundation of the General
Theory of Relativity", Principles of Relativity,
p. 111.
124.
A. EINSTEIN, "Mechanics of Newton" t p.38.
'
125.
A. £INSTEIN, Op. cit., p. 38.
126.
A. .8INSTBIN, Op. cit., p. 37.
127.
A.EINSTEIN, Op. cit., p.
128.
C. HEMPBL, ' "Geometry and Empirical Science 0 ,
The World of Mathematics, Vol. 3, pp. 1637~1638.
1
41.
37.
�-17129.
A. EINSTEIN;
130.
Ibid.
-.
131.
Ibid.
132.
"Mechanics of Newton", P• 41.
.!£i£·
133.
"A. -EINSTEIN, Op • . cit~
,~p. !.42.
134.
A. EINSTEIN, Op. cit., PP• 42-43.
135..
Lou:i.s . do BROGLIE, "A General Survey of the
Scientific Work of Albert Einstein"(translated
from French manuscript. by Forrest W. WILLIAMS)
AEPS, PP• 114-5.
136.
Lorentz called the t' combination .of x and t
the local time of the electron in uniform
motion, · and applied to. ,physical construction
of this concept, for the better understanding
of the hypothesis of contraction. But the credit
of first recognizing clearly that the time of
the one electron is just as . good as that of
the other, that is to say, that t and t•
are to be treated identically, belongs to
A. Einstein.* Thus time, as a concept unequivocally deter~ ined by phenomena, was first
deposed from its high seat. Neither Einstein
nor Lorentz made any attack on the concept of
space, perhaps because in the above-mentioned
special tDansformation, where the plane of x,
t, an interpretation is possible by saying that
the x-axis of space maintains its position.
One may expect to find a corresponding violation of the concept of space appraised as
another act of audacity on the part of the
higher mathematics. Nevertheless, this further
step is indispensable for the true understanding
of the group Ge, and when it has been t~en,
the word relativity-postulate for the requirement
of an invariance with the group Ge seems to me
very feeble. Since the postulate comes to
that only the four-dimensional world in space
and time is given by phenomena, but that the
projection in space and in time way still be
undertaken with a certain degree of freedom,
I prefer to call it the postulate of the absolute world (or briefly, the world-postulate).
�-18*A. EINSTEIN, Ann. d ~ Phys~; 17, 1905, p. 891;
Jahrb d. Radioaktiv~~:; at und Elektronik, 4,
1907, p. 411. H. MINKOWSKI; "Space etnuTimen,
The Principles of Relativity, P• 83.
137.
Cf. supra.
138.
A. EINSTEIN, "The Foundation of the General
Theory of Relativity", The Principles of
Relativity, p. 115.
139.
Ibid.
-
140.
A. EINSTEIN, Op. cit., P• 117.
141.
A. EINSTEIN, CE; '"' cit., P• 117.
142.
Cf. SuEra; P• 63.
OE·
cit., P• 116.
143.
A. EINSTEIN,
144.
A. EINSTEIN, Op. cit., P• 118.
�Out of the delightful drawings done by the
many gifted members of the group, the choice
of ·these four could hardly have been more
arbitrary and was dictated as much by their
suitability for reproduction as by other
considerations. I regret that I could not
afford to have a larger and l.i1 ore . representative number . reproduced, but I consider
these quite worth while.
The artists represented in order of appearance are: Judy Milspaugh, Ted Stinchicum, Brett Fields, and Richard &
Jest.
James Gilbert
�-19-
-
Charles G. Bell's The Married Land:
--
A Review
"I interest myself in the background of my friends."
The Married Land, p. 108.
In this case the best way to praise
Cha~les
Bell's recently
published book will be to exhibit briefly the questions it
raises in its arrangement and thought.
But I confess it is
difficult to know where to begin with a book in which form
and the run of thought which leads to the determination of
form so closely mouify one another.
It is to be assumed that at some point the reauer will
ask himself, "What kind. of book is this?"
If one compares
it with a novel like Tom Jones ( held as a model in the
Preface ), one notes the absence of any direct adventures.
Whereas in Fielding's book a multitude of encounters are
narrated from beginning to end, here the movement is for
the most part one of reflection;
Tom Jones in middle age.
these are the memoirs of
The purpose of Jones's long
journey, to win the hand of a virtuous young woman, involving the discovery of a suitable parentage, is externally
already accomplished here.
What is left to perform is the
"winning" of the wife by the understanding through form.
To be sure, there are also journeys in this book.
It is a
fresh event which proviaes the occasion for reflection,
although it is suggested that this event is only one of
many possible from ,t he past and future.
The routine of
Daniel and Lucy Woodruff Byrne on their farm in Maryland
is broken by phone calls which call each away to a sick
relation, the husband to a hospitalized aunt in Mississippi,
the wife to her Quaker uncle in Pennsylvania, stricken with
a heart attack.
side.
At the end they return, no death on either
There again, it is not what happens in the ordinary
sense that matters, but rather how they make sense of the
meaning of their journeys.
For this reason what happens
becomes extended in imagination into a characteristic
�l
. -20-
event in which, on the one hana, the pair are driven to
North and to South in the persistency of their families
and past environments and through which, on the other hand,
the past by being examined reveals the basis for a successful return.
The .mythic
reenact~ent
of their lives gives
clarity to their present ,selves and also to the characters,
living and dead, who shaped their pasts.
Thus, to give
examples, the husband attempts to clean out the rubbish
of souvenirs and decay that clutters the aunt's house, and
the wife comes upon a missing section of her father's
journal • . Towards the beginning of the book the task is
stated generally:
Daniel faced the day with three questions-The first arose from the image of the spring,
that mystery of water out of earth; it was
addressed to the heart: How~ bring clarity
from the dark house, the opening of its dens?
The second was asked ~the mind,-and for:-lowed from the first: In the face of all the
de D. s would reveal, how hada-bridge~ee;- - · possible from Woodrtiff to Byrnes? The third ·,
neither the heart nor the mind could answer,
.mt only time: When would he be ~ Lucy
again?
( p. 25, author's italics )
The relative unimportance of the third question -- not,
to be sure, of its outcome -- shows ·the way in which matters of time ( history ) are subordinated to matters of heart
and mind (
This is
~ot
po~try
and philosophy perhaps ).
to say that the writer was not concerned with
the novelist's problem of time,
tha~
is, with
p~ottin~.
The time scheme by which the book is arranged is quite
difficult, but nevertheless explicitly intentional;
and it
sustains the relationship between happening· and significance
which is the book's major intellectual problem.
At first
it would seem that past and present events are jumbled
indiscriminately, but by following closely the sequence of
tenses the reader is able to make sense of the scramble.
�-21It then appears that basicaily the booK describes the
husband's thou.gLts and activities in the last day and a
half of his stay in Mississippi, together with the flight
back north in the afternoon of ~he secona day.
spends the morning of the first day,
The hero
I think, going for
groceries, visits his mother in the afternoon, and during the
n~xt
morning measures the family plot in the grave-
yard and finas the aunt's will.
This I should like to
calJ. the metabolic level, owine:, to a preponderant an1ount of
time spent in the su.permarket.
However, above this limited
span of time there is the level of the organism, which
persists by means of habit, stable environment, and memory.
The recollection which took place the previous aay
of the father's death is thus still vivia anu gives the
impression of having occurred in the basic tillie of the
novel.
Similarly the time of the visit to the grocery store
is deceptive:
because it is a repetitive task, it could
have happened almost any time during the three week stay.
For the same reason it aoes not demand any attention, and
the protagonist is free to recollect the past.
These
recoliections occupy the first half of the book ( through
Chapter IX, "The Mee ting 11
) •
In this part of the book
the events of the fiight south are recouuted in the order
they occurred, though with breaks.
Between the
f~ight
north ana the remembered flight south we have all that
happens in terms of motion.
Beyond this, on the way to
Mississippi the protagonist has recalled his first marriage
and second wedaing.
Along side of the narrative of the
husband, there is some account of the wife's simultaneous
stay in Pennsylvania;
but this is for the most part seen
reflected in the husband.
On the most general level of
time major anecdotes in the history of the two
are told.
fami~ies
These are not necessarily in chronological
order, and any but the praise-worthy reader who writes as
he reads will fina the relationships uifficult to follow--
�. -22-
they are probably given more as background than as historical fact.
rt might be objected that in the first half of the book the
wandering of memory takes a little too long.
Certainly the
most excellent moments in the book come in the second part,
in which the description of the
characte~s
of the husband's
parents and the wife's father are given sharper definition
by being connected directly with present objects:
er, a visit, a diary.
ti~o J _
tvoo in the
a revolv-
There the remembered ( and future )
present.
Otherwise the disjunction between
is at hand and what is thought may be amusing -- as
when thP 1111 -~h~nn Jnnks at the airro.rt fJight pl.an and begins
wltat.
arranging the Quaker relatives into
clearly intended.
co~umns
-- -but it is
The effect aimea at is stated in a paren-
thesis:
The encounter of day, reconnoitered
in waking; foreseen and remembered
as real as the deed. There past and
future merge, smeared in present: To
make the actual conditional, and the
~itI'Onal actual, to blur t~ais
tinction.
-- ~~ ~- -~( p. 4, author's italics )
The effect has its justification:
••• in the world of mind , which is
where we live, the road of his marriage had to be discovered, and he
searched for it frantically as if
in fact there was no other way to
reach Lucy again.
( p. 22i' )
But again the "world of the mind" is, I venture
to
say,
nothing other than the world, and the flights of ratiocination rest on particular fact.
The broken time scheme of the book exhibits the difference
between history ana fact.
One might suppose that past
history is the determining
ca~se
of the present fact.
the historical level the book is without doubt a novel,
although one arranged in a curious way, with sequences
On
�placed on top of one another.
However, this arrangement
invites one to question the sufficiency of usual historical narrative.
If events can be juxtaposed out of order,
if, .for example, the taking ~ff of an airplane can be
given simultaneously with a description of southern Aunt
Betsy's uncontrolled driving, one is led to ask what is
common in the pieces of history.
In the example given, it
is suggested the key is that disparate events are driven
by a common wave of energy.
co.n.s~ant
Thus one is led to ask what is
in the connection of historical facts.
still perhaps a question for an historian.
That is
What is remark-
able about this book is that it passes on to non-historical
questions, that is, that it has a metaphysics.
It is the fact that the book occupies itself also with
problems which are not strictly narrative --
~·1£••
with
the hierarchy of memory and change -- that leads one to
suspect in a certain mood that this is not so much a
novel as an allegory in the form of a novel.
suggestion is advanced cautiously.
Divine Comedy instructs in a
But this
For whereas the
theo~ogy
which is detachable
from the poem ( E.!.E_.: the instruction itself is not separable ), here the world view depends on the particular part
of the world selected.
Were another marriage given, the
analysis of its basis in the nature of things would also
differ.
partial
The terms chosen for the analysis are of only
universali~y.
is very often
emp~oyed
Th~s
the notion of the four elements
to give pattern.
It is one of the
joys of the book to read how, as in an allegory, the elements
are given varying description in natural images.
invited, for
examp~e,
One is
to consiue r the lowe r Mississippi
curling about the Delta like a dragon, and the efficient
rush of an Appalachian stream.
Such consiaerations, it
should be emphasized, are not in the case of this book
simplj decorations on the cake.
necessary
~eason
It is aimeu to see the
for apparently accidental differences in
�-24husband and- wife, for the husbana believes that it is only
the discovery and understanaing of this which will make the
marriage stable.
The earnestness with which the intellectual pattern is investigated distinguishes the book.
such as active-passive,
The pairs of opposites
masculine~feminine,
North-South must
be considered seriously if the book is to make any sense.
The fact, for example, that husband and wife come ·from disharmonious parts of the country leads to an
the characteristics of those regions.
of
exp~oration
As the couple
discover their neea for one another, it is suggested that
the North and the South have an analogous
ency.
depend-
In general the South is presented as the genteel
anarchy to which the stable Eastern
liable.
mut~al
co~onial
America is
Here perhaps the intellectual order of the book
weighs more heavily than it should.
It begins to look as
if the capitulation of Mississippi to numbskulls were a
prophecy of some Untergang
were futile to reverse.
~
Abendlands, which all action
It woula, however, be facetious to
deny, in the shadow of the enormous stupidity
~f
the human
animal, that the solution suggested, content with the
"private good", is not worth earnest consideration.
The
assumption that geographical enviroiu11
ent is liable to
produce differences in character is also worth
loo~ing
at.
For example, would not one be moved naturally to aiiferent
sorts of thought
i~
the garaen of an old, established town
and in the desolation of a mountainous aesert?
But it must not be
forgott~n
that action and
also make a pair of opposites.
contemp~ation
It is the author's opinion
that an individual can transcend his environment.
It is not
necessary, then, that a social pattern become stagnant.
Or
rather, even if the society is on the decline, some individuals may escape from
customary way of
~ife
i~.
gi~e
Generalizations about a
way to uescriptions of character.
�-25But on the other hand the characters are not just anybody
off the street;
they are heightened by the pattern in
which they are groupeu.
The heavy emphasis on pattern
leads to one difficulty:
the characters, although re-
lated in idea, do not, except for the husband and wife,
talk to one another.
Nevertheless, as the characters are
seen taken up in the protagonist's
consciousness, they
are admirably large and vivid.
They are of two kinds:
those who define their society and
those who, whether or not consciously, cannot live within
society's bounds.
The Quaker Unc.Le
Stewar.d .~and.the
Aunt Betsy are examples of the first type.
really realizes his liruitations.
Souther.n
Neither
I myself rather liked
Uncle Steward, although the . n<St:r.-l'a..tor ac:;c.uae..s him Qf _
understanaing tragedy.
off into caricature.
Aunt Betsy has a tenaency to veer
That is a danger in this Kina of
writing, as is a way of aropping from iaeas to jokes without
any intervening mora.L .Level.
The husband's father did cotL
prehend tragedy in his Life.
He had the energy and the iaeals to become a great center
of renewing action, but was caught up in the net of a
corrupt society, incessantly
by an odd set of parents.
his own life.
Unab~e
in debt, and confuseu
to break free, he tooK
The husband's mother ana the wife's father ar e
more successful.
incident, is
invo~ved
The mother, except for one very brief
portra~ed
most aelicately.
The beauty of this
miracle fro!il the Kentucky hi.ils is quite moving.
the prototype of the wife.
She is
The activity and complexity of
the wife's father cont£asts with the hentle Southern woman.
The opinionatea and high-i3piritea accou1n in his o'lim words
of his peculiarly rambunctious pacifism in the First
VJar is very much fun to read.
w or~d
I wasn't able to tell from the
Preface whether his journal entries are quotations from an
actua.Lly existing manuscript, but iu any case they ana the
�-26many different k inds 6£ iP.tters and speech patterng
~h ~w
that the author has a fi.ne taste for variations L.1. style•
It is the husband who is the
IDCt11:d:
rJ :if f j r.P-1(,,
to er~sp.
T.t~e
wife is seen objectively, on the practical level, but the
hasband appears, as it were, from within.
Thus we cannot
uetermine just what it is he uoes for a living.
It seems
that he is at the same time writer anu painter, but we
rarely
see
vo~cing h~s
him working;
own opinions.
what he sees, hears,
more often we hear hiru loualy
But it is his attempt to order
thinks~
and
remen1
bers that proviaes
the main viewpoint from which the book is written;
in
other words, the book is the one which the protagoaist
intends someday to write.
One should, however, ctistinguish the author· frori. the pro-
tagonist.
To those who know him, the author reveals himself
on every page.
W
hoever has seen the sharp
eyes
ana heard
the briJ.liant shifts of his conversation will reco6nize at
once the intel.lectual passio.u which is so striking in this
book.
iously.
There are not many writers who take ideas so serOne iri,agines, for exampJ.e, that Sir Charles P.
Snow's scientists talk about novhing but big business
off hours.
i~1
their
But Charles Bell never tires at any time of
exploring the cliffs and caverns of the human intellect,
which exploration is as well one of Life.
W learn in the
e
Preface that the characters have their sources, not only in
the requirement
o~
a pattern, but also in fact.
It wou.ld
seem then that the author !!.ani1ests, as did Goethe. that
singular and accurate Gl~ck in which "everything happens at
the right time".
Eyvind Ronquist *
*Mr. Ronquist, an alumnus, graduated from St. John's in 1961.
�-27-
INNOCENCE AND WAR
First Prize Sophomore Essay, 1962
by
Mary Louise Biggar
�innocence sees
greyness
and desert
because of the other.--
other ridiculous .. --We must
unrelated
two are entire
--Because
its demands
each
fol
to
demand
and
The
books
commitments ... e
tians - are in our own minds
ago believed
be
creatures at peace
hearts
excellence
have an
of con-
so
are
in the world
books say that we are
to some
we see about us:
The nature of commitment is a war
These books
between
a
certain we be
we are
and evil
of
iv es
and
commitment to the
and then as we do when we half believe
at any
\:e
them as futile
for
which saw
theirs ..
state of
innocence.
be
who are young
interes
the
�-29terms of good and evil - out of which there cane.rise only
endless war - is most often fatal to the human spirit.
we become vague.
an·~
Uncertain,
Fe a.re distant, finally, from both the sight held
in innocence and the sight of .good and evil.
accept everything.
He
I know we pretend to
speak of good and evil and justice 8.nd truth
most earnestly, and we also say knowingly that the Meaning of Life
is Life.
Actually we have no notion of good, and evil, or we would
do more than speak of them;
we would,if we knew anything of them,
make some stand exactly and without questioning
wher~
we ore standing.
If we would still believe in life as naturally as we once believed
in it, we would not make such foolish statements about it, for they
really imply resignation.
other.
We have lost each for the sake of the
The fact is, the majority of us continue . to live like pigs,
and with the uncomfortable semi-consciousness of doing so.
In
short, these books and their commitments, which are so full of
life, become a contradiction to it if we do not allow them to
seize us as entirely as they demand.
If the state of innocence were what most people feel its definition
must be - that is, the state of ignorance - the problem would be at
worst the problem of teaching fools wisdom.
But that is not all
the question, as far as I have been able to tell.
are not fools.
The innocent
It is true that innocence in any huwan is concom-
mitant with certain delusions, and that they are delusions characteristic of innocence, but it is equally true that there are certain
delusions characteristic of those who have forced themselves out
of that state, whic'h I shall later enumerate.
The innocent see
the same world, and they see as much of it as the non-innocent.
They simply do not see a conflict in it:
neither between light and
dark, nor what is and what should be, nor humanity and the inhuman
forces.
While they do act, they act well or badly simply in accor-
dance with how much they see;
that is, the fact that they see the
world through the innocent state has little or nothing to do with
the excellence of their actions.
Why is this?
It is discomforting,
�-JOat least.
I~see
two reasons, primarily.
First, although they do
not see in terms of conflict, and perhaps just because they do
not, they have a great love of what is, and on that account they
are tender of it.
Secondly, although they do not see in terms of
light and dark, they too feel the desire to be more themselves.
I suppose the best and simplest metaphor for the two states is
this:
the innocent sees in colors;
and white.
the warrior sees in black
Those are coir.mon mef:aph9rs, but usefuL.·
and black and white separately may cover the world.
Both color
He who sees
in terms of color, will say his higher self is somehow
~
colored,
and he will understand that statement as the vague and the committed
never can.
hi~her
He who sees in terms of black <J.nd white will say his
is more full of light and stronger for the battle.
Neither
can understand the other.
Beside the belief that most people hold that innocence must be
equated with ignorance, lies a second, closely related, that in
innocence we hold the world to be good, and the loss of innocence
is the discovery of evil.
Here innocence is again equated with
ignorartce, and again the problem would be delightfully simple if
it were merely one of teaching the other (evil) side of life.
But Genesis is the paradigm, and it firmly states that the end
of innocence is the discovery of good and evil.
We can hold this
second delusion concerning the nature of innocence only in our
vagueness.
The source of this definition of innocence as "knowledge
mArely of good things" is quite interesting.
upon it later.
I shall elaborate
Briefly, in that fatal vagueness where we see
neither colors nor darkness against light we cannot even bear
to see thet the two states have no resolution, although it is the
very fact that they hcve no resolution which has left us vague
and without a sense of life.
We forget the colors for the memory
of which we distrust the other sight.
We also flee from the
other sight, for any responsible examination of the great stands
would yield the information that good of the type evil can work
�-31against (that is, not The-Good) is never
is also seen.
s~en e~cept
as evil
But we mistrans.l ate everythi.ng, and think thereby
we understand whc.t 'it is
all a.bout, for we have deserted both
posts and are no longer torn between them.
By calling our former
colored state "belief in the goodness of everything" and the
second as "discovery of evil, .. we have an excuse for the greyness
(for obviously, white has been tinted with black).
This sorry
excuse for thinking allows us the most abominable excuse for vitality, for we may boast melodramatically that our
grey~ess
is the
product of the discovery of truth, and furthermore is the reality.
There is an entire kingdom of students enG philosophers launched
proudly out on this discovery.
Greyness is, in short, the great problem.
1 believe it cannot
arise in the conflict of light and darkness, for they have no
intermedie te shades and the nature of perception of them demands
war;
in greyness there is no war.
I believe it arises in the
conflict within our own minds of the entirely separate and
parable views held in innocence and in commitment to
darkness.
incom~
~ar Bg~inst
Seeing how e[ch makes the other ridiculous, we become
vague, and thet vagueness is
fa~al
to the spirit.
The books subtly
lie in pretending that all will be well opce we gain knowledge.
Innocence is not -ignorance.
It will always be impossible to see
by the two states together, for they deny one c- nother in our own
minds.
The fact is, that .t hey have nothing to
but also the fact is, that just by
c~ o
pret~ndin3 \-Je
with one another,
do understand
that they are disparate, as \··ell as by .pretending we understand
they are one, we become ve.gue.
We must plot out the. territory
of ec.ch, which we are for the se.ke of each e fraid to do.
great books and the
~reat
should not y ietd death.
But the
st&nds must be granted life, thz t they
The undertaking is immense.
The axiom
underlying both states is that . something is important, and that
something is not merely our ability to feel.
Th2t is impossible
to prove, but we ccnnot live. and believe otherwise.
In both states,
�we do honor
In t·he midst of the greyness, we stil
would honor
that is our
For the sake
st not be vague.
of that
which I cennot
to draw the
I shal
in this
t, the state of innocence must be marked out.. If
fashion
I define it somewhat more
than it is defined elsewhere,
you will
me if you will admit some memory of a state
all such characteristics at once, and will allow me to cell it
u:innocence 0
also.
·for
sake of s
Its loss must be marked
ic
We must then determine the nature of the stands, the cominnocence and expressed in the
mitments and conventions
books
I
once there is vagueness
mitted to war also ... that because the
we c8nnot stand and
mus
answer the
we are com-
states are entire
to balance them, but we
demands of ee,ch.
�-33The state of innQcence -- Genesis as the paradigm of innocence
and its loss. -- The innocent! loves the seasons, which negate
the possibility of tragedy or nobility. -- out of wonder at being,
sees all things as equally important. -should be.
-~
love~
what is, not what
perceives the world subspecie aeternitatis
-~
in
short, forgives everything because he does not see that there is
anything to forgive. -- The narrowing of our territory as origin
of the desire to act, -- The subsequent loss of innocence.
Innocence is primarily that state in which we see the world in
its wholeness, and not in terms.of good and evil. It. is secondly
.
.
the state in which we (from the Latin innoceo) "do not harm", or,
more li~ely, believe we do not · harm. T.h e paradigm of innocence
1
and its loss is of cou rse found in the book of Genesis. Adam and
Eve are placed in a garden by .God, who in his love allows them to
love all things. For them as for Plotinus only beauty has being,
and all being is beautiful: it is not a beauty to which ugliness
Cc.n be opposed, then~ But ·t hey desire god-hood and they acquire
the knowledge of good and evil.
Ye shall be as gods, then: your eyes shall be opened,
knowing good end evil.
Still in the garden, they re-interpret the same things which had
been given before. lmd so what is the outcome of their new knowledge?
A rather picayune kind of shame, the shame of being naked, a petty
morality of which it is obvious neither God nor the writer approves.
CWe m
ust also be careful at this point not to s r y - "Ch well, t ha t
is some mere law or custom, evidence of a perversion of the knowledge
of good and evil." The writer gives it as exactly the product of
that knowledge. - We have no right to assume it is a perversion.)
But they
are driven out of the garden and forced to act in a world
in which there are curses and commandments.
The pattern is this. The desire for godhood is followed by the
knowledge of good and evil, for we need that knowledge in order
to master others, if not ourselves. Cnce we attain it, our life
narrows, and we are forced to act by this new knowledge as well
;
�-,,; -.-7 ',
as see. In attaching i mp ortance
we are shown our mortality.
to _ rig~~
This makes sense, for
good ·and evil can exist only in _time:
knowledge of ti1em,
"it.Te
action,
if we wish
inust acc;ept the fact tha" we
t
can be masters only in time.
Following soon ·upon the
intellectual loss of innocence is the time in which
we harm.
God more.
Cain kills Abel because Abel has pleased
At this time there is a second cur9e, the
curse of God upon Cain, that we are
strangers
~omehow
from this time forth.
vfuat hast thou done?
blood crieth unto me
thou are cursed from
the ground, it shall
thee her strength, a
shalt thou be in the
The voice of thy brother's
from the ground. And now
the earth; when thou ti·llest
not henceforth yiel.d un.to
fugitive and a vagabond ·
earth.
This harm is of a particular kind, a kind which makes
us strangers to the rest of the world.
W harm because
e
we wish revenge for a mistake we made about what
would be good.
No other creature is capable of such
lies• or is so proudly determined to be "good" that
he commits himself to it over the body of his· brother,
and does not so much honour the good as demand that
he be it.
No other creature destroys be·cause he· cannot
bear imperfection.
God himself will destroy for just
that reason in the flood,
Long after that, He will
have learned a commitment higher than to his own perfection, and He wi;Ll make a covenant ·"of acceptance
of life.
And the Lord said in His heart, I will not again
curse the ground for man's sake, for the . imaginati6n of man's heart is evil from his youth.
The whole story of innocence, the desire to act like
.i
gods, which requires the knowledge of good and evil,
the c6nsequent narrowing of our lives and the ugly
proof (though the theorem be glorious) that we are not
natural lies in this book.
Written out, too, is the
�-35- .
acceptance of commitment to the good, no matter how
much less it seems than what we once had (Adam), the
perversion of commitment which arises out of pride
(Cain), and the final commitment which is to allow
life to continue and somehow to forgive.
The innocent is, he feels, in his entirety in being
both part of and about the seasons.
By the seasons,
I mean the vicissitudes about us, and within us, the
cycles of birth and generation and death, and the
resolution of death and pain into the great oneness
of life.
He who sees purely in terms of the seasons
cannot conceive of tragedy, .for to stand by one thing
when all things are running through one appears ridiculous, a deluded act which nature will resolve.
He understands mourning and grief and ecstasy, but not
nobility.
Before he is required to act, he has a
marvelous flexibility.
He has not classified in terms
of importance, for all things are equally wonderful
and important.
Since all things are sources of wonder
and are of equally great importance - since they do
not have to be otherwise, until he becomes determined
to act rightly - he thinks of the world about him
no t i n terms of "ittt but in some subtle terms of
"you".
He sees things simply, because there is no
requisite for him to put them together.
This will be
lost with the loss of innocence, when it becomes
vagueness.
state.
It is an integral part of the innocent
It is the perception of a single thing, with-
out the use of words.
As we come to believe in dar kn ess
and light and the necessity for action we will have
to put things together , and in becoming means rather
than ends, they will become "it"!
If we are vague
we will become locked in a state in which we cannot
�-36see anything simply but only as a ineans to · an end, or
in relation to other things.
Thus a .. child may love a fairy hero, a snail, a sailboat, and his father with equal intensity.
correct?
Is he not
When he passes out of innocence into vague-
ness he will not' dare, ·and will be ne:I:":9'.<;msly . looking
about for the right thing to love.
But in the inno-
cent state he trusts the importance of 'w hat is
~·iven.
He does not demand that the things he loves be intellectually aware or even particularly alive, nor that
they be useful to him in his search for "higher"
knowledge.
Standing in his first season, he views
· every season as potentially his.
He has the first and
perhaps greatest view o.f the whole, and he demands
everything in it, simply because he sees them as well
as participates in them.
Not feeling truly . involved
yet, he does not see that he has harmed and may
harm; he had one kind of clear sight.
It is in some
sense easier to see clearly a battle you are noting.
feels he is not yet in the battle.
available to him.
~
Everything seems
is not yet a question.
But
we can easily see here a source of the loss of innocence.
Man is both part of and about the seasons.
That is, he both participates in them and sees them.
But the sight of
everything.
~verything
breeds the desire to be
Seeing so much, the fact that we are but
a part of nature with a part to· play escapes us.
~ve
would believe we have the power to be anything • .
We do in a certain sense have that power, but the
fact that we are one part necessitates choice and the
determination of how.
It is in choosing and in at-
tempting to answer how - that is, in painfully compounding the limitations of our physical nature with
He
�tle
er upon
In the innocen
state we love
is
and do not see
But how else should we ever love
we would not care en
is to dream of
for
and even if we could dream of
we could never understand the task of
is
love of
without
At any
which is of course the whole
rate
love of
this
If we do
of ourselves, and love some
not recall the
ourselves rather than
use in our at
to be
is is necessary.
what we
be, there is no
to be better
er?
of
for who is at
alone can
and
and that for the sake
c,.· n tain the secrets
our innocent state we
of
are uncritical, and able
world at a time.
care for one
We do not compare worlds as better or
worse, and we are difficult to bore.
necessary for
The
so
at life have not yet become strong
to
satires
those twisted mockeries of
, used in the narne of
but in fact directed
existence itself.
So, in innocence, we love
for its own sake,
and not yet because we feel ourselves missionaries
about to
the heathen to the
we dv not love it
for the sake of
If there is
concerned with
in our love, it is
of that is contained in
believe
our
of how much
But there is, I
more to this love of what is
its own sake:
we love
of Adam the mediator was God.
love of our
should be
That is,
love
a mediator.
In the case
In childhood it is the
- their desire that the child
makes him contented to be so
and
�-38their love ·at once of him and of what they may give
him enchants the world.
And innocence . is given again
and again, not only to Adam and to children.
The
first stages of love are innocent, rapturous sights,
in which we see a person without dividing him into good
and evil parts, and in which we dream of a love in
which there will be no harming.
That is, in first
loving a human being we love him for his existence
and are lost in wonder at it.
Good and evil have
no place in the higher fact of his being.
We love
him for what he is and for what he contains of what
we had thought before should be, but the two merge
into one.
We have
a dream
of not harming, and we
wonder that we so greatly ~nd corisdiously wis~ not
to harm.
Any man on .first showing his love of
some~
thing to ano"ther, gives the state of innocence,
for he
demand~
not action but sight, and does not
demand that we enter upon the world we have been
shown.
Without some original loving mediator there
is no innocence, but only the _
blind struggle for
survival.
The importance of what has been given is
not seen instinctively.
It is passed on by one who
has seen it.
The innocent state is one in which vie perceive the
world subspecie aeternitatis.
In the first
place~
as I stated above, we believe vaguely we might
ha~e
or be anything and everything, for we are in our
first season {of life, or of a new world, as above)
and do not feel the pressing of mortality upon our
hearts.
We see eternity and our own immortality ' at
one, and we play.
If we are not mortal, and if
we
are loved, we do not believe there is any real motion.
�The
, and
a
to that state of b
coherent truth is for
In innocence we believe in the essence of the moment
tures
childhood in terms of s
- we recall
in terms of actions without
our futures
essences but
ends..
Thus a child understands
a tree without
it and the
he has
it is the essence of the present..
cone
does not conceive of it as
truth
nor
He
another
does he demand it have a
or relation to other
I
the memory cf childhood
to your own memory ..
not moral
If
ask that you ref er to
I can
'
poems cone
He senses
The sense of
not a
~
or even
in b
It is sensed
of war ..
in the essence of each present moment ..
we view et
is
which is without war
In this
and most like
the
is
f ac
in
the essen-
ces of various moments that we take
are
we
see
will assent
that the
Even
if we will not
or wrongness of action, which
is the
for the future, is
divorced from the
What
it
erates will be certain essencesv
These essences are
truth for the innocent.
is not
even a grown man
or angry, he may look for and listen
to the voice of the
child within him and
it e
receive
When we lose txlis
become vague, we become unable
and evil.
exc
said above
r
We chase a
o see
Good and evil, as I
e motion to exist
cannot conflict in
motion.
gen-
for
where there is no
we shall never catch when
�-40we are pleased with nothing except as a means to some
good end.
Whereas. . _
i.nn.ocen-ce, perceiving under the
aspect of eternity and in terms of seasons, forgives
everything because it does not see that there is
anything to forgive, in the vagueness following its
loss, and even in the commitment to light in a war
between dark and liglit, it seems impossible to forgive.
But of that I shall speak more later •
.In summary then, it is characteristic of innocence to
believe all things of equal importance, to lbve
what is exactly as it is, to believe exclusively in
seasons, and to perceive the world subspecie aeteritatis.
Would you deny that such ·a state containing
such characteristics exists?
But if you have ever
honoured the essence of a moment present without
wondering first whether it was worthy of honour, and
have felt a wonder at existence due to
· thi~
essence,
you have approached the state of which I speak.
Later, most likely, you will attempt to evaluate that
moment - you will weigh 1t, determine its cause and
its consequences, and be uncomfortable if you cannot
find any large significance in it - portents of tragedy,
of evil, of creation.
Still in attempting to evaluate
i t you will again be uncomfo r table fo r you will wonder
how it was you then saw and felt so much whereas now,
naming the things ' larger than the essence, you know
no truth.
Finally you will ignore it, as though · it
were delusion.
By the very fact that you in your
vagueness cannot accept that state of being, you have
underlined that it is a state of being, and one impossible to deal with when we are so dull.
I do not
assert that anyone exists absolutely in that state
at any time.
of war.
There are within it always intimations
If there were not, we should hold within
�it a very
There
if the state of
that is the human estate
were
as I describe it we would
not be
into the vagueness.
know the other
we
was somehow
somehow doubted.
But we
with us, that
Because of
we doubt
now ..
Nor do I maintain that the state of innocence is a
necessary
of childhood.
savages as innocent
I cannot conceive of
and neither can I conceive of
a child who was never loved as innocent.
Innocence
is
on from man to man.
not
o wage war for one s existence, for such
a war obliterates
To be innocent one must
One must also be free and
- those who have none who love them
cannot be so, for the law will turn them into its perverse slaves because there are none to
above and b
it.
them
In the New Testament, which
return to innocence, in order that
may become innocent men are first freed from the law
love.
in
There must be one who loves our lives our lives
he mus
love of life can exist
Life cannot be
love life itself
in
of it.
exc
seen in
dark.
The
as it is first
But in
(which
cannot be an absolute act - we have seen some who
were
more
freedom to love
of innocence.
than others) he
and that is
us the
�-42-
I have previously suggested some of the factors which
lead to the loss of innocence, and hence to the greyness.
Primarily innocence is lost when we discover
the incommensurability of sight with the limitation upon
personal action.
There is change, but in narrowing
what was we cannot but desire to preserve it.
not only sight but also memory.
We have
Eventually we note not
only c hange in the world but also in ourselves.
The
magnificance of what we have seen becomes increasingly
impossible to realize in ourselves as we grow older and
as our territory diminishes.
It is less and less likely
that we shall be a companion to Socrates, that we shall
live upon a certain mountain, that we shall be as 0reat
as we saw in the broad view of the first season was
possible.
We begin in horror to see that the seasons
not only take our loves, but that far worse they
may mark upon our faces merely the lines of time.
We grow desperate.
We must somehow seize and twist
the natural flow of the seasons that they should not
merely flow, and that we should become at least some
part of all we saw in the early vision a man might be.
We must act, but to act becomes unnatural, for we no
longer know by instinct how to become more ourselves.
Glimpsing mortality and having lost the vision of
eternity because of that glimpse, we desire to become
masters or gods, of the temporal in the time left us.
To become a master is to make some kind of a stand,
for if we are not born masters (and we are not, as
we see in the seasons will mark upon us more time if we
let them, and le0ve us with nothing), we must employ
a convention to become so.
division of
~
Any convention demands
whole into two parts, by one of which
�-43we stand.
The world must be divided at least into
good and evil of some variety, however vague, and we
must stand by the "good", however vague.
In order to act now we must be more than natural
creatures, as we should see.
and in the middle.
We are past the beginning
The beginning was mostly vision, and
unable to guide us successfully even this far, for we
sense that we are less both than we would and might
be.
Something in us which is unnatural must lead us.
By marking out good and evil it will mark out the law.
It will set limits upon us because we have asked for
action rather than sight.
falisity in the limits.
We cannot help sensing a
But we desire to be every-
thing as well as to have sight of everyt hing, and the
limits and divisions are the price that ·we may be
anything.
Now we have lost that innocent state of being.
now is our state?
What
�-44The state of vaa·ueness -- Distrust of the importance
- ~---
of what is given -- consequent wasteful destruction
Disinterest in what is
If we give blindly
after seeing need, we are refusing even to see the
disparity between what is and what should be -- But
if in the state of vagueness we deny that everything
is demanded, we shall never leave it.
But do I truly need to describe this state of greyness
of o.ur weakness in not examining the
whi.oh ari.s-$a out
territory of both the innocents and the warriors?
We study the great books and hear of great commitments,
but something in us sa.ys that all this is unnatural,
and that any ''real" love is either in.s tine ti ve or
false, and that reality cannot be defined in other
terms than "existence".
On the other hand suppose
we wish to understand or have knowledge of a certain
medieval room:
we cannot do this either, because we
are not plotting out good and evil in this mere perception, and are not engaged in the eternal· war.
We are left "between the devil and the deep blue sea."
Having lost innocence, we cease to trust the
of what is given.
impor~ance
We are so dull that we cannot ·
....
conceive of any state different than our own.
Seeing
how dull we are, and caring, except instinctively,
very little about .ourselves, we cannot see that
anyone else matters either.
This delusion of a
universal greyness co-existent with our own greyness
even seems, when we are so deluded, to be verified by
the books.
They speak of the suffering of one man,
the great man of whom they speak, if they speak of
it at all.
He suffers because he sees.
Because his
�-45sight is so deep, it appears not to be concerned anymore with the ern otions of individuals.
He has put
the things of the world together, and has risen
above them.
We feel we can do the same thing.
Every-
thing is neutral but the sight of great men, we feel.
_, __.-, -
..
Out of this delusion of neutrality we destroy.
is true, Shiva rules.
indiscriminately.
It
But we destroy wastefully,
While ,death is necessary, such
dQstruction is not.
I stated earlier that reason (in its lower sense),
classification according to descending importance,
and the perception of patterns are necessary mainly
for action.
They are also natural human faculties.
They will take innocence if the consciousness of good
and evil does not, for they will take wonder.
For
having employed these faculties long enough, we are
no longer in a state of wonder.
the grey state of half-wonder.
How absurd it is,
We come to wonder at
fewer and fe wer things, and those things are only
ones we have found difficult to deal with by means
of these faculties.
thing, or nothing.
Either we should wonder at everyBut we feel life growing dull
because we see its patterns.
"La Roux is going to
die . " "Well "(wisely)" everybody dies sometime.
I've seen it happen again and again."
To combat this
trading of innocence for nothing at all, we trust some
equivalent of the great books, some knowledge of the
great stands.
To act merely in accordance with our
perception is merely to survive; to act merely in
accordance with our love of the great things may not
be to act at all, for we must be able to apply that
specifically, and not to 6harge blindly through,
waving it over out heads.
Those faculties must be
combined with some knowledge of the great stands.
�-46But suppose we do have the g reat commitments, and some
sight of the great things, before us.
W
hat is the
product in terms of action as well as feeling?
Exactly
what you already know, althbugh concentrating on tnose
things thems elves, you ignore it.
~'
Finding what should
we cannot forgive what is for being what is.
cease to love what is.
We
We know very well that youths
return from their education with a considerable loss
of respect for their very vulgar parents.
While
Confucius suggested that we ought first to be good
sons, good husbands, and good brothers, and then if
we have any time pursue our studies, we pursue studies
first.
We see human fallibility and cease to trust.
Just because we are not just, we rant against injustice,
exactly as Jesus predicted.
It is the mote in our own
eyes which makes us so self-righteous.
help it?
Yet can we
Standing by the light, we are not yet it.
To merely stand by a thing makes one anxious, nervous,
irritable.
To guiltily half-stand by it makes one
more so.
Once we saw the large and the small things inextricably
connected.
love either.
That is, I supp6se, the only way we could
But now we separate them.
That is
really only to say that we see what should be in the
same t hings we saw before.
fects everything.
But what should be af-
We can divide it into parts, and
abstract these parts from what is, but in doing so we
are lying.
The original sight of what should be
cannot come from anything else than from what is:
must penetrate every portion of what is:
an image of what is.
it
it is somehow
We are discontented with every
part of every thing, but we are not brave enough or
do not see enough to admit that.
The actual thing is
vibrant with potential, as Aristotle said.
The
�-47actual never exists without the potential.
to see this potential is unbearable:
Perhaps
at least for me
it has been at times nearly so. · \We must find words
for it, divide and abstract it.
more comfortable to deal with.
Abstracted, it is
I mean by this that
it is More comfortable to think of perfect love than
to realize that everything is demanded of a friend,
not only that he should love in whatever greatest way he
could love(which is certainly different than the vague
idea of perfect love we have abstracted from books
and the love of friends) but also that he should walk
gracefully, and finally that he should demand everything of us.
But because we do not see the depehdence
of what should be on what is, we grow vac-ue.
If we saw
how at one they are we might love each for the sake
of the other.
But conceiving of them as seperate,
we cannot love either one because it seems so foreign
to the other.
Again, we have always conceived of the human gifts as
free.
The dignity of man seems to demand it.
We
have always seen a humanity grandly and freely bestowing
the gifts of love and of giving and thereby creating a
heaven.
This heaven that poets speak of we have thought
was the human glory.
But when we see need, we see
that the gifts are not free.
In the narrowing of our
season, duty becomes evident.
with a sense of pettiness.
W answer dutifully,
e
Many of us cannot truly
respect anyone we suspect needs our love.
Again,
I submit only what y0u must have already observed:
that is, the general if disguised selfishness and
disrespect shown by most students to those elders
whose need becomes evident more, as it is
less.
an~wered
On finding that love in the common life is not
free, but must answer and is willfully destroyed by
every man, we tend to flee to places where there seem
�-48still to be free and grand gifts.
How many years it
will take 1n ost of us to learn what i1ow I can only
state - that the human gifts are most free because
they are not free, and bec.a use need is so seldom
answered - I do not know.
In the books concerning
great men, the gifts again appear free.
We may give
nothin s at all because we are not answering what is
needed, and b y vague giving we may destroy.
The dignity
of man is underlain by the most groveling and helpless
need, and in that need he seems unclean.
The great
men have seen need clearly and answered clearly,
answering not the deluded needs but the original ones.
In this, they may have done the only real asserting of
the didnity of man.
Great men appear to stand alone
and untouched in clear air and give great things,
while we feel that we are almost smothered in a crowd
in which there is nauseating constant, mutual, pulling
and tripping.
The reason for the disparity between
ourselves and themselves and the fact that their gifts
are free not of need but of vagueness, for the most
part e.scapes us.
And so out of vagueness we waste the gifts.
to say that they shrivel within us.
giving remains.
This is not
The instinct for
But whereas, even if we do recognize
that in the great books that instinct is turned to
answer the greatest needs, the anmver of how to do
that escapes us.
Good-hearted
~rnuls,
we merely im-
itate the gifts given by great men, but we are vague
out of the conflict bet ween the small duties which
annoy us and the desiredto give within us.
know what to give or to whom.
We do not
Witness The White Duck
in which a young man searched for truth, the greatest
gift, and at once desire to give it:
yet because
he was overwhelmed with books he was vague - he did not
.L -
�-49carry his search far enough to discover the truth of
a man's reaction to the trugh he was about to state,
and so he destroyed.
Thus in pretending that our
desire to Give in combination with our sight of some
of the great things which may be given automatically
yields a gift, we become vague.
In the blindness of
wishing to give, we pretend that what we have given
will be received exactly as we wished.
We refuse to
see that on account of need we cannot give purely
because we desire to do so.
We refuse to see that
everything is demanded, not merely the things we
can think of at the moment to give.
The greater
the things, the more impossible to give, and in refusing to see that our pain ceases and our life stops.
To see need at all is no longer to be innocent, for
need defines an imperfection in the world.
To wish
to give as grandly and clearly as the great men gave,
and to be disgusted with the need about us is to
become vague.
To become vague is to hide ourselves
from the fact that everything is demanded.
And to
hide from the fact that everything is demanded is the
most fatal thing of all, for then we not only, as
before, uncomfortably fail to truly love eitner
what should be or what is, but lose sight of the disparity between them.
The sight of the terrible dis-
parity between the~ is the sight by which all great
men have lived, and the sight is pain.
a part of our love for what is
To l-0se
when we have seen
what should be is a terrible price, but perhaps it
is one which must be paid.
But to lose actual sight
of the disparity between them (which we will never
admit to having lost aloud, but which is evidenced by
our avoidance of the fact that everything is demanded)
�-50is to acquire the fatal version of the disease I
have called greyness.
Seeing that we cannot have
or be everything, and that we must act to have or
be anything, we must still see that everything is
demanded, however little is possible.
from which we shall not escape.
It is a pain
But only the accept-
ance of it can take from us the fatal vagueness.
�-51The Three Great Stal.Lds -- \,ve must chose one, al.though
a lie 0r convention is requi.cea to do so-- otherwise
we will fail, out of confusion -- the Platonic stand
of reason -- the Christian stana with the infinite
ana the ir.cational -- the tragic committment to an
extreme.
I maintain that you uo not believe in go0d and evil,
and are yet in a state of greyness, unless you see that
everything is demanued, anu I maintain that the sign
that you have seen that everything is
~emanaed
~
first, that you feel sick and desperate, and second,
that you shape your powe£s to answer
very specific needs.
s~ecifical.1.y
I further maintain that in order
to see that everything is demanded and to live, you
must employ a convention, anu
of the great stanas.
yourself to one
con~ . itt
Not to ao so is either to be
already wise beyond reeson or to become undramatica~ly
- confused.
sim~~y
and
The despair which arises
out of confusion is incapacitating.
Each stand
cannot help but l.ie anci we can, . . ot he.1.p bllt see that,
not only from stuaying aiffe.cent stanus, but from
colliparing tneir
p~stuJ.ates
own simple observances.
reject all cruf them?
and conc.1.usions with our
lb this not reason enough to
Yes, but for oue thing.
men saw more deeply into
~ite
than we:
if we
Those
do
not
stana beside them, · we shaLl not see anything except
a certain glory about the fact that they
~ia
see.
If each of them twisted somethinb, what bave we,
committed shaiLow.1.y to The Truth, better than their
depths?
To make sense of the wo£ld demanus a lia,
but not to make sense of it 1tleans nDt to see it, and
to substitute a series of fee.1.ings for sight.
can judge those books
our views.
aloof~y
We
but they wili colour
If we uo not ruaster one of them, together
�-52they will master us.
The same event cannot be interpreted
from a vaguely Christian, vaguely Platonic, vaguely
tragic viewpoint without dissolving the event into a
meaninglessness about which · we only feel something.
Exactly as in the fading of the season's first great
views, we find we cannot be everything.
Not only can
we not remain aloof from the stands, but we cannot,
in love with the grandness of them, attempt to take
every stand at once.
In attempting to do so, we shall
merely mimic symptoms, and the attempt to follow all
is a sign that we do not understand any.
It is true,
each presents a warrior against the dark and each is
committed to the truth.
the truth" mean?
But what does "committed to
Simply that the warriors, like all
men who are not in the greyness, want the truth.
In
innocence we also were committed to truth but believed
we had it.
If we could have remained in that state
there would have been no problem.
But slipping out of
it we lost the truth, no longer being able to find it
naturally.
The whole point is that now a single
convention must be employed;
if that were
~
the
point, we would reach truth naturally, and conventions
and the division of the iriworld into darkness and light
would be absurd.
Behind each stand is a
in words.
sjg~t
which cannot be described
The tragedian does not say "You must stand
by the extreme";
nor the Platonist "You must stand by
proportion", arbitrarily. · If we say grandly "Both
Socrates and Antigone died for the truth", we will be
speaking grandly, but we will certainly disgust Socrates
and Antigone.
They died according to their lights, in
order not to betray them.
nature of man;
Socrates died for the political
Antigone, for his aloneness.
Resolve
�-53the two into one a.s _;_.Jl'etci.iy as you -'-ike, but ;you will
come out 'INith
tvJo
simple-minded suiciu.es.
stan~s
I would define the three main
tment to. an extreme, and
postu.iate.
Each can
quite nicely.
acc~ptance
inc.iu~e
anu
ab reason, commitof an
exp~ain
We have stuaied theru under
iriati~nai
che 0thers
th~
heauinss
of the Platonic philosuphe.-· s, the trat,edIB ns, auu the
Christians.
They a.1.1
postu~ate
a war
01
darkness
light, althouhh some more subtiy than others.
a~ainst
Sorue outline
of · each is necessary in order to se2 the way in which
each demands everything.
The general definition of the Platonic stand is "mastery
through reason", with tb;e very it1:portant c1ualification
that reaaon is not always .iaiu out in the form of a
Euclidean proof, ana may become sight itse.if, as in the
~yths
at the end of the dialogues.
which is natural to men,
sei~es
Just because reason,
only certain thint:,G in
order to aevise "coherent 11 systems, reason is the only
hope for knowledge of all.
That
~
our minds ba ve a
certain pa~r cf ascension, somewre t para.1.iel to the
ability to prove a Euclidean proposition.
But P1sto
clearly sees that we will get nowhere unless we have
been given everything, and in carelessly choosing only
certain axioms, as most of us are wont to uo, we will
lie.
Everything on earth is demanded: as an axiom that
we might reach the truth.
just that Keeps us from it.
But our vaLue rea.iization of
Therefore he must unify
all we see into some i-w catagories - not only is
Same and Other, but also ce£tain Forms, such
and Justice.
Expectin~
a~
the~e
Beauty
ail thinbs to fall more or less
under these forms (for we are not evil but .less good)
we can compound everything for the sake of sibht.
will see the finite infinitely
magnifi~d;
if he
w~
al~owea
us to say the magnification was the i~aLe, we wou~d
�-54-
be miserable for the aisparity - ana so quickly he
turns the tables and. the mag11ification beco111es the
actuality.
in
knowin~
that
wou~d
wi~L
He bolaly states . that we
be happier
more of what is - what a pitiable de.1..usion
appear to the tragedian.
tains that those who have oeen the
But he a.1..so mainrea~ity
must and will
bring it back to the world. of images, "this" world..
The effects are the same as though this were the "real"
world.
In effect, he has aemand.ed that we be glad
that we can see what shoula be and that it exists,
even if only for the sake of sight.
V·e might say he
J
com~itted.
lied, that in transLating image and. obJect he
some heinious crime against truth.
he comfuitted?
Some crime
Yet what crime has
wil~ a~ways
be comLitted -
if it is not perversion, it wilL be never to have tried
at all.
The absoLute truth would be well if it were
accessibLe other than by reve.1..ation, and yet I
be~ieve
the final truth wiLl be what you can d.o.
But whether or not the Christian stand is
a~so
a per-
version it is not possible for those who are 11ot
Christians to tell.
The Christian postulates that
there is a kind of being caLled the blessed. state, which
we who are without it cannot understand, ana
certain~y
which we who have not accepted Christianity's irrational
postulate (as indeed all postuLates are irrational)
could not hope to unaerstanct.
Yet Christianity appears
to offer the least perversion, taAen on its own grounas.
The aesire for wholeness is a strong one, and. I can
unaerstand. how many in the ena would turn to it.
we not all longed. to "become again as
Litt~e
Have
chiluren"?
Take away the sense of grand.uer anu the desire for
glory, and you find the majority of huma11ity aid not
leave childhooa and simplicity out of any yearning
to do s@, and that the greatest longing is perhaps the
�-55o~e
to return to it.
greatest
lon~ing,
Must we out of priae deny
o~r
mibht it not, when answered,
an~
point to the greatest truth?
Misht we not submit
enti.1:ely to the infinite, towards · hich there is a
great pull, ana regain our innocence?
:Men have visions.
There are Dostoevsky's visions oif
human suffering, Rimbaud's visions of beauty, ana our
own lesser visions still overwhelming us.
we do with those visions of infinity?
What shall
Pursued, they will
twist and pervert the pursuer, for his passions rrctch
the things in their infinity,
an~
he does not.
as a statement of a truth to be lived by, they
break one, as the vision of chastity broke
The Greek
phi~osophers
Taken
wi~l
Hip~olytus.
of fer balance and proportion
as an answer, but how impossible and how consequently
dull that can be.
The fourth thin 0 we may uo is to
become simple as a chila, so whole and good that nothing
may pervert it, and that the Father himself in His one
and
on~y
truth may take us into the realm
01
the blessed.
Sick of good and evil, St. Augustine renounced them in
God's oneness.
v have all a sense
1'e
and we are all sick of
of sin ana of de a th.
~imits.
of the infinite
We are sick of law and
And
••• this then is the proper and true definition
of a Christian; thaL he is ~he child. ot grace and
remission 6f sins, which i~ ~ri~er no - . l~~' but.is
above law, sin, death, and he~l ••••
The only way to heal that sickness, I believe, is to
become a Christian.
It is the tragic stanu which is the least natural, and
in which suf1t:::ring is not merely upon the way but ruost
greatly at the end.
For the tragedian the
neither good nor evil.
go~s
are
They are aosolutely inhuman
�-56forces against which
humanity mllst stand, accepting
OUL'
its resultant freedom as it& glory.
thin~s,
rationality ran through all
an
irrationality;
But tor
a
P~~o,
for the Christian
for neither were the forces inhuman.
We had only to unite with the world of truth in order
to become what we shoula be.
But the
tra~edian as~erts
that we are forever st...·angers .Ln the worla. a11uthat
the highest form of life can resu.Lt only from the
acceptance of that fact.
The trageaians see, I feel,
that the co.rtf lict of good and evil is but a prouuct
of time arlci mortality.
WhiJ.e the P.Latonist and. Christian
look somewhere fo1· eternity, the trabic hero wi.L.i. not
compromise with it.
He stands with and sees the pitiful
convention wich which life presents us - mo~tality ana
its granauers rin5ing abo1.1t eternity, its .Litt.Le ..1.ights
and. darknesses m:de out of nothine.,,r1ess.
He stanus by
its most pitiable aeJ.usion, the extreme of com11. ::u,tment,
and thereby wages war with the nothingness.
Only a being
which can feel greatlJ can seize upon nothing and
delusion of something anu
them both, by the
strang~e
greater force m his own life.
On~y
the shortness of life anu make it
~he
AchilJ.es can see
sho~ter,
and by wrenching
himself from the forces which give and take, assert the
magnificence of what it is
tragic stand will aiways be
sirJ pl.y
to ue human.
~onel.y,
l1he
1
for not on.Ly is the
person who takes such a stand at war with Qa.kne ss but
also he is warring With only the f01.'Ce
The~e
is no .League of tragic men;
tragedy negates the
possibi~ity.
says somehow that he .is goa, the
01
his own humanity.
the very iue a
W hi~e
~f
the Platonist
'. ~ hristian
that he is a
creature of God, the tragic hero says onl.y that he is
a man.
To say tha
l,,
you a1·e a man is ne ve ..c to cease
asking "who am I?", for that is the question tram which
the answer "I am a man. 11 has sprung, anQ the two ar·e one.
(I am one who believes we know the great statements
�-57before the great
quest~ons.)
the tragedian has answered th
den~nded
Essentialiy, I believe,
fact that everything is
wiGh the question who am I?, for t hat is his
first translation of the demand.
is as
impossib~e
But because the translation
as the original, he takes upon himself
committment to an extreme (of cha6tity in
Hip~olytus,
indiviaual human di6nity in Anti~one) anu agrees that,
whoever he is, he will pay the fuli price for the sake
of
somethin~
larger than
himse~f.
If these two were
nothing without the committment¥ it would not matter,
for the tragic hero has set at once a price up0n the
thing to which he is committed, and upon himself,
simp~y
by integrating the two, as is unnatural.
of
�-58Conclusion -- In cormr.. i tment we become what we were
not certain we saw -- commitment to large things must become
commitment to another human -- the final conquering of the
seasons -- that men honour life in both innocence and war -that because of that we shall finally forgive them and thereby
give the greatest gift, the belief in the right to life.
There was a
cert~in
naturalness in each of those three commit-
ments, and that consisted in the fact that there is a certain
longing in us for the answers each of them presents. That is,
we strongly desire that Justice be somehow a reality, that
we be children who may return to innocence and eternity,
and that we discover and assert who we are as men. We have had
glimpses of the magnificence of honour, of childhood, and of
humanity pitted against inhuman forces. Yet the glimpses were
uncertain. The primary yearning of commitment is that through
it we become what we were not certain we could trust we saw.
Very simply, if I am not certain that La Roux is honourable
but through him I have seen honour, I must not as the modern
psychologists (answering "because he has guilt feelings from
frustration with regard to his uncle") or as the early adolescents (answering not at all, but very much enjoying the question)
ask only why it is uncertain whether he is honourable, but I
must ask how it is possible for me to be honourable.
We finally
doubt the reality of things concerning which we only ask that
noble question why. We must commit ourselves to honour, without
asking forever whether it is real. In that commitment the
questioning of why must change to how, a question far darker
than why, for whereas why at least implies ananswer, how implies
nothing so much as it implies despair. I cannot help believing that just because how is so desperate,
and commitment so
unnatural, in becoming honourable we will discover, as well as
give life to, the reality of honour.
But
im.-::::.n~l.J(
t;o
ln,..
r, omrn-{
.fo.+.r-d to
Sl](~h
thj ngs
as honour is hardly
�-59to be comn itted at all, although in misreading the great books
we might believ.e it were. We must be committed to a single tl;ling yes, in the danger of being quite ordinary, I mean another human
being- in order to be committed at all. Socrates was committed
to his friends,
Achilles to Patroclus, and Jesus to his dis-
ciples. Only in this can we truly claim to love good or evil
(for they are mortal things) or what should be (for that arose
from, and for the s&ke of, what is) or to answer the fact that
everything is demanded. To make a law more just in the
6
azne
of light and justice is well, but it is simple, for it is
fairly clear, for a law can only become more or less just,
and is primarily two-dimensional. But a man is everything in his eyes the world is reflected and exists, and for
his sake the war between good and evil has been fought, and
because of his gifts we have seen what should be. He is
impossible,
complicate~,
yet in trut u it is of him that every-
thing is demanded, for everything can only be demanded of everything.
r .· books give visions no man can fulfill - of what
it is to be a son, a voyager, a warrior. But we are committed
to one
who is ridiculous, petty, and ugly, as well as one
through whom the darkness runs. This histories portray a
greatness which we who are not great and certainly we who are
young cannot understand. Men such as Aurelius are human, but
they have become so much so that we
fe~l
an impossible distance,
and forget it is the distance · > a greater rather than a
lesser humanity. As to our scorn of men like Tiberius, I can
only say that perhaps we have confused a price which must
be paid
with some terrible envisioned compromise with the
ideal. Destruction horrifies 1s, and we refuse to see that
in traversing the distance to what could be, what is must
be destroyed.
But whereas com itment to a Justice involves
merely knowledge, commitment to a man in the name of justice
demands both creation and destruction. Knowledge will be the
source of what we give, but what we give must be life and that
can only be given to living things.
�But the seasons in which we lived in the state of innocence
have not ceased for our commitments. Nor have any of the great
men failed to · -ee this. Each speak of the final conquering
of the seasons.
In Book viii
of
the Republic, Plato speaks
of the eventual decline of his perfect state:
In plants that grow in the earth, as well as in animals
that move on the earth's surface, fertility and sterility
of soul and body occur when the circles of each are
completed ••• but •.. all the wisdom and education of
your rulers '.1:W 11 not attain the laws which regulate them •••
(the laws) will escape them, and they will bring
children into the world when they ought not.
Sophocles says in Oedipus Rex
All things doth long, immesurable time
Bring forth to light and then again conceal.
repeats
And the Bible/again and again the words of Isaiah:
And the voice said, Cry. And he said, ·vvhat shall I cry?
All flesh i~ gr~?' and all goodliness thereof is as
the flower of the f!eld: the grass withereth, the flower
fadeth: but the word of our God shall stand forever.
In view of the fact that the seasons run through us
and make our stands ridiculous and our final words a
crying out at death, which is the final and encompassing
silence, ho w shall we live?
W shall and must be happy,
e
for only in that will we have answered the horrors of life.
If we refuse to be happy because there is suffering, we
have in reality lost the entire battle.
I know that it
is "impossible" to be happy, but I also know that honour
demands that we should honour what in our feeling of being
nothingness we shall n,e ver understand - that t h ose who
love us wish us first of all to be happy, and second of
all to be good.
Should we turn so quickly from that
gentle voice in the midst of so clashing a war?
I believe
that to do so is not only dishonourable but also exactly
what the forces of evil, had they personality, would desire
that we should
~ o.
W
hat greater deference can there be
to evil t h an that we s h ould acquire long, knowing, and
grey faces.
Bu t if we cannot remember to be happy even
�-61in seeing theclouds overhead in the midst of war,
we are fightin g for nothing.
If men cannot be happy
in this life there is no actual glory, for in what
does glory consist except in the ability to wrench
ourselves back when sight has tHisted us and the things
we held good.
tfu at is hell but heaven's destruction?
If there can be no human happiness, we are entirely
strangers, and so entirely unnatural, that we would
do better not to exist at all.
I stated at the beginLine of this paper that the state
of innocence can have no connection with that state
in \ili ich we perceive and join in t ne battle between
dar,k and light.
Yet the effect of having seeD both
states will be a compronise beb.reen them:
the effect
can only be a compromise because the two states cannot
themselves
c~ . promise.
The end of it all, then, is
a forgiveness.
Not only in the vagueness but also in the war we a ad
lost the ability to forgive.
The loss of that ability
,be
makes us / not only strangers to the non-human things
but also to uen and to ourselves.
Until we fili give, we
will not be able to look into the eyes of another.
There is no need to speak further on thewretchedness
of that condition, or the need to escape from it.
Forgiveness is a miserable COi.!1promise, but it is perhaps
the best thin3 we shall come to.
the eyes of a few of the old.
You have seen it in
If you thou ght to see
i t in the eyes of children, you are mistaken, for there
you can see only trust.
have demanded everything.
It does not come before we
It does not Cvme while we
are c om1": encing· upon the war, for the very nature of war
is one to obliterate universal forgiveness.
Forgiveness
must be lost when we fist separate good from evil, or
�-62we have not really separated them.
It is gained
only when we havegained someidea of who and what men
are.
We cannot know ·that until we haveseparated them
from the forces.
We cannot separate them until we
are ourselves more human.
But by separating them from
the · forces I mean nothing making them less responsible;
I simply mean the realization that men are different
even than good and evil, although they contain and
perceive them.
That they are different is marked out
by the fact that they may or may not choose to honour
the good.
Man is neither li3ht nor dark.
He is not
either gray, for there is no half-goodness, as we are
wont, in aur
p~ctorial
any of these, there
minds, to presume.
~ould
If he were
be no forgiveness, for
although there might be a battle, he would have no
choice whether or for whom to fight.
But whoever
men are, they are capable of a certain kind of honouring.
It is for that capability, no matter how misused, that
we shall for ive him.
0
First, by honouring or desiring
to honour something that is not themselves, they have
set a price upon their heads \;·hich we cannot remove,
and which only in the end we shall see.
Secondly,
and most importantly, this honouring is the only thing
in us that can stand bet\.-Jeen the state of innocence
and the war.
Men honour life in both states, no matter
how incomparable the s,tates may be.
cannot be stated:
What that means
it can only gradually be seen.
.....
Seeing that men honour life we will finally honour l. "'.
W cannut say the honouring is nothing, for by it we
e
must admit, if
1J e
are honest, that man has beyond
our quibbling set himselm at a great price, even if he
were originally nothin g .
honouring lies
for ~ iveness
In our honouring of their
and the covenant with life,
greater than any committment we made before.
Honouring
�-63and forgiving both men and life for the sake of our
seeing that men honour life, we give the greatest
gift we can - the right to live, in all its implications.
Its implications are too many to enumerate, once you
admit that for a long time you have not been sure of
that
right~
One implication of the right to live is
the right to be oblivious to the war, which iB its
heat we could never have granted;
the right to be innocent.
that right is simply
We shall then become the
mediator because of whom innocence may exist.
we should be him is as
necessar~
That
as that we should
be warriors, for life cannot be seen it its full glory
unless it is first seen in wonder.
be~inning
Life in the very
and at the end has a glory and a wonder
it can never have in the wars which begin with committment.
Because of our acceptance of the committment
to everything, we will in granting the right to live
have µssed in Genesis from the role of Adam to the
part of his God, in the end of the biblical paradigm
of the loss of innocence:
And the Lord smelled the incense they had offered
him; and the Lord said in his heart, I will not
again curse the ground anymore for man's sake •••
neither will I again smite anymore every living
thing as I have done ••• And the rainbow shall be
in the cloud; and I will look upon it, tllat I may
remember the everlasting covenant bet '- ~een God
and every living creature of all flesh that is
upon the earth.
�"The
stat
the poet's endeavor must be
itself a poem; in that case
the very requirements of its
form will reveal, as truest
, the way to address
its sub ct .. " -- W H
..
in the
Forever
the sun I seek for shade
for nanna so cold and
my time in summer
you very soon
that
yo~
die!
had known that I
be a mummer.
---J • M .. E
*Mr.
is a
of
��Portfolio :
Four Nudes
�Note:
During the school year of 1962-63, I conducted a Life Class in the st. John's Art
Studio on Tuesday eve nings until the middle o f A. 1 ,d J. .
It was well attended by St.
John's students and faculty and by townspeople as well. The moderate fees more
than paid for the models and the art materials supplied so I have spent some of
the surplus for the four reproductions
included in this issue of the Collegian.
(continued after drawings)
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E
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The Collegian began as a student newspaper; became a college community literary publication in 1952 and continued until 1969; became a student newspaper again in 1969; discontinued publication from 1980 until 1989 when it again became a student literary publication.<br /><br />Click on <a title="The Collegian" href="http://digitalarchives.sjc.edu/items/browse?collection=26">Items in The Collegian Collection</a> to view and sort all items in the collection.
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Freis, Richard (Editor)
Lachterman, David (Editor)
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The Collegian, June 1963
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1963-06
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The Collegian
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CONTENTS
Page
t .
Montaigne:
Ecco Homo · •••• • • • • Jeffrey ter Meulen,
64 • •
1
Two Portraits of Augustus • • • • • • • • Richard Freis, •63 • •
(University of Cci.l.ifornia, Berkeley)
7
A Note on Ptolemy's Tacit Assumption. • • • John Hetland, •65 • •
8
On the Theatetus • • • • • •
.• • • •
Neal Weiner,
1
64 • •
10
Three French Poems • • Translated by Christian Harrison, •64- • •
Sonnet For Helen
A Cassa.ndr.e
Ma Boheme (Fantaisie)
24
A Note on the Golden Section
• •
.,. Sanford Feman,
0
•64 • •
30
Bruce Collier, •65 ••
35
Introduction to the 11th, 12th and 13th
Propositions of-Apollonius., ••.• • .Robert Sacks, Tutor • •
36
Humpty Imnpty on ntscourse
Un-Matrix
• • • • •
• • • • • • •
R. Thomas Ing,
• • • • • • • • • •
On the Metaphorical -- Postscript • •
1
67 • • 42
Charles G. Bell, Tutor ••
***********
Editor ~ • • • • • • • • • David Lachterman
Business Manager • • • • • - Da\rld .RasnratJsen
Faculty Ad~sor • • • • • • • • • • Eva Brann
43
�Malcolm
has suggested the fol
An
an ordered
L:.
chain.
Simila
Given
there is
fixed order
n
tted
The
appear
the order of
1
elements
�MONTAIGNE: ECCE HOMO
An Essay on Method
Jeffrey ter Meulen
If I wrote a book called The World as I Found it, I
should have to include a report on my body, and should
have to say which parts were subo~dinate to my will and
which were not, etc., this being a method of isolating
the subject or rather of sho~dng that in an important
sense .there is . no subject, for it-. alone could not be
in
·
mentioned _ that book.
The subject does not belong to the world: rather, it
is the. limit of the world -Ludwig Wi ttgensteil'.l
In the end one experiences only oneself -Friedrich Nietzsche
I
In his essay On Presumption, Montaigne announces for the first time
that he is making a study of man. He has already denied in an earlier
essay the possibility of knowledge, since the inve~tigation of nature
had been rendered vain in his eyes tn)that "so · many interpretations
disperse the truth and shatter it. n( 1 There was nothing in that
inquiry which was of use to man -- there was no truth, no being in it.
"• •• there is no existence that is constant, either
of our being or of that of objects. And we, our judgment
and all mortal things go on flowing and ~olling unceasingly. Thus nothing certain can be established about one
thing by another, both the judging and the judged being
in continual change and motion."(2)
.
And so MontaiBne turned his inquiry in toward himself.
What is the purpose of these essays? I propose to investigate that
question from the vantage point of the pr~fatory note To the Reader.
It is Montaigne himsel·f who tells us that ••each particle, each
occupation of a man betrays him, and reveals him, just as well as
any other. n(J) The writing of these essays is his occupation. He
betrays his most intimate self to us. In contrast to other authors,
he is the first, he tells us, to communicate_with people by his
'entire being 0 as ¥nchel de Montaigne, not as a grammarian or a poet
or jurist. He is himself the matter of his book, he writes in the
preface; we would be unr~asonable to spend our time on so frivolous
and vain a sub,ject. ~ suspect here we are the victims of his
�- 2 ·-
Democritean mockery,his gay science. "You can tie up all moral
philosophy with a cummon and private life, n he writes in the essay
On Repentance a "Each man bears the entire form of man's estate. n{ 4)
His 'respect ·for the pubbic' he says, inhibited him from showing
himself naked. Yet his announced aim is a private one -- the tb.i os
He has made the Socratic precept -- Know Thyself -- his own. And
if the world complains that he speaks too much of himself, he would
complain that "it does not even think of itself."(5) He thinks
"the worst c9gdition of man is when he loses knowledge ·and control
of himself."~ )
•
')I(
The
ld£OS
must be kept intact, a.~d because he cannot keep his
subject still, he· must keep constant watch, and spy upon it in
different circumstances. Our aim is to find ourselves, not to lose
ourselves, he says.
It is primarily from these considerations that he develops his
method. "1-tr history needs to be adapted to the moment; ":-.lae -writes,
"I ·take hold of my subjects in different circumstances and aspects. n(7)
II
I wou)..d like to leap ahead for
"The whole)difficulty is as to
itself. n~b
To speak in these
inquiry and, in a sense, to go
that it is relevant in dealing
experience with Montaigne's.
a minute to repeat Kant's statement:
how a subject can inwardly intuit
terms is to change the level of our
beyond Montaigne. But I believe
with the subjective to match our own
It is to be understood that Montaigne is looking at him-self, whatever is concealed beneath the word. As he himself describe'S it,
(in the essay On Renentance), his method is a ceaseless listening
to the rhythm of his inner being. His essays vary in tone as do his
moods between reticence, self-satisfying ·irony, and an emphatic
seriousness. It is an artless method which obeys no preconceived
plan, but adapts elastically to the changes of his oivn being. We
see here that this strictly experimental method conforms so aptly
to his subject. His acknowledged ignorance and indifference to
'things' is part of his method; he seeks in them only himself. He
tests his subject by its responses to many things: books, ideas,
people, or situations; he illuminates it from every direction; he
dances around it. The result is not, however, a mass of unrelated
snapshots, but a spontaneous apprehension of the unity of his person
emerging from the multiplicity of his observations. The totality
of his becoming is his being. He may contradict himself, but the
truth he never ·c·o ntradicts. It is the fluctuating subject which he
contradicts' 'never the truth of the subject • .
Let us try to explicate in more lucid terms, using our own experience.
Men, man-made objects, and products are perceived as bodies within
the spatio-temporal world, but they differ from rocks and trees in
�- 3the expression of a soul. A bed, for instance, is more than a simple
body; what it is can only be understood by a reference to men. An
individual is not perceived in quite the same way as a rock; there
is involved an interpretation of what is perceived which indicates
the presence of a soul, the subjective, the 'I' or 'self' of this
other thing. This 'self' is understood through the interpretation
of simple perceptions, as being 'in' or 'with' what has simply been
perceived as a body.
But what more can we say about this •self'? What is it? Where is
it located? It is evident from the examination of Montaigne's
method that the subject is rather elusive. The necessity for his
method of irony lies in the nature of the subject • .
The self, however, is no-where to be found. Montaigne, _as his
method indicates, sees it only in the world of things, the circumstance, the .things of the world. What happens in the world points
to something which we might call our self. What we call the
activities of self come to represent the 'I'. Every· act betrays
and reveals the self, Montaigne said. The pronoun 'I' seems to be
a sign of this perception of centeredness. We predicate the
actions which we think of, to this subject. In this perception
of centeredness, we separate ourselves from the world and think of
the center as something apart from the world of which it is the
center; the world, after all, is only what we perceive. "Things do
not lodge in us in their own form and essense or make their entry
into us by their own power and authority," Montaigne writes, "external ooj~cts surrender to our mercy, they dwell in us as we
please." (CJ J
In the everyday world -- before we begin to philosophize -- none of
us is a private self confronting a world of external objects. The
mine-ness of my existence does not consist in the fact that there
is an I-substance at the center of my circumstance, but that this
mine-ness permeates the whole field of my being. ~ being is spread
over a field which is the world of its care and concern. This is
why Montaigne's method is successful. In a sense, the 'I' or 'self'
is our only world. Montaigne made himself the subject of his
physics and his metaphysics.
Being, however, still escapes us; though we are porn to seek out
. truth, "to possess it belongs to a greater power." It is knowledge
that Montaigne calls the foundation of being. But with the world
in · its cqnstant .f lux, it is impossible to know anything about it.
We only have experience, which the "infini t~ confusion of opinions
that is seen among philosophers themselves"~10) demonstrates .to us
is capable of endless interpretation. Interpretation, rememb~r, is
the mode of subjective understanding. hlhat has happened, and what
was done is for Montaigne always capable of being understood in a
new way. As things are interpreted anew, they become a new reality;
temporal existence can never correctly be understood by man. The
mask of being, the appearances, is all that we see in the world.
Even reason cannot penetrate beyond experience, . into the essence of
�III
�•.
- 5I relate this because it conveys Montaigne• s .a ttitude, one of
humorous superiority. His scepticism did not lead to despair, but
to freedom. He has broken the chain connecting himself with the
outer world. This freedom has given him his privacy -- the
of which I spoke before. Self-knowledge or this freedom relieves
the individual from a forced obedience to imperative moral command.
The individual .must a?sume the responsibility and dignity of becoming a self, and '15,os
• Montaigne looks upon self-possession
as the highest good. The aim of self-knowledge is to keep the
intact. Montaigne avoids anything which might jeopardize his selfpossession. The limits of the individual are dissolved in tragedy,
ecstacy, drunkenness, madness, selflessness and excessive self-love.
What Nietzche called the Dionysian element is avoided by Montaigne.
Conversely to what he considers the highest good -- "the worst
condition of rnan is when he loses knowledge and control of himselr,n(13)
His essay On Drunkenness is a cautious discussion of this Dionysian
urge. It is to Apollo that Montaigne commends himself for the
protection of his 1 gay and sociable wisdom. 0 ·"The most beautiful
lives to my mind are those that conform to the common humCJl:l pattern
with order but without miracle and without eccentricity."~14J This
is the closing thought· 6f his last essay, On Experience.
1
Montaigne disparages the seriousness of the world which would like
to push ''us out of ourselves and drive us to the marketplace for
the benefit of public safety.n(15) The problem of virtue then is to
find a w~v "to give myself to others without taking myself from
myself.-"~'16) It is this which is the source of his moral philosophy.
Integrity is self-possession. A man limits his freedom, which is
synonomous with self-possession, when he loses himself to possession
by something other. "They want to get out of themselves and escape
from man," he says "that is madness: instead of changing into
angels, they change into beasts; instead of raising themselv~s, the~
lower themselves. These transcendental humors frighten me.n{17) For
Montaigne, if man were to know his nature and live naturally, he
would be moderate. !
IV
I have come a long way from the .prefatory note To the Reader, which
in its simplicity told us only that we were being given a man in
his natural form. But the thought which I have just outlined is
only an introduction to something which seems to me ver;J important.
It is something which may have a connection with what we call
Morttaigrie's •scepticism'. His scepticism is a natural doubt in
view of the endless debate of philosophers. "What rule rrry life belonged to, I did not learn" he writes "until a~er it was ~ompleted
and spent. A(new figure: an unpremeditated and accidental
philosopher." 18 J.
In his philosophy "we have emancipated ourselves from nature'~ rule
to abandon ourselves to the vagabond freedom of our fancies."~19)
�P• 220
p
p
p
1
�Statues
of Art
New York
Dick Freis
construes
Likeness in these
featured the same reveals
The subtler difference. The
man
Eludes us: nor may
s be true
About this man who wa.s so many,
So
see this:
Grandiose:
Man-and-a-half
gazers
Who crack their necks toward his indifference,
And
fall back until his
focuses.
Grace of stone: intell~~-~··-~ moves
Nowhere
power balanced
Down.on
whose muscles groan
Beneath
of Rome; intell.~~··~~
Moves nowhere; nor does blood beat toward the heart.
Arms are
in stilted
pose:
arm
Lucretian skies, slate and
God ... hollow; left rests toward the hollow
eros tacked on at his feet is Amor
Hard
; other swords rise
the blind
death
His breas
tells it all
center, Rome victorious
, and Dmm and Deu; Earth rests
at his side ride Sun and Moon;
The universe: all circled round
Beautiful; but one is
comfortable:
The senseless comets of Vesuvius
Fall
seem as human. Then see this:
An older face -asides
Fires of ambition
The brows
Necessi
Now thin
The chin relaxes into
Here
and mercy live: and therefore steel
To hold the Roman peace
ceaseless war;
But no more
the fiercer battle flares,
himself a man from
The unknown
�- 8 -
NOTES ON ·PTOLEMY 9 S TACIT·ASSUMPTION
John Hetland
On page 16 of the sophomore Ptolemy manual it is stated that, for
any outer planet, the angular movement in longitude plus the angular
movement on the epicycle is equal to the angular movement of the
mean sun. From this fact, three consequences follow, provided a
certain assumption is made. It is with this assumption, and the
proofs of the consequences, that I ~tlsh to deal.
The assumption, as stated in the manual, is that at ~ time the
planet, the mean planet, the mean sun, the apogee of the eccentric,
and the earth are all in one line. However, r;the apogee of the
eccentric" should" be struck from this list, as will be shown. The
importance of this seemingly trivial correction will be seen when
the strange coincidence is accounted for by Copernicus. For while
it is necessary, in the heliocentric theory, that the. planet, the
mean sun, the earth, and what will correspond to the mean planet,
be all on a straight line at some time, it by no means follows that
what will correspond to the apogee of the eccentric be on this line.
Thus the coincidence would still be unaccountable under the heliocentric theory, were it not for this change.
Although the demonstration becomes more complex, the three consequences still follow, as is shown below. In the diagram I have
drawn the earth E, the mean sun S1, the mean planet M1, and the
planet P1 all on the -same line, but the apogee of the eccentric not
on this line. I have shown these points at any later point in time
as E, Sz , M 2• and P2 • I have also drawn the line through the
equant Q and the mean planet M1 to the mean apogee F and called the
angle in the epicycle between the mean and true apogees angle b. I
wish to prove the first consequence given in the manual, that the
line joining the earth and the mean sun is always parallel to the
line joining the planet and the mean planet; that .is, that ES 2 is
parallel to M P2 •
_
2
As the epicycle moves from M to M 2w:lth speed 1, the planet moves
1
from P1 to P2 , that is from G to P2 (for. the planet is moving with
respect to tne line through the equant and the mean planet,* and
it has moved through the angle b before crossing this line), with
speed a, and the mean sun moves from s 1 to s 2 with speed .i + a. I
have drawn EJ parallel to ' QH; therefore angle M EJ equals angle
1
M:1NM2 • But angle I11NM2 is the exterior angle of triangle MQN, and
tnerefore it equals L :f. b. Therefore angle M EJ equals L 1+ b.
1
Now angle s1Es 2 equals ~t+ a. Subtracting from it angle M EJ equal
1
to £ + b, we have as the remainder angle JES 2 equal to a - b.
But ·in the epicycle, angle HM2P2also equals a - b, and EJ is parallel
to QH. Therefore ES 2 is also parallel to M P2 , which was to be proved.
2
The consequences involving opposition and conjunction now follow
directly from what I have proven.
* See
Ptolemy, ~x.6, para. 4.
�- 9 -
.
I
; r.
A briefer and less rigorous .demonstration is as follows:
Since QM rotates with spe,ed J2. with respect to any stationary point,
and MP rotates in the same direction as QM with speed a with respect
to any stationa~; poirit,
·av
.
therefore MP rotates with speed ,R t.Jwith respect to any stationary
point. But ES also rotates with speed
+ a with respect to any
stationary point, and Es is at some time in a line with MP. Ther efore
ES . is always parallel to MP.
.e
�.....
is
�- 11 - .
trying to use that rough whole it will be found that it requires
modification and refinement. We then arrive at a dialectical
interplay between whole and part-between theory and fact, which
moves towards the completely unified goal. This paper is only
the first timorous step in that direction.
******** ***
Let us begin this examination by looking at the character Theodorus. Theodorus, a mathematician from Cyrene, reveals in his
very first words that characteristic of his which will most concern us. Socrates has asked him to tell of young men of Athens
who are devotl.Q.g themselves to mathematics "or any other fonn of
philosophy".{lJ Theodorus replies:
"Truly Socrates, it is well worth while for me to
talk to you about a splendid young fellow, one of
your fellow citizens, whom I have met. Now if he
were handsome I should be very much afraid to speak
lest someone should think I were in love with him."(144)
What is revealed here is a high sense of respectability in Theodorus. Al though what he had to say may have been perfectly true
and merited by Theatetus 0 s conduct, he would not have said it if
it were to involve him in the shameful act of chasing a beautiful
young boy, even if there were no more truth to the involvment than
idle gossip. Let us compare this to a passage from the great
myth of the Pheadrus:(2)
"Now when the charioteer beholds the love-inspiring
vision and his whole soul is wanned by the sight and
by the ticklings and prickings of yearning, the
horse that is obedient to the charioteer, constrained
as always by modesty, control9 bimself and does not
leap upon the beloved."(254A)~3J
It would seem that both the modesty imaged here and that brand of
respectability evidenced by Theodorus are the offspring of t he
. same shame. In his first words Theodorus identifies himself with
·the white horse, and hence with that sort of respectability that
is opposed to eros. But perhaps this is because he sees nothing
beautiful in Theatetus' s face. ·
This is not so. Throughout the first third of the dialogue,
Socrates endeavors to get Theodorus into the conversation. At
one point in his attempts he compares the conversation at hand to
a Spartan wrestling school. Theodorus is accused of sitting in
the bleachers watching the naked wrestlers and refusing to strip
himself. He replies: "Why not, if I could persuade them to let
me do so?"(162B) What a preposterous perspective he has on the
whole affair. He, an old man, most likely with an aging body,
i ·s going to try to persuade the beautiful bodied youths not to
drag him into the ring. Now clearly the wrestling itself is
symbolic of the sexual act. How then, can Theodorus sit there
�2
• •
were
�- 13 - .
the cave, it is Socrates, the philosopher, who is doing the pushing.
Hence, the "philosopher" described here is repudiated by Socrates in
his own actions, and certainly Socrates is a true philosopher. Then
who is- this "philosopher"? Thales, the prime example., was an astronomer who fell into the ditch ·while studying the stars. According
to Pindar the "philosopher•• is . "above the sky, measuring the stars
(astronomy) and the surface of the earth ( 7:G.Lv~tr1:>&;'ryci'-) (175E) •
These are the things which Theodorus is said to be able to teach
Theatetus. Also, early in the dialogue it is mentioned that Socrates
knew Theatetus's father (of his own generation and hence his neighbor)
while Theodorus did not, but ·knew Theatetus. Again, at the end of
the digression it is curiously asserted by Socrates that the
"philosopher" knows "how to drape his coat like a freeman". This· is
certainly out of place with the rest of the description; why should
one above the sky care about his cloak? There are two reasons.
First, the cloak represents clothing in. general and by contrast,
nakedness. Secondly, the proper draping of the cloak evidences the
social respectability of the wearer through indicating his social
position. So again we find the image of nakedness occurring in
conjunction with respectability. Again we must point our fingers
at Theodorus as this "philosopher". But the quotation from Pindar
points to him in his capacity as mathematician. It is as mathematician that Theodorus shares the activity of the "philosopher".
The relationship of eros to knowledge here begins to reveal itself -can we now find some relation between these two images: -mathematics
and nakedness?
At an earlier point in the dialogue (165A), when Theodorus is begging
off from entering the conversation, he offers the following excuse:
I
,
.
'
"As for me, I turned too soon from tµ 1.. A c:.J v /\ ~ ;rov to
geometry."
.
a
Now ? l ,..\ c:.: .S
-J/
in its primary sense means naked. In itself this
is nothing new; Theodorus is once again fleeing the erotic. But in
this case, the· nakedness is directly opposed to geometry, or in
general -- mathematics. We now have two reasons for associating
his lack of eros with mathematics, the one just given and the fact
that it was Theodorus as mathematician who was the "philosopher" of
the digression. There remains one more incident with which to weld
the link.
As stated before, Theodorus spends the first third of the dialogue
avoiding involvment, but at 169 he finally enters. Why? Immediately
after Theatetus defines knowledge as perception and Socrates tells
the Protagorean _p- J{;, .s
, Theodorus asks if all this is wrong
after all. Socrates, forgetting Theatetus, addresses bis next
question to Theodorus. He begins by pointing. out that if this
is true, then one man cannot be any wiser than another man (160A) or
even another animal, but to illustrate his point Socrates relegates
himself and Protagorus to the dogs. At this point Theodorus admits
that Protagoras is wrong, but since they were friends Theodorus will
not contribute to Protagoras 0 s defeat. Socrates then makes a speech,
in the name of Protagoras, saving the f'- :,.;"'6os from his own criticism!
�- 14 -
Next Socrates refutes it again by means of memory and again tries
to involve Theodorus -- . again he fails. So, Socrates makes another
speech in Protagoras's name, reinstating the ~:()()o:, • In that
speech Protagoras demands that he have a man, not a child. to defend
him. Again Theodorus refuses, but here a new twist occurs. Socrates
again brings up the question of ·the equality of men's wisdom as a
result of the tu-v'6o
, but this time he illustrates it differently
5
"But come my good .man, follow the discussion just
until we decide whether you must be the measure in
respect to diagrams, or whether all men are as sufficient
unto themselves as you are in astronomy and the other
sciences in which you are alleged to be superior."(~)
'Fheodorus yields. He will enter the discussion long enough to answer
this and only this question. Clearly it was for this purpose that
Socrates kept defending the µJ{J os after he had refuted it. Only
if Theodorus's position of r~spectability and security which he had
as one knowledgeable in mathematics were threatened would he ever
enter the argument. Hence, Socrates could not allow the ;-t:Jt5)o s
to be defeated until he entered. So then, Theodorus comes in in order
to save his mathematics from the chatter of the many and chaos of
the fl.ux. As long as his mathematics was secure from assault he would
not enter, but realizing the threat posed by Protagoras, he condescends
to the "act of love", Socratic dialectic, in order to save it. The
chain is complete, and his main characteristic, lack of eros, is bound
to his mathematics. We must endeavor to come to(sQme understanding
of this discovery. A passage from the Symposium 5J will be helpful
here:
"The truth is this: no god seeks after wisdom or
desires to become wise -- for wise he is already:
nor does anyone else seek a~er wisdom if he is
wise already." (203)
The most curious thing about this entire dialogue is that two mathematicians (men of science-scientia-episteme ) are unable to define
knowledge. !bes not the above quotation tell us why? it is a part
of Diotima 9 s explanation of love to Socrates, the conclusion of which
will be that eros is a lack. It is an emptiness and a seeking a~er
what one lacks, and hence it is the lover and not the beloved who
embodies eros. So then, since we confirmed the connection between
Theodorus's lack of eros with regards to both sexual and intellectual
objects, would it not then seem reasonable to say that, for the same
reason that the wise seek not wisdom, he seeks not knowledge? This
is not to say that he has knowledge in the full meaning of the word ,
but he thinks he does. We said that Theodorus, as mathematician, was
the "philosopher" of the digression, hence it is as mathematician
that he should have knowledge.
It was only when the Protagorean doctrine of universal flux threatened
his status as mathematician that he entered into the conversation.
Why, in non-dramatic terms, is this? If there is one thing we know
�- 15 - .
about mathematical works, it is that they stand still. The words,
the theorems, the whole system stands in its beauty to be understood, appreciated, and remembered. It is in virtue of this stasis
that mathematics is here threatened by the flux. When he describes
the Ephesian followers of Heraclitus, Theodorus rails against them
because they let nothing stand still, and says we should not act as
they do, but we should treat the problem mathematically (181) (as
was previously demanded by his friend, the sophist Protagoras). The
mathematical course fails, but the interesting thing is that Socrates
makes a left-handed defense of the Ephesians by saying that they
teach their real doctrines in private and only to their friends who
are explicitly not Theodorus but implicitly Socrates. As further
evidence for this, we noted earlier that Socrates assumed the guise
of Protagoras in his defense of the j)- v&l .s
• It must be because
in some way they are alike. Now if we look at the dialectic as
presented in the dialogues we see that it never stands still. It is
a constant search, never affirmtg~ but always denying and refUting
while moving towards the truth.l J Just as Socrates' diamon only
says "no", so works the dialectic, only refuting but never affirming.
And yet we have Socrates's own words at 15JC:
"And what of the soul? I:bes it not acquire information
and is it not preserved and made better through practice
and learning which are motions?"
Because of the identification of Socrates and Protagoras, we cannot
take this as simple irony. Is it not true that he who learns ler~rns about
that of which he is ignorant? i.e., that which he lacks (the
question of knowing and not knowing will be taken up presently).
The analogy between loving and l ·e arning is complete. Both the lover
and the learner must lack. But just as Theodorus is unnaturally
continent, so has his mathematics staais given him a false sense of
knowing (stasis). Thus we see why lack of eros was picked as his
characteristic. The only time he expresses any interest, eros, is
in order to hear about Parmenides who denied the existence of motion,
which negates dialectic and hence is a negative sort of eros. We
shall return to mathematics later and a more detailed examination of
its relation to knowledge will be taken up then, but now we must turn
to Theatetus.
Since we began with Theodorus's first words, let us try to be consistent and do the same with Theatetus. Socrates asks him whether
we should inquire about Theodorus 9 s qualification for saying that he
and Socrates look alike. His reply is "We should enquire" ( 145E).
Whatever we say about him, we cannot put him in the same class of
non-erotic beings in which we put his teacher, for by his reply he
seems the exact opposite.
VJhereas in the case of Theodorus there may have been some doubt about
eros's being his defining characteristic, there can be none in the
case of Theatetus -- it is timidity. Throughout the entire dialogue
Socrates is constantly trying to arouse courage in him, and he sinoerely wants to be courageous (187B). The whole midwife tale is
�- 16 - .
told for the purpose of inducing Theatetus to have confidence in his
own abilities through belief in the devine authority of Socrates as
an infallible destroyer of bad children and deliverer of good ones
(151D), When Theodorus disdains being made equal to the dogs,
Theatetus is too modest to accept equality with the gods (161c-162A
and 162C respectively). To list all or even more of these examples
is needless, it is the exceptions and ·variations that will interest
us here. As we went to th~ Symposium before, let us now take a
passage from the Laches.(7J
"Then the answer which you have just given, Nicias,
includes only a third part of courage, but our question
extended to the whole of courage, and according to
your view ••• courage • . •• is knowledge of nearly
every good and evil • • • ". ( 199C)
However playful we may take this to be, we must recognize the problem contained within this passage. Action in ignorance cannot be
called courageous, but only foolhardy. Our old saw about fools and
wise men does not mean that the latter are cowards, but that unless
one acts with knowledge of the circumstances under which one is
acting, no matter what the situation,- he cannot be courageous. It
is easy to walk off a cliff into a net five hundred feet below, if I
do not indeed know that I am at the edge of a cliff. And yet, if I
am in ignorance of the situation, but nevertheless realize that there
is danger ahead, I must fear. There ·may b.e fear without courage,
but not courage without knowledge.
Now Theatetus does fear, but is he ignorant? Clearly the answer is
no, at least no more than he should be. He is, a~er all, a young
boy and should not be expected to hold forth on great matters. But
more than that, he is extremely capable. Several times throughout
the dialogue he exhibits his ability to deduce from given pre~~es
by seeing the conclusions that will follow from what he says.~ 0 J
Also, in the example of correct definition at the beginning of the
dialogue, he exhausted an infinite group of numbers into a general
theorem, while all Theodorus was evidently able to do was to give a
few particular examples by drawing them. In addition to all this
innate capacity, he has heard all the prevalent theories of the day
concerning the subject of knowledge and, although they may ultimately
hinder him from reaching his own understanding of the questions, he
is not only talented, but "learned". How then, if what we said before
is true, can he lack courage?
The point is, I think, that however good he may be, he nevertheless
thinks himself ignorant. In all honesty he admits that he did not
understand the Protagorean doctrine, and the third definition he
offers is one he had. heard, barely remembered, and certainly did
not understand. The only definitions of knowledge that are his own
are that it is many things and that it is right opinion. The first
of these was quickly shown to him to be worthless, and the second
is self-defeating, and he only mutters it half-heartedly. Before
offering the last definition he says that he is dry and has no more
�- 17 - .
to offer (148E), even a~er Socrates has told him that he is
pregnant. Unlike his teacher, he does not lack eros, for we are
told that he wondered about this question even before he met Socrates,
and Socrates quickly fills him with more (155C), but his eros stems
from his thinking himself totally ignorant. It is for this reason
that he is too modest to approach these grand questions -- he feels
himself inadequate and unworthy of them.
Can a connection be made between his timidity and his position as
mathematician? A~er Theatetus has given the first mathematicarexample, the dialogue.sgoes as follows:
Soc.
Most excellent, my boys, I think Theodorus will
not be found liable to action for false witness.
Theat. But really Socrates, I cannot answer the question
of yours about knowledge, as we answered the
question about length and square roots. And yet
you seem to want something of that kind. So
Theodorus appears to be a false witness after all.
Soc.
Nonsense! If he were praising your running and
said he had never met a young man who was so good
a runner, and then you were beaten in a race by a
full grown man who held the record, do you think
his praise would be any less truthful? ( 148B-D)
Theatetus, although he was able to find the unity in the manyness of
these mathematical objects, fears that he cannot apply the same method
to non-mathematical objects. Socrates does not deny the distinction,
~ut he adds that the study of mathematical objects is a prelude and
training ground for the more important and ultimate objects of knowledge. And this is the crux of the matter; Theatetus is aware of a
special nature belonging to objects of his inquiry, whatever it in
fact be, and hence is fearful of his ability in other fields and
therefore thinks himself ignorant and incapable. Socrates affirms a
similarity between the two fields- but Theatetus does not understand it.
,
So both Theodorus and Theatetus feel the limitedness of their positions
as mathematicians, but in the former case this feeling resulted in
complacent acceptance ·of it, and in the latter it resulted in a desire
to go beyond but also a fear of treading outside of the mathematical
limits. Thus we perceive the ·similarity and difference of their characters. The · study of mathematics has given to Theodorus an attitude of
knowing, but to Theatetus an attitude of not-knowing or ignorance.
Now in a dialogue about knowing we W"Ould expect this dramatic antithesis to reveal something about the nature of knowledge. If we look
at the center of the dialogue (9) we find this same antithesis expressed in other terms. At 181 the Pa:mnernoean philosophy· is opposed
to that - f the ~hesians. Wa cannot go into his doctrine in any
o
detail, but it is clear that they are opposed to Protagoras in respect
to motion and rest. the former maintaining universal flux, the latter
universal stasis. The former of these presented itself as a challenge
�- 18 -
to the possibility of knowledge since nothing could be know because
nothing was, all was becoming. If then, we posit complete stasis,
there should result complete knowledge, for if non-being does not
exist how can there arise the possibility of error? Now the
possibility of error is perhaps the main theme of this dialogue.
Each of the three definitions as they are expounded reflects upon
this question. In the second definition, it is found that if we
assume that a thing is either known or not known, there is in no
way the possibility of error. There will result either complete
knowledge or utter ignorance of the object in question. At the end
of the third definition of error, interchanged opinions, this assumption is rescinded, but nevertheless we have not seen the end of it.
At the end of the aviary analogy (which began as a distinction between having and possessing as a way to solve the problem of knowing
or not knowing) Socrates comes to the following conclusions:
Soc. Then a~er our long wanderings we have come round
again to our first difficulty. For the real
reasoner will laugh and say 'Most excellent sirs,
does a man who has both knowledge and ignorance
think that one of them which he knows is another
which he knows? Or knowing neither of them he is
of the opinion that one which he does not know
is another which he does not know? • • • Or will
you go on and tell me that there are kinds of
knowledge of the kinds of knowledge • • • and thus
lead us in an endless circle? (200B-C)
The assumption that we either know or do not know is clearly then
still with us. A~er this, the search for false opinion is dropped
and a new definition of knowledge is advanced, that it is right
opinion plus . .\ 6 - o.s • The question immediately becomes what ;s
r
,.\,J ~f'OS • Now in the first of the three definitions of A6ff 0 ':3'
offered by Socrates it is called "making one's own thought ( fu( volv<)
clear through talking by means of verbs and nouns, imaging the opinion
in the stream that flows from the lips as in a mirror or water" ( 206D).
This is probably the true one of the three (Socrates has said (206C)
that one of the three is true) since previously ( 190C) ~ t.~ vvc...d..
was defined as silent ...\D'/[.;:iS
• But why is it then rejected? It
is rejected because under those circumstances there would be "no
possibility of right opinion apart from knowledge". Hence we are
driven back to the possibility of false opinion and thence to the
problem of knowing and not-knowing. We see then that his question of
knowing and not knowing casts its shadows over the whole of the last
two definitions of knowledge and prevents any conclusion from being
attained.
Just as this question is the prevailing one in the arguments, so is
it reflected in the dramatic characterizations of the two interlocutors, Theodorus representing, as we have seen, knowledge; Theatetus,
ignorance. This then provides a means for viewing the sequence of the
arguments through the entire dialogue. As we said, the bulk of the
time given to the consideration of knowledge as perception is given
to Theodorus or is at least for his sake, while once knowledge is
�- 19 -
de fined a-s right opinion he never speaks again. Taking that point
as a natural dividing place, we note the following: in the first
part the definition is viewed as reducing all opinion to equally
true sensations, but it is always true to someone, never in itself.
Hence the threat is that there be no knowledge at all, for truth
must be simply true. However, .in the second part, the assertion to
be denied is, as we have seen in both its definitions, that there
is no false opinion, or, in other words, that all is knowledge. In
accordance with the principle that one must either know or notknow, the dialogue is then divided into two parts the first of which
corresponds to not-knowing and the second, to all-knowing. As we
said, Theodorus is the chief interlocutor of the first part, and this
·is because he must be shaken from his knowing mathematical security,
and so he is by the Protagorean
(.).$
•
On the other hand
Theatetus thinks himself ignoran • and he therefore is in the half
where the possibility of ignorance is quest_oned. Finally, at the
i
end of the dialogue (205A) he gains courage, and this is because the
atmosphere of the whole section suggests that none can be ignorant.
c· (.)
V
But if the mathematicians are at the opposite ends of the stick, where
is Sdcrates the philosopher? Let us return to the same passage from
the Symposium.
"Then who are the philosophers, Diotima, said I, if
those who seek after wisdom are neither the wise nor
the ignorant? That's clear enough even to a child, she
answered, they are the ones between these two, as love
is. You see, wisdom is one of the most beautiful things,
and love is of the beautiful, so love must be a philosopher, and so being he must be between wise and ignorant.ff(203)
So then, the philosopher, as the truly erotic man, stands necessarily
between knowing and not-knowing. \rJhat about courage?
Soc.
• •
. ~~
You seem not to remember that our whole search
from the beginning has been for knowledge because
we did not know it.
.•· : . • r~ •
•
Theat.Oh yes, I remember.
Soc.
Then is it not shameless to proclaim what it is to
know, when we are ignorant of knowledge? But
really, Theatetus, our talk has been badly tainted
with unciearness all along; for we have said over
and over again 'we know' and 'we do not know' and
'we have knowledge' and •we have not knowledge',
as if we could understand each other while we were
ignorant of knowledge; and at this ve-ry moment have
used the terms 9 be ignorant• and 0 understand 0 as
if we had any right to use them if we are deprived
of knowledge.
Theat.But how will you .converse, Socrates, if you refrain
from these words?
Soc.
•I
Not at all being the man (;;(v -17f) I am • • • • (196D-197A)
�- 20 :JI
.
~1
~/
f) .
The use of the word ~If 1f ( "1'· n • ~ v o;> ~-s) for man inst~ad of a<ll /)-i..urro~
indicates Socrates as the possessor of courage ( ~v6 f ~ L-°'
)•
So then, Socrates, as the courageous man, also stands between
knowing and not-knowing. In both cases he is the mean between
the extremes, Theodorus and Theatetus. This whole affair is summed
up in his well known epigram oil>~
al,,1< o~~~
•
("
o,-'-
But does this dramatic characterization reveal, as before, something
about the arguments as a whole? !bes the addition of Socrates the
philosopher tell us something more about knowledge, something that
could not have been told by Theodorus and Theatetus? If we return
once more to the early part of the dialogue (145E) we find Socrates
and Theatetus engaged in the following conversation:
Soc.
And does this differ at all from knowledge?
Theat.
Ibes what differ?
Soc.
Wisdom. Or are not all people equally wise in
that of which they have knowledge?
Theat.
Of course.
Soc.
Then knowledge and wisdom are one?
Theat.
Yes.
Soc.
Well it is just this that I am in doubt about and
cannot fUlly grasp by my own effort -- what knowledge really is.
1J'e tend to forget that the purpose of the whole dialogue is here
.
r
clearly shown to that of distinguishing knowledge from wisdom. The
word "wisdom" occurs many times throughout the rest of the dialogue,
but no direct mention is ever made of the question again. Now I
would like here to quote Aristotle on the subject of wisdom.(10)
"Such and so many are our notions, then, which we have
about wisdom and the wise. Now of these characteristics
that of knowing all things must belong to him who has
in the highest degree, universal knowledge, for he knows,
in a sense, all things which fall under the universal.
Now these things, the universals, are the hardest for
men to know, for they are the farthest from the senses.
And the most exact of the sciences are those that deal
with first principles." (Metaphysics Bk. 1, Ch. 1,
982a 20-25)
How does this bear on this dialogue? To see this we must look for
a moment at the divided line in the Republic. Th~ mathematician is
the pictured in the section whose faculty is <5 '-r;( v uL.d-,
•
He uses
the objects of perception in his sc~ences, but not as things in
themselves, but as images of other things about which he is truly
concerned. However, there are principles which underly his own
�- 21 - .
science -- his suppositions which he does not consider as objects of
inquiry, but which he uses, assu.ming them to· be understood. These
suppositions are the first principles of Aristotle's introduction to
metap~sics just quoted.
So when Theatetus is afra~Ei to examine one
of these, viz., knowledge and all that it involves,t11) he reaffirms
the Republic's image of the mathematician. Mathematics ( a<..:_ Voul(.)
is, as we have seen before, the subject of this- dialogue~ Let us
take one more look at the whole in the light of the divided line.
First we must recall the; sequence of the divided line. The first
division has as its object of cognition images ·or perceived things;
the second, the perceived things themselves'; the third, the perceived
things as images of more intelligible entities. But · the fourt and
highest, the realm of highest knowledge and hence wisdom, has as its
objects of inquiry those principles which underly the &1_r/ vo<-cA of
the third section. Now let us look at the sequence of the three
definitions of knowledge in the Theatetus. The first presents perceived
objects as the results of unseen motions which are the "realities",
as images of them. The second, on the whole, deals with perceived
obiects, ~aken simply as such, and their identification or being
mistaken.~12) The third deals with the logos and its nature, and, as
we have said before, the A.6,ro s is a reflection of £ <-~ 11 OL°' ,
the mathematical mode of coghition in the Republic. These two sequences parallel each other exactly! It is all there .but for the
absence of an analogue to the fourth · part of the divided line. But
the whol~ dialogue is climbing up, the divided line by means of the
.,16 S P1 the dialectic itself. It therefore must stop at the
third part because the interlocutors are mathematicians and cannot go
beyond dt.o("v'o1..o<.
to the realm of the eye of the mind (which in a
curious way leads us back to perception as knowledge).(13) Just as
this dramatic sequence must here stop, so are we unable to reach any
conclusions about knowledge until we examine· the various objects of
knowledge.-0 which requir~. s a study of being as such. The very statement of ot~ .1\ 0n_ o ~ K. 0 ~~ ·)!.,
implies ontological necessities
which stagger the imagination.(14) Also then, just as the dramatic
action is carried into the Sophist, so does the subject of the
Sophist, being-non-being, same-other, motion-rest, correspond to the
fourth part of the divided line. And so, because we must identify
dialectic with A 5 0 H
and ~' 1.. . ~ "''.) 1-')(, in the realm of discursive
reasoning, Socrates will sit silently in that dialogue, yielding to
the god-like Eleatic stranger.
ro
1
1
And yet there is still a greater reason for all this. At the end of
the dialogue Socrates goes to the porch of the king "to answer the
suit· which Meletus has brought against me." Throught this entire
dialogue he has known that he is about to die. What will becom of
e
philosophy when he is dead? hlhat will become of Athens without its
greatest politician? In his first words Socrates demands to be introduced only to a promising Athenian youth. When he looks with his old
eyes on the youthful Theatetus and perceives his own form proportionately
scaled down, he finds hope in Theatetus's possibly being the one to
replace him as the gadfly of Athens. But Theatetus must be saved from
Theodorus and mathematics before he becomes as hopelessly dead as his
teacher. In death Socrates takes the role of midwife to give life to
�o.
�- 23 - .
Aristotle to interpret Plato, but I feel justified in this
particular case. There seems to be no reason for this King
first of all that Aristotle disagreed with his teacher on
this point. Secondly, it is a common enough notion of wisdom
for us to have arrived at it on ouw ovm. Thirdly, the fourth
part of the divided line should correspond to wisdom as it
is clearly the highest knowledge.
11 •
Namely the principles enumerated in the lists of 18~187
plus motion and rest which p~rvade the whole dialogue.
12.
It is only in the aviary analogy that we begin· to deal with
what may be called "pure noetic entities". In the wax tablet
attempt they are dismissed as being somewhere else above the
tablet, and are not mentioned again.
This is hinted at at the end of the aviary affair where the
result is that is must be discarded for it would require kinds
of knowing of the kinds of knowing. The aviary was conceived
for the purpose of explaining 7 plus 5 equals 11, after the
wax: tablet had taken care of mistakes as regards perceived
objects. The mis-addition is not of dogs or · other obj'ects of
sense, but is of the pure monads and their ;;f"&f-"- ot. . • Hence,
what is required is an explanation of a mean ·between knowing
and not-knowing the "pure noetic entities". The obvious conjecture is, why not a wax tablet for them also, only let it be
different in its "matter" than the first? This leads immediately
to the question of how and where the no·e tic imprints were gotten,
and suggests the eye of the mind and the myth of recollection.
The existence of non-being, and resultant degrees of being are
two such implications and reflect the symmetry between knowing
and the thing known, i.e., between epistemology and ontology.
13.
14.
�sous
ombres
Vous serez au
Pierre
�bones nor
�-
I
��crevees
���2
=
::::
=
=
��- 33 - .
HUMPTY DUMPTY ON DISCOURSE
Bruce Colli.ar
"The question is," said Humpty Dumpty, "which is to be master."
APOLOGY
I intend to take two or more statements from Lewis Carroll's works
Alice• s Adventures in Wonderland · and Through the · Looking-Glass and
explicate them in terms of discourse. This is not meant as an
interpretation of the t.Jorks in question, or even of the passages
from which the statements come or of the characters who utter them,
al though I may speak as if it were. I may seem to be reading too
much into the statements, but I should rather be thought of as reading
out of them. I make no claim to follo1dng the thoughts of the author.
The problems of discourse are deep; and the pitfalls and byways are
many. rwould hope to avoid the pitfalls and byways, and, perhaps,
to hint at a few of the problems. I will be saying rather more or
less than I mean.
***********
In confronting the problem of discourse, we are presented with three
focal points for our inquiry i the sounds that make up speech, the
thoughts that give rise to speech, and the objects in the world about
which our thoughts are formed. We shall- be concerned with the
relationship between these three points.
The following two statements will be taken as representative of two
points of view on the nature of discourse.
The Illchess:
Humpty Dumpty:
"Take care of the sense, and the sounds will take care
of themselves."
"When I use a word, it means just what I choose it
to mean, neither more nor less.·~
The approach of the Ihchess is an innocent one. What is primary here
is the sense: the meaning or thoughts in the mind of the speaker.
The sounds uttered in speech are a reflection of these thoughts: a
means of conveying them from a speaker to a listener. The actual
form that the sounds take is unimportant, merely conventional; insofar
as they are more than noise, they ~ the thoughts that they represent .
In a sense, they pass out of the picture entirely. In many ways they
are similar to the electrical impulses used in radio transmission.
But the world is left out. Words re-present thoughts about objects
in the world, but not the objects themselves, Since, then, thoughts
can be formed about these objects only on the basis of sensation, words
are no more than expressions of sensations and opinions• The Dlchess
�are.
the
�- 35
nature and structure of discourse reflects the nature and structure
of the world, and can lead us to see it; indeed, there is no other
way.
Humpty Dumpty tells Alice that he pays words for using them. We
too must pay them -- pay them reverence •- submit to their mastery
before we can master the problem of discourse and rise to the truth.
EPILOGUE
It may seem strange that Humpty D.nnpty, realizing the problem of
rhetoric, should himself be so poor a rhetorician as to impress
Alice as highly •0unsatisfactory." .Alice herself resolves this
problem in commenting on the fact that Humpty llunpty is alone.
Since the power of rhetoric consists in knowing the available
means of persuasion, it cannot be developed in isolation from
other men. Humpty Dlrnpty, shrewd as he may be, cannot fully
pursue rhetoric or dialectic, outside of a political context.
"~
can°t, perhaps", said Humpty Dumpty;
"but . ~
can."
�is
us
have been aware of
from the
were more
the ones he
of human
also be
even
cases
from the most
from any
conic may be
be
conic
back
cone.
was not
For the
case
have known
in fact be
conic
cone
from any
to
case in which the
of
the nature
section was
the vertex
at the vertex is a
Thus
be a
the
and if
(
to one
the
cone.
were as
in the
of the
the
cone
if acute
, the
the section
be a
be an
�- 37 "Apollonius the geometer, my dear Anthemius, nourished at Perga
in Pamphylia during the time of Ptolemy Euergetes, as is related
in the life of Archimedes written by Heraclius, who also says
that Archimedes first conceived the theorems in conics and that
Apollonius, finding they had been discovered by Archimedes but not
published, appropriated them for himself, but in my opinion he
errs. For in many places Archimedes appears to refer to the elements
of conics as an older work, and moreover Apollonius does not claim
to be giving his own discoveries; otherwise he would not have described his purpose as •to investigate these properties more rul.ly
and more generally than is done in the works of others.• But what
Geminus says is correct: defining a cone as the figure formed by
the revolution of a right-angled triangle about one of the sides
containing the right angle, the ancients naturally took all cones to
be right with one section in each -- in the right-angled cone the
section now called the parabola, in the obtuse-angled the hyperbola,
and in the acute-angled the ellipse; and in this may be found the
reason for the names they gave to the sections. Just as the ancients,
investigating each species of triangle separately, proved that there
were two right angles first in the equilateral triangle, then in the
isosceles, and finally in the ocalene, whereas the more recent.
geometers have proved the general theorem, that in any triangle
the three internal angles are equal to the two right angles, so it
has been with the sections of the cone; for the ancients investigated the so-called section of a right-angled cone in a rightangled cone only, cutting it by a plane perpendicular to one
side of the cone, and they demonstrated the section of an obtuseangled cone in an obtuse-angled cone and the section of an acuteangled cone in the acute-angled cone, in the cases of all the
cones drawing the planes in the same way perpendicularly to one
side of the cone; hence, it is clear, the ancient names of the
curves. But later Apollonius of Perga proved generally that all
the sections can be obtained in any corte, whether right or
scalene, according to different relations of the plane to the cone.
In admiration for this, and on account of the remarkable nature
of the theorems in conics proved by him, his contemporaries called
him the "Great Geometer." Geminus relates these details in the
sixth book of his Theor:v of Mathematics.
The precise method which the pre-Apollonians used is not known, but
something like the following proofs has been suggested by Archimedes' Conoids and Spheroids; Prop.
7.
�the
Given a
to
a
and
L.
0
I say that
the base
the cone at
I
Draw
Draw
Now
:::::::
I may
BAG and BCG are both
a
as
G
BN
=
bisects
But
is
to
= AF
=
= FG
= NG
and
NG
=
=
and since BN
=
=
�- 39
I say that
NQ2:AN,2AL::A'N' :A'A
or that the original
equality has been contorted*
by the ratio A'N:A 0 A, and I call 2AL
the parameter.
The ratio A'N:A'A I
call the ratio of contortion of the section.
Let the construction be as before
Now
But
; .t. ::. .
;
Thus
But
And
And
NQ2 = BN,NC (Euclid VI, 13)
BN,NC = AN,NG (part 1)
.1'jQ~
= AN ,NG
NQ :NG: :AN :NQ
NG : AF : : NC : AD: : A' N: A' A
NG:AF: :A 0 N:A 0 A
NG:AF, AN:NQ comp. A'N:AA', AN:NQ
NG:AF, NQ:NG comp. A'N:AA', AN:NQ
0
NQ:AF comp. AN,NQ, A'N:A'A**
Or NQ:AF, NQ:AN comp. A'N:A 1 A
NQ 2 :AF,AN::A'N:A'A
But AF=2AL and 2AL is the parameter
. NQ 2 :AN,2AL: :A 0 N:A 0 A
* Contorted, i.e., the original ratio of
equality which existed between NQ2 and 2AL
has been changed to the ratio A'N:A'A.
**
This comes from the general proposition that
if AB:CD comp. EF:GH, JK:LM
Than EF:GH comp. AB:CD, LM:JK
It can be proved as follows:
Given AB:CD .comp. EF:GH, JK:LM
AB:CK, LM:JK comp. EF:GH,JK:LM,LM:JK
EF:GH comp. AB:CD, LM:JK
(Q.E.D.)
Thus the noble root of the ugly word "invert".
G
�us
to OD
AN
is
and
to
:BN
DA: = NC
:BN
BN
=
is the
F
that
this
to the
a line dralNTl
section was dralNTl
the base of
section
the vertex of the
drav.m
the third
to
the vertex
.............. r-. .......... 11
and the
base
formulation so
to the cut.
that he can
:CO
or
on
construction of
I
the
�- 41 - .
The central sections:
(Sarne setting out as previous central sections, page 39 • )
Construct OK parallel to AA'
Continue AD to K
Since
and
But
OK is drawn parallel to A0 A
OK:BK:AN:BN
OK:CK: :A'N:CN: :A' A: :AD •• CK2:BK,CK::AN,A 0 N:BN;CN
. N. CN =·NQ2 . . ·· . ··
B
OK~:BK,CK::AN,A 0 N:NQ2
0
also
.OK2:BK,CK::AN,A A:AD,BN
Thus
NQ2:AN,A 0 N::AD,BN:AN,A'A
Or
NQ2:AD,BN::A'N:A'A
Construct AF such that
AN AF = AD,BN
NQ2 :AN ,AF: :A'N :A" A
.And thus AF is the parameter. A
This formulation, however is ~:::::-t----1~--------=~~
useless because it depends
K
upon the point N:
but
AD:AF: :AN :BN
and
AN:BN::OK:BK
Thus
AD:AF: :OK:BK
0
\
\
We now have the first solid
G'~A
formulation for the parameter. If it
is compared with the first formulation of the
para-meter of the parabola (AD:AF: :OD:AD or AD:AF:OC:BC), we see
that the only difference is that the ratio OC:BC has been replaced by the ratio OK:BK, or that in some sense the point C has
been replaced by the point K.
Finally, Apollonius finds a way of fitting into the formulation
those lines which are not relevant to the cut.
Sine
But
But
or
OK:BK:AD:AF
OK2:BK,CK comp. AD:AF,OK:CK
OK:CK::A 1 A:AD
OK2:BK,CK comp. A'A:AD, AD:AF
OK2:BK,CK: :A',A:AF which is the final formulation
Note on the construction of AF
Since
and
AD is parallel to Be
OK is parallel to AN
Angle DAF = Angle OKB
Now if
I let Angle FDA = Angle BOK
The two
tx-ian·g le s
FDA and BOK will be similar
Thus
OK:BK::AD:AF
~Q.E.F.)
(Q.E.D.)
�- 42 -
UN-MATRIX
R. Thomas Ing
Hold in thy mind's eye an image
of sand held high in tightened fist
that slowly falls in formless drift.
See it caught, grain by grain, by wind
which cares not what the sand intend.
But for an instant are there grains, ·
and then the sand is nothing more
than proof of standing on the shore
where sea does wear upon the earth.
Stay as rock, do not venture forth.
Go, thou moment of my knowledge -into the earth from whence thou came.
Ib not linger, nor show thy name.
For wind might tear it from my sight,
and names become but more·of earth.
�- 43 - .
ON THE METAPHORICAL -- POSTSCRIPT
Charles G. Bell
To have spoken badly might be a boon if the stammer necessitated
writing.
No doubt it was hard to make out what was being said in the lecture
on Metaphor, ~h and ~bol. · One had to search for a theme underlyiµg sallies of argument, fragments of example.
Conceive a spectrum without limits or clear divisions, the continuum of rese~blance in which we operate. ·As always, groupings
have defined themselves, species, separating from others, have
received tpe stamp of tradition. These are the basic modes of
discourse, which we .try to hold distinct (or they, against dissolving
currents, reassert their distinctness): mathematics, the sciences,
philosophy, fiction, poetry. Cutting across these, subgroupings
have appeared, peculiarly related to the main thrust of symbol:
mythology, prophecy, allegory, the symbolic poem, the symbolic novel.
Devices of analogy have been refined and named: personification,
metaphor, simile. Over all such fruitf'ul specialization rides the
unifying drive which is the creative life of man.
Within each range of the phenomenon we may draw out poles, which
merge again in particulars, interbreeding as we try to hold them
apart. Thus with the distinction which dominated the question
period: the symbol as precise actuality (Mr. Allanbrook' s Beatrice),
or as the stripped abstract (number). Tempting as it is to call
the specific symbol poetic and the generalized symbol philosophic
and mathematical, and so clarify the realms, I cannot help seeing
a catenary between these opposites, including such abstractions as
the points of the compass, the mythopoetic numbers, the circles and
gyres, each of which, loaded with all kinds of content, can take up
procreative residence in mathematics, science, history, religion,
poetry, art. Even the irreducible particular -- that woman, Beatrice
bears a somewhat doubtful relation to the powers released, may only
precipitate what has been concentrating, perhaps for centuri es, in
the cultural ambiance (so Beatrice out or Virgin worship and Troubador
love; D:m Quixote, Hamlet, Lear, out of who knows what).
In such an inwrought field I seized on ·.a group of illustrations,
which when fitted together adumbrate a kind or history:
Even number, in the first ecstacy of its outcropping (Pythagoras),
carried with it the whole complex or what was later separated into
poetry, religion, philosophy, science. So, too, in Renaissance
science (Leonardo), or wherever imagination, with germinal images,
working like a spermatic logos in the rational ear, gives evidence
of penetration into the stricter disciplines: thus with Harvey and
Kepler, with Newton• s "Nature as a perpetual circulatory worker",
with Kekule•s molecular snake swallowing its tail -- thus necessarily
with current attempts to make sciences out of history, mythology,
the psyche.
�- 44 - .
It is true that there are places in nature where the under-girdil]g
of number lies at the surface -- crops out -- like crystal rocks
from the so~er mottlings of earth and vegetation. It was here
that the ancients seated gods and angelic intelligences, in the
divine regularity of the stars. Here, too, mathematical· physics
contrived the triumphs of determinism (the Principia and return
of Halley's ·comet)which have lured all sciences in their wake, and
which the naive . are always taking as a paradigm of knowledge -while the uni verse of the Bible and War and tragedy and flesh and
marriage eddies around us and in us -- how simple -- the paradigm
of knowledge.
What opposes it is not only the cry of romantic poet_ : What
s
'Whitehead called Wordsworth's "modal presences", make' s: "God
forbid that knowledge should be limited to mathematical demonstration"; it is what we know to have happened in the strongholds of
physics and mathematics. As if, in the suspensions of the organic
universe we had managed to dry up a small area of causal rationalism,
. only at the expense of deepening at its center those paradoxes of
space, time, iogic and number, which the present century has revealed. (And how late what we call reason appeared on the scene,
after some organizing w.ill or blind chance had already put the world
and us, with that reasoning mind itself, together.)
So it is not surprising if in our time we have auguries of a new
convergence (Thoreau• s bug boring out of the dry table), the sciences
gaping again, pregnant w.ith the philosophic and mythopoetic (Whitehead, the Jungians, Teilhard de Chardin), while poetry and fiction
(Blake to Yeats; Hawthorne and Melville to Joyce and beyond) hint
at a new world-epos. I doubt if the need that set the symbolic
powers in motion has yet reached fulfillment, even in Yeats, though
his may be the most burning achievement yet available.
That which is to be fulfilled rests upon us as a creative COillJltand,
a divine obligation, drawing us on -The half-read wisdom of daemonic images,
Suffice the aging man as once the growing boy.
�
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Text
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�C0 NT E N T S
Page
The Meaning of Regular Solids • • .Robert Neidorf, Tutor
. •.
1
• • • • • • Lawrence Feinberg, . '64 • •
9
A Strictly Euclidean Demonstration .Samuel Kutler, · Tutor • •
12
Si tu t'imagines
13
14
A J:trth for Our Times
• • • • • • • • • • • Raymond Queneau • •
Translation by Christian Harrison, •64 • •
Rousseau and the Ancients • • • • David Lachterman,
Correction to Page 41 of the
October Collegian • • • • • • •
1
65 • • 15
Robert Sacks, Tutor •·
************
Editor • • • • • • • • • David Lachterman
Business Manager • • • • David Rasmussen
Faculty Advisor .•• . • • • • • Eva Brann
.
33
�EDITORIAL
In order to encourage excellence in creative writing the COLLEGIAN
has established a short-story contest. All St. John's students
are invited to submit short stories on any theme to the editor
before the end of the first semester. The contributions will be
judged on the basis of imagination, coherency of theme and skill
in using language to display ideas and characterizations.convincingly. The absolute and not the relative excellence of each contribution will determine the selection of the winning story; if no
contribution meets the judges•' standards the contest period will
be extended. . The author ~f the winning short story will be awarded
a twenty-dollar gi~ certificate for use in the College Bookstore.
The judges will-be Miss Eva Brann, Mr. Richard Scofield and the
editor.
*************
The following is the solution to the mathematics problem in the
October COLLEGIAN submitted by Mr. Malcolm 1~att:
Proof: Form the longest possible ascending chain,
beginning with the first number. Now take the first
number ~ in this first chain and form the longest
possible ~scending of numbers, none of which appear
in the first chain. Then take .the first number which
does not appear in either of these two chains, and
proceed as above. Eventually· all of the numbers are
used up. If any of the chains thus formed have
~
n+v elements, then we are finished. If not, if
all of these chains have length ~ n, then there
must be at least n+1 of them. Consider the last
element of the last chain. It cannot be greater than
all of the elements of the next to last chain, or it
would have been a part of that chain. In particular,
it must be less than the last element of the next to
last chain. Again, this element must itself be less
than the last element or the last-but-two chains, or
it would be an element of that chain. Continuing,
we see that the last elements of the chains themselves
form a descending chain, and since there are at least
n+1 of these elements, we have found a descending
chain of length ~ n+1 •
�THE MEANING OF REGULAR SOLID
Robert Neidorr
In the last part of the last proposition of the last book or Euclid's
Elements, the claim is made that the so-called regular solids, or Platonic
solids, are unique. In the Heath translation he enunciates that •••
• • • no other figure, besides the said five figures,
ean be constructed which is cont~ined by equilateral
and equiangular figures equal to one another. (SIII, 18)
By the phrase "the said five figures" he refers explicitly ·to what are
commonly callsd the Platonic or regular solids, which have been con5truoted one at a time in the earlier portions of Book XIII. The fact
is that this enunciation is defective; the purpose of this note is to
indicate the defect and demonstrate its po·ssible remedies • .
1. The defect - First we review the five ·solids which are said to be
unique members of a class. They are: ·( 1) The cube, a six-sided polyhedron contained by mutually congruent squares. Or, in Euclid's terms,
the cube i~ contained by six equilateral and equianglllar quadrila~erals,
equal to each other. Each vertex~1) of the cube is composed of three
faces. (2) The dodecahedron, a twelve-sided polyhedron contained by
equilateral and equiangular (i.e., "regular") pentagons, mutually congruent. Each vertex is composed or three races., (3) The tetrahedron,
a four-sided polyhedron contained by ;equilateral (and hence equiangular)
triangles, mutually congruent. Each vertex is composed of three faces.
(4) The octahedron, an eight-sided polyhedron contained by equilateral
triangles mutuall congruent, Each vertex is composed of four faces ·
(5) ·
icosahedron, a tvrenty-sided polyhedron contained by equilateral
triangles mutually . congruent. Each vertex .is composed of five faces~
'
.' '
'
We see that each of these solids . is bounded by a set of mutually congruent faces or surfaces, which are in every case regular polygons.
A so, i t i s clear that ·Euclid's entire discussion is intended to be
l
·restricted to .convex polyhedra, which can be defined -as those polyhedra
which lie entirely to one side of the plane of any face. Hence we are
ternpte.d to characterize a regular or Platonic ·solid as a convex p·o lyhedron bol.lnded by . mutually congruent regular polygons. Although Euclid
does not use the terms "regular" or ttp1atonic'', it is evident from the
cited enunciation that he means to describe some general class of
(convex) polyhedra, of which the · listed five constitute unique exemplars.
The enunciation .itself is the only clue as to' how he intended to describe
that general class;· taken literally, the class it 'describes !,! the ciass
or (convex) polyhedra bounded by regular ("equilateral and equiangular")
(1) By vertex I mean the. point, a.nd the reg'iort around it, on .the surface
of a polyhedron where three or more faces and edges converge. Euclid
calls this a solid angle.
�- 2 -
polygons mutually congruent ("equal to one another"). The defect in all
this rests on the fact that there are more than five such figures.
As a preliminary to further discussion we require a fixed terminology.
We shall say that solids bounded by congruent regular polygons are rhoregular:
Df. A rho-regular solid is a convex polyhedron whose
faces are mutually congruent regular polygons.
Next, we will use the term "Platonic solid'~ to refer specifically to the
five polyhedra listed above; thus the term "Platonic solid" should be
understood as having only a denotative meaning. The terms "regular solid'~
will be defined later. Euclid's enunciation amounts to the assertion
that the Platonic solids are the only rho-regular solids, and it is this
assertion which turns out to be false.
We begin by restating Euclid's uniqueness proof. From Book XI, 21 it is
known that the sum of the plane angles which meet at a vertex must be
less than 360 degrees. It is also evident that a vertex on a solid must
be composed of a minimum of three faces joined together; hence at least
three plane angles must meet at the vertex. It follows at once that there
is no rho-regular solid contained by regular hexagons, since the interior
angle in a regular hexagon is 120 degrees. Similarly, no vertex could
be constructed with regular polygons of more than six sides, for their
interior angles are even greater.
The angle in a regular pentagon is 108 degrees, so a vertex can be built
up with three and only three such figures; this corresponds to the dodecahedron. For a similar reason a vertex can be constructed from three
and only three squares; this corresponds to the cube. Since the angle
in an equilateral triangle is sixty degrees, a vertex can be constructed
from three, four, or five such triangles, corresponding to the tetrahedron, octahedron, and icosahedron. On the basis of these considerations,
Euclid concludes that "no other figure • • • can be '.~ constructed which is
contained by equilateral and equiangular figures equal to one another."
Or, as we should say, no other rho~regular solids exist. But his conclusion is false.
If we seek to build a polyhedron(2) with a stock of -regular pentagons or
squares, it is clear enough that each vertex must be formed from a junction
of just three such faces; hence the dodecahedron and cube are the only
such figures possible. If we now tty building polyhedra from a stock of
equilateral triangles by joining three together at each vertex we get a
tetrahedron; by joining four at each ·vertex an octahedron; five an icosahedron. But suppose we try to build a· polyhedron from equilateral triangles in which some vertices are composed of three faces and some of four,
(2)
Or better:
the surface of a polyhedron.
�- J - .
or some of four and so~ae of five, etd This possibility is left ·out of
account in Euclid's text. And if we try such constructions we shall
succeed; that is, contrary to Euclid's explicit assertion there exist
rho-regular solids other than the Platonic figures. We describe two
such -solids:
First, lay two identical tetrahedra face to face. The result is a rhoregular figure of six sides. Two of its vertices consist of a junction
of three ~aces, and three of its vertices consist of a junction of four
faces. Second, take two equal squares laid together sandwich-wise.
Around their common center rotate one with respect to the other 45
degrees (Figure 1). Keeping them parallel, separate them by some con-
Figure 1
Figure 2
venient di stance. From each corner of the upper square drop lines to
the two nearest corners of the lower square; in this way a belt of eight
triangles will be formed around th~ squares (Figure 2). If the distance
of separation is suitably chosenlJJ the lines joining the squares will
have the same length as the sides of the squares, and the triangles will
be equilateral and congruent. Next, on top of the upper square and
under the lovrer one erect four-sided pyramids with triangles of the same
size (each of the pyramids will be half of an octahedron) ) The resulting
figure, having a total of sixteen sides, is rho-regular.{ 4 Two of its
vertices consist of a junction of four faces; the rest of five faces.
2. The first remedy - To escape this difficulty, we need to tighten the
specification of the class of solids of which the Platonic figures are
to be unique members. The easy and obvious way to do this is to add
the stipulation that every vertex ·must be composed of a junction of the
same number of faces; or, briefly, that the vertices must be homogenous
in type. We shall use the ' term "Regular solid 0 to refer to rho-regular
figures which have this property. Rho-regular solids with heterogenous
(J)
.,'Ir-:~
It must be S/ v 2 , where S is the length of the side of the square.
(4) It is not obvious (unless one builds a model) that this polyhedron
is convex; specifically, one worries about the dihedral angles between
the triangles around the: .b elt and the faces of the pyramids top and
bottom. However, calculation shows that these are convex junctions; -the
angle is about 154 degrees. .
.
It should be noted that here and at other places throughout this
discussion we are assuming the validity of Euclid's Df'. 10, Book SI,
which states in effect that a convex polyhedron is uniquely determined
by the size and shape (and arrangement) of its faces; this proposition
is notoriously provable.
�- 4 -
.
vertices (such as the two described above) will be called "quasi-regular."
Df.
nr.
A Regular solid is a rho-regular solid with homogenous
vertices.
A quasi-regular solid ;s)a rho-regular solid with
heterogenous vertices.~5
It is clear from Euclid's uniqueness proof that the Platonic solids are
indeed the only Regular solids. To render the text precise, we should
add the property o.f possessing homogenous vertices to the characterization
contained in Euclid's uniqueness enunciation. Using his terms, it might
read as follows:
No other figure, besides the said five figures, can be
constructed which is contained by equilateral and equiangular figures equal to one another, and in -.which every
solid angle is contained by the same number of planes.
It may be argued that this is obviously what Euclid meant. Perhaps.
Indeed, I shall argue below that if we are to polish up Euclid's text
at all, it should be altered in this way rather than in other equivalent
ways which will emerge shortly. But in any case we are here concerned
with the logical accuracy of what is written, not with what may or may
not have been meant. Furthermore, one often hears it said that the
Platonic solids are the only "regular" solids, and that a "regular"
solid is (merely) a polyhedron bounded by identical regular polygons:
~ assertion is wrong.
J.
Other remedies - One of the significant properties of the Platonic
solids is that they can all be inscribed in a sphere, as Euclid shows
throughout Book XIII. It is also evident that the two quasi-regular
solids described above are not spherically symmetrical. This raises
the following question: Among rho-regular figures, are the Regular
solids the only ones which can be inscribed in a sphere, or not? To
answer this question we need to establish two theorems.
(A)
In any rho-regular solid which can be inscribed
in a sphere, the dihedral angles between adjacent
faces are ,all equal.
Proof: Suppose first that the polyhedron is contained by equilateral
triangles. Consider a pair of adjacent faces ABC and ABD (Figure 3).
The edges AB, BC, CA, AD, and DB have the ~aine length, say s. Point
(5) I have avoided the natural term "semi-regular" solid, as this
already has two other meanings. It ·has been used to refer to~ ..polyhedra whose vertices and edges are identical, and whose faces are
regular polygons of different types; these are also called Archimedean
solids. The term has also been used to indicate polyhedra whose
vertices and edges are identical, but whose faces are not regular polygons.
�- 50 is the center of' the circi.lmscribed sphere;. herice the lines joining it
to the vert.ic·e s at ·A, B, C, and D are all equal; let them have length R.
M is the mid-point of AB, and lines MC, MO, and MD are filled in.
0-:-.:\
/,/;/'I ',,.,...
,.1
,// / II1I I ""''
. . .-
C~- . . ~
\ " '.
\
"
..
I
I
f-1--- ' b
~~I
· ,/'
\ I'
.
'\
;
.
~
.
I
I
))-~·-:-.- ··7 0
7
.
I
I ......... ·" -- _,/
\\/ :~/
; ;V
.
Figure 3
Since ABC is an equilateral triangle, CM is perpendicular to AB; for the
same reason, IM is perpendicular to AB. Since AOB is an isosceles triangle, OM is again perpendicular to ABo Hence CM, OM, and DM lie in one
plane (cf. Book XI, 5). (~~xt, we see that the lengths of CM and IM are
un~q~ely determined by s.
J Also, OM is uniqueiy determined by S and
R.~7) Finally, OC and OD have length R, so the sides ~f the triangles
OMD and OMC are uniquely functions of S and R, and therefore so are the
angles in those triangles. Furthar, the triangles have been shown to
lie in one plane, and the angle IMC is a measure of the dihedral angle
between the faces (cf. Df. 6, Book XI). Hence that angle(8) is determined
by S and R, and since S and R are the same for all faces, all the dihedral angles must be the same. An exactly similar argument will hold
if the faces are squares or regular pentagons.
The second theorem we need is the following:
(B)
In any rho-regular figure whose dihedral angles
are equal throughout, the vartices are homogenous
in type.
·
Proof: Take any two vertices on the surface of such a figure, and think
of them as juxtn.p~sed in such a way that two of their faces are coincident (or ·"superimposed'°) • ·Since the dihedral angles are equal all
around both vertices, and the angles in one equal to ~he angles in the
other, all the faces inthe one must coincide with all :the faces in the
other. Hence there must be the same number o.f faces ·.'in. each.· ..
Combining theoDems· -A and B:- we can now assert:
(6) . · CM
= IM = · S -y:J/2· ·: _, ~ .
.·,
(7)
OM =
( 8)
Angle Il-m
I
'\
l/4R2 - s2/2 •
= 2~r·c~s
(S/ '{ 12R2 -
3~2)
•
�6
be
the
�constructed which is contained by equilateral and equiangular figures egual to one another, and in which every
solid angle is contained by the same number of planes.
Although this is logically adequate in .conjunction with the proof which
follows it, it is not ideally elegant; specifically - we can show that it
is partly redundant. For the phrase "equal to one another", which is
underscoped above, evidently means that the faces of the polyhedron in
question must be mutually congruent. But it happens that if a convex
polyhedron is bounded by regular polygons of the same type (all triangles,
or all squares, etc.) then it follows that the faces· are of the same
size as well (and hence congruent or "equal to one another.") - ·
To prove this we first establish a lemma:
Lemma: In a convex polyhedron there can be no junction.
between polygonal edges of unequal lengths.
Proof: Suppose there were a polyhedron with adjacent faces F and G
having unequal edges meeting along the line AB. In the Figure 4 it
is convenient to imagine that the surface of the polyhdron is viewed
from the outside, and that F lies in the plane of the paper.
Figure 4
Since the entirety of a convex polyhedron must lie· to· ·one side ·of the
plane or· any face, the whole of the polyhedron in question will be on
or behind the plane of the paper.
Consider the vertex · at V. If this were formed .by a junction of just
three faces, the third face would have to be . n .the plane formed by _
i
the lines AV and VC; but this is also the plane of G. Hence there
must be more than three faces meeting at V, and there must be one or
more additional lines (i.e., edges formed by the junction of two
faces) radiating out from v. One of these lines, call it VD, forms
with VC two sides of the face adjacent to G along the line VC. We
will call that face H. Next consider the line of intersection between
the plane of H and the ~ F. Since that line passes through the
�- 8 -
point V, it must fall in some direction across the face F.(9) Hence
part of F will lie to one side of the plane of H, and part to the other
side, which is impo: sible in ·a convex polyhedron. . This establishes the
s
lemma.
Now suppose there exists a convex polyhedron contaiped by regular poly•
gons o·f ·the· same type, but of at least. two different sizes. The faces
wuld· be ·mutually similar; hence if two differ in size, all of the edges.
of one would be shorter or longer than all of the edges of the other.
,Thus somewhere on the surface of such a polyhedron there would have .to
be a junction between two·polygonal edges of differing lengths. But the
lemma shows that this is impossible. Thus if arry convex polyhedron is
bounded by regular polygons of the same type, they must be mutually
congruent as well.
With this result it ·emerges that the conjunction of properties indicated
by Euclid's phrase ."equilateral and equiangular figures equal to one
another" is partly redundant; it could be replaced by the weaker phrase
"equilateral and equiangular figures having the . same number .o f sides":
it would· follow that the figures (i.e., the faces) would be "equal to ... ·
one another."
·:.:
I certainly do not mean to suggest that this refinement ought to be
packed into some ideal and ideally-perfect edition of the Elements, for
it is not really relevant ·to the spirit and purpose of Euclid's effort in
Book XIII. On the other hand, for Euclid and for Greek mathematics
generally, the important conception of a "regular" geometrical solid
turns on the notion of a convex polyhedron bounded by regular polygons;
I am arguing that in the spirit of that approach a "regular solid" is
most adequately and economically defined as a convex polyhedron bounded
by regular polygons of the same type, with the same number meeting at
eech vertex. It follows that there are only five such figures, and that
each one has identical faces, equal dihedral angles, and spherical
symmetry.
(9) Unless it is coincident with AB. But then AB would be the line
of intersection between the planes of F and H, and also between the
planes of F and G. Then, as the planes of F, G, and H would all meet
in the line AB, AB would also be the line of intersection between the .
planes G and H. But VC is that line • .
�- 9 A MYTH FO!t OUR TIMES
Lawrence Feinberg ·
Not long ago, I had a few conversations with someone who swore me to
secrecy concerning them. For reasons which shall become evident, I may
not reveal who that ·person ~s·f·. however I have his permission to relate
to the public the substance of a particular conversation we had, shortly
before we parted. It was· not actually a conversation, for he spoke and
I listened without replying to him in any way. Times are such that I
can no longer refrain from telling others what he told me, and though
hesitant about the veracity of his words and the public's credulity, I
here make that conversation known to all, to stand or fall by rrry reader's
judgment of it.
·
An elder of a certain tribe, a~er much deliberation, decided that he
and his fellows should end their existence as speedily as possible. Why
he reasoned thus, or what his moral promptings were, no one knew; as a
wise man amongst his people, his counsels were sought in all important
matters, consequently it was not without much concern and fear that the
people learned of his grave decision.
Now the persons of this tribe were not of the same species as you and I,
or if in fact they did bear us some resemblance, it will never be known.
For each individual lived, from birth to death, in a box the dimensions
of whose. each and every- side was 10 feet by 10 feet. Their way of life
mµ~t se$.m a mystery to beings like us -- certainly there could not have
been propogation of the species as we understand it. Yet every individual
of that tribe was most intimately acquainted with li- e in all its formal
f
aspects: When movement was heard outside of one's box where no movement
had been heard before, this was a sign that life had been generated;
likewise the cessation of external sound was construed as the · cessation
of life. In this way every one knew that his fellows would regard hinias no longer existing when they failed to perceive movement in the place
t~ which he was. ~The knowledge of .one's own death was nonetheless in- ·
comprehensible, for how could there be cessation of movement without· its
being perceived?
Language as We know it was unknown to this tribe. Their grammar of
~xpression. consisted of certain knockings and rappings -on the wa.lls of
the box. Since. there was no direct confronting of one individual with
another like himself, this language could· not be taught in the same way
that our language is taught. But only those of the feeblest intelligence
failed to learn the language; for the most part i~ was only a~er one was .
advanced in years that he was able to grasp how the various knockings ·
ware used and ·himself. put into practice that ·knowledge of knockings which '
had taken so l .ong to . acquire. The language in its · comprehensible forms
of expression was Qhieny· used by the tribal elders, and consequently th~re
existed the possibility of knowledge of ·a · state of affairs • . (Let us not .
forget this point.)
- · -·
.
·
·
.The techniqu_ for using .·knockings ·was intricate:
e
various shade·s of meani_g
n
��- 11 '
.
-
.
.was no such thing as outside. that every individual was inside.. But, he
argued, this was not a blessing but a cu..t·se, for communication lost all
meaning when it was shown that there wq:: nothing that could be communicated.
The knock~language was a sham.
Thus for the first time the tribe learned of its coll~ctive existence,
but it further realized that this existence was being threatened by the very
person who had informed everyone. Hatred for that one spread through the
entire people -- pandemonium was everywhere. Without exception the tribal
members furiously threw themselves against the sides of their boxes, to reach
and destroy their betrayer. Boxes, undergoing such violence, collapsed, and
their occupants were at once annihilated. The frightened philosopher at last
began to stir when he perceived that all motion had stopped -- everyone was
dead but he. Thereupon, the philosopher was seized by a fit or tncontrollable
laughter, and he then trod over every inch of his dwelli~g •. rapping gently
over the smooth surfaces~ '.
· ·
· ·
·
.t
,'.t
�AC a
are
to AC
For
(X.
G be the
as E is to F.
measures E
G make
G measures E
therefore as P is
to F so is
But as
to
as P is to Q so is AB
let K and L be the square numbers for
the
and
as K is to L so is the square on AB to
the squares on
the square on AC is
BC are
square on
, the square on
of the square
is
the
of
Since Q is the
of
K is also an even
P
is the
since p
Q is also an even
since L
of
the
p is an even
of
are each
are
a
since
E and
measures E
F.
Q.
*
, we
an
from
�-
!
3 Raymond Queneau
Si tu t'imagines
si tu t'imagines
fillette fillette
si : ~tu t' imagines
xa va xa wa xa
va durer toujours
la saison des za ·
la saison des za
saison des amours
ce que tu te goures
fillette fillette
ce que tu te goi.ires
Si tu crois petite
situ crois ah ah.
que ton teint de rose
ta gaille de gu~e
tes mignons biceps
tes engles d'email
ta cuisse de nymphe
et ton pied leger
si tu crois petite
xa va xa va xa
va durer toujours
ce que tu te goures
fillette fillette
ce que tu te goures
les beaux iours s 1 en vont
les beaux jours de fete
soleils et planetes
tournent tous en rond
mais toi ma petite
tu marches tout droit
vers sque tu ne vois pas
tres sournois s'approchent
la ride veloce
u
"
la pesante graisse
le menton triple
le muscle avachi
allons cueille cueille
les roses les roses
roses de la vie,
et que leurs petales
soient la mer. 8'tale
de taus les bonheurs
allons cueille cueille
si tu le fais pas
ce que tu te goures
fillette fillette
ce que tu te goures
�- ff Translated by
Christian Harrison
Chinka chuhng, chinka chuhng, chinka chuhng chuhng chuhng
Hey sweet thing in that skintight sweater,
If you think your lovin 9 s gonna keep gettin' better,
If you don't think that time is runnin' out instead,
Then baby you been misled, misled, baby you been misled.
Hey sweet thing with them high priced hats,
Try your painted toenails in these two-bit flats,
Take them nylon stockins off your sexy legs,
And see how they fit in size 28 pegs,
Cause if you don't think that they will fit in time,
Then honey you cornmittin' yourself a crime,
You been waitin' around for a rich man's bed,
But baby you been misled, misled, baby you been misled.
Yes sweet baby you are off the beam,
Thinkin' party party party is an unendin' theme,
Cause the sun and the moon may go round and round,
But you are headin' straight for a hole in the ground,
And there ain't a single man irt the world can save
Your sweet round fanny from the cold cold grave.
Chinka chuhng, chinka chuhng, chinka chuhng chuhng chuhng
And before you get there, rrr:J good lookin' friend,
You gonna rest your lips on a big triple chin,
You'll get a mighty lot o' wrinkles in that rosy cheek,
And need a big, strong girdle cause your muscles are weak,
Now baby you been savin' a sweet, red rose,
And its ripe for pickin', says the man with a nose,
So baby lets you and me pluck it today,
And let the petals fall baby, where they goddam may,
Cause if you don't baby, ,yes if you don't,
If you keep messin' round with will and lilTOn't,
If you keep on waitin• for that rich man's bed,
Then baby you been misled, misled, baby you been misled.
�- 15 . ;.
ROUSSE~U ·i~ltNIHTHE ·~ANGIENTS~
David Lachterman
Introduction
The central problem of modern political philosophy, political
philosophy a~er Machiavelli, is power. As the doctors of the
Church wrestled-valiantly with the enigmas of the Trinity trying
to elucidate the identity, individuality and province of the
Persons. so political philosophy -- secular theology -- must
determine the relationships between prince and people, ru1er and
ruled, or more generally' part and whole. It is the common .
assumption of theorists such as Hobbes, Locke and Rousseau that
civil society is artificial, a work of man and not of nature. In
passing therefore from his original, a-political state into civil
society, the individual sacrifices whatever privileges he may
have enjoyed in the state of nature for the sake of something
new although not necessarily something better. It becomes the
task of political philosophy to understand the new relations that
do or ought to arise among men in a political community: relations
involving the distribution and legitimacy of authority and power
and the ·obligations of the ruled to their rulers. Thus, a complete
account of . society · must include a description of man in the state
of nature ~- his rights and responsibilities -- and an eXplanation
· of what man acquires or loses by deciding or being forced to unite
in political societies.
Rousseau is chiefl.y concerned with explaining this transition
without introducing the exercise of constraint or force on the
part of any individual. · His problem is to describe a form of
politieal association in which the advantages of the civil order
fully recompense the loss of natural independence. However, his
intentions go beyond the solution of this particular problem. In
several, central aspects of his political thought, Rousseau reveals
an indebtedness or, more accurately, a sympathy with the ancients
.i .e., Plato and Aristotle. This sympathy requires a break with
the tradition of modern political theory laid down - y Machiavelli.
b
His political construction is in part determined by an understanding
of the true end of civil society that few of his contemporaries,
especially Hobbes, would . share. At the same time, ·however, he
accepts the notion · of consent or contract, the meqhanism invented
by the moderns to explain the transition from nature to society.
He is .concerned, as, perhaps, Plato and Aristotle were not, not
only with What the city ought ·to be but also with how it can come
to be. In brief, Rousseau seems to adopt modern means to achieve
ancient ends. Perhaps his greatest concession to the modern spirit
would be the admission that the ends. justify the meari's.
In presenting And interpreting the thought of Rousseau· I shall make
use of five categories which represent the fUnqamentai issues that
he investigates: the state of nature, the social contract, sove•
reignty, ·the general will, and law. Underlying .each is the .idea of
liberty; it is in the gradual unfolding o~ the meaning of th~s· idea
that the spirit of Rousseau• s thought can best be . grasped. · ·
�- 16 Section I
The .most cursory examination of the Discourse on the Origins of
Ineguality and the first book of the Social Contract will undoubtedly reveal what seem to be two fundamentally opposed understandings of the state of nature. In the first treatise we find
a panegyric on the nobility of savage man; in the second, an
eulogy of social man. In the first, the establishment of society
entails the depravity of the human race; in the second, it brings
about its ennoblement. If however we attempt to distinguish
Rousseau's purpose in each TNriting it may appear that the t"WO
understandings correspond to two different intentions. As long
as we adhere to Rousseau's advice to "lay facts aside", that is,
to refrain from confounding history and philosophy,(1) we should
be able to regard each understanding not as a categorical assertion of (historical) fact but rather as an hypothetical construction designed to serve a particular end.
In the Discourse the abusive, tyrannical condition of present day
political society is given; philosophic inquiry must account for
this condition, it must explain the origin of society and its
evolution until the present, a present in which "we see around
us hardly a creature in civil society who does not lament his
existence". The main argument of the Soc1al Contract, on the
other hand, does not assume the existence of any politi~al society;
it proceeds within the realm of the ought not the i[.(2) Rousseau's
initial remarks in the first vhapter of the Social Contract explain
the connection between the two TNritings quite clearly: "Man is
born free and everywhere he is in chains • • • how did this change
.come about? I do not know. What can make it legitimate? I
think I can answer this question." The first sentence is historical, that is, it represents as an actual fact the enslavement of
man in society.()) It echoes the description, in the Disc.ourse~
of the final degradation of society -- the conversion of the
legitimate into arbitrary power or, more briefly, the state of
slavery.(4) However, Rousseau does not intend to examine the
root s of t his condition , he forsakes the historical method used
previously in the Discourse. The last sentence could be misleading if we regarded Rousseau as proposing to render 1egi timate
the actual condition of . civil society, the condition of master
and slave. Rather, he must be understood as bringing into
question civil society itself, apart from any historical instances of it; the form of his question is thus what can make
any civil society legitimate, taking man as he is and the laws
as they might be? The anstrer proposed in the Social Contract is
meant as an ideal basis for the founding of any society.
( 1 ) Cf. esp. Introduction to the Discourse on the Origin 1 ·o f
Ineguality (hereafter D:iscourse)(Everymans ed.) p. 175-176; also,
end of First Part p. 206.
(2) In violation, it should be noted, of Machiavelli's basic
methodological restriction, cf. Prince, Ch. X:V.
(3) "all ran headlong to their chains as hopes of securing their
liberty.'' Discourse. p. 221°.
(4) Discourse p. 2)1
�- 17 I have devoted so much space to this distinction because most of the
confusion regarding Rousseau's political theory seems to arise from
the failure to separate the Discourse and .Social Contract as I have
done. Indeed, the preoccupation with the "noble savage", the conviction that Rousseau intended man to return to the idyllic and
pristine state of nature(5) must ·have been the result either of a
hurri~d and superficial reading of the text ( 6) or of a misapprehension of Rousseau• s purpose in the Discourse: an in. ictment of
d
the illegitimate e~ercise of political power.
Despite the difference in purpose between the two writings, the
axioms of the •science of mankind•{?) set forth in the Discourse
are for the most part unchanged in the Social Contract. Since
Rousseau claims that his political construction is based on the
"nature of man" it will be essential to our purpose to uncover
these axioms tdthin. the description of the "state of nature". In
doing so we are likely to discover that nature in these two phrases
has two distinct meanings.
Man in the state of nature must be stripped of every d1sposition,
passion and talent that he possesses and can only possess in
society. It was Hobbe's mistake to attribute to his natural man
passions, pride and the fear of violent death for example, which
only came about as the result of communal life. Thus hi·s identification of the state of nature :with the. state of war is
spurious; man's life prior to any form of association or mutual
dependency is "simple, uniform and solitary". All intercourse
with other men, even the most casual, is rare .and insignificant.
The ·great store of nature supplies each individual's physical
needs without demanding to;l Man thus lives only in the consciousness of the present,~8~ an animal like other animals stronger
than some, weaker than others.
What of the moral and metaphysical side of savage man? Rousseau
believes that he has discovered the two fundamental operations of
the human soul prior to reason: the desire for self-preservation
and compassion at the sight of the pain or death of any sensible
being, particularly of any human being. Man in the state of
nature is ."destitute of every. species of intelligence". Since
"the y.nderstanding is greatly indebted to the passions" and viceversa~ 9) and since the passions originate in our wants of which
we mu.st . have some idea or· to which we are· directed instinctively,
it follows that savage man's desires are limited to physical
wnnt. Man is a creature of pure . sensat~ons, lacking .evenythe most
sifilI:?le knowledge.
·
(5) Cf. for example, Otto Gurbe, Natural Law and the Theory of
Society 1500-1800 (Eng. tr. Cambridge, 1950) P• 109
(6) Cf. esp. the concluding paragraphs of the Discourse 1~ere
Rousseau -imptites this interpretation for his adve~saries.
(?) Prefac_ t .o. Discourse, p. 168
e
. .
. · .-···
· ··
·(s) Disc· m.·50 ·~. 187 · ·· · ·
a
~
This ·re.ciproeity :Hobbes -.see~s tc) have ignored. Cf. :.Leviathan
Bk•· ·I, Ch • . J, 6. .
-. .
·
. <9).
�- 18 However Rousseau makes . two crucial distinctions between man and
the ·other beasts. The beast is directed solely by nature -instinct -- whereas man in his capacity of a free agent can choose
between acquieseing and resisting the impulse of nature. Man's
liberty, his free will, is natural and his consciousness of this
liberty "displays the spirituality of his soul". Secondly, man
in contrast to the beast possesses the faculty of self-improvement ,
of almost unlimited perfectability. It is this faculty that
gradually "draws man out of his original state,produces his discoveries and errors,his vices and virtues". Nevertheless, it is
important to recognize that in the state of nature, before any
inconveniences or deficiencies impel man to improve his faculties,(10)
these two distinctive qualities are largely irrelevant. Man's
free will is rarely exercised; his perfectability is, in a true
sense, pure potentiality. Here we begin to see two possible meanings of t~e word 'nature': pristine, original state and essence
or entelechy -- the full actualization of possibility. It is in
this latter sense that the nature of man is understood in the
Social Contract -- what man ought to become if he is to be a true
man. (11)
I mentioned previously the. feeling of compassion which Rousseau
attributes to man in the. state of nature; this innate sentiment
is the spring of all social virtues -- generosity, clemency,
humanity, friendship~ Although Rousseau denies that men in the
state of nature have any "moral relations or determinate obligations one with another" the natural virtue of compassion i's the
one feeling that contributes to the preservation of the species.
This virtue is especially interesting bec~use its analogue in
civil society is conformity to the law(12J and because the corrupt
and debased civil society thrives on the profit every man foresees
in the misfortunes of his neighbors. The development of existing
seciety entailed the extinguishing of compassion; the success of
the rational society requires its preservation in a different
form. It is because of this virtue that Rousseau can characterize
man as naturally good (although actually wicked) -- a fundamental
axiom of the science of mankind.
I have tried in the preceding paragraphs to collect the essentiaal
descriptions of ·man in the state of nature as given by Rousseau
in the Discourse on the .Origin of Ineguality. His own words can
·best summarize what I have been arguing: "Let us conclude then
that man in a state of nature, wandering up and do'Wll the forests,
without industry, id thout speech, and td thout home, an equal
stranger to war and to all ties, neither standing in need of his
fellow creatures nor having any desire to hurt them, and perhaps
even not distinguishing them one from another; let us conclude
•-
..
(10) "· •• the fortuitous concurrence of many for·e ign causes."
Discourse, p. 205
.
( 11 ) Cf. Social Contract, Bk. :t, Ch. VIII -- "1' instant qui fit
un etre intelligent et un homme."
( 12) As . Rousseau· puts it: "it supplies the place . of law; morals
and virtues."
�- 19 that, being self-sufficient and subject to so few passions, he
could have no feelings or knowledge but such as befitted his
situation; that he felt only his actual neceqsities, and disregarded everything he did not think himself immediately concerned to notice, and that his understanding made no greater
progress than his vanity." One thing more: liberty is the
noblest faculty of man.
Whereas in the account of the transition from the state of
nature to civil society given in the Discourse, man's faculties
and natural goodness are progressively debilitated, the Social
Contract (Book I, Chapter 8) views the change as an ascent that
affects a radical change in the nature of man or, rather, as I
have argued previously, fulfills for the first time tha nature
of man. "file passage from the state of nature to the civil
state produces a very remarkable change in man, by substituting
justice for instinct in his conduct and giving his actions the
morality they had formally lacked. Then only, when the voice of
duty takes the place of physical impulses and right of appetite,
does man, who so far had considered only himself, find that he
is forced to act on different principles, and to consult his
reason before listening to his inclinations. Although, in this
state, he deprives himself of some advantages which he got from
nature, he gains in return others so great, his faculties are
so sti..~ulated and developed, his ideas so extended, his feelings
so ennobled, and his whole soul so uplifted, that, did not the
abuses of this new condition often degrade him below that which
he left, he would be bound to bless continually the happy moment
which took him from it forever, and, instead of a stupid and
limited animal, made him an intelligent being and a man." Here
civil society is represented as the highest good man can achieve
and the state of nature, as a positive hindrance to the fulfillment of all that is best in man. At this point the distinction
made previously between the Discourse and the Social Contract is
valuable:because all existing states have from the beginning
been wrongly constituted, it was necessary in the Discourse to
commend the state of nature by- way of rebuke;(1J) now that civil
society is to be constructed anew and properly, it is possible
to regard the state of nature in its true form. The two accounts
are connected by the parenthetical qualification regarding the
frequent abuses of a ci'vil society that is not founded on legitimate authority.
Perhaps the most significant substitution brought about by the
transition to civil society is that of. civil and moral liberty for
natural liberty. Rouseeau has argued that liberty belongs to -man
by nature in one sense, namely, that man in his original condition
enjoyed the freedom to follow his own inclination; it will be his
task to show how rational. civil society guarantees this natural
liberty in another sense -- as the actualization of man's
possibiliti.e s as man.
(1J)
P• 176
This is explicit in the final paragraph of fhe Introduction,
�- 20 -
Section II
Turning now to the construction of a rational civil society,(14)
Rousseau attempts to discover the legitimate conventions that
support political obligations -- the duty owed by citizens to
their rulers. Two terms in the foregoing must be explained.
'Legitimate 0 is opposed by Rousseau to 'arbitrary' and has two
complimentary connotations: first, that to which a man can
freely acquiesce and second, that which conduces to the good of
those whom it serves. A convention is an artifice, a work of
man not of nature. However, the conventional in Rousseau is··.htgher
than the natural, in the sense of original, becaus-._ it testifi· s
e
to the perfectability of man, to his ability to escape the·
thralldom of instinct.
From what has been said -about legitimate it should be clear that
force or compulsion can have no part in the institution of the
rational political society. A major part of the first book of
the Social Contract is consequently a refutation of political
theories that set up force as the origin and prop of political
obligation. Such theories invoke alleged rights -- the right of
the strongest, the right of the conqueror -- which Rousseau shows
to be meaningless: a right is based on a reciprocality of
interests and responsibilities; where one party is all powerful
the other · yields to him not because he ought to obey but because
his desire for self-preservation forces him to obey. The •ought'
in this analysis will become increasingly important; for the .·
moment it ·need only be pointed out that duty is always a moral,
never a physical obligation. Hence the exercise of physical power
can n~ver legitimize itself; right can never be established by
fact.~15J
If right, not force, is the legitimate foundation of society, the
·end pf the political community must be adjusted accordingl¥,
Under a despot the people are said to enjoy tranquility,l1°J
violen~e is curbed and men°s lives are no longer threatened from
every side; but, Rousseau asks trenchantly, "What do they gain
i f the very tranquility they enjoy is one of their miseries?
Tranquility is also found in dungeons, but is that enough to
make them desirable places to live?" As long as a people is
merely · subject to a ruler, as long, that is, as the interests of
ruler and ruled are not the samE}, power will be arbitrary and
obedience a physical necessity.l17J What is to be secured in
{14) In the Discourse, civil· society is largely a matter of
chance,· er. ·p. 223
( 15) ·An additional instance of the 'idealism' of Rousseau's
endeavour, in contradistinction to Machiavelli's. See also
Grotus, The Laws of War and Peace, Bk. I, Cn. III, paragraphs
VI-VII for the argument of the supremacy of the prince over
the people.
(16) Compare Hobbes Leviathian, Part II, .Ch. XVII-~ . o.egi.nning
(17) ·See the discussion in the Social ·contract, Bk. I." Ch ·~ · II
of whether the rulers rule for the sake of their subjects·~ :
�- 21
civil society is not merely life, but rather. ~hat freedom which
man.enjoys by nature. Alienation of liberty can never be the
basis of society, Eobbes notwithstanding. "To renounce liberty
is to renounce being a man." Civil society must be a refiection
of the essential nature of man (and liberty is the essence of
man) or else it will inevitably degrade and debase man until he
will look back with regret on his primitive, a-political conditions.
Rousseau finds man equipped for nobler ends than mere physical
existence; .i ndeed his freedom, which is one with his perfectability, makes it possible for man to become a moral being,in a
sense which I shall explain later. Therefore the crucial
question for Rousseau is how
the existence of the state can be
compatible with human freedo~ g~• in other words, how can liberty
and obedience be reconciled.~1 J
.
In the Discourse the gradual diminution . . of nature's abundance and
the concoraLtant" . rise of agriculture and industry combine to introduce equality between men: inequality of possessions and
resources and thus of power. The state of primitive society(19)
became a "horrible state of war". The rich, desiring to secure
their lands and wealth, conceived the "profoundest plan that ev~r
entered the mind of man": to ally themselves with their enemies
in order to use the combined force of their attackers for their
own protection. If it was the profoundest, it was also for Russo
the most treacherous plan that man has conceived. "All ran headlong to their chains, in hopes of securing their liberty" -- a
~ope soon and irremidiably disappointed.
In the Social Contract natural incommodities outweigh the resources of each individual for his self-preservation; man then
realize that it is only by combining their individual forces
that they can save themselves from perishing. No ment.ion is made
of property, wealth, compulsion or the state of war.
What form should their association assume? · If any individual is
dependent on the will of another individual, hi~ liberty is abridged; if any indi vid.ual retains for himself privileges which
his associates. do not share, their liberty is abridged. Each
associate must remain as free as before yet with the advantage
of h~ving the common force of the whole for his defense. The
fulfillment ·o r these two requirements is provided for in the
terms of. the .cont. act: "each of us puts his person and all his
r
power in .COI1lnlon, under the supreme direction of the general
will, and, .in ou:r corporate capacity, we :'r eceive each member as
an indivisible part of the whole." Although the ·c entral term --
(18) Cf. Social Contract, Bk. III, Ch. XIII (p. 80 in St. John's
text): "l' essence 4es .corps politique, etc." ·
·
·
( 19) Not civil ·society in the full sense, ., but ah aggregation of
~amilies living on the same land.
�- 22 -
the general will -- will only become meaningful in the subsequent discussion,, it's possible to see how this contract eliminates personal dependency: the individual alienates his person
and possessions to the corporate whole, the "moral and collective
body" created by the act of association and not to any other
individual; each individual in turn is accepted as a part of
this whole, enjoying its protection and having a voice in its
deliberation.
The social compact however -- and this is possibly Rousseau's
most striking contribution to the political dialogue -- does not
establish arry particular regime, any constitution such as a
democracy or monarch. The' discussion of government is postponed
until the third book. Having united themselves into a public
person, the people do not constitute or even elect b¥ this act
a government; instead, they create the Sovereign.(20)
Section III
Rousseau commends the philosophers, especially Hobbes, who realized that to understand the foundation of p9litical society it
is necessary to go back to a state of nature.l21) In this sentiment, at least, be is firmly leagued with the moderns against
the ancients. Political philosophy, then, must not merely describe how the best or most stable order might be constructed; i~s
real task is ta justify the authority exercised. by the ruler.
This modification of the fundamental political question is the
outcome of the modern conviction that man is not by nature (i.e.,
originally) a political animal.
Rousseau's Sovereign satisfies this requirement ina9much as all
who submit to any act of authority are its authors;l22) they will
be, in effect, obeying themselves. Rousseau expresses this
reciprocality of authority and obedience in the distinctions given
in the Social Contract Bk. I, Chapter 6: the active aspect of the
body politic is called sovereign (this activity is legislation);
t he passive aspect , state . Citizens are those who share i n the
sovereign power: subjects, those who are under the law; but,
every member of the people is both citizen and subject and hence
those who obey the law ,w rite the law.(23) · By justifying political
authority in this way. Rousseau can quickly dismiss that ancient
question: whether the ruler rules for his own sake or for the
sake of the ruled. · If 'the sovereign is a collective body whose
members are the citizens, it clearly cannot have interests opposed
to theirs, for the same reason that a living body can maintain it( 20) Compare the wording of the covenant in Hobbes, Leviathan
Part II, Ch. 18 (p. 143, Liberal Arts text). Especially noteworthy
is the notion of rep'r esentation, expressly rejected by Rousseau.
( 21) Discourse, p. 175
·
(22) Compare Hobbes' account of authors and actors, Leviathan,
Part I, Ch. XVI
(23) Cf. Social Contract, Bk. III, Ch. XIII: "the words subject
and Sovereign are identical correlatives, the idea of which meet
in the single word 'citizen'.
�- 23 self only when all the members, or organs are healthy.(24) "Merely
because the sovereign exists,(25) it is always what it should be".
There should be, in the rational society, some legitimate source
of authority; that is, as I have explained above, a· source of
authority that it is right for men to obey; but this is what the
sovereign is, for it is always rj,:ght for a man to · conform at his
own will and thus the proposition, is true.
In spite of the perfection of the relation between sovereign and
citizen, there is a grave difficulty in establishing an equally
successful relation between subject and state. An individual may
think it proper for him to enjoy ''the rights of citizenship"
without being pre-pared to fulfill "the duties of the subject", in
short, he may refuse to obey the authority of the sovereign.
Consequently, the body politic must reserve the right to compel
a man to obey. In Rousseau's paradoxical formulation this means
that a ·man is forced to be free. The full significance of this
statement will hopefully become apparent in the discussion of
Law (Section V).
Before passing on to the general will, I should like to clarify
two issues involved in the notion of sovereignty. Sovereignty
is a central concept in Hobbes, too; but how great is the
difference between its meaning there and in Rousseau! For
Hobbes, by the original covenant every man alienates his right
to govern himself, that is to obey what his own will . dictates.
Instead, a single man or a body of men (or the whole body of the
people, an alternative rarely considered) is given the right of
acting in the name of each, while each in turn "owns and · acknowledges himself to be the author of whatsoever he that so bears
their person shall act or caused to be acted". "He that ·carries
this person is called smtereign. t1( 26) In every case the will of
the sovereign is what Rousseau~ calls .a particular will, to which
each .must submit his own will. In the Social Contract, quite to
the contrary, it is to dissolve the body politi·c to promi9e to
obey any particular will, that of a monarch, for example.t27)
Sovereignty can never be transferred to an individual or a group
of individuals for by its very nature it belongs to all the
people; indeed, it is the very bond that makes a people, a
single corporate being, , out of an aggregation of men.
Consequently, government, which is the bearer of sovereign power
in Hobbes, becomes in the Social Contract an intermediary between the sovereign and its subjects. · For the determinations O
·f<
the sovereign, that is to· say, the will of the people, to be put
into action by every individual, some force is necessary; this · ·
( 24) Rousseau himself recognizes the partial.. iriaccuracy of this
comparison. See Disco~rse ~n .Po.liti?,al E?on?mv p. 252 (Everym~s
ed.), for the reservation and comparison in :i,ts fullest fo. m. . .
r
(25) Translating "par cela seul qu'il ·est''' existentially, . not .
qualitatively.
(26) Cf. Hobbes Leviathan Part II, Ch. XVIII, P• 142-143
(27) Cf. Social Contract Bk. II, Ch. II
�- 24 force, which brings the people as subjects into conformity with
its or,m will as citizens, is the government or supreme administration. (28) Its power is executive while the~ of the sovereign
is legislative. From this it follows that the only valid or proper acts of the sovereign are laws; whereas the government acts
legitimately when it takes steps to secure "mutual correspondence
between subjects and sovereign", in other words, when it makes
every man free.
Under closer scrutiny sovereignty is made to reveal its essence:
the general will. It is this that we now have to examine.
Section IV
The social compact creates a moral body, moral, because it has a
will: an act forced upon us, one9 that is, that we do not will
to do, can never be mora1.(29) The terms of the compact name
this will: it is the general will, to whose authority every
associate entrusts his person and his possessions. In what
follows I shall be primarily interested in assembling and explicating the various notions Rousseau associates with the general
will; in the final section a discussion of the positive acts of
the general will (the laws) will introduce an analysis of the
fundamental issue in this paper: the similarity between Rousseau• s
political ideas and those of the ancients.
While the social contract provides a quasi historical, and
sovereignty a political, explanation of social obligation, the
notion of the general will presents a psychological or philosophical
account. Sovereignty is the active aspect of the city; Rousseau
illuminates what this means when he writes that the sovereignty
"is only the exercise of the general will".(30) The ground of
political rights and duties thus becomes not so much something
that is explicitly political (as institut.ions, constitutions) as
something corresponding to a pschyological faculty.
Rousseau in the preface to the Social Contract declares that his
purpose is to reconcile right and interest, justice and utility.
The immediate or explicit argument behind the notion of the
general will does just that; it demonstrates that submission to
the conditions one imposes on others is both equitable and in
one 9 s .own- ~in~·~re-st. For the general will must be distinguished
both from the will of all and the will of the majority. The
generality of the general will is fundamentally qualitative, it
is defined less by the number of votes then by the nature of
(28) This administration takes the collective name of 'Prince' -surely a 'r eference to Machiavelli.
( 29) Social Contract, Bk. I, Ch. III
(JO) ibid. Bk. II, Ch. I
�- 25 the voter and the object of the vote. The voter is ~ citizen,
a member of the sovereign and is therefore concerned with the ·
"public advantage" rather than with his private interest.
(Rousseau wants to show, of course, that public advantage and
private interest coincide.) Thus a unanimous decision reached
by a body of men each guided by his private interest is not a
decision of the general will; nor, a fortiori., is a majority
decision under similar circumstances.
The g·e neral will considers only · the common good and hence is al ways
right -- because it pursues the object for which it was instituted.
The question ·p roperly -gut to each citizen is "is it to the advantage of the state?" f31donsequently whenever the issue relates
to some particular or determinate object -- an individual, a
profession, · a class of subjects -- the will of the people lo·s es
its generality, ·f or in that case each citizen is judging. something
foreign to himself·; particular interests replace the common
interest that unites all. The mathematical metaphor that Rouseeau
uses to describe what happens when the general will is being
determined is somewhat obscure!J~rom the footnote we gather .that
the common interest must make itself felt in ·opposition to various
private interests. Two voters with contrary private interests
meet together ·in the perception of the .·common interest; thus
cancelling their private interests.
Every valid act of the sovereign recognizes all citizens .collectively and all actions in the abstract. The carrying out of
these acts is- obligatory because each has agreed to fulfill the
cenditions he has imposed on others; as long as the will remains
general, each man is obeying, in effect, his own will.
Now the special effect of this arrangement according to Rousseau
is that "in fulfilling them (social obligations) we cannot work
for others without working for ourselves"!33Every man by nature
prefers himself above all other men; in casting his vote every
man thinks of himself -- each man constantly wills the happiness
of all because each man thinks of himself when thinking of all.
Certainly no man will impose burdensome or injurious conditions
on others which he himself is obliged to fulfill. Every sovereign
act is thus legitimate because based on the social compact,
equitable, because common to all and useful, because it has the
general good as its object. Notwithstanding the . absolute power
of the body politic over all of its members, the general will
cannot impose fetters that are useless or even harmful to the
community.
·
In exchanging the state of nature for the social order man gives
up his natural independence for civil liberty, _liberty limited
.. ··
(31)
(32)
ibid.
ibid.
( 3).) . ibid.
Bk. ,IV, . Ch. .I
Bk. II, Ch. II
Bk. II, Ch. IV
�l
- 26 only by the general will. Far from being a renunciation this is
an advantageous exchange, "instead of an uncertain and precarious
way of living they have got one that is better and more secure,
instead of the power to harm others security for themselves," and
instead of their strength, which others might overcome, a right
which social union makes invincible".
I stipulated previously that the foregoing presentation contained
the explicit argument of the social contract. The obscurities of
that argument along with its utilitarian tone might provoke
questions concerning the fundamental character of the society and
the people who are to live under the social contract. 1rJhy does
the general ~dll refrain from imposing useless fetters on the
community? Why will particular 1dlls meet in the recognition of
the common interest? Is self interest, the preference each man
has for himself, the sole ground of political obligation? If
so, is this interest noble or base? Is civil liberty --freedom
as Hobbes understands it -- the only fruit of social existence?
In short, what is the relationship between the general will or,
more precisely the law and the moral character of those subject
to it? The very fact that Rousseau attempts to answer these
questions, both in the Social Contract and in the Discourse on
Political Economv, testifies to his deviation from modern political thinking, or, at least, from the conviction of the true
end the city common to the moderns. Whether his answers correspond to the solutions given by the ancients is the subject of
the next section. Perhaps I have prejudged the issue by calling
Rousseau's political construction a rational civil society.
Section V
By way of prea,mble I should like to exhibit two passages from
Rousseau's writings which demonstrate his awareness of the
quarrel he tried to reopen.
"As nature has set bounds to the stature of a well-made
man, and, outside those limits, makes nothing but giants
or dwarfs, similarly, for the constitution of a state
to be at its best, it is possible to fix limits that will
make it neither t'oo large for good government, nor too
small for self maintenance." (Social Contract, Bk. II,
Ch. 9) "I shall. suppose myself in the Lyceum of Athens,
repeating the lessons of my masters, with Plato and
Xer.ecrates for judges and the whole human race for
audience." (Discourse, Introduction)
The first reminds us of Plato 0 s similar discussion in the
Republic; more significantly, it suggests that the context or
field of Rousseau 0 s political c..011~t.:ruction is the ancient polis,
not the modern Leviathan. (34) The seconcf'advises us that
(34) This suggestion is already implied in the demand for periodic
assemblies of the whole people and is strengthened by the contents
of the 'Dedication to the People of Geneva' at the head of the
Discourse.
�- ·27 ,..
Rousseau's arguments here and, by extension, elsewhere, are to
be judged according to the principle$ of the ancients.
In Rousseau as in Plato and· Aristotle virtue and reason are
inseparable and, · moreover, necessarily involved in any determination or the best political order. Rousseau adds to these the
concept of liberty. for him the essential element of the nature
of man. To see how these three ideas are interrelated and how
their interrelationship established Rousseau's allegiance to the
ancients is the principle task of this section.
Any decree of the general will which relates the whole people as
sovereign to the whole people as subject -- any decree general
both as to subject and ·object -- is a law. The state governed
by laws, whether it be a democracy, aristocracy or monarchy is
a republic; in 0th.er words, a state in which t.he public things
or interests are foremost. Ho-wever Rousseau forsees the
possibility of conflict between the general will and the particular
wills of the subjects; will compulsion alone bring the subjects
into ·· conformity with the decisions thev themselves made as . citizens?
More generally, what ·kind of men ought to live in the republic?
Government does of course compel obedience in exceptional cases;
nevertheless there is reason to suspect that the majority of
subjects obeys not out of fear of punishment but from some positive sentiment or .consciousness. We recall that the political
equivalent of compassion is obedience to the laws. Obedience can
no longer be associated exclusively with self interest; some form
of' fellow-feeling some real consciousness of the common interest
as common must be taken into account. What kind of men might
be expected to have such a consciousness? It would .be instructive
to compare Aristotle's description of homonoia (being of the same
mind) with Rousseau's General Will, without necessarily trying
to locate the roots of .the latter notion.
"The citizens are said to have homonoi a ·'trJhen they t 'h ink
similar thoughts about what is advantageous to them and
choose after .deliberation the same things and carry out
the things opined in common. Thus when all the citizens
thi9k the._
public offices ( d/~ ,(_a(L
) ought to be elective
( rlfL/ETo( l) there 'is said to be homonoia between them" •
. And here some light is shed on the arithmetic metaphor Rousseau
uses to explain .the operation of the _
general will:
"For it -is not .to be of one mind whenever each thinks
the same .thing but when each thinks the same thing in
relation to the same thing; for instance when both the
demos and the nobles think the best should rule."
Unless I am mistaken, . this is ,a·· reasonably clear description of
what Rousseau envision.ed in his explanation of the general will.
Aristotle goes on to qualify the notion of homonoia: it can
�- 28 -'
/
only exist between good men (£.7Tt £t t(fr'- v) "for they are of one
mind with themselves and with one another ••• the desires of
such men are constant and do not flow back and forth like the
tide; they desire just and advantageous things, which they aim
at in common. The base on the other hand cannot be of the same
mind .except to _ small degree. "(J.5)
a
If it is only good m.en who can perceive the common interest and
vote for it, surely only good men will conform to their own
decisions. Compassion was for Rousseau the sign of man's natural
goodness; through obedience to law and what it presupposes -consciousness of the common interest -- that goodness persists in
the rational civil society although it has been fully extirpated
in the existing civil societies. This conclusion, however, is
of little value until we have discovered how Rousseau understood
the good man or if, indeed, he admitted his existence or, perhaps,
his indispensability.
For Plato the account (logos) one gives of the just city corresponds to the account of the just man; for Aristotle ethics and
politics are inseparably correlated. It is indeed a constant and
distinguishing feature of ancient political thought that the
virtue or depravity of a man's character has an essential influence on the character and permanence of any regime. The best
~tate should therefore contain the most virtuous men.
The best
state, furthermore, is the one in which wisdom -- either living
(the philosopher-king) or traditional (the laws) -- rules: the
rational state; just as the -best man is the rational man, the
man whose actions are directed by reason. Virtue is a kind of
knowledge, a mode of activity determined by and in conformity
with reason.
The terminology of the Social Contract (moral liberty, moral
equality), the .-1·daa of the legislator and the entire Discourse
on Political Economy (Rousseau's answer to the Prince of
Machiavelli) make it abundantly clear that Rousseau ~ concerned
with ethics and in much the same way as Plato and Aristotle were.
Consequently we might expect Rousseau to understand the good
man, the citizen of tae Republic, -as the man whose actions are
guided by reason -- his own or that of another.
The general will always wills the public good but sometimes it
fails to understand what that good is that it is willing. Likewise, the individual · always desires his own good and in acting
thinks that he is doing what is good but he too is often deceived.(J6)
Both ·are in need of guidance. And here I may allow Rousseau to
speak for himself:
(35) Aristotle, Neomachean Ethics 1167a26 ff. (My translations)
(J6) This argument may be examined in greater detail in Plato's
Gorgias 466E-468E
�- 29 ..
"The individuals ·must be. compelled to bring· their wills
into conformity·with their reason: the general .'Will must
be taught·· to know what it 1,-.71.lls. If that is done, public
enlighte?IrBnt. leads to the union of understanding and will
in the .social body; the parts are made to work exactly
together, and · the whole is · raised to its highest power. ·
This makes a legislator necessary."
Here we have reached a crucial point: Rousseau accepts the
·modern notion or contract with its denial that man is by nature
political, yet he also accepts the ancient requirenient that
reason. direct .the. operations of the city-- a situation only
brought about by the intervention and supervision of a god-like,
sublimely wise man who sets up the laws for a people. Contract
alone is insufficient to assure the foundation of a rational' .
political society, for the many are not wise or enlightened,
they are blind.
The legislator -- and Rousseau is thinking of Solon, Lycurgus,
and perhaps r;:IJ.µnahl?o~ilius-- at the appropriate time in the
history of a people{J?) establishes a system of laws based on
a thorough understanding of their passions, capacities and circumstances. The laws he sets up impose continual deprivations,
the advantages of which no young people can be expected to understand. Hence he cannot appeal to reason in order to have his
laws accepted; reason is the product of his enterprise. Nor does
he have any actual authority, being neither sovereign or prince -"his office has nothing in common with human empire". Therefore
he · prefers the authorship of the laws to the gods, hoping that
the ·greatness of his own soul will certify the "miracle of his
mis·s~on"(J8) and in'. .this he '"persuades Nithout convincing".
The lawmaker thus creates the social spirit; he in effect recreates ·
men through the laws bringing it about that "each citizen is
nothing and can do nothing without the rest". The city comes to
be what it ought to be through wisdom~ · ·
· .. · ·
It is presumed that after the departure of the legislator t he
people as a whole will be sufficiently enlightened by his precepts
and example _to . ~11 its true good therea~er; at the same time
each subject will recognize the coincidence of his private interest and ~ the interests of the city.
The law becomes the form of rationality in the city,(it)is _
the
depository of the (divine) wisdom of the legislator. 39
.(37) . Rousseau i discusses this point in Bk • . 2 1 Ch. 1-0 . of the
Social Contract.
.
(JS) Plato's ·Laws begins. with the· question: "Do you take a god.:·
or some man as· the cause of the setting up- of your laws?"
( 39) The secularization. of the Divine becomes complete when
Rouse.eau calls the '~voice of the People" the "voice of God". The
imminent God of Spinoza's metaphysics -"" the laws of nature -corresponds in Rousseau to the general will of the city. Adequate
reasons, I think, for calling political philosophy secular
theology, as I did in the Introduction.
1
�- 30 When each subject acquires the habit of obedience to the laws,
when each is educated to "the due observance of what is proper",(40)
the state becomes solid and lasting for then the law merely "assures,
accompanies and rectifies · the natural relations . between men" -relations ·. that are grounded in the practice of virtue. . The word
'nature' has certainly taken on a· new and intriguing meaning which
I shall explore in the concluding paragraphs.
A manual for rulers, a new and totally revised version of Machiavelli's Prince, must make the rulers aware of the supremacy of
law and the necessity of obedience to the law.(41) Such a manual
Rousseau wrote under the title A Discourse on Political Economy.
In it he makes explicit what was beneath the surface of the
Social Contract.
The general will is found here both under its own 9ame and under
the name of the "Public Reason, Which is the Law''.~42) It is to
this Public Reason that the Prince must listen at all times, for
government here is legitimate and popular, having for its object
the good of the people (which the public reason determines). "The
power of the laws depends still more on their own wisdom than on
· the severity of their administrators and the public will derives
its greatest weight from the reason which has dictated it." Thus
the Prince who is under the law and not its master must be its
guarantor and must use every means of inspiring the love of it.
"The first· law is to respect the law."
Thus the government, the legitimate executor of the general Will,
can pres·e rve peace and order in the Republic, assure tranquility
and respect for law in the state. To what other ends could it
properly aspire? Does not the fulfillment of the being of any
civil society consist in these very ·.,-things? Certainly, for
Hobbes, for those who took the "satires of Machiavelli" seriously.
(40) Compare Aristotle, E.N. X, ix 1179b20-1180a15.
(41) Rousseau's interpretation of Machiavelli is quite fascinating. I shall quote his most significant remark and· most of the
appended footnote: "He (Machiavelli) professed to teach kings;
but it was the people he r~ally taught. · His Prince is the book
of Republicans." "Machiavelli· was a proper man and a ·good citizen; but, being attached to the court of the Medici, he could not
help veiling his love of liberty in the midst of his country's
oppression." · Note also .that he calls the writings of Machiavelli
"the Satires.'' · ·
(42) This Public Reason determines the rule of what is just and
unjust in the city. We might preo.ipitately suppos.e that justice
is relative to each state. · Hence, it is well to recall Rousseau's
statement in the Social Contract: "Doubtless there is a universal
justice emanating from Reason alone." Rousse~u is perhaps think~
ing of the lex naturalis of the Roman juris consults or even. of
Cicero's "Law is transcendent Reason, implanted in nature, commanding what should be done · and forbidding what. should not be done."
(Cicero, de Legibus !-,. 6) ·
�- J1 ·"But if .noth_ng ~ore is done, there will be· in all this
i
more appearance than reality; for that government which
confines itself ·to mere obedience will find difficulty in
getting itself obeyed. For if it is g·ood to know how to
deal with men as they are, it is much better to make them
what there is need that they should be. The most absolute
authority is that which penetrates into ·a man's inmost
being, and concerns itself no less with his will than
with his actions."
The virtues of the subje.c t of the Leviathan are extrinsic, they
do not involve his inner character, nor do the laws or acts of
the Sovereign attend to this inner character. Rousseau stands
here quite resolutely with the ancients.
"This was the great art of ancient governments, in those
distant times when philosophers gave laws to men and made
use ·or their authority only to render them wise and ·happy •. ·•
. • • .~ ·BUt··,our •mocle:rm .. gove1mments, which imagine they have ·
done everything when they have raised money, conceive that
it is unnecessary and even impossible to go a step further."
The government which seeks to have the general will accompli~hed -and this is the true office of any legitimate government -- must
bring all the particular wills into conformity 'With it, "in other
words, .as virtue is nothing more than this conformity of the
particular wills with the general will, establish the .. reign of
virtue" -- true virtue, the hapit of acting in accord with what
reason declar.e s to· be good. (43) Government, by enforcing the law,
teaches men not to be inconsistent with themselves; it teaches men
to be free. "It is not only upright men who know how to administer
t .h e laws .; but · at bottom only good men know how to obey them. tt
Civil liberty is not all the city gives to men for they also acquire in their renunciation of their natural (i.e., original) independence moral liberty ·"which alone makes a man truly master of
himself; for the mere impulse of appetite is slavery, while
obedience toa law which we prescribe to ourselves is liber t y" .( 44)
What could be more in the spirit of Plato and Aristotle?
The greatest good of all, which is the true end of legislation,
consists in liberty and equality. The former we have described
already; the latter is not, according to Rousseau, uniformity of
wealth : ancl power, but ·the proper use of these: "power shall never
be great enough for violence -- and no citizen shall e. er be
v
wealthy enough to buy another nor poor enough to be .forced to sell
(43) It must be noted, however, .that in most cases this Reason
does not belong to the particular wills as such; in p·raising ..
Socrates and Cato ._:R.ousseaU: "·say13 "we should be taught by the one
(Socrates) and led . by the other; and : thi·s ·a lone is enough to ,determine which to prefer: for no people has ever been made into a
nation of philosophers but it is not i~possible to make a people
happy." The people of Rousseau's Republic will be "upright and
si~le."
(44) Social .Contract, Bk. I, Ch. VIII
'
��- J3 CORRECTION TO PAGE 41 COLLEXJIAN, October 1963
Robert Sacks
And now the Central Sections
Let the same things be set oat as before, but let it no longer be required
that angle A'AO be a right angle; and again let it be required to find the
relation of the parameter to the lines involved.
Now since
BN,NC = NQ2
and
AA 0
1
AN
therefore
AA'
A'N
Or
NQ2
BN ,AD : : NA 0
... AD : NC
.
... BN,.AD BN,NC
.
A'A
As in the case of the parabola, if I draw AF making angle ADF equal to
angle BAN meeting AA' at F triangle ABN will be congruent to triangle ADF,
and thus
BN, AD = AN, AF
therefore
NQ2
AN,AF :: NA 0
A'A
Or
NQ 2
AN,NA' :: AF
0
AA
Thus AF is the parameter.
But this formulation is useless because its
construction is dependent upon the choice of the point N. Therefore
Apollonius draws the line OK parallel to AA', meeting BC at K.
And since
AD
AF : : AN
NB
and
AN
NB : : OK
KB
AD
AF : : OK
KB
We now have, etc.
�
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••
COLLEGV\N
ST. JOHNtS CLLLEGE
J ANUA;Y, 1964
I
�TABLE OF CONTENTS
A Sense of Honor·••••••••••••·······•······ Laurence Berns, Tutor
1
Varia on Apollonius •••••••-•••••••••••••••••• Bryce Jacobsen, . Tutor
7
Two Poems •• •• ••• •••• •• ••, •• ~ ••••••• •• ••••••• Beverly \.'ood,;vard, Tutor 11
Civility and the Law ••••••••••••• •·•• •• •· •••• Daniel Carl Schiff '65
Rci>us seau and the Ancients:
1\ Reply~.........
2c-rmeniscus
?
27
-.)
.coem • ••••••••••••••••••••••••••••••••••••••• Susan Roberts '66
Comments on Mr. Sparrow's Lecture ••••••••••• Larry Silverman
1
30
66
Essay on Ducks •• ~ ••••••••••••••••••••••••••.• Jeremy Carl Leven '65
Editor •••• De.vid . Lachterman
Business hanager ..... David ..asrnussen
,Editorial .·.ssistant •••• Susan Roberts
Faculty i\dvisor. • •
Eva Brann
C The Collegian sends its best wishes to Nrs. Audrey Kempton with
hopes for her speedy recovery.)
12
31
36
�lri the editorial · to the September, 1963 Collegian I
suggested that members of the community submit questions
·or criticisms to our Friday evening lecturers through the
medium of this publication. this month Miss Brann and I
· decided to implement this suggestion by inviting a
studen~
to review Mr. Sparrow's lecture Rights, Law, end the Right •
In the follouing weeks
students and tutors will be invited
to contribute reflections or challenges concerning future
lectures. On occasion more than one review of the same lecture
will be published for purposes of comparison and controversy.
Lecturers will be invited to submit restatements, counter-challenges
and elaborations of their positions. The record of such debates
will be, I think, ··~f vclue a~d interest. Mr. Silverman's
comments on t-ir. Sparrow's lecture set. an unusually high tone for
future contributors; it is hmped that what he began others will
continue.
Note: The deadline for
the Collegian's Short Story Contest
has be&n extended until March 15, 1964.
ErrDta to this issue:
p. 17 cheif should be chief
17 6mvalries and add 'spars'
19 (better called an
) insert ... . }:~ .~. : , .
20 Footnote two = Let II, sc. vi 1. 54
21 Footnote three= Act IV, sc. i 1. 145
25 Footnote one=
27 in seiner add
29
; ~ct
V, scene i, 1. 1-6
/J..1At d\ S
promenus should be promeneur;
Vaugh~n
ed. add pp. 75-86
�El.l:ATA TO
JANUAf~Y,
1964 COLLEGIAN
the following title was missing from the Table of Contents :
The Relationship Between Appositives, Restrictive and Non-~estrictive
Attributives
•••••••••••••••• Pattie 7urner 1 66
12
The followmog should be added to the secona paragraph on p. 32
ending
11
thus agreeing in part with the traditional liberalism
he was trying to undermine."
Add:
One might counter this objection by remarking that those
actions permitted by the laws Dre approved because the actions
are right. The square is quite explicit on this point.
By calling certain voluntary actions 'right', do not the
laws imply that one is duty-bound to do them ?
To first p2..ragraph on p. 34 after the
'the peculiar work' "
add:
ra~o" l-'pyov
words "In Plutarch's phrase,
�i'\ SENSE
OF
HONOR
Laurence Berns
· ur
o
One of .the .saddest things ·about the lrUrder ·of .
President is that we
do not realiy or fully kriow what we have lost. So much of what we
admired in the I'!lan lay· in the promise he held out .for future greatness: .
his intelligence·, 'that is,- his capacity _to learn; his high . style, the
grace and fluency of his discourse; his sense ·o·f htimot"• ·the subdued
irreverence. of hi.s "deadpan" comic style; his freedom from, or rather,
distaste for sentimentality; his sobriety in acknowledging the aspirations of the more articulate members of the polity while at the same
time being able to appreciate why the resistance·of the less articulate
made it wise to forego the implementation of those aspirations.
Being both ambitious and well-bred, he could be at the same time both
gracious and hard; ·happy in the exercise of highest authority, he
·
could be grateful for being provided with the opportunity for living
up to, as he. put it~ that ancient .Greek definition of happiness, "the
full use of ~our powers along lines of excellence." Like every
-. natural politician he greatly desired and greatly sought the esteem
.of his fellows, arid 'like any man whose soul has ever been enlightened
. by a sense of honor~ - he knew that the .prize was - not worth the winning
·
if he did not make himself worthy '.of that esteem.
II
However, the injunction of our new President obliges us to turn our.
attention away for a time from memories of John Kennedy to the grim
circumstances or conditions .of his assassination, to see if :we might
learn anything from them. We shall in all likelihood never know 1:~hat
was going on in the mind of the President's assassin, to what extent
. he might have been influenced by the atmosphere- of alarm created by
the political murders in Birmingham and Mississippi and by the ·rabid
charges propagated by political extremists, charges which gain conviction among the dupes of the extremists 'becausG they remain urirepudiated and uncondemned by people ·who know better. , (It is the
duty or those who · stand to profit · politic ally from such charges to
be the fi~st and the most vigor~us in denouncing them). .
·
. .'
~
Regar dless of what went on in the assassin·• s mind, the assassinat ion,
the murder of Oswald, .the events just referred to, all are signs of
danger. Are there any general conditions whi'ch have been contributing
to ·this tendency to take direct political action, to take .the law into
one's own hands, . thi_s tendency toward the subversion of the rule of
law? It .is hard to be verj exact about such matters; but perhaps the
knot.Yledge r-e seek does. not yield itself to overexact methods. . It
1
could be that the m~st articulate elements of the nation and the most
-· prominent objects of their loathing, the right-wing extremists, have
been working in unplanned cooperation to bring about the same conditions.
The effects of the extremists and their not so unr.dtting allies, those
who have gone into the tawdry business of investigating political
opinions in public, are not too . difficult to understand: by sowing
�"" 2 -
distrust and suspicion they tend to sp r ead the feeling that Americans
can no longer trust themselves to behave iike free men, that what is
required is extensive official supervision by them and their cohorts.
The accusatorial atmosphere not only opens up new fields for bullying
but is also expected to reform the situe·tion left us by our traditions
and institutions of civil liberty. It does not require a great deal
of subtlety to see that what they would reap would resemble most
of all, in its political essentials, _ the despotisms admired by their
brethren of the far left.
To expect any society to be completely free from fanatics, those brooding enthusiasts, to turn Lincoln's phrase, would be unreasonable. The
problem is always one of keeping them under control. So long as they
present no clear and present danger to free government, it is probably
safest to provide · them and their brethren of what they regard as the
opposite extreme opportunity for keeping themselves occupied by organizing and meeting peaceably. But wherever unlawful violence breaks out
the p~nishment should be swift and severe. Leniency in such matters is
likely to function as encouragement. It is equally or even more important
than the control of violence that the leaders of respectable opinion in
the nation and in the various communities make it perfectly clear how
far removed from the serious political life of the nation these people are.
This requires, to repea.t, that the primary responsibility for diminishing
their influence should fall to those within the pale of respectability who
might stand to profit from their efforts. These are the people who are
most likely to have some influence on those who are about to join or leave
their ranks. It probably is 11 too much to hope" that anythin.s ..migbt ·
"soften the hearts of those who uould themselves recoil from assassination,
but who do · not shrink from spreading the venom which kindles thoughts of
it in others." It would be safer to place our hopes in strong anti-toxins.
The case of those whom we have spoken of as more articulete, our writers,
social scientists, journalists, artists and "communication specialists",
is -more difficult and more important. They might be expected to know
better. By wallowing in the seamy and sentimental side of Ufe, indulging
in and habituating us to that invasion of privacy called pornography,
identifying misery with profundity, glorifying vulgar, thoughtless and
even perverted passion and preaching its liberation, by all these things
our writers tend to undermine the pride, self-respect and self-confidence
of the educated public, those who they should be preparing for leadership.
One wonders why these supposed divers into the depths of the human psyche
never seem to have noticed that it is precisely those peoples who have
been most distinguished for self-restraint, self-censorship and selfcontrol, qualities now fashionable to disparage, the English-speaking
peoples, who have also been most distinguished for being able to make free
republican government work over long stretches of time. Free men
need confidence in and encouragement of their ability to control
themselves . Our writers and the producers of our mass media drama tic
arts for the most part, produce the opposite. To the extend to which
free men lose their dignity and self-respect and cease to hehave like
free men, like men who deserve free institutions, to that extent the
~
�.. 3 -
will to pre.s erve free ins.t i tutions will naturally wane·, to that extent
it will seem _ oth right .,and natural to eliminate free institutions.
b
It is almost pathetic to see hot~, when some of our writers do strive
to present something of the noble or heroic, it often turns out to be
of the nearly mindless variety, as if deepened understanding can lead
only to the low or bestial. This is not too surprising, for when the
writers turn to the authorities, the scientists, the "social scientists",
for enlightenment, they .find them incompetent, for the most part, to
deal w.ith much besides the· low~ the mechanical and the bestial. To
speak of the noble and the base, the good and bad, would entail substantiating "value judgments", and that they say has nothing to do with
science. This is not .the place to go into the sophisms usually presupposed by those holding to this notion of the science of human things;
our concern here i~ primarily with its effects. Yet perhaps it would
not be amiss to suggest that if these social scientists believe that
the principles of their science cannot be derived from their oim:
proper subject matter, that they must .be borrowed by analogy from the
more prestigious natural scie·nces, it might be more fitting to go not
to physics or mathematics but to a science like medicine which makes
qualitative distinctions like that between health and sickne·ss.
The effect of the intellectual orientation we have been describing on
our journalists manifests itself by the increasing disrespect of
respectable periodicals for the privacy of any apparently newsworthy
subject. - Ought we to be peering into the astronaut's living room,
staring at his wife on the day of his · fiight? . Do we have a right to
know as much as possible about the private life of every public figure?
Are not the press and media men partly responsible for making the
Dallas authorities feel that everyone had a right to know all the
details of Oswald's transfer to the county jail? Should the question,
as to whether the public's "right to know" should be allowed to
jeopardize a man's right to a fair trial, even have arisen? !bes the
press have a duty to reveal to us everything they can possibly find
out? Or is it not rather the duty of ever;J responsible reporter and
journalist to, at least, consiqer whether 1...rhat he says might make his
audience better or worse citizens, better or worse human beings? There
are times when a personal and private tragedy mecomes an occasion
where it is appropriate for the public to know about and participate
in the events. Such, of course, were the events leading to the burial
of the President. The press and the communications media, for those
three days, following that example of proud -and compassionate selfre straint set by the gallant former Fir st Lady and the Kennedy .
family, showed us to what heights they are capable of rising by the
part which they took in giving the late President the farewell he
deserved. One of the incidents for which this writer is most grateful occurred as the dignitaries gathered about just after the President's
body had been placed in the Rotunda of the Capital Building. A CBS
radj_o reporter, his voice very low and heavy with emotion, noted that
most of the mourners were still dry-eyed. Then he said "Just across
the way from me s·omeone' s eyes have just filled with tears." He
hesitated and finally said,. "I don't think I'll tell you who it is."
·_,
�- 4 -
Unfortunately, We must now turn to the dreflriest subject o·f this essay.
Perhaps the best commentarj that could be made was made during those
three days following .the assassination when any person of some sensibiiity knew that this was no time for cheapness, pettiness and triviality,
.and consequently that vulgar intruder, · advertising, was expelled from
the airwaves. Unfortunately the debasing effects of this continual
stimulation of and appeal to every kind of petty desire do not end with
periods of national mourning. Assas$inations are not the only occasions
for which serious people have a need, perhaps even a right., to ·sustain
a serious mood. The advertisers realize their purpose-s most when they
imbue their unwary audience, the largest part of their audience, with
the feeling that they owe it to themselves, as if by natural right, to
gratify the desires the advertisers' products cater to. The American
. way of life, American freedom, begins -to s_ m to mean ·the freedom to
re
amass as many possessions, gadgets and creature comforts as possible.
We will not elaborate on the kind of invasions of privacy that are
perpetrated by the cosmetics industry. .Can we afford to allow such
as they to play so large a role in forming our tastes? To the extent
that the advertisers succeed in_forming the national character, it
becomes increasingly difficult to insist that we be treated with the
dignities befitting free men.
What necessity dictates that the communications media should be
dominated by predominantly commercial motives? What about the
educational role of the media? Ed~cation is gratifying, but, unlike
salesmanship, never nattering. The reason is simple: Education
involves confronting oneself with minds or spirits that one acknowledges are in some decisive respect superior to one's own mind or
spirit, it involves a continual· striving to raise one's own under-·
standing to the level of that of one's teachers. Education, then,
frequently, if not al~ys, reminds us of our defects in a ·way · that
makes us apt to be ashamed of them. It moves us towards overcoming
whatever is petty and selfish about ourselves; salesmaship, on the
_
other · hand, caters to and ·thereby encourages the selfish and the
petty. Educati_n is not likely to rN.in out on the open market.
o
The problem is complicated by the fact that. a great deal of advertising
in this country is not stupid, much of it is rather clever. Obviously
considerable artistic, literary and musical talent goes into its
production. The sad result is that young budding artists w should be
ho
.· directed towards working for _he elevation, perhaps even the exaltat
tion, of the human spirit become inured to the prostitution of their
talents.
Someone might reply to the positions we have set forth in this section:
Is not our sense of privacy connected to our sense of shame and is not
sl;tarn.e·lessre s _ after all, both· the precondition for and the natural
s
effect of enlightenment? If shame and tact, respect for another's
sense of shame, are nature's ways of protecting the intimate, the
vulnerable, the· naturally exclusive in man, then sham.elessness would
seem rather to be proof of ignorance. Furthermore, i-f our self.
respect depends upon sue~ protect:i,.~m and our freedom. depends upon our
self-respect, then our freedom depe· ds as well upon our sense of shame,
n
our sense of privacy.
�- 5 III
Our -concern has _been .the conditions t~nding towards the subversion of
the rule of law. in America. · Throughout our history there has been a
tension between a tradition of violence and the · tradition of respect
.. for. the la1,i'. Bot the least manifestation of our failure -to come to
.grips ad~quately with the probl_e~ of violence is _the widespread
· . tolerance for those .home-grown forms ·of military dictatorship called
organized and unorganized crime~ On the frontier, it has been said,
violence was necessary and the tradition made sense. But now there
are too many of us. and we are too close together to tolerate habits
appropriate for by-gone conditions. Yet ·it would be truly sad if
thanks to the progress of ·medical and technological science we have
become so crowded and so inte·rdepertdent that the very physical conditions for -"rugged ,individualism" and privacy are disappearing.
However .this may be, · :it ought to be said that the . roots of.·our
tradition of violence are not altogether _
ignoble. · Violence is not
in itself W:rong, obviously it is required sometimes for the defense
·. of our noblest interests. According to the Declaration of Independence
no particular form ,of government· or institution, or adherence or ·
conformity thereto, is sacrosanct. What is spoken of as sacred ·is
honor and certain inalienable rights, properties of separate human
beings. Our sacred .honor and our natural rights may.~ under-certain
very rare conditions, . require that rebellion and Violence be .undertaken on their behalf againsttha established order. Rather than
·simply deplorin'g all . forms of vioierice our task would seem to be to
try to understand the difference between fanaticism ·and noble dedication. The ti:..ro. are often confused t for reasons alluded to earlier and
because they do share at least ene iroportant trait in common: they
both seem to involve forgetting about one's self. The difference may
have something to do with the reaso_ ableness of the goais of each.
n
0
·. The greatest doc.uments f,'rom · .the most v~ried source·s of our tradi tio· ,
n
. _or . example, · the Old and New ·Testarrients, Plato• ·s Republic and the
f
Declaration of Independence are unanimous in teaching that perfection
is not to be _
sought for in particuiar ·institutions, at least human
institutions·, that there -will never be heaven on earth. They point
to what kind 'of order we ought to aim for, what kind of order should
provide us with the standards for improving those actual orders we ·
find in the w
orld, but they w
arn us not to expect the realization of
our highest hopes. The warning servep not only to prepare us against
disappointment and frustration but also to help us from being diverted
from the. pursuit.of that perfection "which might be feasible for us:
·'.for example, in t~e ~~p_qbl~.~. Socrates shows ~s why the chances _or
f
instituting · a perfectiy J~st order aniong a community ·o£men are
·
completely, or almost completely, ni.1", but he does it. while illustra~
ting in what way it might -be feasible· !or a man to institute such an
order, a heavenly ord.e r, namely,- by instituting it "in his own soul.
Perfection is not to be ex,pected .in the ordering of other men, but,
if at all, in the orderi~g of one's· self. The latter, not the former,
might. be in our power. The fanatic does not make distinctions: he
does not distinguish between possessing rights and knowing when it is
wise to exercise those rights; he does not distinguish between what is
�- 6 -
good simply,what good is realizable generq.lly and what goodness might
reasonably be expected in ·some given situation. The latent fanatic
expects heaven on earth. He is inevitably frustrated, and indignation
joined to envy and resentment swells into hate against those who he
supposes are or represent the causes of his failures. Could one not
say that perhaps the nihilism, the bitter resentment against all
society exhibited by some of our writers is also a function of their
original overexpectation, a function of their divorce from the sobriety
of the tradition and hence their failure to consider the immense
obstacles that always lie in the path of man's attempts to improve
himself and his situation? The fanatic is certainly no respecter of
the rule of law, its blessings are far too modest to please him. The
rule of law is not going to bring heaven down to earth, the rule of
law by itself cannot even produce nobility of soul, though it may go
far towards creating the best possible conditions for the cultivation
of nobility of soul. Despite these shortcomings a moderate appraisal
of those blessings may not be out of order. It might not be too great
an oversimplification to say that the trouble ~dth most men is that
they tend to bully and or cheat each other. The English-speaking
peoples seem to have concentrated on preventing men from bullying each
other, and have been blessed with considerable success in this regard,
in great part because of those devices and that spirit which we sum up
under the head of the rule of lar..r. We must also coneern ourselves
with the problem of ·cheating, but not in such -a way that we concentrate
so much power in the hands of our protectors that they are then in a .
position to bully us. Besides the fact that he who is in a position
to bUlly us is also in a position to cheat us, bullying hurts in a
much 'deeper way t~an cheating.
What should we expect from men? Probably one should save one'.s highest
expectations for one's self. One should hope but not expect that men
will behave as well as it is possible for them to behave. Yet cynicism
is not the answer, for although one should take precautions against the
possibility, one should not .expect that men will behave as badly . as it
is possible for them to behave. The proper mean probably · lies in_
acting as if one expected men to behave better than they probably will
behave. ·
·
What we seem to be recommending is · a kind of puritanism, but puritanism
with a sense of humor, for high comedy thrives on · w
hat the·. fanatic · ·
cannot abide, the disparity between human goals and ; human achievements.
It mollifies our disappointment and our anger while ·a t the same time it
keeps before our minds those goals from which we ·fall short.
Let us sum up this paper with a warning and a suggestion. The warning
first: If we want to remain free, we cannot allow ourselves,. to become
vulgar. The suggestion: If we want to become virtuous without becoming
dull, we could perhaps do no better than to consider that highest and
. noblest form of "de'adpan" humor, Socratic irony.
�- 7 -
VARIA ON APOLLONIUS
Bryce D. Jacobsen
The following article includes three separate items:
I
II
A construction fitting any ellipse into any cone,
.
The completion of Apollonius' (partial) presentation of
circular sections,
III A classification of sections with respect to the cutting
plane.
I
Anv Ellipse in Anv Cone
Apollonius, in P~op. 52-58 in Book I, solves the problem of generating
a cone and cutting it so that a section will be produced whose diameter
and parameter are equal to two "given ••• bounded straight lines".
He does not, however, address himself to the more general problem of
cutting any given cone such that the resultant section is identical to
some given section. This form of the problem was mentioned i_n Mr •.
Sacks' article in the October, 1963, CollePian, when he said:
"For Apollonius, any size conic may -be derived from any given
cone and, in fact, any given conic -section may conversely be
placed back into any given cone."
The problem as stated has solutions for the parabola and the ellipse.
No general solution exists for the opposite sections, unless the ratio
of transverse side to upright side is given as greater than unity.
The solution for the parabola is fairly simple. (We will not present
it here, since it makes a nice "original" for those addicted to
Apollonius.) We do, however, pr.esent the solution for the ·ellipse.
Notice carefully that no restriction whatsoever is put on the cone,
o
. r on the given section.
(The fact that, in our given ellipse, the given diameter is the axis,
and the ratio of transverse side to upright side~ greater than .unity
ts not a restriction on the possibilities of the given ellipses. For,
if the . "figure" of the given ellipse is no-t that of the major axis and
its parameter, then by II-47 the major axis may be found, and by I-50
the parameter to this axis is given. So an e~lipse given by any
diameter and its parameter is ~given by its major axis and its
parameter. And the ratio of major a.xis to parameter is greater than
unity.)
Problem: In any given cone, to pass a plane through it such that the
resultant section is identical to a given ellipse.
Let MRN be the given ellipse, with axis MN and parameter MO.
�- 8 -
Therefore there exists a cirele Nhich can be circumscribed around
quadrilateral BAFD. (Converse of Euclid III-22. See Heath's note.)
Therefore AB and FD are chords of this circumscribed circle, and E is
necessarily outside this circle.
Therefore rect. DE, EF equals rect. BE, EA (Euclid III-36).
Now
And
Or
Or
Or
DE : EF :: DE,EF : sq.EF :: BE,EA : sq.EF
BE,EA
sq.EF comp. BE : EF, EA : EF
BE,EA : sq.EF comp. FL : LH, FL : GL
BE,EA : sq.EF :: square FL : rect. GL,LH
MN : MO:: sq.FL: rect. GL,LH
Now let sq.FL : rect. GL,LH :: AB : Z
Therefore the section produced by a plane through AK and XX will be an
ellipse 1dth AB as axis and Z as parameter (I-13). And since AB : ·z : :
MN : MO, this ellipse.~dll be similar to the given one.
Now if AB equals r1N, the problem is solved.
If AB does not equal MN, then mark off on FL (or FL extended) a line
FS equal to MN. From S draw ST parallel to FG. From T draw TW parallel
to FL. Therefore TW equals MN.
Now let sq.FL : rect. GL,LH : : TW : U
And
sq.FL : rect. GL,LH : : MN: : MO
Therefore MO = U
Therefore the section with TW as axis and U as parameter will be
identical to the given section.
QEF
(The proof is the same if the point D is taken on the other side of F,
thus reversing D and F. In this case the cutting plane and line FL
meet the base of the axial triangle on the other side of the base extneded. Thus it follows that there are at least two sections in the
gi ven cone which are equal to some given section.It se.ems probable, moreover, that for any axial triangle in a given
cone, a section equal to , a given section can be found. :If this is
true, then there are infinitely many so. utions to this problem for a
l
given cone. I will not try to prove this. I leave this for later
consideration, or for others to prove, or disprove! . ·
II
Circular Sections
There is a "gap" in the early propositions- of Apollonius.
he proves that:
In Prop. 5
�- 9 -
If
a) in an oblique cone the axial triangle is perpendicular to
the base
b) and the cutting plane is perpendicular to the· axial triangle
c) and the section is subcontrary
Then the section is a circle.
In Prop. 1J ·he proves that, in any cone:
If
a) some axial triangle is given (not necessarily perpendicular
to the base)
b) a cutting plane is given whose common section with the base
is perpendicular to the ~ of the axial triangle
c) and the cutting plane is neither parallel to the base nor
sub contrary
Then the sec~ion is an ellipse
The question naturally arises, "What is the section when the following
are given"?
a) an axial triangle, as in Prop. 13
b) a cutting plane, as in Prop. 1J, except that it 12.
sub contrary
It cannot be concluded from Prop. 5 that this section is a circle, since
conditions a) and b) of that proposition are absent. Proposition 9
is no help either. The section 1§. a circle, but this is not provable
within the Apollonian context. However, a revision of Prop. 5 solves
the problem. First note that Prop. 5 is not used at all in proving
Prop. 6. Thus we may use Prop. 6 in proving our revised version of
Prop. 5. The proof would then be as follows:
If a cone is cut by a plane through the axis, and is also cut by
another plane such that, on the one hand, its•·common section with
the cone's base is perpendicular to the base(or base extended)
of the axial triangle, and, on the other hand, it cuts off on the side
of the vertex a triangle similar to the axial triangle and lying subcontrari wise, then the section is a circle.
�- 10 -
Let FGH be any cone, and let axial triangle FGH be perpendicular to the
-cone's base. ·
Through F draw IFJ'.parallel to GH. On IJ take any .point 0, and then
take point E such ·that · DE : EF : ; MN : . MO. ·
On ED at D set up 00 . uch that angle QDE equals angle EFG. Now pass
s
the circle EPD through points E and D, such that QD. is also tangent to
circle EPD. (Only one ·such circle satisfies these 'conditions.) Let
circle EPD and lirie FH intersect at ·B•
.Join EB, cutting .GF at A. Extend EB;· cutting GH (or GH extended) at
K. Through K, in· the plane of the cone's base, draw XY perpendicular
to GK. · Through F draw FL parallel to EK~ Join BD.
Now angle EDQ equals angle EBD (Euclid III-32).
angle EBD equals angle EFG.
Therefore angle GFD + angle EBD = two right angles.
{And thus angle FAB + an~le FDB = two right angles.)
~erefore
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�-11 -
TWO POEMS
Beverly Woodward
I wrot~ her a long poem in prose~ I told her that a
pomegranate has many seeds. I told her that it was an
agreeable fruit, a fruit which ·a man could enjoy. - I wrote that one day when an autumn wind was flowing,not knowing which of the mul ti·col'ored threads she
would choose ~s the transmitt~r of her response.
I
was surprised that she chose ··to play in so many keys.
The song was simple, pure, free and melodious,
It did not anticipate it could be frozen
By the builders of systems
Made a foundation
For an immobile structure.
The song knew ·no rancour
It found its new garb very strange
And then, it had never been meant
To support such a great weight
Or to live in darkness under the earth.
�-
12 -
RELATIONSHIP BETWEEN APPOSITIVES, RESTRICTIVES,
AND NON-RESTRICTIVES
Pattie Turner
Although in the grammar manual apposition and restrictive and
non-restrictive attributions are discussed quite apart from one
another, it appears to me essential to con~ider all three when
discussing any one of them. While apposition is said to be
distinct from predication pr attribution; it is also explained
to resemble a non-restrictive attributive in signifying a
"condensed, additiona],.:pre,d:ication". · So~ obviously, attribution
and predication do . play a role in apposition.
At the same time
that a combination ·o·f signs may be considered in apposition with
another sign;- it may also be considered a restrictive attributive
as well, although the manual states that it resembles a nonrestrictive attributive.
An appositive is described in the grammar manual as a "a substantive signifying the same thing as another substantive •••••
" The substantive which signifies is said also to "resemble
a non-restrictive attributive in signifying a condensed additional predication." So, here in this definition, two parts
of grammar must be considered. First, the appositive must be
accounted for, and secondly, the appositive with .respect to a
non-restrictive attributive must be considered.
An appositive may be a single word (e.g. a proper noun), a word
with a modifier (e.g. noun plus an article or adjective), a
phrase in which a combination such as a prepositional phrase
is employed and which a combination such as a ·prepositional
phrase is employed and which does not indicate a complete thought,
or a clause which does signify a complete thought -- a unit in
itself. An appositive may be present in a great many forms
since it is the loosest form of combination.
However', while,
it is the loosest form of combination,it is the most intimate
c onnection of one thing to another, i . e . identity .
It is now
in order to look at the different types of apposition.
The simplest and perhaps the most frequently used type of
apposition is that of one word, e.g. "It is hard to believe that
he, Jack Waters, is ten years older than I." In this sentence
the proper name "Jack Waters" is in apposition with "he".
In other words "Jack Waters" . and "he" are one person, an
identity.
It would be easy, however, to use both terms "Jack
Waters" and "he" in a similar sentence and have each signify
two entirely different people: "It is hard to believe that
Jack Waters is ten years older than he." In studying these
two sentences it becomes apparent that the position of the
sign in each sentence is different, thus indicating that
position in a sentence plays an important role in apposition.
In the first sentence where there is clearly apposition, "he"
and "Jack Waters" can interchangeably be the subject of the
�- · .. 13 the .'cl. use-..·"that .he. '. .. . . u In the . seco.nd .sentence, . however, only
a
:t.he proper . n _ime . 0 Jack Waters" is :the subject of :th~ ...analogous
:
·clause 11 that Jack .W aters ••• =. 11 • · Thus the position of the apposit~ve is essential to the meaning of the sentence; in point of
.fact the appositive is µsu~lly set beside that which, .i t describes
or identifies. · This :fact could be considered ·part 0:£ the close
relationship between the appositive and that which i t signifies.
Similar .to the on~ - word- appositive is ·th~ two word, a noun plus
.its :artic.le, : appos:i tive: "We took our pet, a dog, to the veterinarian for ·a sho.t •• ~ ·
In .t his example there is no doubt that
"our .pet" and "a dog" are the same thing, and inde.ed they .are
set . nex.t to one another as has been shown to be essential ...
Next let examples of .the other. two types of apposition be explo. r:-ed.
:
First, an appositive phrase:
"Donald Duck, a creation
.o f Walt Disney, ·i s ·a :favorite cartoon character of children all
over the world."
Surely, : "a creation of Walt Disney, ••••• n
cannot stan<:l al·one, but it c . n replace the name "Donald Duck".
a
The .phrase as .the subject _ f the sentence would not have as
o
significant meaning as the proper name (this type of complication
wil·l · be discussed later), although each signifies the same.
thing.
Second, an apposi tiv.e clause:
"The realization, that
I was now .on my own,. was somewhat :frightening." Again the
subject and the claus_ are interchangeable, but the use of one
e
is· more meaningful than the use o:f the other.
Since the purpose of this paper is to observe the correlation
between the appositive and the restrictive -and non-restrictive
elements . of the ,sentence,, j, t will be necessary to consider the
restrictive and non-restrictive as separate elements and then
:to examine the connection or subtle ass?ciations between the
. three • . Let the restrictive be considered first.
The restrictive is an . attributive which is significant and
. essential to the meaning of the sentence; without this element
the sentence would have little or no meaning • . - The restrictive
can be..one word, a phrase, or a clause.
An . example of a single
word restrictive is:
"The extende_ curf~w was . a favour to
d
those who had to travel a long distance."
In this .sentence the
word "extended" is essential to the proposition in which i t
figures.
It indicates , that without the. increase of time allowance, those who had to be~ route for an unusually long . time
would not meet the requirements of the plac.e t~ which they were
returning • . Surely, withc;:>ut the word - "extended'' the sentence
would tend . to sound extremely sarcastic, for i t is not clear
that the curfew alone would be of any help {help i~ . adhering to
the rules ., that. is) to the t .r avellers.
Therefore the word
"extended" is essential to the meaning of the sentence,and must
be classified as a restrictive attributive.
Similarly, in the
sentence, - "The prisoners who were . sick were sent . .to the hospital,"
the clause "who were sick" •• is essential.
If . the clause did
not appear in the sentence, . the meaning of.- the sentence would
change.
This new meaning would be that all the prisoners were
sent to the hospital.
This, however, is not what is . meant,
and .the.re:fore the claus~ is restrictive.
�-14In t:P,e sen. ence "The girl wearing a pi.nk wig looked . partic.1:J.larly
t
· p ·e culiar, n it. is obvious that the phrase "wearing a pink wig"
is .o:f cardi:nal importance to· the . meaning o:f the sentence.
If
the phrase were left out, the .. girl would look ·pariicularly
peculiar under . any circumstances. . Therefore, ·.necessarily, the
phrase ·is restrictive~
Unlike the restrictive, the non-r.e strictive is ne1the·r · ess.ential
nor particularly significant to the meaning of' the sentence.
Strictly speaking a · non-restrictive is a form of attribution but
,i t may; be thought of as a "cond,ens ed' additional predication."
Let us consider the three most common forms of the noh-restricti ve:
a singie word, a phrase, and a clause.
The one word
non-restrictive is often used more .as an attributive which
attributes something to .a specific word or defin~s a s~ecific
word.
Thus it is not meaningful in the light of the sentence,
e.g. "The child wore his blue snowsuit outside t ·o keep warm.-"
In this sentence the word to be explored i.s -"blue".
As an
attr.ibutive "blue" indeed defines the snowsuit as far as color
is concerned, but · it does not define the . snowsuit in re.g ard to
the purpose for wearing the snowsuit i.e. warmth.
As a "condensed, additional predication," the word "blue" certainly says
something about .' the snowsuit, i.e. that the garment partakes .of
the quality blueness. This participation in the quality blueness,
however, is irrelevant· in the proposition; whether the snowsuit
be blue, red, or .green, the child will keep warm.
Thus "blue"
in this sentence is a non-restrictive.
A phrase also can be a non-restrictive; an example of this is
contained in the followirtg sei;itence: . "Having arrived from
Boston, the lecturer spoke to us about .anabolism and katabolism."
Obviously the lecturer's arrival from Boston had nothing to do
with the lecture on the constructive and destructive processes
of metabolism.
Strictly speaking, one might argue with this
statement by saying that unless the man had arrived from Boston,
there ·would be no lecture.
In this sentence, however, what is
important is the material of the lecture. Theref.ore th.e opening
phrase is non-restrict~ve in that it is not an intrinsic part ·
of the sentence , but is rather incidental to the significance
of the sentence.
A clause too can be a non-restrictive; an exampleof this is
c·ontained in .the ·following sentence:
"I heard that Mrs. Martin,
whom I dislike, will be at :the same party as we."
"Whom I dislike" is the non-restrictive clause.
It is non-essential to the
sentence in that whether I like her or dislike her has no bearing on her anticipated presence at the party.
In this sentence
the clause is a ma'tter of opinion and is meant as a . passing
remark.
The relationship o:f restrictives and non-restrictives to apposition shall now be examined.. Three main cases o:f apposition
with respect to the restri ·c tive and non-restrictive must be
considered with reference to the sttributive and predicative
value o:f each.
The three different cases to be accounted :for
are (1) the appositive as·a non-restrictive, (2) the appositive
�- 1 .5
~
as . a r .estrictive, and .(3) the .appos.itive as a restrictive and
at . the same time.
. _ n.on~ 'restri'cti ve
a
· The - appositive ·as a non-restrictive is the most generally
accepted case.
As a non-restrictive attributive it signifies
a "conde:n.sed, additional predication." An example of this is
the fo,llowing: ,. Lyndon. B~ Johnson, the President of the United
s·tates·~ arrived in Washington yesterday after a Christmas
v·a'<~~ttion in Texas.-" . I~ this sentence "the .President of the
United States •••• " is . non-restrictive · in that ·it really is · riot
essential to the meaning of the proposition in ·which it figures
since it is hoped that the name implies the position of the
Presidency.
In this case, as in attribution, there is present
an "assumption of prior unification." Not only does this
identity imply attribution by defining the scope of significance,
but it also implies predication in that it says something about
something else.
It asserts the existence of the Presidency as
well as naming it. Thus, this is one case of a non-restrictive
appositive which includes attribution and predication.
An appositive may also be restrictive.
The best example of
this is one which is similar to an example in the manual:
"I,
Carole Hocker, do solemnly swear that I have received no help
on this exam." Is the name needed to clarify the statement, or
could it be omitted causing no detriment to the meaning of the
oath? Indeed the appositive is an intrinsic part of the
significance of the sentence. If "Carole Hocker" were left
out, the sentence would read "I do solemnly swear ••• ," To this
sort of oath anyone could fix their signature. Therefore,
although the personal pronoun is used, the statement remains too
general.
On the other hand if "I" were omitted, and the sentence read "Carole Hocker solemnly swears •••• " this indeed
would give no indication of personal integrity with respect to
the oath, and therefore it would be almost meaningless. Thus
the appositive, the name, is of cardinal importance ., and the
appositive is restrictive.
Under certain circumstances an appositive may be either nonrestrictive or restrictive. An example o:f this appears in the
:following sentence from the grammar manual:
"lle saw Keane, the
actor." In order to label "the actor" as a non-restrictive or
restrictive appositive, it is necessary to deviate from the
strict practical rules of grammar and consider the reader.
Do
"We saw Keane ••• ," and "We saw Keane, the actor," indeed signify
the same thing? There are several different ways to look at
this sentence.
Does the speaker of the sentence want to indicate that he saw a man named Keane who happens to be an actor,
or that he saw an actor whose name~ oh second thought, is
Keane {but the name isn't really important because "it's not
what you know, but who you know.")? Perhaps "the actor" was
attached :for those people in the same category as I -- those who
didn't know that Keane is an actor--.
At any rate it seems
that the appositive may be either non-restrictive, :for those
who are ignorant of the field of acting.
It is also both
attributive and predicative in that it defines the scope o:f
signi:fance of Keane and predicative insofar as it asserts the
�- 16 being of Keane not as .a pers o:-.1 , but. as an actor. -It is,. however,
more to my liking to think of it as a restrictive since if it
is considered otherwise , i t would probably be more appropriately
omitted.
Thus, I have endeavour~d to .show that there is a link ·which
connects apposi ti·on to restrictives and non-restrictives more
intimately and intricately than . the manual allows, . and that
attribution and predication play. a decided role in the u.se of
restrictives and non-restrictives which in turn are an essential
part of apposition.
�- 17 . CIVILITY AND THE LAW.· ·
Daniel Carl Schi:f:f
· Near the beginning of' the sixth scene of' the s .econd act .of'
· The Merchant o:f.: ·venice the ·masked Gratiano tells the masked
Salerio·}hat "'11 thin~s that are, are with m?re spirit ·chased
than enJ· yed".
o
By this he means t~at men are more aroused to
action and emotions when striving :for something they . desire than
when they . are ac·tually enjoying . the thing they · haye sought.
It
is. when he is in serious conflict :for something that he esteems
that .the passions, crafts, and foibles o:f a man become most
. evident ., and his inner st:t'engths and weaknesses are rev~aled.
In attempting to throw light on the nature o:f life iri the
Venetian Republic {and in :fact in all similar societies),.
Shakespear has taken some f'i:fteen residents of' that comm~nity
· and involved them in a series, indeed a labyrinth, o:f embriolments and conflicts in which ev~ry character . becomes strained
~nd somewhat misshapen.
However they are misshapen only insofar
·. as .t h_
eir dominant characteristi~s become more dominant, and
thus their natures, f'ree :from - ~he clouds of' Unstudied actions,
are mo~e ea~ily seen, analysed ~nd understood.
I: .do not. have the time o.
r
space to .concern myself' .w ith al _ the
l
encounters, rivalries and described in this play
·· or to :fully deal · wi-th all the combatants.
I will _~heif'ly . deal
with what is commonly considered to be the central· theme o:f the
play, that is, the conflict between the sons and daughters o:f
Jacob and . their Gentile hosts in the diaspora.
·
- ~ntagonisms,
The chei:f antagonists in this conflict are Antonio, the
"Christian" merchant, and Shylock, the Jewish moneylender. Since
both of' these ·men are involved in :fi nance and trade on the
Rial to, .it is necessary :for them to have some sort o:f contact.
It ~s to be expected that· the Jew would have ill :feelings
.to~ards the merchant because Antonio hinders his business by
.lending money to his :f~iends gratis.
It is strange that the
two .would ever ent ·e r into a contract together, and this is only
brought about by Antonio's ·desire to supply his :friend Bassanio
with enough money so that the latter might become a suitor to
fair -Portia, "a lady· ·r ichly le:ft". 2 Thus,' during the :first
scene, a p·l ·ea·siilg picture of' Antonio appears.
He is a man who,
although a trader, . has the·" highest o:f principles and w:i,..1 1 . nly
o
.deal in usance when · it i ·s necessary to do so :for a :friend' .s
benefit, . and at that time will spare no expense or personal
e:f:fort · to supply · his · needs.
1 'Act · II, s6ene v, line i4
2 Act II, scene i, line 65
�-
18 -
The image o:f Antonio as a Christian gentleman, however, begins
to :fade quickly when Shylock reveals the true reason behind his
hatred o:f the . merchant. The Jew, in his :first address to the
audience, :' gives two major causes o:f his hatred :for Antonio;
(although both .o :f them are, :for Shylock _
merely manifestations
o:f An'.ton:io' 5· he'ing ·a Christian)~ The :fi_
rst is that Antonio
· in his "low ' simplicity ••• lend.s out money gratis and brings
doWI1 ·t he
t e o :f usanc e here with us in Venice" • 1 The second
_i's · tha~ .·;'he ·rails ••• on me my bargains, and my well .w orn . thrift ,
which he c_alls interest". 2 In other words, Antonio, in his
"simpl.: ici.ty" (and :for Shyla ck this is true _
stupidity) ruins
~ · shyloc'li: i· s bu.siness and then, in addi tfon, insults Shylock for
·n ot b· ~ing as :foolish as_ a Christian • . (For Shylock a Christian
is, not to mention other more despicable things, one who lends
money wi th_ ut .. interest to other Christians.)
o
r·a
When we first see Antonio and Shylock together, Antonio again
·implies (it is the first time· in the play} his contempt of
·· Shyloc~' s money 'policies. by 'telling the Jew that ~ (Antonio),
· und~r no~mal cbridition~, - does ~ot borrow or lend by giving or
taking excess.
Shylock · answers tp.is by :firs_ getting Antonio
t
involved in the loa.n , by making him state .the term, and then
by telling him t:tie. s :tory o:f Jacob and Laban.
For Shylock this
story implies tha·t · a man can do anything to increase his fortune
so long as he does not break the law. Antonio's rebuttal is
that Heaven and not Jacob controlled the birth of the lambs
and that animals are not the same ~s silvei.
The two obviously
cannot constructively argue Scripture together .•
This interlude once again forces Antonio to ask for the loan
and Shylock nowreplies by stating .his deepest grievance against
the merchant, namely, that Antonio continually insults and
degrades Shylock and his tribe.
It is in this passage (Act I,
scene iii, lines 195-129) and in a similar one (Act III, ~cene
ii,' lines · 56-76} that .Shylock i~ - ~een in his most wrathful and
vengeful state. It is the .wrath of an oppressed man who has his
:former o·ppressor at .his ·mercy. When he asks "Hath a dog money? 11 J
he is._ striding over· the stumbling merc~ant, for Antonio must
either adrhi t t ·h at the Jew is not a dog but .a man like himself,
or . that. dogs, ewes and lambs have much to do with money., c _ ntrary
o
tp what he _ had first said.
Antonio's reply that he is likely to
spit ·on Shylock again, sharpens a question that has been looming
since the be.g inning of this scene, i.e. what kind of Christian
is this Antonio.? Can a man who so openly hates another man,
wi ·thou~ - the least ·sign of compassion, be in any _ sense called
.a :followe·r of Christ? Antonio can act in _
love towards his
:fellow Christians and not loan money at interest, but in not even
attempting to love the Jew, and to see the image o:f God in him,
it seems that Antonio is de:finitely :failing · as a Christian.
1 Act II, scene iii, lines J9-41
2 Act I, scene 111, lines 44-46
J Act I, scene iii, line 121
�-
19 .
It is this :fail:ing and i 'f;e outward manifestation·, that· is,.
Antonio's constant rebuke and open show . a~ hatred . a~ainst the
Jew, that has fanned the :flqme.· o:f Shylock's ·hatred;; -. a:nd . this
same neglect o:f Antonio's Christian duty is what nearly cost · the
good merch~.nt: his li:fe, a li:fe ~ertainly not saved by his own
sp"l.:1:so . wit and :fig~ting nature.
'
.
I:f the animosity betwe~n Antonio. and Shylock can be- laid' ·to
Antonio's -not being a true Christian, · it -must also be attributed to Shylock'. s not being a true Jew, or at least ·not acting
as a Jew sJ:iould a~t.
Shylock _describes the proper role a Jew
should :fill when dealing with Christians when he tells Bassanio,
"I will buy with you, sell with you, talk with you, walk with you,
and so :following, .b ut I _will not eat with you, drink with you,
nor pray ·with you •.1" . Shylock realizes that he should only deal
with the Chris,tians :for the purpose of pro:fi t.
He must, and does,
call a Christian good only i:f lie is substantial'· and . bad i:f he
cannot pay his debts (-s.ee Ac:G. .J:_,._ _ s _ _ ne,_ iii·-, iines ~1~~2:5}• ·
oe
Shylock shouid,. and even must, ~o-neLa.lJ..i:'21.nsu!.:: t:IS anti b-Ofmp<:liments
of' the ·christians that do . not affect his commercial standing with
them. This is what he seems· to do at the opening of this scene~
However, as soon as Shylock sees Antonio, he stops talking about
money and ~r~:fit and starts recounting his hatred.
Antonio's
constant railings, coupled with his free loan policy, has struck
deep at the old Jew.
By taking active offence at the Christian,
Shylock is committing a grave sin (perhaps better called an
), :for ~e is engaging a powerfully supported enemy in a
method of :fighting :foreign .to Shylock, and is doing it on his
opponents ba~tle:field.
Shylock. how~ver, has not completely lost his wits.
He realizes
that if he is ever to avenge himself against Antonio, it must
be within the law, in :fact, it must be by the law.- He states
from the first that if' he "can catch him (Antonio) once upon ·
the hip, I will :feed :fat the ancient grudge I bear him.2 "
He then enteres .into a contract with Antonio, a contract which
can yield no financial ·reward for Shylock, . but only gives him- the
hope o:f hurting, indeed destroying, Antonio. To be sure, Shylock's
hope is small, but · it is not ·non~existent, as Antonio thinks it
is, :for there are, as Shylocl~ himself bas said "land rats and
water rats, water thieves and land thieves, I mean pirates; and
then there is the peril of the waters, winds and rocks ••• 3"
In short, Shylock sees this slim opportunity :for .re.v enge and
takes his 'chance. The bond o:f ~a.· pound ()f :flesh is cl_ a'rly not
e
a "merry boll.d"' and Shylo?k in arrart~i.Hg "ii~-, ~£s '::-~hyt11.irl€f ' but a
"gentle Jew ", who, to quote the :fair Antonio, "will turn
Christian":-·. becoming so ki_ d. Thus Shylock has done the · seemingly
n
1
1 Act I,
scene iii, line.s 31--35
2 Act I, scene iii, lines 42-43
2
.3 Act I, scen,e 'iii' line·s . 20- - 3
.. . ..
4 Act I, scen·e
~.
111,
lines 180-181
�-
20 -
i ·mp.o ssihle. · He has gotten his arch-enemy to legally agree to
.t erms which might. . enable ·Shylock to. exact vengence upon him,
with the power of the· Republic of Veni .c e helping and protecting
the . crafty ·Jew.
Before I examine the trial of Antonio and try to understand the
wonderful intercession from · Belmont, I feel that it is necessary
tp examirie the other major meeting of Christian and Jew iri the
play.
This, of course, is the marriage of Jessica, Shylock's
darighter, and Lorenzo, the Christian friend of Bassanio and
Antoriio.
(Actually Lorenzo is somewhat lower in station than
these two gentlemen.)
The first question that comes to mind when trying to understand
· this couple is how they originally met. The answer to this
question is never given in the play.
What we do see is that
Jessica is the motivator of the elopement.
She is the one who
arranges the time and the place of the meeting, procures her
disguise, and steals the money from her father.
Her reasons for
loving Lorenzo are easy enough to understand.
His life is
young, gay, a ·t tracfive and liberal {with the money stolen from
Snylock}. This is in sharp contrast to the dreary, stingy life
that Jessica lived while in the Jew's house. What young girl
would not · prefer to go with Lorenzo, rather than stay with
Shylock?
The time she . chooses to depart is when her father is attending
a feast at the house of the Christian Bassanio. This is indeed
symbolic, for it shows the extent of Shylock's social involvement with the Christians, and it foretells the utter ruin of
his household.
If Shylock himself begins to associate with
the Christians, in non-financial matters, how can he expect his
daughter to stay away? It is obvious that the Christian gaiety
and vitality would be much more attractive to a young girl than
an old man.
So if he goes, she must necessarily follow.
Why Lorenzo loves Jessica is less clear and certain.
He says
"She is wise, if I can judge her; and fair she is, if mine eyes
be true; and true she is, as she hath proved herself."1 This,
coupJ _ed with the girl's willingness and her father's money,
make ' Jessica .appear to be quite suitable as a bride for the
young man.
But Lorcnzio doos more than simply accept ,Jessica, he loves her.2
I believe that there are two main causes of this.
Firstly,
Lorenzo desires 19ve its~l:f,. and by a clever pun (Act II, scene vi!
lines 42~46) indicates that Jessica is obscure, and love is
what he is discov_ ring • . Secondly, there is mystery, adventure,
e
and intrigue in his courtship of, and elopement with, the Jew's
beautiful daught.er.
Their love, however, once consumated, is ~ot simple, but complicated by the very causes that engendered it.
Jessica is a
Jew's daughter and Lorenzo is a Christian that has ' stolen her
away.
Lor~nzo backhandedly admits that he will have to answer
1
A,..+
TT
�- 21 - ·
to the commonwealth for his marriage (Act III, scene v, lines
30-35), thus showing that he realizes that the political unwis dom in his marriage must one day be accounted ·for, and that
politics will become involved in his: l ·o ve and home.
Jessica,
sensing this, shows signs of uneasiness, which are . shown by the
constant sparring of wits between her and Lorenzo.
(The
question as to whether or not their love can survive is dealt
with in the final scene. Sin'ce this takes place after the court
scene, both according to Shakespear anq my argument, I will
deal with it after~ consider the trial in Venice.) ·
The marriage of Jessica and Lorenzo and the contract between
Antonio and Shylock can be thought of as two polar instances of
the associa·tions of Jews and Christians, or of a:ry similarly
ethnic groups.
In the marriage we see the case in which what
should be purely emotional and private, has become involved
with political considerations. The tragic aspect of this
involvement comes about when political strife, and not merely
political action, is introduced.
The contract between Antonio and Shylock is an example of what
can be the result of the passions' becoming involved in what
should be a simple civil affair, . such as business.
What could
have .been a profitable relationship for bqth parties becomes a
senseless battle, a battle from which both sides (particularly
Shylock, the villian) limp away wounded.
At the beginning of the court scene (Act IV, scene i) Shylock
is at his strongest. He knows that Venice must uphold the bond,
because the commerce on which the city depends is itself
dependent on foreigners like Shylock, who carry on trade in the
city.
The city cannot afford to set the precedent of voiding
a legal contract, and therefore the bond can only be broken by
Shylock's consent. Thus even though the Duke himself desires
Antonio's freedom, he cannot overrule Shylock, but must try to
convince him to relent.
The Duke appeals to Shylock to show mercy to the downtrodden
merchant, and not only 'forgive the forfeiture, but "forgive a
moiety of 11he p~incipal". 1 The appeal falls on deaf ears, for
Shylock has not yet learned about mercy.
He has learned to
hear and take offence at Christian insults, but he has not
learned to forgive with Christian charity.
(Obviously Antonio
was not a good teacher.) To Shylock mercy merely means giving
up what is rightfully his.
He knows that according to the
laws of Venice, Antonio is in his power. When Shylock tells
Gratiana "I stand here for law. 211 He seems to be remembering only
the laws of the commonwealth, and forgetting the Laws of Moses,
particularly the sixth commandment. When the appeal for mercy has failed, Bassanio offers Shylcok
twice the principal that was originally borrowed.3
(It is
1 Act IV, scene i, line 27
2 Act IV, scene i, line 27
�- 22 interesting, but o:f doubtful signi:fi°cance, to remember that
Portia said that she would give Bassanio gold to pay the debt
twenty times over, 1 and yet Bassanio, at this time, only o:ffers
twice the payment.) Shylock refuses this, and says that he will
refuse payment even if twelve times the p~incipal were offered.
It must be noted here that this was no small sum (a ducat had
a purchasing power equal to seven of our dollars), and that
Shylock by himself did not even have ·t he original princip- l of
a
three thousand ducats when he was first approached by Bassanio
and Antonio. 2 Thus Shylock is publicly restating and therefo re
re-enacting his first sin 0£ forsaking profit for vengence.
The Duke then tries a slightly different tack, and asks Shylock
how he hopes to receive mercy if he does not render it.
Shylock
quickly answers that he does not need mercy, having done no
wrong.
~~l ~_xi t l ~u eo~ , Vl ~3~ l
After this reply the Duke seems ready to give in to Shylock.
Bassanio then tells Antonio that he will defend him by force3,
but does nothing, either then or later on, when matters appear
blackest for the merchant, to show that this was anything but
an idle threat.
Perhaps B~ssanio was quieted by Antonio's
apparent readiness to die.
The good merchant, having long
ago withdrawn :from the affair, seems to feel that it is his duty
to calm those striving to save him.
At this point the Christians seem to be completely vanquished,
and only have one hope left.
The Duke has sent for Bellario,
a learned Doctor o:f the law,5 to help him with the case.
The
Christians do not seem to realize that this is the wisest thing
that they could have done, that is, fight the . Jew with things
. h .e understands and fears, e.g. civil and earthly punishments.
Bellario, of course, does not come himself, but Portia (Bassanio's
wife and Belario's cousin) disguised as a young l awyer comes t o
defend Antonio.
It is unclear to me how Portia knew that
Bellario had been sent for, but the fact is that she does arrive
with a letter of recommendation from Bellario. ,
Portia's first speech. again asks Shylock to show mercy, basing
the plea on the majesty and beauty of mercy, and the fact that
mercy is necessary for salvation. These arguments are more
ignored than rebutted by Shylock, whose lack of charity at this
point surpris-es no one.
Portia then asks if the Jew will take
the principal and forget about th'e -bond.
Shy 1t:,··c 'k ohce ~again
r ·e mains adamq.nt.
So far, it appears as if the young lawyer has no new defense for
Antonio, and Antonio himself heartily "beseeches the court to
1 Act
2 Act
3 Act
4 Act
5 Act
IV,
IV,
IV,
IV,
IV,
scene
scene
scene
scene
scene
i,
i'
i,
i,
i,
line 86
line 90
lines 114-116
lines 118-121
line 107
�- 2.3 give the judgement.1" However, there is something very strange
in Portia's speeches",
at the end of each appeal for leniency
she tells the court that it is powerless to alter a decree, and
that if Shylock does not relent, the court must rule against
the merchant.
The effect of these lines is to make any relin-
~~~~::~n=h~:s s:~~:c~~~
!::! :::~~e: t~ ~~~!ea~=m~fs:;;~~~
8
by
2
11.
Thus he clearly shows his murderous intent.
Portia, seeing that the Jew will show no charity, recedes for
a few moments, while Bassanio and Gratiana express their love
of Antonio.
When they are finished, Antonio explains that he
is ready for death, fortune having already impoverished him.
Portia, however, is not at ali · ready t~ · see the merchant destroyed
In fact, it seems as if her initial appeals to Shylock to show
mercy, were in themselves merciful offers, which, having been
accepted by Shylock, would save- him from the onslaught to come.
Portia's defense is principally composed of restrict.i ons. of
Shylock's actions.
The first restriction she · cites denies
Shylock "one drop of Christian blood3 11 , lest he lose . his land
and property.
Shylock immediately senses his defeat and asks
payment of thrice the principal, the sum Bassanio had previously
offered and is still willing to pay.
Portia, however, will not
leave off and let Bassanio pay.
She now tells the Jew that he
must take exactly one pound of flesh or he will be killed.
Shylock asks for the principal, which Bassanio is still willing
to give him, but Portia stops him, claiming that the Jew will
have only justice and his bond, and none of the mercy he him- ·
self did not show.
At this po.int Shylock wants to give up th~ suit and leave, not
wanting to act against Antonio if there will be reprisal against
him for it.
Portia and the law, houever, are not through, for
they " hath yet another hold on him. " For plotting against the
life of a Venetian citizen, Shylock must give that citizen
(Antonio) half of his fortune, and forfeit the other half to
the state, his life being put at the mercy of the Duke.
The
Duke, in order to show Shylock what mercy really is like, spares
the money lender and only fines him, instead of confiscating
half of his fortune.
Antonio also shows mercy, and agrees only
to use the half of his estate that he will receive, and upon
Shylock's death to give it to Lorenzo and Jessica, p r o v ided t ha t
Shylock will do the same with the property the Duke has allowed
him to retain.
Antonio also makes the further merciful stipulation that the Jew become a Christian.
Shylock, however, fails
to c.omprehend the mercy bestowed on him, and only mourns his
1 Act IV,
2 Act IV,
3 Act · IV,
·4 Ac'i; I_V''
scene
scene
scene
scene
i,
i,
i,
i,
lines 249-250
line 200
line 320
line 360.
�- 24 :fallen poa~~~on • . ~e is not ~om£orted by the f~ct . that he could
have fallen further.
An analysis of' Shyl·o ck' s· :fall. shows a great deal 0£ ironic
justice. The most obvious example is that Shylock, ·the man
who claims to champion the law 1 , is destroyed by it.
The cause
0£ this is twofold. The :first is that Shylock tries to use
the law £or purposes thatwere never intended by the original
lawgiver. Thus in trying to ,rise above and master the law,
Shylock is trying to s~bvert it, the thing which is most unwise
:for a Jew·, whose only defense is the law.
So it happens that. when. a wiser person tha~ Shylock becomes his
adversary, he is doomed• For this person, understanding the
intent of' the law, can show where Shylock is misinterpreting the
law.
(In t~is · case he is trying to use a law t6 kill someone.)
Thus Shylock's only def'.e.n se is to try to justify ·niisinterpretation
and if'· he. succ.eeds, by the .saµie arguments• the laws protecting
him can be misinter:p.reted. · Thus., _ matched against a thinking
· adve_rs~~y • Shy lo ck fs doomed •
0
. · he - se,cond · reason tha·t . Shylock fails before t .h e'· law is that
T
·· he .. doesn·1· t fu- .ly un~e~stand:· its · workings. -... Unlike the Mosaic law
1
. (as · Shylock ·sees. it)", .-' the . -V.enetian statutes, and_·in·· fact the
Veneti~n stat·e-, · require : a: · cert a.in· amount· of' . "mercy" and
nchri s ti an.· charity; " in . order . :for i ~ . to . work .: p·r~pe·rly •.
:
.
.
.•
'Social life has become much more complex : since the times 0£ Moses.
· I:f every man in Ve~ice were to be prosecu:ted every time he broke
a· law, _ the state cou.~d do · nothing .-except arrest its own ' citizens.
Commerce and thus the state would soon disappear.
· he way to avoid this problem is to be willing to· :forgive
T
offenders provided .. they · can be useful to the · s.t .ate ~
There is no
heed to rigorously press the people as long as everybody is
flourishing, and no one . gets too :far out . 0£ hcnd. Legal mercy,
then, is the great g~ossing over of' irksome details, the oil
that helps the state run smoothly and keeps it prosperous.
Sliylock cannot see _
the ' reasons behind it ·, and so must learn them
by barsh example~
The play seems _o have rea·c hed its logical end with Shylock's
t
becoming Christian, and indeed, i:f the problems discussed in
. this paper so far 'were :the only problems, or even the central
p _oblems o:f the play, perhaps Shakespear would have ended it here
r
. and ~ot have· his characters :feel compelled to go back to Belmont.
Bas,s anio and Gratiana go . because they b-elieve their loves to be
tnere.· ·I do not kho: why Portia · and·Narissa chose to return;
w
perhaps ·it is becau·s ·e it is their home, or perhaps they :feel
their love will best flourish there.
When the scene shif'ts ' back to ~elmonti we see Loren~o and
Jessica, the :fugitives :from Venice, who stayed behind when
everyone else returned to the city, engaged in a strange, sad,
1 Act IV,
scene i, line 145
�-- ,
- 25 dialogue.~ ·
Lorenzo begins
....
The mo'o n .shin.es bright: . fri ,such :a ·n ight as this·,
When the. sweet wind did: gentl.y kiss the trees
And they did· make no no.ise, in ·such a night
Tr.oilus methinks mounted the: Trojan .walls,
And sigh' d .his soul toward the Gre;cian tents,
Where Cressid lay that night.
(1)
but beauti:ful·lY.· moving
·. ~.
~·
It is - no accident that Lorenzo chose thS · tale o:f this couple.
For although they loved, they met only :for -a night, not because
Troilus did riot want to love forever, but because: the lovers'
:fathers were o:f opponents camps.
And so they were separated·,
and so, uncared for, Cressid proved untrue.
Next the stories of Dido, Thisbe and Medea : are told bi the
love~s.
All o:f these ancients chose their lovers from oppo~ing
political camps; all passionately loved :for a while, and all
ended sorrowfully.
Lorenzo and Jessica then recotint = th~ir bwn
love story, knowing the ·pattern it has so :r-ar fo ! lowed, arid
sensing that the end that has come :for the others will someday
come :for them. They know that when they are alone in Belmont
under the bright moon, Jessica, under th.e guise of · a teasing
lover, can state her :fears about the truth of Lorenzo's vows of
love, and .Lorenzo can forgive h~r.
Jessica's fears are not
foolish and ungrounded, for . in marrying the Christian : s~e has
had to forsake everything else that . she previously had • . Her
father's house, people and way of life are closed to her now;
she only has Lorenzo and without him she is completely abandoned .
It is no ~onder that Jessica fears the end of thi~ b~ight night
at Belmont.
A:fter each of the lovers has given four speeches, they are
interrupted by messengers announcing the return o:f Portia to
Belmont. When Lorenzo hears this, he orders the house to prepare :for her coming by :filling the air with sweet music .
This
music adds further glory to the night at Belmont, and moves
Lorenzo to give two b~autiful speeches, one explaining the
celestial harmony to Jessica, and the other describing the joys
and effect of the less perfect, but still powerful, earthly
harmonies.
Portia does not return without a gift for the couple, for with
her she brings the news that Jessica and Lorenzo are now heirs
of Shylock's fortune, and consequently they are no longer
dependent on their parents and friends.
They are now able to
establish their own home where they can rule themselves.
They
can now live during the day as well as love during the night.
Thus with Shakespeare's story of the conflict between Christians
and Jews brought to a happy close {only thirteen lines before the
end of the play itself), perhaps we should ask what, i:f any
thing, can we learn about this struggle :from the play.
The
happy endings do not :fool us for a moment, :for we realize that
the problems were only solved by the mistress of Belmont , wise
Portia, a women of singular virtue. But, as I said earlier.,
�- 26 these two cases are polar extremes, misshapen by embroilment
and conflict.
In most cases where the emotions become involved
in what should be a purely civil affair, a small show of mercy
and charity on the one hand, and continence on the other will
usually reconci1e the antagonists, provided there is some profi t
f'or both • . There is rio need :for a Daniel to judge them, nor
for one, if not both of' the opponents, to be destroyed.
In the ~ case of lovers, seldom is it necessary
actually flee thei~ homes and go to Belmont.
their civil problems can be borne through the
se.rve to sweet en the love they :feel at night,
bright and music prevades the air.
· ·,
·~
·-
f'or them to
In most cases
day and will only
when the moon is
But what if the civil becomes so strong that i t begins to strangle
love, and not.nurse and accentuate it? In that case it seems
a pi].gri_
mage to ·B elmont must ~e l" maq~ . •;_--;·~ ffow ?... ·,~: l::e -~- ~t ~~s~est
. to ' go wi .th 5trong :f.riends who ' kriow the way, -- · this is "
the means
Gratiano . uses; . or to come With . oi:ie's love to sojourn there for
· a t-ime, -' a 's . fugitiyes from the city - like Lorenzo and Jessica.
· Howev.er, , ·some, ... and they · are usually brave princes or noble
·:"ge,µ.t ·l -eme~,. make th~ir way alone, ·driven by a strange sort of
iove • .[f ~ this be you.r ' journey, be sure that you do not look
. f'or Belmo~t en6ased in iold ~s . di~ t~~ black Morrocco and the
." · ~ld ·shy- ock; ·. or' searc.h :fo:r .i ·t ' . _thi·nkj;n~~( that it is your just
l
d?.~ e:r-t :and·· na t-liJ:;"al · ~.ue,. ··as · did th~ ., :fo_ ,iish Aragon and the merchant
o
AnJ;·o nio •. Bu.t ·i:r your .wish is to · be.- ·success:ful like the good
Bits~·ani~ :. i ·you .mus.t . b~avely. g:lye · and, haz~rd all you have for this
strange ,.something, whose ca.sement ·seem·s quite worthless.
And
. if' yo.u' g.:~t t ·hat· :far~ · do . ot try" to · make the · right choice by your
n
. wits aI:o~e, but· li;st~ri. to · the · music in the ·air, for even if' it's
spi'rJ.,..t ' do~s no .t move you, .· :it.s inspired rhyme may turn you in
the rig~~ di~ection.
•
I
-~- ")
.
�- 21 · ROUSSEAU AND THE ANCIENTS: A REPLY
Parme~iscus
(Editor's Note: The following contribution was received through
the college mail under the indicated· pseudonym. ·T4e note and
the mystery surrounding it intrigued me as editor.although
hardly flattering to me as the author of ·the paper under fire.
I was tempted to find out more, if not about the true author,
at least about the pseudonym. After several unsuccessful
attempts, I located the following brief mention in the encyclopaedic Pauly-Wissowa Real Encycloplldie der ~lassiches
Altertumswissenschaft, Achzehnter Band, Zweite Halfte, p. 1569
Ferner erz~hlte Semos -in · seiner ·
, _Parmeniskos sei ein
vornehmer Mann gewesen, der einestages in die Trophonsh8hle zu
Lebadeia hinunterstiegen. -sei und, als er wieder . heraufkam, die
F~higkeit des Lachens verloren hatte.
{Loosely translated, the
sentence · reads: · "Moreover Semos in his (work on) Delos recounts
that Parmeniskos . was · a· · man of eminence who one day decended into•
the cave of Trophon at Lebadeia and when he came up again had
lost the ability t·o laugh.") · Whether Semos' Parmeniskos is the
same as our contributor's, I do not really know; nonetheless,
the humorlessness of his piece 'seems to me to be in harmony
with the name _and its classical connotations.)
Mr. Lachterman's paper, Rousseau and the Ancients {Collegian,
Dec. 1963) sins, I should say, more by e~cess than by omission.
The comparability of Rousseau and Plato and Aristotle in ~
cardinal aspects of political thought . i~ · established very persuasively through what seems to have been a ·careful reading of
the relevant texts.
Nevertheless, this one-sided and at times
belabored emphasis on the areas of agreement tends to obscure,
to my mind, certain more ambiguous notions which enter nonetheless i .n to the total fabric of Roussea'l;l' s political and ethical
philosophy.
I understand .t he ambiguity of these notions to
have arisen from fundamental tensions iri his manner of thinking ,
the result, perhaps, of his own mode of life·, or, qui t ·e possibly,
of an imprecision and ,hesitancy determined ·by the distressing
character of the conclusions he seemed led to and for whose
modern, more revolutionary offspring he must accept partial
responsibility.
In order to buttress these critical and, it
may seem, unwarranted generalisations, I shall now make brief
mention of three: instances of ambiguity that lie close to and
thereby imperil the heart of Mr. Lachterman's thesis.
Dr. Leo Strauss in his justly celebrated Natural Right and
History speaks frequently, in his chapter on Rousseau, of an
i~resoluble conflict between society and the individual, that
is, society and nature.
I would say that, although the conflict seemed to Dr. Strauss irresoluble, Rousseau himself
thought that he had found a solution in the elevation of the
People to an {unjustifiably) high status, making it at once a
collective mystical body and the sophisticated voice of political wisdom.
Connected with this god-like status of the People
is the idea of public enlightenment which Rousseau never fully
abandons despite, as Mr. Lachterman argues, the introduction
�d
-28of an oDll')iscient Legislator .in B0 ok .II . of ..the Social Contract.
To those readers :familiar with classical political thought {and
Mr. Lachterman appears to be one o:f these) the myth o:f the
People and its corollary o:f Au:fklRrung must seem egregiously out
o:f _
place in th~ writings, o:f .a ·. thinke:r so :imbued ·with · and
-"inde.b "
ted" . to· the · ideas . of the ··anci.ent_ . . In any case :i t seems
s
-qui t.k 'clear that ·Rousseau's. "assertion _
that · ea·ch ·man in obeying
th~ · 1~~ ~ollo~s his . own w~li i~ rooted - ~n the·~dea o:f the People
whose g 'e neral· will always_ act in ~ the interests of all citizens •
. I
The n.ot_
:.Lori of ... a. cont.ract which brings into being this mystic
· pody reinairis essential t .c)' the · supsequent ".elabor'ati9ns· of the
·g .e nera1 will and the-. law present.ad_ by Rousseau .in - the· Social
Cohtr·a ct', .n otwithstanding ·t .he suggestions · ri · the·· Discourse on
1
· Pali ti cal Economy · that:, mo~al · goodness i .s · t ·he ·true. foundation
o~ ~dlitical obligation, suggestions which · Mr. Lacht·erman re- ·
ceived with ·obvious and unmistakable . rel- sh.
i
The simiiari ties
bet·we~n . R 0 usseau and the ancients in this . .latter work do not,
I . daresay~ oirershad_ow' and ultimately negate the principia of
· ·the· Social · Con.tract, on the basis of which the - whol·e of Rousseau's
w· rk must be evaluated and the relegation o:f which to a seemingo
ly· inconsequential place in Rousseau ' __§j political theory is the
· mos~ - disturbing element in ·Mr. Lachterman' s thesis.
1
The presence of these two contradictory sympathies--with contract on the one hand and the ancient's conviction of the
naturalness and moral ultimacy of the polis on the other-creates 'the £1rst of' the afor~mentioned ambigu~ties in Rousseau's
work ..
In the next place, however enthusiastically Rousseau (~nd Mr.
Lachterman) ·may stress the role o:f reason in the rep-µ.bl-~i'c , - i t
is obvious that sentiment rather ·t han reason is. · the· supreme
political faculty.
Compassi.on--the symp·athy each . of' us should
hav'e ' for the miseries o:f our fello~s--is inculcated in man by
hattl'.r~ Eihd can only be "extirpat.e d". py the onslaught of' civili zatidrt•
Rotisseau' s 0 ideai cons:truction" makes i t possible :for
compassion to erltltire wi th:lri. and indee.d hold together society.
It Ls thi.s sent:iment which; more thart self-interest; is mean.• , ·
to support political obligation.
In addi ti.on to this, . we ttii'ght
merttioh that ih Rousseau~-in marked contrast to Plato a,ritf "
Aristotle-•there :1.s rio ~ntologica.l · and_ epistett1ql 9gical jUstif'icatit>n :for t4~ supremacy · of reason i_ri t>oii.tidai society•
This
·s hortcoming seriously weakens the £orce of his asser'tion that
the ideal society- is. governed by r~l~$.<ln ,..incarnate ih the Law.
At most Reason he~e can only mean ~ . k~,~·;.ot sentimehtal wisdom
. or the. ·common sense o:f the noq}.e'' 'arid f.iJ..pright peasaht. • 1
.
£_
1
The . :finai issue I should like .t ·o raise with. Mr. Lachterman•s at
times ·su~spiciousiy naive interpretatiQrt has . to do with freedotn
Let me say first
that eneomi~ms of virtue have a peculiarly - unpleasant sound in
the mouth of' a mor~l profligate, Maritain's censure of' Rousseau's
counterfeited moral rectitude seems t'o me well-intentioned and,
an~ moral · responsibility in political - society.
1~
C:f. e~pecial~y Social Con~raci, Bk. ~V, Ch. I, Page 1.
�-29as one sees in leafing through the Confessions, accurate,
Freedom meant for him (and continued to mean after him) freedom
from constraint and authority and·it is on this conception of
freedom that the image of the natural and therefore good man is
based.I The free spirit can never be successfully integrated
into society without sacrificing his cherished liberty- a
liberty not in the least harmonious·with the civil and moral
liberty that the contractual society makes possible and indeed
enforces.2
To ignore, as Mr. Lachterman has done, this side of Rousseau's
character and though+.- the side that influenced German and
French roman-ticism so greatly - is as much as to close one's
eyes to the obvious in the hope of raising the unclear and, it
may be, inconsequential to a ra~ that it scarcely deserves.
By this I mean . that History saw fhrough Rousseau's pose as the
ally · .9 f the ancients, while Mr. L~cht ·~··r~an, if he put forth
'his ·thesis seriously, did. not.
; , ,
l~
2· .
Cf. Les Revenes du promeneus solitaire {Rousseau's last work!)
~aughan ed of Rousseau's Political Writings)
Cf Social Contr.act Bk I
Ch VII - a passage frequently
referrea to in Mr. Lacnterman's paper.
�COMMENTS ON MR. SPARROW'S LECTURE: Rights, ~ ~ the Right
Larry Silverman
J"n. v-evi ~wi.ng and r .om.me. nting on Mr. Sparrow's lec~ure, it was
:necos .~~1·:y :f'.oi~ ~ to paraphrase and deduce from his words.
If,
in so doing I have distorted any of his opinions, I can only
'
.
hope that that distortion will lead to a further clarification
of them:·
The lecture, on Rights, ~ and~ Right, began by pointing out
the need for its existence. It contended that the present confusion and conflict among civil, natural, social, and economic
rights, culminating in the 'unthinkable' proposition that the
same thing is both right and not right, may, in. the future,
subject civil society to a turmoil from which " ••• neither the
rei t era ti on of once-understood relationships nor man:i :fes ta tions
Of
good-nat:l.11'0d SP.Tii:i..ment:aJ.i .ty Will be . able to extricate USe 11
This c~isis seemed to stem from the peculiarly modern notion
that the "endless worth" and "infinite dignity" of each one of
ll.f3
e~t .ii:l.Prl hini to natural and ina. . Pnable rights~ "limitless
U
in nnmher." Hence the lecture tried " ••• to suggest another
:f':t·amework than that of rights within which political issues can
be framed and pr_ ori ties assigned •• "
i
a
The suggested framework seemed to rest on the notion of the
"common good," rather than a theory of private rights. Hence
one. of . the characters of the mythical dialogue expressed surprise and skepticism at hearing that his 'right' to walk down
the street was simply the law's approval of that action. This
· approval "is grounded on the prior determination that it is all
right to do the contemplated act ••• in view of the common good."
The skepticism arose from the belief that each individual man
had a natural and inalienable right to exercise his individual
will, and that the law's approval is only an implement to that
right.
The lecturer traced this notion back to the philosophy of Hobbes
and Locke.
According to that philosophy each individual desiring
passionately to live, " ••• is conceived as a point surrounded by
'natural rights' some of which he lay down or- transfers to a
communal authority when he 'enters' society, but others which
he retains because of their inalienable character." It is
precisely what Mr. Sparrow called the "inhuman .. necessity" to
transfer authority that gives rise to a self-eontradiction within
this view.
For, if the good is defined as self-preservation,
and the right as that which naturally enables or empowers a
man to preserve himself, how then can an individual man be so
powerless as to be forced to relinquish some ot his powers in
order to be enabled by another to exercise these powers? In
other words, my right, .or that power which enables me, to walk
down the street must he· understood concomitantly with the
obligation of others not ·to hinder me.
There is n~ entological
or historical priority of one over the other.
�-32-
Mr.
·To clarify this argument,
Sparrow made use of something
he ..cal·l ed the "square of right."
(See next page).
He used
this device to illustrate with some precision the relationship
between: duty and right.
In the top half ·of the square, the
prohibitions and commands of the law become tbe duti..es and hence
the rights of the individual. · This . can· be s .e en .i n . the · cited
example of the policeman, who has . a right to direc .t traffic
because he was so commanded.
At the same time i t is, of course,
his duty to direct traffic.
f
But for all its pre_
cisi.on, · the square contains t~.o _ serious
· defects. _ In the :first place, if we are to isola~e dutie·s : in
the top half · of t .h e square, what are we to :say of _men who
_i.nsist ·upori (.ioing their duty not simply by" obeying commands
but by exercising those rights permitted them . by tbe ·law. Socrates " was p~rhaps - the paradigm of such a man_ . If the laws,
.
for ·a · time, permitted him to speak free·ly, he .spoke fre'ely,, not
to -exercise -J1i s rights as an :individual' but . .to do his duty as
a ci tiz·en.
Indeed, today we are permitted to ·vo.te; is i t not
our dtity to do so? Yet · Mr. Sparrow, fo~ the sake _of · lotical
rigor, restricted duty to the class of obedience,. thus agre.eing
:in par·t; with tlie traditional liberalism he was trying to undermine.·
This reply might have validity were it not _for the second ··. __
deficiency in the square.
Mr. Sparrow, as was stated earl~er,
maintained that the so-called approval of the law was gro.u nded
in the prior :determination that an action was ali right.
:Wha't .he.· mea:Ilt by 'all right' is still unclear.
Here is one of
several ·- defini.tions given in · the lecture: " ••• An action which
does not harm. or only slightly harms the common good~"
But
. voluntary acti~ns which are "all right", (e.g., walking down
· t.he street; growing a beard, listening to music· , etc.) are '_ very
·d _:fferent - frpm voluntary actions which are right. (e.g. voting,
i
·Speaking -One·' s mind fQr the sake of the common good, etc.).
It
ca.n make no sense, therefore, to cal 1 all permitted ac ti o:ris'
'right', as the square does.
We. might overlook the deficiences o:f the square and view i t as
an aid in revealing the absurdity of saying that one ·empo·w ered ·
by nature is constrained by necessity to enter into an artifical
bond in orde~ - to obtain · his nat~ral powers.
But assuming that that stat ·eme~t is absurd there .are stil-1 many problems before us.
For if one's power stems not from natural rights but fro~ the
approval of· others, or more to .~he point, of the state, ' how
then is tyranny · to qe . avoided? Mr. Sparrow might answer that
the approval ~f the laws of - a sta~e are properly based upon .
the notion of the _
common good and not the arbit_
rary will of a
tyra:rit, .(who i 's of' all men the ,most private); a tyrant is not
evil because he de-pri ve.s ·men o.f their 1 -right, ' but because·
he makes men incapable of doing the right.
Thus, a man is only
free insofar as he is free to be a man; and the faculty of
manl.iness is the ability to do the right, which is defined as
action "tending" towards the good, and the inability to do the
wrong, or actions tending towards nothing, and hence "meaningless"
agitations.
�-JJ...;.
THE MODAL .SQUARE OF OPPOSITION UNDERSTOOD AS
THE
.I
.
SQUARE OF RI.GHI'
.
Forbids:
Commands:
~
A
A MUST Nof"\J3E DONE
I have a DUTY not
'
to do A; bu~ also
· --..J have a RIGHT not
to do A; and it,is
--;;RIGHT not to do A
MUST BE DONE ... .
I have a DUTY ·to do . A;
but al·so I have . a BIGHT-to do A; and it is
RIGHT to do
':;
:'%-..>..
~'
4
:
'
~
,_
~/
\~
<v-r-
-----.
<:,
o"
~
L,Q-,~ .
~--
Lt
A MAY BE DONE14 .
_,... ---··
I have a RIGHT to do . A;
and it is RIGHT..... to do A
I
~---
·Perniits: /-
--~-·
./
./
-.... ' -..". LAW, the
~/~
,,
/
expression
and determination o:f
the RIGHT
/
.JA NEED NOT BE DONE
I have a RIGHT not
to do A;/and it is
RIGHT rtot to do A
/PPermits:
* * * * * * * * * * * * * * * * * * * * * *
STATE OF CIVIL SOCIETY
Law,
Compulsion, Constraint
DUTY (OBLIGATION TO DO)
. DUTY (OBLIGATION NOT TO DO)
I
~
SOCIAL
RIGHT (PERMISSION TO DO)
CONTRACT
f
RIGHT (PERMISSION NOT TO DO)
STATE OF NATURE
Rights, Liberty, Freedom
.l
�-34But if' the :faculty o:f manliness is the .ability to do right -and
that ability is ·somehow obtained :fro~ an external p:ower, are
we not then confronted ~ith the same problem as confronted the
partisans of naturals rights? I think Mr. Sparrow· would ;ans~e-r·;
"No." The reason :f'or this answer is perhaps tJ:ie most -significant and elusive implication of the entire lecture. For the ·
community and the law enable a man to .b e · :free not only by
authorizing and approving his activities, but _
by pro.vfding a
sphere and an object necessary for · those - a ctivities to take
place.
In Plutarch's phrase, "The pecul.iar work
of a good man is political." -* Thus, a community enables a
man t-o be a man in a way _
similar to that in whic·h wood and nails
enable a carpenter to be a carpenter. There is no longer a
contradiction.
" ••• Right. and ~ight, necessity and :freedom,
mer~e in the depths of the mind and heart o:f a true human
person."
Near the beginning o:f his lecture, Mr~ Sparrow spoke of the
'common good.'
As he went on, he s6mehow managed to unite the
common good with the "indiYidual good." Towards the end, the
term, "rational supreme good" was introduced. The lecturer
seemed to be saying, by implicat1on at least, that in the :final
analysis the three were one.
.; .
This is a most provocative and rather dangerous view.
Before
we can allow ourselves to dream and to speculate :further we
must check the cianger . which _was spoken o:f previously--the
danger o:f tyranny.
Could not a sixteenth century inquisitor,
_
adopting Mr. Sparrow's suggested :framework, justify his
-activities by ~ayi:µg, "Some of us have a ·greater knowledge o:f
the Supreme Good than o,th_ rs do.
e
It is our duty, . there:fore, . to
conform the political body and the private · man .t o that Good, .
with any means whatsoever." How can we repudiate the inquisitor
except by replying, No man can be truly :free unless he is :free
in the conventional sense to choose or reject the truth.? _
Whether an harmonious_· polity can be established in harmony with
the Supreme Good, and whether · the myth of 'i~alienable rights'
is necessary :for men in order . to learri arid'. _
to will the Good,
must remain, for the time being, open questions~
Just ben eath the surface o:f all the lecturer's remarks was a
principle e·x plici-tly :formulated in the last part of the lecture.
The terms 'right' and ·• wrong' bear . o action the same relationt
ship that 'true' and ':false' b~ar to . sp~ech • . A :false statement is meaningless, and therefore no statement.
·" If' ••• transcending, containing, and ordering human ends is possible," he
said, "human acts will be constituted as such precisely to the
extent that they tend to or mean, that is are means, to it.
And hence, :for them to be truly human actions, :for them to
be meaningful, and :for them to be right will be one and the
same thing." The so-called wrong actions are meaningless and
therefore no actions at all. " ••• What seems to present itself'
initially as a wrong action is in :fact mere agitation." Evil
is privation of good.
*
Plutarch, LIVES, Cate, p. XIX, 2
1'
�-35This position .caused much comment during the question period.
Mr. Sparrow's analysis . was interesting, but it seemed to deal
only with one part of the phenomenon of evil.
For surely,
Adam, after having eaten of the fruit, became aware of his
nakedness, or privation. But it is very difficult .to read that
story without :feeling the reality and the potency of the
Serpent. · Though the lecturer acknowledged that it is " ••• all
too possible for members of a divided and discordent humanity
not only to mutilate being but ·also to iead others to think
that such sub-rational agitations are instrumental to the
attaining of the proper end o:f the human person," he did not
succeed in expJ.aitiirg how this is possible.
taking his view, the problem o:f indifferent or
'all right' actions becomes even more inexplicable.
If we
are to call the thousands of trivial and harmless acts evi'!
because they are meaningless, we had best get a new word to
describe those actions which are really evil.
Furthermore~
Mr. Sparrow ended his lecture by saying, "However, it is not
quite so clear that it is she (dialectic), revealing the
ultimate absurdity o:f false actions, that by making us at one
with ourselves, can lead us out of the cave and so restore
meaning to action.
I suspect that instead the cure will have
to be :found in another dimension altogether.
The Word may .
have to be made :flesh and come to dwell, to die, among us."
Somehow those last sentences gave the lie to those preceeding
them.
It is as i:f the lecturer were really saying) "Before
the nature of man can truly . be understood as I would have you
understand it, before evil can, in truth, be called privation,
some Supernatural Being must descend to earth and teach us the
two precepts wherein all the law and all the prophets are
contained, and say clearly to each man, 'He that is not with
me, is against me, and he that is not against me is :for me.'"
�-36;..
Ali ESSAY ON DUCKS
Jeremy Carl Leven
Mr. Lamb notwithstanding, this essay shall deal primarily .with
the ·animal "imparatis", for the nobility .o f this animal is
most present, not when served, but when serving.
I divide
my essay, therefore, into six parts: the animal, . himself; his
relationship to his peers; his relationship to people and . vice
versa; hi~ influence · on the American w~y of life; his humor;
and the .duck as an explanation for the order of the kosmos.
The work "Duck" is derived from the Old English 'duce" which
meant 0 a . diver" • . This shows that evolutionarily the Duck
has changed relatively little since the days when he spolte Old
English, still diving and sti11 · enjoying it, if one is to
judge by appearances. Much like people, the Duck also belongs.
to a family, one that is known as "Anatidae", a name that may
make a Latin duck quite proud, but currently is so despised ·
among American ducks that they seldom use it; and it has,
therefore, become almost obsolet ·e among all but the most
conscientious du.c k-lovers, drakes included.
Generically speaking, we must ·refer to the · Duck as an "Anas", a name which undoubtedly has caused many ·a .w eb-footed animal
of the family Anatidae to turn her head away in a deep c-r1mson
blush. Contrary to the opinion of those who have kept these
animals as house-pets, there is no relationship, entomologically or otherwise, between the name of the genus and the
alimentary . canal.
The Duck has often been described (of. Amer~can Co·llege
Dictionary and my friend; Morris' mother) as a "web-footed
swimming bird characterized by a broad flat bill, short legs
and a depressed body". Perhaps it is better to describe
him as a ":feathered biped"; this points with pseudo-Platonic
directness to the close link between the Duck and the philosopher, a similarity that becomes even more evident when we
listen to the speech of both.
This obvious l y brings us to our next topic: the peer r elatio ships of ducks. As a rule ducks get along with each other no
better than do men, or, in other words, not at all. For ducks
do not share their food with each other, nor do they assist
each other in any way. Even a duck who may fancy himself a
leader in an activity such as flying South finds that he is
constantly overtaken by other ambitious ducks until he :finds
himself last in formation. This bureaucracy explains why
ducks deem it necessary to start South so early in the F all
and do not return until late Spring, this situation is
known colloquially as the ducks' "migratory plight".
,
�-37Concerning his relationship to people and vice versa little
can be said, Ducks are· ducks, and p·eople are people.
People
seem to notice the difference, and the ducks appreciate this
perspicacity. Man also seems to revel in the throes o:f
bread-tossing, a splendidly humane sport, enabling the Duck
to see his way through the cold Winter, while it is a wellknown :fact that Man cannot live by bread alone. While on the
relationship of Man and Duck, a human acquainta:nce o:f mine
should be mentioned, a brilliant Audubon scholar by the name
of Seymour Duck.
It appears that he felt the sole advantages
of his name were that it was :fairly easy to spell and presented
little difficulty with pronounciation.
However, Seymour,
now the chairman-in-charge-o:f-reevaluating-the-point-systemo:f-classi:fication :for the American Kennel Club, disliked his
name so much that he changed it to "Poodle", and, consequently,
was asked to turn in his binoculars. The irony of this is
that Seymour can best be described as having a broad, :flat bill,
short legs and a depressed body.
We now approach the subject o:f the influence of the Duck on the
American way o:f life, a way of life to which many refer as
"ducky", or something to that effect. Ask yourself, what
American woman has not wanted to own a genuine duck-feather
pillow, a pillow so light that, when one throws it up in the
air in delight, it is difficult to realize that what went up
can ever be down? And the American Man :finds no sport as
enjoyable as sitting in cold marshes from six in the morning
until dark, waiting :for his friend, the Duck, to appear so that
he may :fill him with virulent lead, a typical show of American
affection, a display of human love that calls for ducks to
have, if nothing else, a good sense of humor.
This brings us to our next subject: Donald Duck, and I am
reminded of a comic strip I read last week which went something
to this effect.
Daisy Duck to Donald Duck, "Who was that
cute-looking duck I saw you with last night?" Donald's reply,
"That was no duck; that was my wight*!" This points to the
wealth of humor the common duck provides for the common man,
bordering only slightly on the esoteric.
And this naturally brings us to the :final and most essential
topic.
From this essay the careful reader could not help but
be impressed by the :fact that the true value of the Duck, is
that in no way does he provide an explanation for the order
o:f the' kosmo s.
*
{Archaic, obsolete)
A human being or person
�
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THE
'-......._
~
c-OLLEG . IAN
A PR I L
1964
.______..--_.-/"
�C 0 N T E N T S
AN ANATOMY OF PLANETARY ORBITS
..... .
HERACLITUS: THE THAUMATURGY OF LOGOS •
THE TRAGEDY OF KING LFAR • • •
*
*
David Lachterrnan, '65 •
...
*
..
1
• 29
Jessica Hoffmann,'65. • • • 50
A SELECTION FROM BACON 1 S SYLVA SYLVARlJ11
*
Eva Brann, Tutor • • • •
*
• • • Introduced by • • • • • 65
Laurence Berns, Tutor
*
*
*
David Lachterman •
• • • • • • • • • Editor
Eva Brann • • • • • • • •
Faculty Advisor
David Rasmussen
• • • Business Manager
Susan Roberts • • •
• • Editorial Assistant
�AN ANATOMY OF PLANETARY ORBITS*
Eva Brann
In reading astronomical texts it is ver1;1 profitable to stop
now and then to fix the attention on the mathematical diagrams
themselves, not insofar as they assist the course of demonstration
but insofar as they are the incarnation of conceptions perhaps
never made quite explicit in the text -- to inspect them, as is
sometimes said, "quali tati vely v
'.
No manner of lookinCj is more
useful in the effort of gathering that budget of insights into
the ways of science and the being of its objects which forms the
capital of reflection.**
Ptolemy under·wri tes this point of view
when he explicitly speak. of applying the consequences of his
s
conceptions by demonstrations '9using the diagrammatic approach"
a classical distinction between a diagrammatic and a numerical,
tabular method, cf. Theon, Exposition 2.£ Mathematical Matters
Useful f£!:. Reading
~.
ed. Hiller, p. 177).
In general, two basic kinds of diagrams may be distinguished
in our astronomical texts .
The first pictures a mathematical
hypothesis devised to "save the
appearances ~ 1
under the constraint
of the axiom which requires heavenly bodies to move in circles
and uniformly; the diagrams, in other words, are constructed to
rationalize or correct the apparent anomalies of their motion.
Such diagrams are drawn by Ptolemy _
and by
Co~ernicus.
kind pictures the analysis or generation of
the heavens by real bodies.
~
The second
orbite traced in
Such diagrams are drawn by Kepler and
*The relation or· such orbits to cosmologies is surveyed in the
POSTSCRIPT, pp. 1&ff. .
**Some consequences will be drawn in. a note -on astronomical~
thesis projected for a future Collegian.
�- 2 -
Newton; they meet the
99
great need of imagining the true figures in
which the routes of the planets are arranged". 1 )
The characteristic figure of the first kind of diagram is the
circle, of the second, the ellipse.***
I.
CIRCULAR h7POTHETICAL DIAGRAMS
A thorough study of these ;,yould begin with a characterization
of the planetary diagrams in Ptolemy 0 s Almagest and would then
tTace their transformation in each corresponding chapter of
Copernicus'
~
Revolutionibus Orbium Coelestium, that is, it
would detail the mathematical Copernican revolution.
But that
is too great a work to attempt here, especially since Copernicus'
circular devices, falling betwixt and between the old and the
'°New
Astronomy 0 ~
as:
are they properly to be conceived as mathematical hypotheses
are very hard to interpret, raising questions such
or as approximations to orbits? has .his ·attempt to restore the
axiom of circular motion in all its purity a "physical" motive? can
his diagrams really be fitted into his cosmological model? (See
POSTSCRIPT.)
I shall therefore confine myself in this section ·to a brief
review of a typical Ptolemaic figure such as precedes all determinate adjustments to the · appearances.
This inventory of charac-
teristics will certainly yield nothing unfamiliar, but it will
serve to illustrate what I mean by an nanatomyn of diagrams and it
will provide a contrast to the ·Keplerian and the Newtonian orbital
figures:
1.
The paper plane in which the dtagram ·is drawn represents
an ideal geometric
m,
or what might best
be
called "Euclidean
***All three-dimensional elements, i.e., those inclinations of
diagrammatic planes to one another which account for lat~tudinal
variations of planets, will be omitted here.
�- 3.
. ..
un-spacett , for Ptolemy's figures, al though they have a direction
(see b. below), represent neither a particular place nor a locus
of positions in the world.2)
This is a consequence of the pri~
marily mathematical, that is, non~physical nature of the figures
they certainly do not image the real motion in the heavens.
2.
Each diagram is a separate and isolated device, for there
is implied neither a common scale in accordance with which the
determinate ratios of the different parts of each diagram are
calaulated, nor a planetary system into which they fit as wholes.
3. The diagrammatic
~
of the basic regular planetary
ou~c.c-
motion (r;,hich varies -in speed for each planet), is evidently ob"
tained from those spherical drawings, projections of the heavens
.
unto the earth, in which the ecliptic lies horizontally, the
vernal equinox is front and center,
and the sphere is tipped forward to
bring the European latitudes int.o
prominence (II, 5 and 6).
If the
tipping is continued until the
paper plane · coincides with the ecl ip- ·
tic as seen_from the north, the basic
planetary motion, which is from west
to east (see POSTSCRIPT), will be
counterclockwise (contrast
motion 2.!l
~auxiliary
~
Caelo, 285 b 15).
The sense of the
circles i§_. !!Qi unitary but is either the
same or opposite to the basic motion-- (for instance, in the equ:fi;/alent planetary hypotheses of the epipycle and the moving eccentric,
the former has to move in the same, the latter in the opposite sense
�- 4of its deferent, XII, 1).
4.
The parts of the diagrams differ . :-.somewhat for different
planets and somewhat more for the planets above and below the sun,
but the tyPical elements are alike.
headings, a. circles
They are enumerated under three
2f movement, b. lines of direction; c. special
points:
a.
a circle of appearances (ecliptic)
having the earth as a center and
therefore "homocentric with the
cosmos" (III, 3); of indefinite periphery since the e·arth is to it
a
point; about its center are measured
the angles of observation.
as
a circle off-center with respext to
the earth (eccentric deferent)~~of indifferent size, which carries the
~planet in its geometric path; it
corrects an anomaly with respect to
the ecliptic; its 120th part is the
common measure of the diagram.
a smaller circle (epicycle)' borne
on the deferent and found in terms of
its radius, the geometric path of~
apparent planet; it corrects an )
anomaly with respect to the sun.3
a center of regular motion (equant) situated on the deferent's
diameter; it 0 equalizesn a discrepancy between the zodiacal (ecliptic)
appearances of the mean planet and its correct motion in the diagram
so far constructed (IX, 2). Its periphery serves as no geometric
path -- it is solely the , point about which alone the planet moves
uniformly, the clock-work of the diagram; this is expressed in its
na.n;e: Hthe ceayer which does the revolving" ( TO ITE..fL"-yov
KEVTfOV
).
.
b.
the radii of the above circles, forming, as rays of angles, the
measure of distance traversed, which is never a linear but always an
angular quantity in these diagrams. The radii of regular motion are
19
thought of as revol ving 17 the planet ( n.C v o o 0rE v a..\,,. 1\~ r ~ a...-yt.Lv
f..08£'l~L
III, 3). The line from the earth to the
apparent planet is the line of observation.
�- 5the line containing the centers of the ecliptic. the eccentric
and the equant (line of apsides) which gives the diagram a direction
with relation to the ecliptic; anomalies are shown to occur
'S'Yilmietrically ab'ol'i'.tit; its very slow movement (IX, 6) indicates
a shift of the plane of the whole _ ypothetical diagram against the
h
circle of observation.
·
an (implicit) line showing that the radius from the mean sun to
the earth is always parallel either to the radius of the equant
(inner planets) or of the epicycle (outer -planets); this means that
each diagram is coordinated with the sun.5}
c.
there are a number of special p(ints such as the farther and
cl.o ser poles of the line of apsides apogee and perigee), corresponding points on the epicycle, ·p oints of ™passage (I, J), etc.
the most interesting of these are the station points which
bound the planet's retrogradations and returns, found when. the line
of observation is cut by the periphery of the epicycle in a ratio
dependent on the ratio of mean to epicyclic speed (XII, 1~ since
this ratio and this point have to fall out of the diagram after
the numerical determination of the-rat"iO-Of the epicycle's radius,
they represent a kind of corroberation of the hypothesis.
If such a diagram is set in motion an epicycloidal orbit of
fairly. fantastic shape is described.
Ptolemy, of course, never
attends to these traced paths at all within the · Almagest -- the
parts Of the diagram are only an imaginarjr (
passim) machinery of motion (see POSTSCRIPT).
that Ke-pler
Ch •. T.)
~
v
oO
r
(;
f.V O .v' >
.
(It is significant
M"-q' .
trace"' nperplexissimae spiraen , Astronomia
llirY:!J
Indicative of that is his willingness to admit the equi-
valence of the epicyclical hypothesis described above to an alternate
hypothesis, that of the moving eccentric, for although both save the
6
same appearances, they sometimes generate qui te different orbits. )
While both the Ptolemaic and the Copernican diagrams fail
either to produce real routes or to fit into ·a true system, they are
nevertheless fundamentally bound to a cosmological
model~
In fact
the bloodless part of the ·cop,ernican revolution is ·nothing but the
�6
from
the center of the
center
s
see
WO''
both
orien-
tation but
IL
causes of
the
This is
s causis motuum
p
s concern
new
The
20
external
of mere appearances with
cal consequences of the nature of
in the
of
His
to us in the
in these terms is most
Newton's
a much more
certain ways
of
the basic
features
not about a
books are
combines its
may have
as the
thus actual orbits are
as
to be
in the
ways from the
The
of the
is
for an
the ancient
a
�- 7true viewer's perch on the world's top. Thus not only is a common
measure found for the planetary intervals, but their absolute
magnitudes are also determined; the mean speeds of the planets can
furthermore be related to these.
2.
The diagrams are no longer constructed to Hsave" apparently
irregular motions, but rather to explicate
~
and lawful motions;
consequently there are no circular, i.e., closed auxiliary motions
either same or opposite, but only continuously varying components.
From the point of view of the fi.gure accomplished, the sense of the
motion in such diagrams is indifferent and the time of the diagram
therefore reversible.
Since, furthermore, the common planetary
direction is not, as in Ptolemaic diagrams, determined from the
basic spherical model, its unitary character calls for a special
cosmogonic -- account.
3. Since the mathematical explanation is no longer a mere
hypothesis, the diagrams now contain parts representing and measuring
physical quantities, such as lines of force, centers of force,
inertial velocities, etc.
4.
Since the center of the orbital diagram now represents a
source, or
at least a center, of force working across the orbital
plane at the periphery, the mediating
~of
the figure will,
contrary to that of the older figures, turn out to. have a function.
5.
While in the old ·diagrams all changes of speed ( accelera-
tions) were only relative to the observer
and all measuresof
speed r,rere angular, the orbital diagrams incorporate absolute
accelera.tions along the actual linear
6.
~
of the planet.
While the hypothetical diagrams exist only as total figures,
�- 8 having certain special places such as the apogee, perigee and points
of mean motion, the elliptical diagrams can be analyzed anywhere on
the periphery, being everywhere generated according to
7.
~
.fil!2.
the
hlhile analyses of motions are not absent from circular
astronomy, they yield, in accordance with 6., whole figures such as
the
w~ic'-"
ecliptic,~is
a component of the sun°s spiral (the only impor-
tant actual path in Ptolemy) after the daily revolutions have been
analyzed out; only in the new, physically determined paths are
motions literally generated in terms of small components; these
differ according to the conception of the causes involved in the
generation.
A comparative analysis of Keplerian and Newtonian elliptical
orbits is therefore subjoined:
NEWTON
KEPLER
(References to the Principia,
(References to the Epitome,
ed. Cajori)
E.B. ed.)
SINGLE ORBITS
i. ~ orbital figure defined
Orbits are "properly speaking,
that line which the planet describes around the rn" ' (p.999)
ii.
center
~dynamic
•
2. The real, bodily
895, 91o;:-
~
(pp.
Orbits are described by any body
revolving about a center of
force (p. 40.)
of~~
1. A mathematical point acting as
a theoretical center of force in
mathematical demonstrations ( p. 40).
2. The sun, in the physical interpretation-or Bk. III (p. 420).
�- 9 -
KEPLER
NEWTON
iii.
~
place 2.f
~
ceriter
1. As a mathematical point it is
fixed in geometric space at the
focus of the ellipse.
2. As a body it is on a (tiny)
ellipse, relative and similar to
the planet, with its geometric
center at the center of gravity
(p. 164).
J. At the absolute and exact
3. In absolute space, near the
center of the finite, spherical world and at the focus of
all orbital ellipses (pp. 857,
center of the world (p:-419).
987).
iv.
~bodies
in planetary diagrams
1. The sun, formost in dignity
(p. 8571.fixed at the world 0 s
center (p. 897) , · endot'10d with
a motor ~ (p. 896),. in rota-
_
tion, and both possessing and
giving all light, heat, life
and motion (p. 897).
2. The planets, having these
2. All bodies have the same desproperties:
cription (p. 398):
a. volume (p. 1).
a. volume (moles), which varies
according to observation(!),
as the orbital radius (p. 879).
b. amount of matter (copia),
compounded of volume and
density, and varying as the
square root of the radius
(c
r Y~ ) both for arc he. typal reasons (p. 881) arid to
suit the Third Law (p. 880).
°"'
. .
b. mass, the measure of matter,
compounded of density and volume
and found to vary directly as
weight (pp. 1, 411).
I
c. powerlessness (6.dvvo..rLo.)
or natural inertia, an inability to move (p. 894).
c. primary properties among which
are impenetrability, hardness,
etc. ( p • 399 ) •
v. The forces assumed
Active
1. Active force
ac~~
untlate-
1 • Active force is reciprocal
or
�sun is
source
immaterial outflow
which conveys
mo....,.tor
motrix) effecting
a turning
arising in
of the sun
895ff.
its effect
in
2 ..
change
induces
mass of the
Law II, p
center of force the mass
not a factor: f o< a
.. 5 •
Motor virtue
is
a
.; ;. . ; ;. .;. .; .; .; . ;.:. . sweeping
vectoria which
the planet attempts
to carry it in a circular orbit
.. 899 ..
another.
the geometry of
2, the
of force ac)ts as a center
;;;;...;...;,...........,..............
6 .. Planets possess certain
a. a stubborn resistance to
the.;;....;....;............
terial inertia
2c;
894) , by which it
s
the grasp of the
s motor
virtue and makes delays in
p ..
p ..
135.
�·- 11 -
KEPLER
NEwrON
its orbit.
b. a passive magnetic ~
(p. 936) with a ~
"friendly" direction in the
plane of the orbit. The more
nearly this pole points toward the sun the more effect
does the sun's (active)
attraction have to cause
"libration~, i.e., tho~e
0
small apprp.che s towa.rd the
sun which deform the circular orbit (cf. v, 1; p. 965),
(The permanent posture of
the magnetic thread at right
angles to the line of apsides
is slightly deflected and restored in one revolution
. (p. 941). 'This motion is
nothing but a calculatory
device, p. 9L~2.)
b. Magnetic force differs from
the power of gravity (p. 414).
~
iv.
~
shapes £!
~
ol"bits
.
·---
Depending on the bodies and the
. precise ~ law. involved .the
.
ellipses are differently generated :
1. In purely mathematical diagrams
with a poinf center the orbit is
a stationary ellipse (p. 56).
2. If the force law is slightly
altered from the inverse square
law (perhaps by a distant body's
interference) , the planet moves as OV\
a prototype ellipse (whose line of
apsides;~major axis J changes direction in the sky as the ellipse
rotates about the focus)meanwhile
tracing out a more complex (looped)
path (Ne~"rton H
anual, pp. 127, · 148).
3. If the center of force is itself
another (reacting) body, it will
itself describe a similar (small)
ellipse; the geometric center of
both bodies is their common center
of gravity (p. 165).
4. The true orbit is a nearly
4. If there are three or more bodies
exact ellipse about the sun as
involved~the
true orbit cannot be
found but approximates _fill ellipse
�2
the sun at
focus
focus
vii.
.e.
circular
are
be a measure, for
the oband hence
, with the
i;d th which the solar ray
strikes the
969
-<~
measure can noi,r, beof the deflection of
is
Let there be
circle PD
the
of
P is the apogee
is
Let there be a center of force
the
an inAB in the first in-
�·\., ,
- 13 KEPLER
NEwTON
D
.
I
." \
\
''
"'
\
\
\
\
·B
\
\
I
I
·A
\
F
I
l
IxM·p
CtY1T~r
Then 2AJ3;PB is the total libration since R is the closest
approach of the planet to the
sun.
r
Divide the circle into least
equal arcs PK, KG, GD, • 7-:-:-i.e., continue the 'division to
infinity (p. 973). The comparative libration in the arcs
is given by the sines LX, HF,
EB, • • • (vii , 1b) , and it is
shown (p. 974) that these are
in the ratios of the sagittae
PX, XF, FB. In particular, as
the whole sagitta PR of the
whole circle is to the total
libration PB, so is each sagitta PX, XF ,. FB, • • . ·: to='' ' the
·
corresponding increments 2.£ libration, which are thus founO.
and laid off on the diameter
as PM, MI, IF, •••
s
A
Now let the force act all at
once to draw the body toward-Sby the amount BF. In an equal
second time interval the body's
uniform inertial motion would
have carried it through Bc=AB.
Instead the two motions BF and
Be are addedVectorially (p. 14)
to give the resultant BC.
The actual path is \the polygon
whose sides are BC, CD, etc., a
series of resultants obtained by
. composing the inertial motions
Be, Cd with the measures £!
attraction BF, CG, etc.
If the time taken is
least (infinitesimal), the orbit
becomes curvilinear; if the force
acts according to the inverse
square law, · it is an ellipse
with illi:, center £! force & illi:,
focus.
Using the intervals AM, AI,
AF, • • • as radii, mark off
points L, H, E ••• on the
sines. These µoints can then
_ shown to be on an ellipse
be
(p. 9 7 5 ) . - - - viii.
~
1. The orbit's µlane is comµosed of infinitesimal ~
torial areas of shrinking
radius determined by the equal
elements
1. The triangles described about
the center of force in the polygonal orbit are equal for equal
times (p. 4o).
�NE1rVTON
For
= BC
since
~SAB
bases
=
£::,,.
same
and
heights
Therefore
:::::
The area law
to
• 983) so as to
of the
of time
the
a sum
ix.
composed
v
b
etc
�- 15 KEPLER
in the direction of the radii,
measuring the effects of the
attractive p~~r of the sun
(Cf• V, 5; Vl1 •
NElrJTON
petal effects of the impulse
atB(p.41).
2. But the curvilinear orbit can
also be analyzed in terms of
(Newton Manual, p. 83):
o... B
S
a. an inertial or centrifugal component, tangent
to the curve.
b. a centripetal component, the subtense of the
tangent and the curve,
drawn parallel to the line
of action·and showing how
the planet is drawn back
on orbit.
3. But it can be shown (Newton
Manual, p. 85) that the diagonal
(1b) ultimately equals twice
the subtense (2b).
This is a sign of the fact that
the limits of polygonal orbits
are not coinctdent with curvi:..
linear-orbits, sin·c e their
.measure of fore~ is not identical.
In order to identify them one
· must make the special. assumption
that "ultimately" the impulses
of 1. merge into the continuous
force of 2., i.e., that the
'fO'r'Ces are identical in kind.
4. It should be observed that
the Kepler's divisions are
actually infinite and his integrals are sums of real
infinitesimals (p. 973).
4. All components are understood
to be evanescent quantities in
ultimate ratios as the time becomes an .instant (p. 39). W'.nether
this means that they themselves
are limits or infinitesimals is
not clear (Principia,Appendix,
P• 653).
·
.
(In the limit all these displacement vectors are proportional
to force vectors.)
�choice of the creator:
in our
xi
time
as the
the inverse
l
.... c
c. the motor
)
are
system
�- 17 ·
-
KEPLER
NE WI' ON
Now c. and d. cancel each
other since as each higher .
planet receives a weaker virtue,
it absorbs, by reason of its
greater volume, a larger amount
of it (cf. iv, 2a). And:
1
cl..
c
o/.
l•c
R (circumferences are
as radii)
RJ:'~ (iv• 2b)
R~; ~
But l • C: c:A T, since distance
and material resistance compound to decrease the speed and
increase the time.
: • T
xii.
oot.
~
R~ •
numbers,
~ ~
altitudes
All these have 0 archetypaln,
mathematical causes (see
POSTSCRIPT).
xiii.
~medium
2f.
~planets
These are not mathematically but
theologically accounted for
(pp. 544, 566).
of
~
orbits
1. The planets move in a limpid
ether, scarcely or not at all
resistant (p. 857).
1. The planets move in a rare but
resistant medium which slows them
down imperceptibly (p. 419).
2. The motor virtue traverses
this ether instantaneously,
i . e ., i t is t r ansmitted nonmaterially (pp. 901, 902).
2. This ether may perhaps be the
medium for the mechanical transm
ission of force (p. 547) .
III. ANALYTICAL VECTOR DIAGRAMS
As a contrast to the figurative view of orbits taken above, compare
the analytic treatments in the Junior Mechanics Manual (IV B, ii) and
the Appendix to the Newton Manual.
Attending here merely to the analytic description of the orbit,
two sets of terms are to be distinguished:
�- 18 -
1. a large,polar coordinate system whose
origin is the center of force about which
a radius of variable length (r) sweeps
out uniformly increasing angles ( !::.
~ )•
2. a smaller, roving system of
orthogonal vectors, one of which always
lies along the radius.
These vectors measure small displacements (
b,..
s) of the planet
(which can also be given in terms of the x and y axes).
The accelera-
tions of such a path are given in a differential equation.
In this context the point is merely that such planetary routes are
studied mostly in terms
of~
vectorial components:
the orbital
figure is no longer the center of attention.
POSTSCRIPT ON THE RELATION OF PLANETARY ORBITS TO
COSMOLOGICAL MODELS
This paper has so far noticed only tha.t part of astronomy called
the "doctrine . f schemata" ( Ik>ctrina Theorica) which deals with plane
o
diagrams rationalizing the "secondary'', that is, planetary motions.
Since, however, such diagrams are obviously determined from the outset by models of the whole world, there should be at least a cursory
comment on usphaerics 99 , the doctrine of the cosmological container,as
well.
(On the size of the sphere of the fixed stars in each model
see Note 8.)
�- 19 PTOLEMY: In the basic cosmic model two main features, the first
physical and the other mathematical., very ill adjusted to · one another,
can be distinguished: 1. the traditional geocentric, moving-sphere
cosmology of the Timaeus and ~ ~ (I, 1-8) and 2. the professional
astronomer 0 s planetary hypotheses, which do, indeed, take their departure from cosmological and physical considerations (for such
first gave rise to the axioms of regularity and circularity, III, J;
IX, 2; cf. Aristotle Physics VIII, 8), but which have, as the ancients
themselves remark (Eudemus and Geminus, in G. de Santillana, The
Origins£[ Scientific Thought, pp. 253ff.), long since became divorced
from these. The main connection between these two is that the practical,
observing astronomer coincides with the philosopher'in having a
naturally geocentric point of view (I, 6).
The physical part of the model is presupposed (I, 9) in the
technical exposition. In this model (VIII, 3) the earth is fixed at
· the center while two spheres of prime movement turn. about it, the
starry outer sphere with a regula.r daily mo:ti~n westward about the
main (north-south) axis, and the inner sphere, whose axes are oblique
to the first, in the opposite direction -- these are the Timaeus'
motions of the "~", the source of regu.lari ty, and of the '~~",
the source of diversity. On a great circle perpendicular to the axis
of the second (ecliptic), the sun has its yearly path, 1v-hile the
planets' route is in the zodiacal band about the ecliptic circle.
The sphere of fixed stars imparts the ultimate motion to the world and
serves as its astronomical clock (I, 3).
The planetary diagrams fit, or rather, fail to fit into this
model as follows: although their center of reference is the earth,
they are not conceived according to a common scalejso that their sizes
in relation to each other are indeterminate. Nor is there a harmonic
rule which would allow them to be fitted into a system of proportions
(at least not in the Almagest; as for Ptolemy's Harmonice, Kepler
devotes· an appendix of his own Harmonice Mundi to showing that it was
a failure). Even the very order of the planets from the center is
somewhat arbitarily settled: the inner planets shall be those whose
elongations from the sun are limited (IX, i).
As far as the construction of a moving · model of the complete
planetary system is concerned, it is, even when a common scale for all
orbits is invented, not feasible within the ancierit framework of
spherical physics -- as ' Ptolemy himself admits in ·a work in which he
attempts to construct physical models of the hypotheses of single
planets.9) On the other hand, the feasibility and simplicity of such
co·nstructions in the new astronomy (with the orbits taken as circular
or almost so) is its great point of pride: e.g., Galileo, Chief
Systems (Title page); Kepler, Mysterium Cosmographicum (Tab. I, IV).
The difference which this fact renders concrete is that between motions
·which have mathematical complexity ( a u/. vrr/\ ov..~), :which are a mixture
( ~~~t5 ) and whose actual simplicity is inaccessible to human
understanding (XIII, J), and motions which are visibly and really simple
and decomposed only in the mathematical analysis.
COPERNICUS: The most immediately remarkable aspect of his system
is, of course, the subversion of appearances in ·the case of the primary,
�- 20 -
vv.-H.
I
the ·.day-and-night ( \/ u )\~
fl v "S ) circuit of the heavens which is
now attributed to the rotation of the earth (De Revolutionibus, I, 11)
~ motion 2f ~ Hsame~ 9 is located ill~ ~· +h.,e,
As far as the planetary orbits are concerne~~first, most significant
consequence of this revival. of the npythagoreanu (I, 5) heliocentric
model is that the earth is among the "wanderersn and these no longer
move in a plane oblique to the horizon of the model: rather it is the
earth's tilt which is now the cause of our oblique view of things-the constituents of the motion ._... the nether" are located in the earth,
of
....,_
.........
_. ._..
which is consequently the source' of all appearances, while the true
center of motion is the sun, which-, "resting on a kingly throne, governs
the family of stars which wheel around" (I, 10).
Next, both the ~ and the of'bital radius of the planets is now
given through the "first law •••· that the magnitude of the orbital
circles should be measured by the magnitude of time" (I, 10), so that
they have in their motions"a sure bond of harmonyn.
Now also the single orbits recover their pristine circularity and
are either "truly circular or composed of many circular movements"
(i.e., the equant is banished) -- but this not done only to purify the
mathematical hypotheses but to eliminate a "physical" incongruency: for
any deviatfon from truly uniform circular motion must occur 'gon
account of the inconstancy of the I planet's] motor virtue • • • "
(I, 4), and such inconstancy is unthinkable. Even the planetary paths
themselves, although still composed of epicyclical and eccentric movements, do now approximate smooth circular orbits without loops; this
is effected by keeping the epicycle small and giving it a speed equal
to that of the eccentric.
And finally, Copernicus 0 planetary diagrams contain an important new
i tern -- the circulus maximus, the orbit of the planet Earth whose center
is the origin of all planetary diagrams (see below) and whose radius
is their common measure.
---
-
·~
So far Copernicus seems to be a modern, an "orbital" astronomer. But
several difficulties arise on this score:
First, the geometric centers of the system of planetary orbits are
not in the sun but ·form a cloud of points near it. (See .t he diagrams
in Koyre, La revolution astronomique, P• 65) -- the system is neither
"physically" heliocentric nor is1 it really a tight system.
Secondly, Copernicus sometim&s slips into the language of solid
spheres as bearers of planets -- in fact in the very title of his book
"On the Revolutions of the Heavenly,..-.S pheres 91 (see J. Copernican Treatises,
ed. Rosen, Dover, pp. 12ff).
Third, the devices needed to save the single planets' appearances,
Le., the technical parts of the work, are more complicated than
Ptolemy's (Koyre, pp. 47-48) and might hence be regarded as even more
"hypothetical 70 • (This does not justify Osiander 0 s unauthorized contention that the whole system is a mere hypothesis see ne· Revolutionbus,
"To the Reader Concerning the Hypotheses of this Work". It is, incidentally, significant that it was Kepler who first exposed the imposture,
cf. Astronomia Nova, back of title page).
Finally, for Copernicus the center of each single planetary diagram. is not . · referred to the sun, b:vt to the center of the earth's
orbit. (Cf. De Revolutionbus V, this is the reason for the disjointed
aspect of the system mentioned above, for this center, which is in fact
the ~sun, lies differently with respect to the true sun for every
�---,
- 21 -
planet.)
The result is that the sun holds the true center in the
speculative, cosmological (I, 10) but not in the technical parts of the
book. Thus again the hypothetical diagram diverges from the real
picture.
The true character of Copernican orbits with respect to the criteria
of this paper can therefore scarcely be fixed · and their discussion
has been omitted above.
The works of the three astronomers that follow may be regarded
as
justificatio~
and demonstr·a tions of the Copernican system, as the
following quotations show:
1. Galileo, Dialogue Concerning ~ Two Chief World Systems, "To
the Discerning Reader": ". • • the celestial phenomena will be examined,
strengthening the Copernican hypothesis, until it might seem as if this
might triumph absolutely." (It must be remembered that the book is
written under the -- transparent -- fiction of an impartial comparison
of the Ptolemaic and the Copernican systems.)
2. Kepler, Astronomia Nova, Introduction: 0 • • • from which consideration [that of celestial physics) arise certain clear argwnents
by which on~y Copernicus' opinion on the world (with a few changes)
is shown to be true, and the other two are convicted as falsen.
3. Newton dedicated a manuscript of the Principia to the royal
society in which, it was recorded, "· •• he gives a mathemati.cal demonstration of the Copernican hypothesis as proposed by Kepler • • • "
(Isaac Nevrton°s Papers~ Letters 2.!1 Natural Philosophy, ed. Cohen,
p~ 489 : this is not to say, however, that for Newton himself the basic
facts of the heliocentric system were any longer in need of··.justification;
for him, "demonstrating the hypothesis" means, strictly speaking, to
deduce from the Keplerian period and area laws a force law, . and hence
. -the Keplerian or bi ts).
It follows that the basic diagrams of all three are heliocentrically
determined from the very beginning.
GALILEO: In the Two Chief Systems (ed. Drake) the discussion
centers largely on thatnewly ordained planet, the earth. However,
enough is said about the other planets to make it clear that all
actual planetary orbits are considered to be perfectly circular
(pp. 28ff., 321ff.), not, I think, merely to make the exposition to
l aymen ea· ier , but because the circle is Galileo's line _Q! inertial
s
motion. Inertia is for Galileo a purely kinematic notion, quite distinct
from the resistance of material bodies which was for Kepler one of the
causes of the deformation of circular orbits; Galileo 0 s orbits remain
circular precisely because his bodies have no brutely .material, unreckonable, 11 conturnaciousH properties (ibid., p. 207). (The. suggestion
that Galileo's· orbits are circular because he had a classicizing
esthetic preference for circularity, . proposed by Panowsky in Galileo
i l ~Critic Qi~ Arts~ Hague ·1954, pp. 20ff., is, accordingly, insufficient.) Galileo derives his notion of inertia from the (idealized)
�- 22 terrestrial phenomenon that a body neither gains nor loses velocity
along the horizontal plane
(considered as a small arc of a large
circle about the earth), because there i t is everywhere equidistant
from the center of gravity (Chief Systems, pp. 27-28ff). This insight he transfers to the heavens, not completely realizing that
this implies that the sun is, in fa.ct, the center of gravity for the
planets -- though he suspects that the causes of motion are the same
in the heavens as on earth (ibid., p. 234).
This same inertial motion:-taken simply as a straight line, enters
into Galileo's analysis of terrestrial projectile orbits (Two New
Sciences, J:bver, Fourth tay,pp. 244ff.). His treatment there marks
the beginning of the analysis of orbits into two rectilinear co~po
nents(one representing displacement under inertia and the other under
some acceleration toward the center) and of the notion that such
orbits are conics, in this case, parabolas.
KEPLER: His is the last and most enthusiastic attempt to fit
the planetary orbits into a closed cosmological model. He finds three
patterns:
.
The first (and his earliest discovery: Mvsterium Cosmographicu..m)
is the cosmological or '0archetypaln model proper, a solid geom.e tric
construction accounting for the number of planets (6) and their intervals in terms of thick spheres containing the planets' (eccentric)
orbits which are circumscribed about and inscribed in the five regular
Platonic solids nested within each other (Epitome, IV, p. I, 3).
Kepler cherished this Timaean artifiact, the purely mathematical,
invisible structure· of the world, throughout his life, finding a
rationale for every discrepancy ~nth the facts (Harmonice Mundi, V, 3 -the ruinous seventh planet, Uranus, was not discovered until 1781).
The second, properly systematic, bond fits the planets into a
harmony, a "system" in the Pythagorean sense of 0 scale". In this
pattern the velocities at the perihelia and aphelia of the .elliptical
orbits are taken to correspond to vibrations producing (inaudible)
consonances. It has a 99 manifQld kinship" with the solid model ·
(Harmonice Mundi, V, 2ff.).10J
A third rule is the°'Third Law" (cf. II, ix, 2) by which the periods
of all planets are to each other as the three - halves .power of thei r
mean radii. This is the only one of the three that has survived,
since it is implied in Newtonian dynamics (Principia, Bk. I, Prop. IV,
Cor. 6; Note ?).
Within this system of planets there is for Kepler, the try.e. Qop~:rnican .
one orbit of prime importance -~ the earth's (for now the ' ernbhasis is ' oh >·
the "geoperipheral" along with the heliocentric aspect' of the system).
among his earliest labors was that of establishing its correct
~
eccentricity as a preliminary to finding Mars 0 true orbit (Astonomia
~' Ch. XXVIIff.).
Henceforth the earth's orbit becomes more than
a circle about the diagrammatic center -- it becomes a moving observation post, occupying a middle station between the inner ·and the
outer planets, so. that its inhabitant, the us-Peculative creature"
(Epitome,IV, Pt. I, 3, 4) can, knowing its own route, rise above it, as
it were, to plot that of the other planets with .respect to the true
center, the sun.
r
�.,
- 23 ..
NEWTON: Through two books of the Principia no particular reference
to the heavens (except in the scholia and, tacitly, in the lettering
of the diagrams: S (o11 , T [erra1 , . L (una}) is made. Furthermore,
when the celestial application is finally made in the third book, we
find that Copernicus' and Kepler 0 s much-embattled theories may now be
presented as -- appearances: the. Copernican system and the Keplerian
period and area laws have become "Phaenomena" III, IV and V respectively~
(This vantage ·point, permitting him to observe as phenomena··
the theories behind the common sense appearances, must have been in
_ Newton's mind when he said that he stood on the shoulders of giants.)
· .These two circumstances signify that Galileo's demand for a physical
theory, uniform for heaven and earth,has been once and for all met;
there are no special proofs for or patterns in the heavens, and guided
by mathematical theory, it is easy to 0 see 0 the planets obey the laws
of motion. In fact, the whole vexed question of the place of the human
observer is, for the technical parts of the book, once and for all
superseded in Nelvton' s notion of the relativity of "apparent" space:
"the dimensions of the orbits are the same, whether the sun revolves
about the earth or the earth about the sun'1 (Phae~·~"TV).
The plan, then, of the first two books of the Principia (Preface,
p. xvii) is ~ 7 from the phenomena of motion to investigate the forces
of nature, and then from these forces to demonstrate the other
phenomena'°. This requires that the causes admitted must be simple
and universal (p. 398); Newton speaks of "universal bodies" (corpora
uni versa), ' 7uni versal gravitationn (p. 400). Therefore the third
book, "De Systemate Mundi", which is the Principia's "example" of
mathematical deduction applied to phenomena of motion (p. xviii), has
to do not with a cosmic edifice (mundus) bonded by a harmony of ratios
(system), but with a "universe''-- the homogeneous locale of motions
performed by bodies all, indifferently, subject to the laws of motion:
a world of physical quantities ruled by mechanical principles.
Against this background and within the context of the anatomy of
orbits certain queries concerning the nature of the Newtonian enterprise arise in very particular terms:
Al though Newton explicitly says that •0lines are descr ibed, and
thereby generated, not by the opposition of parts, but by the continued
motion of points; ••• These geneses really ~place in the nature
of things, and are daily seen in the motion of bodiesu
(!!::r2. Treatises
on the Quadrature of Curves, trans. Stewart, London 1745), his mathe;;-ti'C'al analyses are· not, in fact, conformable with this view. For
.while curvilinear orbits are said to coincide ultimately with the
rectilinear elements (e.g., Principia, pp. 30-47) of which the mathematical analysis requires that they · be composed, nevertheless :
1. this very mathematical requiremant shows that his passing attempt
to make the process formally accessible to the understanding by regarding the ultimate orbits as "limits" (p. 39) is vain, for it is
. haracteristic of limits that they cannot •0really take place'° or be
c
"daily seen", i.e., they cannot become actual at all;
.
2. the ultimately diverse measures of force for polygonal and
curvilinear orbits brought out in II, ix, 3 above (cf. p. 192; P.
Frost, Newton, Principia, Ii£.2i ~' para. 145) show that such orbits
are ultimately different in generation and kind (not to speak of yet
�- 24 -
another kind of force tacitly introduced in the case of the't>rototype"
orbit, II, vi, 2, which rotates about the center of force) 3
3. although the Laws of Motion, which require that the ultimate
simple motions, inertial (Law I) or under acceleration (Law II),
shall be rectilinear, and their first corollary (really a 11 Fourth
Law", A. Sommerfeld, .Mechanics , p. 6) which does the same for their
resultants, are said to be induced from the phenomena of nature
(pp. xvii, 4oO), such ultimate motions are certainly not :r eally to
be 0 daily seen'1 , i.e., are not among the phenomena; they are rather
abstractions from or the assumed constituents of real motions, as
the explicatory· paragraphs under each law (p. 13) bring out-~
consequently there is a gap between motions as experienced and as
understood;
4. Newtong s frequent lapses into the langu· ge of infinitesimal
a
indivisibles (e.g., p. 45, para. 4: "least arcs"), although excused
beforehand by a cautionary statement (p. 38), nevertheless bring
out what is inevitably the actual vimv of the calculator.
In the face of this ambiguity it is legitimate to press the
inquiry into the true original nature of the motions whose determination
i~ the very end of the Principia (p. 12).
One possible means for
discovering the ultimate character of Newtonian motion~is to conjecture
about them from Newtongs cosmogony, whose stages may be assembled
as follows:
1. the 0 universal mechanics" which teaches that "description of
right lines and circles, upon which geometry is founded" (p. xvii) is
presumably given prior to the world;
2. then are made the universal bodies (Rule III, p. 398) with
their universal properties (Opticks, p. 400);
3. the future planets are then put in a sufficiently isolated
place, (p. 544) at distances appropriate to the design (pp. 566) about
a preponderant body, the sun (Isaac Newton~s Papers and Letters .Q.ll
Natural Philosophy, ed. Cohen, pp. 281 ff.), where they remain at first
at rest (ibid. P• 296);
4. thei1the "cause well skilled in Mechanicks and Geometry"
(~., p. 287) imparts such initial velocities as are calculated to
allow the planets to describe closed, nearly circular orbits about
the sun (ibid, pp. 286, 297), at the very same instance infusing into
them a certain active principle, the power of gravity working
according to the inverse square law (ibid., p~ 296; Ooticks, pp. 297,
401; Princinia, pp. 4oO), selected out of an infinity of mathematically
possible measures (p. 46, Cor. VII and Scholium),
Now the ~'causen that knows . at genesis the future courses of
the planets, comprehends, in whatever manner, the whole of the
temporal consequence (p. 545; Ooticks, p. 40J), that is, the. true
motions of ·a bsolute space (p. 12). I conjecture that the ultimate
nature of such true motions is that which we apprehend as ~hole
geometric configurations. For such objects underlie the reasoning
of the Principia as beginnings and ends, much as they do the cosmogony;
this notion is supported by the following items:
1. the description of such figures is regarded as the basic mathematical science (p. xvii);
�- 2.5 2. the mathematic~l calculus of the generation of motions has
"no regard to time formally considered", i.e., true time (Method of
Fluxions, p. 20) -- .presumably because in true space this generation
is somehow qualitatively different;
3. after the establishment of the area law (Bk. I, Props. I-II)
and of a general formulaic relation between the derived physical
quantities (velocity and acceleration) and the radii of orbits
(Prop. IV) nthe determination of centripetal forces" is undertaken
for special, selected geometric figures; in particular central and
focal orbital ellipses are investigated (Props. X, XI). This mirrors
the, indeed obvious, fact that forces became determinate only within
a geometric context -- given an ellipse, if the focus is the center
of force the inverse square law can be shov.111 to obtain; within the
Principia the converse is not proved independently, and the generation of such an orbit (Prop. XVII) proceeds analytically (the conic
section is taken as given and the initial velocities which will
produce an ellipse, ·a circle, and a hyperbola respectively are then
established in terms of the latus rectum);
4. the expression of force derived in this section (Prop. VI)
is in terms of the "curvature" of the orbit (p. 61, Cor. I, see
Courant, Differential ~Integral Calculus, II, p. 307), which is a
purely geometric formulation of the shapeliness of the orbital curves;
in these propositions the center of force is merely a point to which
the force is directed and rectilinear generating elements are not
involved;
·
5. the shape of the heavenly orbits is found at the ~ of the
.c ourse of inquiry (pp. xviii, Bk. III, Prop. XIII); planets are
consequently said to"pursue their revolutions in orbits given in !s1!1£
(specie) and position" (General Scholium, p. 543);
6. a last speculation, indeed not to be found in the Principia
but rather suggested by future developments, is based on t1·JO features
of · N~wtonian force: a. that it is the only criterium for distinguishing
true motions (p. 10), its effects being-:ui'e only appearances knor'l7!1
to originate in true space; b. that its nature is quite unknown (p. 547),
its effects alone being measurable, and that, contrary to Leibnitz'
~~,it supports no essential methaphysical role.
In view of
this, might not Newton himself have been amenable to the suggestion
that it is the geometry of orbits which underlies as a (formal)
. principle the dynamic phenomena, i.e., the appearances of force?
Tt...ro final items give rise to more radical questions related to the
guiding distinction of this paper, that between mathematical hypotheses
and real orbits: first, the ninth section of Book I presents the
peculiar concept of the "moving orbit", a hybrid orbit composed of a
geometric archetypal orbit which itself, as a whole, rotates about the
center of force while the planet moving , on the archetype traces out
a true path (cf. above II, vi, 2); second, it follows from the eleventh
section (Prop. LXVI) that the real orbits in systems of more than
two bodies are indeterminate, so that, although they are very nearly
the ellipses they would be "if the sun were at rest, and the other
planets did not act upon one another" (p. 421), no accurate path becomes
known for any planet. (See the Junior Mechanics Manual, Ch. IV, E on
the insolubility of the three-body .problem.) The first .item implies
the collapse of the above distinction,forthe "moving" orbit is similar
�- 26 to Ptolemy's epicyclic hypotheses: in both the planet, moving on
a geometric figure, traces out an actual orbit. The second goes
even further to suggest that the very nature of the objects analyzed may
prevent accurate knowledge of real orbits and true motions. If so,
"true 19 and nmathematical 11 are not -synonymous (Principia, p. 6) -Timaean 6... v 0..7' K vi and not Newtonian lawfulness ultimately characterize bodies and · a thor~hly mathematicizable
reality may
itself be a hypothesis.
NOTES
1. Kepler, Epitome Astronomiae Copernicae, V, Pt. I, beginning.
2. Although Ptole~y begins by asserting that astronomical science
deals with motions and seeks "place, time and similar things" (I, 1),
in the face of proliferating hypotheses he admits that no humanly
construable motions are thus generated --" for it is not proper to
compare human matters to the gods" (XIII, 2); see aiso Note 9.
3. to which the large moving eccentric borne on a small circle
is the equivalent alternate hypothesis (Ptolemy Manual, IV, 1, p. 36).
The equivalence of these hypotheses is not proved in general, but
only for the particular case of retrogradation (XII, 1). I . is to
t
be noted that in contrast to the two hypotheses of the sun (III, 3)
which are genuine equivalent alternatives, the two planetary hypotheses
are in principle identical, both being epicyclic.
4. This is, of course, a name transferred to the equant from the
radii (see b.). The device of the equant is generally taken to be
Ptolemy 0 s own innovation; the inappropriAteness of the name he gave it;
which consists in the fact that a suggestion of physical agency is
attached to the merest geometric point, expresses the equantPs
illegitimacy -- much urged by Copernicus (V, 2).
5. This pnrallelism is one of the brutejunrationalizable facts in
Ptolemy (Ptolemy Manual,' II, 2 (3), p. 17). It' points up the
suspiciously special role which the sun plays in every planetary
diagram of the Almagest.
6. Cf. Note 3. A sample of the paths of a planetary retrogradation under either hypothesis is reprinted in Claggett, Greek Science
in Antiquitv, Collier, p. 122.
7. Kepler 0 s inquiries concerning the physical causes of motion
are thoroughly intert~nned with his researches concerning orbits.
Roughly speaking, one may say that the former played both a prior,
heuristic and a posterior, rationalizing role with respect to his
orbital diagrams. Conceiving early(Mysterium Cosmographicum,1596)
that. since a planet's speed depends on its nearness to the sun, the
sun must act as a center of force, he imagined that the sum of rays
�- 27 ..
from the sun to the planet included in any angle about the sun and
interpreted as an integral area must be an (inverse) measure of the
velocity and therefore a(direc~- measure of the time (so-called
"Second Law0 , Astronomia ~' 1609). - Only then, having tried many
figures, did he find that · for Mars .at _least an ellipse with the sun
at the focus ("First Law") both saved the appearances- and obeyed the
area law: "0 me ridiculum, ••• I had omitted no figures among
planets in orbit except the perfect ellipse" ( Astronomia Nova IV,
Ch. 58. I have r :.ead somewhere that the term focus -- "hearth" -- for
the corresponding point in the ellipse was firstli'sed by Kepler; the
choice of this term is an acknowledgement that one feature of his
great discover-y goes back to the ancients: certain Pythagoreans
believed that the planets turned about a fiery center of power which
they called Hestia-Hearth, e.g., Diels, Fragmente der Vorsokratiker,
I, 403, 11. 14, 19, 28). He then went on to think out causes for the
compound of simple motions needed to generate the ellipse (Astronomia
~; Epitome, 1621 ) • His "Third Law" (periodic time2 o<. radi us3 for all planets) was found entirely empirically and the physical
explanation is purely after the fact (Epitome IV, ii, 4). (Kepler
himself called his rules not "laws", but "axiomata astronomica'', see
Harmonice Mundi, V, iiiJ
.
.
--
'
Newton began by supposing terrestrial gravity to extend to the
orbit of the moon and then 11• • • from Kepler 0 s rule (Third Law] • • •
deduced that the forces which keep the planets in their orbs must
be reciprocally as the squares of their distances [ inverse square
law] • • • " (Newton on the discoveries of the plague year of 1665-1666,
Hall, ~Galileo 12, Newton, pp. 278ff. and p. 360, notes 4, 5).
The next step was to demonstrate geometrically that planets in fact
move in Keplerian ellipses; Newton had done this by 1684 (i!2i9,.,
p. 293). The Principia appeared in 1687.
8. The size assigned to the starry heavens is not of immediate
importance in planetary diagrams; nevertheless here is a summary of
opinions:
Ptolemy (Almagest I, 6): the earth is, for purposes of observation, as a point in the center of the heavens (except in the case of
the moon which is too ne.a r, VI, 1 ) •
Copernicus (De Revolutionibus, I, 6): the heavens are immense
at leas't in contrast to Ptolemy 0 s~ it is not the earth that is infinitesimal but the heavens that are indefinitely great. This is a
necessary presupposition for a system in which the earth moves if
no sidereal parallax is observable, as Aristarchus, Copernicus' ancient
precursor,had already acknowledged; see Archimedesv comments on this
in his Sand Reckoner (~, ed. Heath, Dover, p. 222).
Kepler (Epitome, IV, end): the dimensions of the starry sphere are
exactly known -- its diameter is 60 million earth diameters and its
thickness(!) 2000 German miles.
Newton (Principia, p. 6): from its nature we may infer that
mathematical (true) space is boundless (General Scholium, p. 544; First
Letter to Bentley, Ne~rton's Papers, p. 281); the material universe in
this space is likely to be infinite and to contain other planetary systems .
��- 29 -
HERACLITUS:
THE THAUMATURGY OF LOGOS
David Lachterman
Ou1<
tJ
of
ffA-<,a ct~~~ lo~ Ao 10J ~.t..oJef,1.VTo(S or~o~oyE'ZV
I{;,
C.J
I
~
Cl
oV
£ () r L V 'i.. V 7l d. \/ T °" t <.. v' cU.. .
1
F r c:· j
(\11~
Yl
+ .5 o
"Listening not to me but to the logos., it is wise to
speak in correspondence with the logos: 'all things
are one'."
"All things a:re one" -- in this dramatic utterance three words
clamour for our attention: hfill, panta, einai. The utterance
as a whole seems more like a solution than the setting out of a
problem; nonetheless, I hope to show that the dia-~tic of the
~ and the panta adumbrated in this fragment is the fundamental
problem with which Heraclitus is concerned. Furthermore, out of
a consideration of this dia-~tic of the ~ and the panta emerges
the possibility of cosmos and · it is of this possibility viewed from
many sides that most of the Heraclitean fragments are speaking.
Finally, this dia-lectic determines the form of human utterance
itself, that is, o"f'human knowledge; man is the primary implicate
of the logos in the sense that he, his words and his thinking are
woven ~ the. fabric of the whole of things in the most responsible ,
that is, most accountable, way.
Three phases (statements/manifestations) of this dialectic may be
conveniently distinguished: its immanence in the visible,
'material' world (pvr·, tropai PY.!£.[, phvsis); its invisible
presence as the structuring principle of ordered (and hence; intelligible, -ent) reality (harmonia, 'Dike/ polemos, 1£ sophon); and its
re-presentation in human discourse (nous, onomata). The interwovenness of these three phases· through the logos brings 'being' as
'well-regulated, measured strife' (Dike/ polemos) to light. ·
In order to confront the ~-panta dialectic which is the basis of
Heraclitus' thought, it is first necessary to clear away several
Aristotelian distinctions and 'laws of thought' (Denkgesetz.e) which
obscure our apprehension of the fragments. (Cf. esp., .Physics A,
ii 185 b6 ff.; Metaphysics I, iii 1005 b23 ff.; Ibid 1012 a 24 ff.)
Heraclitus presumably listened to . 0 what is' speak to ·him through
the logos, rather than presuming to speak about 'what is 0 through
'logic 0 l); consequently, Aristotle's discrimination of substance
1 ) M. Heidegger, Was ist das -- die Philosonhie, p. 52 Herakli t
und Parmenides weren grQ's;en in deID Sinne, dass sie noch im
Einklang standen mit dem A~ros
'd.h. dem t: IJ:., rrlvTa<.
�- 30 -
and its accidents2), or, more generally, the division of reality
into categories, the concept of unity as identity in defining form
( A cf,t~ )3), and the inviolability of the principle of contradiction as applied to a substance and the pairs of contradictory
accidents potentially predicable of it4) must all be overlooked if
we are to come to terms with the force of the hen in hen panta
einai and, through it, 'With the 'dynamics' of the log~
PHASE I
Immanence of the hen-panta dialectic in the material, visible world
Aristotle (Met. A 984 a8) classes Heraclitus with the other preSocratic 'physiologoi' (986 b14) who sought a 'material cause' out
of which all things come to be and into which they are ultimately
resolved -- the substratum which persists through all change
(983 b8-19). Heraclitus is said to have chosen fire as his 'material
cause•. It was the shortcoming of these physiologoi that they
distinguished only this aspect or factor in the constitution of the
real, neglecting the other three causes which were left for Aristotle to discover (993 a10-15). The insufficiency of Aristotle's
treatment of Heraclitus will become clear, if it is not already so,
as soon as we survey the extant descriptions of the role of fire in
the whole of things. This insufficiency is only another instance
of the inadequacy of Aristotelian distinctions (e.g., the~
causes) for the study of his predecessors.
Fragment fifty speaks of panta -- 'all things'; otger fragments
also 0eak of panta or ta panta: rr °" viwv N 1.. v 1J t.v £ v w v
7
(
Fr. 1 ; ,Ti~ v ,.-rA. .,.~Lo(. ~ v I ;Ai v £I<. v ~ t, pv ') o..
w
at I
Fr. 41 ) ;
T d.. rr ell\/ Tot 0 L ~ Kl r£1,.. K f \> °' I) v 8 s
(Fr. 64) ' and so
forth. What meaning m~st, we giv,e jo _this word? Frag!J.lent seven
provides the answer: ~l iTi:Av'Tdt. TrA. 0V1ol 1~irvJ<, 0 £"vCiL-ro
••• ;
ta panta are ta onta -- the exisfent things, the things that are. -and it is of these that the logos says: "they are one."
(
I
'
r
-
Heraclitus tells us more than this; he speaks of the manifestation
of this oneness of ta onta in the world accessible to the senses,
the 'natural'world, as we should say, This world is for Aristotle
the world of hvle; for. Heraclitus, it is the world o·f pvr, or, more
specifically, of the tropai pyros -- the transformations of fire
(Fr. 31). The foundation of the oneness of this 'natural' world,
the world in which all things come to be (Fr. 1) is said to be fire:
2) Physics, 185 a24.
3) Physics 185 b8-9.
4) Metaphysics 1005 b19-26
�- 31 -
I
u All
' things are exchanged for fire and fire for all things,
just as goods are exchanged for gold and gold, for goods."
(Fr. 90)
How can such an exchange take place? More fundamentally, in what
sense does Heraclitus understand the relationship between fire and
ta pa~ta, that is, ta onta?
If
of
of
us
we were to accept Aristotle's judgment, fire would be the matter
all existent things, the persistent substratum of the manifold
things
rivers, mountains, clouds, plants, and so forth. Let
listen to Heraclitus:
first of the transformations of fire is sea; and of
sea, one-half is earth, one-half, fiery storm-cloud."
(Fr. 31)
19 The
Three terms are given in this fragment: sea, earth and fire (the
fiery storm-cloud). Their relations may be schematized as follows
(following Kirk, The Cosmic Fragments, p. 332):
Fire
r
le
~H ~ r-\,<f u
I
lff VJuff] f
Sea
r
Earth
The right-hand column is based on the second half of fragment
thirty one:
"Earth (following Kranz) is melted into sea (or, as sea)."
One additional fragment must be taken into consideration here -with what seems to me, following the persuasive arguments of Kirk,
(op. cit., p. 343 ff.), a necessary emendation:
�- 32 -
nv r-1s &:v:.•oV' 1<~ F1[!' .,~5 ·1
IJ\/ TfvfO~ ff~vci1.To-;J u~wf )·yi Tb\/ c:H fOS
rr v ro s &J....v~To ,., ) a~ , o "
os .
55
n-Cf
\
I"'
\
<_I (
I)
cJ. .-.. T
"Fire lives the death of earth and (air lives the death of
fire), water lives the death of (air) fire, earth (lives
~death) of water."
(Fr. 76, in the version of Ma.ximus Tyrtaeus.
Cp. Fr. 36 in which air is not mentioned.)
Deleting the mention of air (which seems to have been added by the
Stoics in order to bring Heraclitus into line with the traditional
four-element cosmology handed down by Aristotle), we are left with
a cyclical description of the transformations of fire in which the
change from one 'element' into the one immediately next to it in the
schematism above is metaphorically represented as 'living the death':
the disappearance or dissolution of one element or world-mass coincides with the appearance or formation of its successor.
Nonetheless, fire is given a pre-eminent role in both Fragment 31
and 90 (the exchange of all things for fire). The fragments
already exhibited make it clear, I think, that this pre-eminence
is not to be associated ~nth material causality in Aristotle's
acceptation, that is, fire is in some way actually transformed into
sea, thus beginning the cycle which eventually turns earth back
into fire. This 'eventually' cannot .be emphasized too strongly,
for it indicates that the process of the tropai pyres takes place
in time; in other words, fire is not the actual material constituent
of all existent things at all times5); rather, all things are
eventually exchanged for fire and, reciprocally, fire is eventually
exchanged for all things. (This description, however, does not
intend that the complementary processes be understood as consecutive (as in the Stoic £101 (· ~ i.v(ft. ~ interpretation); instead, both
the way down (fire-sea-earth) and the way up (earth-sea-fire) are
always going on at the same tims.) Consequently, another sense
must be found for the pre-eminence of fire in this fundamental
cosmo-logical process; this requires a discussion of the cosmos and
the logos as revealed in the transformations of fire.
Fragment 90, which provides the most explicit statement of the
relation between fire and 'all things 0 , furnishes an essential
clue to the manner in which a cosmos can come to be out of the
-----------~~-~,-~-------------
e
5) Fr. 67 ( LI Wf-J. l'a\ ) presents special difficulties; I feel sure,
however, that it does not fit in with the notion of fire as the
material substratum of all things, even though it might be said to
be the substratum of the process which comprehends all things. Cp.
also Plutarch, Consolatio ad Apolliniurn 10, 106E (Kirk, op. cit.,
p. 135) where Fr. 88 is cited. The Heraclitean fire is obviously
confused with the image of gold and the moulder of forms in Plato,
Timaeus 50 A-C.
�- 33 transformations of fire. The exchange of fire and ta panta is
analogous to that of gold and goods; in the later case, however, we
know that the value .received is equal to the value given, that is,
so much gold purchases just so many goods, and vice-versa. · If the
analogy is strict, there should al~o be some equality or proportionality governing the transformations of fire. Fragments 30 and
31 remove all doubts concerning the intimations of fragment 90:
< > s:)."- tfo~
")(;,
!i,l
fl~
~V
I ,. . , o/.
fo
v
i
7_ {,,
IJ
I () V
.. dL~'/Jt:lil
A 6<J v ) 1>' Ko ... o s
yo
~
.
r~Vtc(£r-ZL
~ •
/4~1 J\L<i.TfttT~
IT A? o
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J. 8 '- v
L
"Earth is melted into sea and is measured out in the
same proportion as before it became earth."
(Fr. 31)
"This cosmos (Weltordnung, Diels), which is the same
for all, no god nor man has created, but it always was
and is and will be, an everliving fire, kindled in
measures and extinguished in measures. 99 (Fr. 30)
The logos which supports the hen-panta dialectic in the material
world-order is thus revealed as metron -~ measure, or, taking into
account one of the meanings of logos itself, proportionality. The
cycle of the transformations of fire accomplishes itself in a
measured, that is, orderly, fashion, so that the dissolution of one
world- mass coincides with the formation of an equal or proportional
0 measure 0 of its successor.
The 'measuredness' of these transformations is responsible for their unity: because all things are exchanged for fire, and vice-versa, according to the same measure or
p~oportion ( .A ~o o s ) and because this process never stops ( rru p
~t f J i.v o"
), the 0 collected 0 whole, which is the successive
manifestations of the measured changes of ta panta, is the cosmos,
that is, the world, the comprehensive order of all things and the
activities they perform.
I cannot disagree more with Reinhardt 0 s interpretation of the
meaning of cosmos as "ein bestimmter Zustand, eine Phase dieser
Welt in Gegensatz zu anderen 1<-.rf6' fA-- o <...
, anderen Phasen,
vergangenen oder zukunftigen. (Parrnenides, S. 174)." It seems to
me that the emphatic eternali ty of the cosmos ( 1<60 fUJ v 1 ;vJf.
)
and its uncreatedness establish it as the unique and enduring world
order, although within it the manifestations of fire are continually
�says:
L. '
Fr ..
~
o <:)
as
\
os
that is
f,
o .s
, there
s
�as the
, sea and
the measures'
opposed to one
and, hence,
It would be well to
s
Heraclitus says:
is opposed (
together) is
and
from things that are at variance with one another comes
the most beautiful
and
come to be through
(Fr. 8)
�s
where war
is
�some sense in a
says:
way
...,
~
£L
L
d~ Vd..L
~L~
&-~'
'
'
To
'L
it
/
E o vT a....
no
I
't. v' cl_
\Td, VIJ..
s
-?
<..5
u
o
'7)
l'--o\ T )
war is common and
come to
that
have
,.,
\
sun
exceed its
if it does the
the servants
search after it and find it out.
The
the
of the
is the intention of this
If we take the
of the sun
the
the
makes some sense but
however, we call to
the antithesis ~1
"' J.. I
and think of the sun's exceeding its
£"urpoV1"'J
measure of
be
to
in the summer,
the
is
here the
function as
to
Now that most of the fundamental relationships or
this phase have been exhibited, it is
to
some
more specific examples of this 'harmony' of 0 opposites 0 in order
to come to an
of the oneness of the real that
supposedly emerges
four
of oneness
come to
in
�found
the hot grows
becomes wet
and
one and the same.
way of the
s
is
motion of the fuller's
towards a
end
con-
��.d-.,
\<'-a',
"
-,
0 v
,..~c
are whole
the concordant
oneness comes from all
oneness
t...
c
0
winter and summer
is
surfeit and
05
war
sense of the
The
the later
-- God as the
Whether
s is the sense
when the nature of '
all
here and
The one and
to be called
wise
the
is
observances and
the
god of the
and does not
Fr.
the
seems to
What Heraclitus seems
of most human reof the
in some ways
�cosmic
correspondence it
associated
Therefore
\
0
says:
such a structure
which variance and
its source in
therefore, there must be a wise
the cosmos and it is to this
name of
, if
under-
arts or
is not
such as an artisan
is,
the intelligence that 9 fits things
is looked upon, then, as
source of human
enables man to bring an orderly
is this same ""'""',.·"
the cosmos.
0
....
�7
0
ever is
�wise to
cosmos:
v
was
3
and scornful references
::::.
�ETOL
J
c;\11...
occurrences of the
connected
see ..
of most men is
together
remarkable
in
-- an
of these
they do not
make them one ..
to
encounter
c.
0
/
C'
0
OOd..
5
men
awake escapes the notice of other
what
do when
.. 1)
moreover
from the
What are the consequences of this
all men's deeds and
the
�those who are awake responsive to the
is one, common cosmos, but each of those
to
turns
Along with deafness
as those who are asleep 11 seems
to have been
reproach of the
The sense
here and in fragment
is that each man creates in his
a
world unrelated to the world of the waking.. However, it is
precisely this latter world which the
maintains and holds together which,
not be a
if
for the
1
Nhat is more, the common cosmos is
as a
the strife and contrariety which is everywhole
in it; on the
the world of
the
sequence of fantasies
no inner
there is
order into the confused images
then,
the true
like the
It is not to
with the
nature
hotrever, that
necessary if men
nature of the world
into the nature
one
the
not
one will not
the
since it is not to be searched out and is
Fr .. 18)
If we must
a subject to the
seems
the wisest choice. IJfuat is meant then, is that
tractable
and contention of all
one to
structure which knits
whole,
s, one would not expect to
Consequently, the evidence of the sense is not
it
one to see some forms of the
of opposites, but
especially not the most unexpected -- the invi
For
other clues or
�for who have
many
who
to
not
awareness
is
the name of the bow is
We are not
its work is
here
1JJi th a mere
is an
sense
s
is clear
�rather~ the true
the
of the words
To such connexions we must have our
utterance
one another is no mere
it is
art
cleverness with
as a cosmos ..
most at variance
of
on
of the same
Thus
, more than the
than the continuous
life
more
summer and Tuanter
cohere
all Greeks that
to all and as
With this
is
and of
common become
furthermore is common to
much the same
as the
the
in
the fact that
follow what is· common..
the
live as
(..,
with sense it is
what is common to all,
as the
with even greater reliance. For
nourished by one
For it
wi
is sufficient for
above.
Fr .. 11
But
�overtake
�proper
does the 0 fitting-togethera
remain hidden; the specific
as
until it is
what is other than it. All
of this
to me but
se to
50 of
which manifests itself in
with what the
attempted to show in the
existent
itself in
and as the
�Jessica
that wear rags
make their
that bear
their
are nowhere
pursue what he
s not
fend a
every
the basic
and
he feels and to
he is free to express
if he
On this level, man is
and wit necessary to secure and de ...
among the
�the active element of
the
is
The
�nature
mutinies; in countries
and the bond
twixt son
the natural
unnatural force of evil
of
own
and act wisely in
circumstance
He must see that,
the attainment of that
to the mandates of the
of his own
S to any
not the master,
own ruin ..
on man's fortune:
a
He must be aware
external
of nature
and
.J..l.J....l..!.l.\AlJ,\:iv
He
wit,
the
and the rain
content 1iiiith his fortunes fit
........"', . . . "" . . . the rain it raineth every day ..
With
natures is
s role in the total
To
The
the substratum, they
use
to
obligations on that
nature bond of
the
act of the
' I
of nature
�the love Lear
to advance themselves as ruthless women
of the burden of a
them his land, he says:
we
The name and all th 0
10
to the
and Goneril are
obligated to
father, their king; but they
not
his knights,
he had demanded.
of those titles in the
necessary and
to
o-wn wishes. Thus they
of nature wi. th the powers allotted them in the substratum under
But
the dictates of their
natures. They are evil
of
s rejection
they are not
Goneril sees the
of
He
loved our sister
and with what poor
hath cast her off
Not
are they aware of the
but they use its weakness to their own advantage ..
Lear at the very
their own
Vision, then, even in
men,
them to mould their own
fortunes. Shakespeare paints such a black portrait of these two
Lear off into the
out Gloucester 9 s eyes
he sees the force of evil in human nature as
the most
in the Natural Order.
of
also contributes to the
their
in the tragedy ..
not
that
vision
that
rashness:
The
of Oswald and
are also
I
think, worthy of
the
Let us
as the agent of his mistress 9 s
Although it may be
argued that, in
true to his mistress, he
s his
ti.on as servant in the suprastratum, one cannot forget the fundamental obligations to honor courtesy, and devotion as a
subject that he betrays in siding with
, being of
less wit and power than Regan, is also an agent of his mistress~s
evil nature.. He expresses their evil use of
to
the
order of
suprastratum when they are about to
Gloucester's eyes
�me
All with
structure
have
I can
5
the
�is one of
with the
is
that when we
surfeits
of
9
The first
mind,
but
have vision. She
the devotion
harm she
is
to circumstance:
to Lear in the
but rather
in a fruitful
I
out frown
s
�and Kent seem to me
to
merry.
as a
man.
in
him
Kent is
on the
••None but the Fool
The
is
the substratum
He says to
ne 0 er fear to
se
have that
your countenance which I
would fain call
That
se
Here we
of nature. His vision
comments to
on
�thou art
me who I
seeks for
for
to rain
in the storm.
But I
The
Gloucester
he is
action of the
If I
The
as no
master
work the means
To make
so much
�gods
to wanton
they kill us for
He
to a crowd
in a
blaze his
of nature
but
says
I have no way, and ther~fore want no eyes;
I stumbled when I saw.3b)
master, in
character.
for the
view of the
in
cuss later
has
nature
although his final
is not a blind statement:
of
time we
we feel, not
we
Let us
s
this flaw
natural forces
is of the
as
trusted it
So blind was
in
of nature beyond that level, that
extreme cruelties of
and Goneril
of the force of
in human nature) and the fiercest tempest
of the most fundamental power of the
the total vision of nature
control of his fortune to save him from his
fall
the moment he
fall from the words of his own
0 most small fault,
How ugly didst thou in Cordelia
my frame of
Let
�was
frame
nature in its
was
in the suprastratu:n of nature
He was· King i;\rj_th power and
possession of all his country men paid tributes to
told
him he was
up v-Ji th all his whims, and shmrnd
respect to every aspect of his being. Ideally he was
as
because his person was every inch a
But
idealistic view is a blind one. If all men were good, if they
all selflessly used the qualities allotted them in the
to support the suprastratum, this idealism would be the
But in the
of nature, every man is out for
and in the
natures of men, the force of evil
s basic
the
pampered
was not aware
of
He idealistically, blindly,
the natural. course of events.. He had
than his other daughters, but when she
avowals of
he
ected
the crucial moment, he relied on the outward
known and
He was
to the
He was as blind to the ruthless condition
of nature as he was to the
natures.
was
his
to nature
made
s
so
By
From
Here
the
of the orbs
cease to be,_,
care .. J9
prey to foul fortune as
natures of Regan
Goneril
substratum of nature. In the above
Gloucester, expresses the 77 excellent
by
fortune to the orbs above
He
is
fact that the operation from whi 'L he exists and
ceases to be is that of nature; the
·virtue of which
he is born, the suprastratum in
he has t;.
and his
own individual nature which brings on his
t.:T1r::::,: _cin ..
to nature is his
fault; so nature
be U1e
ect of
his
1
1
of king in the supraoccurs simultaneously
in the
, he was so fixed in the
we have
so unaware, that
the other
by
forms could he
of nature in
, he
When he is
the cruelty of his
to m~n°s
sh and evil
is
l'J2ver
instincts, he could not foresee their trcJ.tmont of
showed him, he
questioning the causes of the
always accepted it at face value as genuine respect for his noble
He is
rather than for his
and
says:
and baffled by Regan's and Goneril's
�11J'Or se
than
murder
such
of nature
s reaction
and we know that
Doth
Save
When is
Natural
any cause in
The answer to the
is forced
and that
When the rain came
1rJhen the thunder
I
�I am even the natural
see
of fortune
that men meet
in their natures.
the force of
I
as the cause of
nature
that
We see
our nether crimes
realizes that there is an
nature; he
the
of
force of
, well mv-are that
is clear when he says
Know thou· this
that men are as the time i
when he is
sins
see that evil men can
of nature the
that
out
in the
escape the ~n,=~·~
source. No human
Lear says of this:
breaks
to men
for his
our
us
where thee
vices
cer
�and Goneril kill each other on
of their deaths is
Yet
the evil
nature is seen
However
in this
when Lear cries out for
at the end of the
have
should a
, a horse,
And thou no breath at all
the
as
the
fe
The good are
that we must remember
vision, if he is both
has every
to live
rat
virtue of his
if he does
is
him from the
have to live'? I feel
............ . . , ... _,_ ng the
Order
nature 0 s
It is at this
If a man
in nature
not have
for bethe form
if man were not
Lear s blind exi
It would have been
Lear himself
this
men
- ,, ·:::t•xre have upon
in the
witl1 the
clone by means of the awesome
of human existence and action.
of
man. In
- : demands
threatened by the challenge of a
to be
through their understanding
Man is a
proelements of the substratum of nature.
tects
the construction of a
in nature.
existence in the suprastratum raises
high above the other
creatures of nature. Man is the
creature. In his
nature is
forces of nature.
and Goneril s
��22
25 ....
26
28
29 ..
II, scene i,
Act I, scene i
scene ii, 11..
6
Gentleman, Act
scene vi 1 • 20 -203
Kent, Act I scene i 11 155-157
scene
11 26 and 28
. ..
I, scene iii, 11. 1 17
scene i,
line 158
.. Fool,
scene
1
183-185
220 ... 221
, scene
11.. 76. . 83
" ....
III, scene 111 1
7
II scene i, 1 ..
»~
scene i, 1 ..
11. 9-20
..
v, scene
.. 324-325
Act I scene
257-260
. .
.
32
33
J4
35
36 ....
37
.
38
3
....
.. .. ..
Act
Edmund, Act
Act I,
Lear
Kent
58
....
"'
scene
scene ii,
�SOLITARY TOUCHING THE SECRET PROCESSES
From Francis Bacon
Laurence Berns
One question that
arises in connection with 'the
between the ancients and the moderns , concerns the
role of sense
in the attainment of scientific
to Bacon, and in contrast, accord
to
One text of Bacon's which I have found
in
reach some c
about the issue is not to be' found in
popular selections
the market.. It is from the
98 .. The
the
reliance on
reliance on
to say that
Bacon Aristotle was too
, and therefore
; he relied too much on
.) The more interes
question it seems
to me, concerns
views of nature and the relatic•:J: of man 1 s
mind to nature that underlie these differences.
98. nThe
of man hitherto hath been determined
the
view or
; so that whatsoever is invisible, eitLer in
of the fineness of the
itself, or the smallneBs of its
, or of the subti
of the motion, is little
yet these be the
that govern nature.
and without which you cannot make any true
dication of the
of nature The
or
that are in all
bodies, are scarce known. Sometimes
whereas
are the most A'~tive
take them for air; :Cro!Il ·which
, as
as
water
from earth. Sometimes
will have them to be ~atural heat,
or a
of the element
fire; whereas some of them are
crude and cold. And sometimes
will have thme to be the
virtues and
ties of the
which
see;
whereas they are
by themselves. And then, when
come
to
and
call them souls. And such
, that
inward, when
• Neither is
this a question of words, but infinitely material in nature.
For
are nothing else but a natural
, rarif ied
�as were
et
seen at alL
if you
you
a number of
within the
before, pass bet'<Teen the
as
at all handled
natures
existence is
, for no one
reason
�
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The Collegian
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Text
T HE
C OLLEGIAN
tv.iA y _JUNE 1964
�C0 N T E N T S
A Rational Extension of the Fifth Book of Euclid 0 s Elements
David Stephenson, Tutor.
Poems
. . . . . . . . . . . . . . . . . • Charles G.
The Gnomon:
.....
Bell, Tutor •
7
A Note on the "Knowern. • • • • •• Eva Brann, Tutor ••• 10
Fear and War or Fear and Peace?
*
*
...
*
*
• Andrea Jacobson,
*
*
Editor • • • • • • • • • • • • • David Lachterman
Business Manager • • • • • • • • David Rasmussen
Editorial Assistant • • • • •
Susan Roberts
Faculty Advisor
• • • • • • • • • Eva Brann
9
65 ••• 39
�'
·.. -r
•
It is my sincere hope that the Collegian has been of
value to the community during the past year.
My endeavor
has been to present the best writings from every area of
the Program along with outstanding independent work.
In
addition, an effort was made to encourage creative writing,
specifically in the medium of the short story.
ness of the response to the announced
0
The meager-
Short Story Contest 0
led me to give greater credence to the oft-expressed complaint
that the requirements of the Program enervate literary
energies.
In the hope that the summer vacation might witness
a revival of those energies , Miss Brann and I have decided to
ext end t he cont est unt il t he first week of the coming school
year.
Stories may be submitted to either of us through the
college mail.
The prize is still $20.00 for use in the
Bookstore.
DAVID LACHTERMAN
�A RATIONAL EXTENSION OF
T~E
FIFTH
~OOK
OF EUCLID 9 S ELEMENTS
David H. Stephenson
"!
ratio is a sort of relation in respect of size between two magnitudes
of the same kind. n "When of the eouimultiples, the multiple of the first
magnitude exceeds the multiple of tl'-~e secc.:-id, but the multiple of the
third does not' exceed the multipl8 of the fourth, then the first ( ·.~agnitu~)
is said to have a gr~ater ratio to the second than the third has to the
fourth. "
-;-- -In comparing these two definitions, one cannot help but be struck by the
·comparative adjective "greater" ( /'-'i ({c:- Vrf.. ) applied to ratios, for it
presupposes that ratios themselves have size. And if they have size, is
it not possible to determine a ratio of ratios consistent with Euclid 9 s
fifth book?
Definition 7, quoted above, is apparently included by Euclid to giv~ a
name to one class of ratios which are not the same, but also to distinguish
this class from the other class of unequal, or rather nnot samen, ratios.
That is, given any ratio, there are innumerable ratios other than it, and
these fall into two classes: those which Euclid would call greater than
it, and those than which it is greater, i.e., those less than it. These
three classes, the same, greater, and less, could of course have been
distinguished by adjectives without quantitative connotations, such as
same, light, and dark, Therefore the use of the word, "greater;t, to
describe a relationship of ratios implies a common conception of them in
some way akin to the conception of magnitudes.
This kinship can be explained in two ways. · First, Euclid and his con. temporaries may have felt that in the case of ratios to the same, as in
propositions 7-10 of Book V, the relative size of the two antecedent
magnitudes obviously determines the relationship of any two such ratios.
Thus a greater magnitude should be said to have a greater ratio to the
same than the less has. Since all ratios can ·be compared by finding
proportionals to the same, they can be called greater, less, or same
according to this reasoning.
.J
Secondly, the definition of ratio quoted above.implies more about the s"ze
of a ratio than 1 is immediately apparent in the translation. In particular
t< 1'T ~~ ff 1:I /~ l K o 17! ,-(x , which Heath prefers to .translate "in respect
of sizen gives insufficient indication of what kind of relation between
two magnitudes con$titutes their ratio. There are two possible ways in
which the size of two unequal magnitudes can be basically compared: one
can exceed the other by a certain magnitude, or one can be a multi?le of
the other, Regardless of any ambige.ity in the term {t-11)L.1c..~11·/ <;
,
Euclid could not have meant a relation with respect to difference of size
as in the former comparison. Therefore a ratio is in some way dependent
on the ~u~~titpltcative relationship of two magnituaes.
This is clear in the case of number3 and commensurable magnitudes, so that
Euclid does not bother to define either ratio or greater ratio for numbers.
Such magnitudes (or nUJ.'nbero) obviously have rati.os 'greater than, the same as'
or less than each other according as th- first antecedent magnitude contains
e
more, as many, or fewer pnrts of its cons$quent magnitude than the other
antecedent contains of its consequent. (That is if the parts taken are
�- 2 -
equal to the largest common measure.)
Moreover the definitions of same and greater ratio for incomrnensurables
in Book V hardly differ at all from the above definition for comrnensurables.
Definition 5, for example, can be restated in the following way:
Magnitudes are said to be in the same ratio, the first to the second and
the third to the fourth, when the first magnitude contains as many parts
(submultiples) of the second that the third contains of the fourth for all
equisubmultiples of the third and fourth.
That this is equivalent to Euclid 0 s definitions is evident from the fact
that according as the multiple M of one magnitude A exceeds, equals, or
is less than another multiple N of a second magnitude B, the first magnitude A itself must exceed, equal or be less than a multiple p of a part
of the second magnitude B, ·where the part BQ is the same submultiple of
the second magnitude B that the first magnitude A is of its multiple M,
and P is the same multiple of BQ that N is of B.
In modern notation :
if mA ~ nB then
~ nB = n
~
m
M - - - ·----·--+-------.
A
/If----+---
B
m
A------
13
- ·---T-
---r----
({
But this means that the relationship of two ratios is determined by the
relationship of numbers of parts of the consequent magnitudes contained
by the antecedent magnitUdes. If the numbers are the same for all equisubmultiple parts then the two ratios are the same. If in some instance
the nu.~ber of containable parts in the first ratio exceeds the number in
the second ratio, should we not say that the first ratio is larger than
the second? (This is equivalent to Euclid 0 s definition?.)
Although the above arguments are implicit in Euclid 0 s Fifth Book and are
justifications for his assumption that ratios have size, they also point
to other similar asaumptions which Euclid nevertheless refused to admit.
For if the fact that ratios have size is deduced from the quantitative
relationships between magnitudes or numbers inherent in different ~atios,
then their nrelation in respect of size" , viz. the quantuplicative
relation of these ratios should also be prescribed by these numbers or
magnitudes. So it should make sense to speak of a multiple of ratios or
a ratio of ratios.
Ratios of Ratios
Consider the following ratio of ratios: (A:B):(C:B) and the ratio of
magnitudes A:C (A,B. C therefore being of the same kind). Then if A
equals C, it is immediately apparent that (A:B):(C:B)::A:C since A:B::C:B,
therefore A:B has the same size as C:B, i.e., the magnitude A:B equals
the magnitude C:B. By dint of the com..mon notions equimultiplesof equal
magnitudes are equal; larger multiples of equals being larger than
smaller multiples. And Definition 5 establishes the above proportion.
�- 3 However if A does not equal C, (A:B):(C:B) may be greater than the same
as, or less than A:C. For instance, assume (A:B):(C:B) exceeds A:C for
all A greater than C. Then this is true in particular when A is itself
a multiple of C. By Euclid~ s De±;inition 7 there are equimultiples -- say
W;X of A:B the same multiple as K of A, and Y:Z of C:B the same multiple
as L is of C, -- such that i:v:X exceeds Y:Z but K does not exceed L.
Symbolically depicted:
W:X::(A:B + A:B +
K= ( A + A +
... + A:B)
...
+
A )
> (C:B + C:B +
<.. . ( C + C +
... + C ) L
... + C:B): =:Y:Z
Then since A is a multiple of C so is K. But K is less than or equal to
L. Therefore L is a greater multiple of C than is K, or else L and K are
equimul tiples. Whatever multiple K is of C let that multiple be taken of
C:B, and call it P:Q. Then K and P:Q are equimultiples; so are L and Y:Z.
Since L exceeds or equals K, Y:Z exceeds or equals P:Q, and 1~:X must
exceed P:Q since it exceeds Y:Z. Let S:T be the same multiple of C:B
that A is of C. Then since K and P:Q are equimultiples of C and C:B, they
will be equimultiples of the equimultiples A and S:T. And W:X and K are
also equimultiples of A:B and A, so W:X and P:Q are equimultiples of A:B
and S:T. Therefore since W:X exceeds P:Q, A:B exceeds S:T.
Hence a necessary condition that the ratio of two ratios (with the same
consequent) exceed the ratio of their antecedents whenever the first antecedent exceeds the second is that the multiple of a ratio be always less
than the ratio of the same multiple of its antecedent to its (unmultiplied)
consequent. That is, if (A:B) :(C:B) > A:C for all A.greater than C then
E:F > G:H whenever E is the same multiple of some magnitude K that G:H
is of K:F. (Algebraically, E:F: :mK:F > m(K:F): :G:H for m > 1)
It also follows from this that if A is less than C, this condition requires
that (A:B):(C:B)
A:C. In other words (A:B):(C:B) exceeds, is the same
as, or less than A:C according as A exceeds, equals, or is less than C.
Such ratios exist already in Euclid's work: the duplicate ratio or ratio
of the squares on two magnitudes, for example. Thus since the duplicate
ratio of A:C does exceed, equal, or become less than A:C as A exceeds,
equals, or is less than C we might simply equate or define the ratio of
two ratios having the same consequent, (A:B):(C:B), as the duplicate ratio
of their antecedents, Duplicate (A:C). But any such definition pr esumes
the necessary condition stated above concerningmultiples of ratios.
<
Such a condition raises the following question: when one ratio is greater
than another, h£:d: ~ greater is ii? The multiple of any magnitude, including ratios, is so many times (viz. double, triple, etq.) as great as
the magnitude of which it is a multiple;. if then one ratio is a multiple
of another, the larger ratio, considered as a magnitude, must be so many
times as large as the smaller.
To answer this question is it not most consistent to continue in the
direction begun by Euclid in the seventh definition of Book V? That is,
as was pointed out earlier in this article, Euclid's assumption that a ratio
can be greater than another is based on the fact that some magnitudes (in
the limited sense, i.e., excluding ratios) numbers, or multiples of magnitudes are greater than others. In particular it probably struck Euclid
as obvious that, as proposition 8 states, '~the greater (magnitude) has to
�- 4the same a greater ratio than the less has". This proposition along with
the preceding one therefore imply that the relative size of two ratios with
~ ~ consequents i§. determin~d 2:z. the relative size of their antececten'ts.
And thus a ratio R:S, where R is a multiple of another magnitude Q, is as
much larger than Q:S as R is larger than Q, i.e., R:S is the same multiple
of Q:S that R is of Q.
Accepting this as a logical consequence of Euclid 0 s definitions and propositions, one must also agree that (A:B):(C:B) is not greater than A:C for
all A greater than C and less than A:C for all A less than C, because we
have just proved that this would require that for any R a multiple of Q,
R:S must be the same multiple of Q:S, and the ratio of the multiple R of
the antecedent Q to the consequent -- (R:S) -- was supposed to exceed the
same multiple of the ratio (also R:S), which is impossible.
With multiples of ratios so defined Euclid 0 s propositions in Book V can be
easily proved, and in addition the following four propositions relate
ratios of ratios and ratios of simple magnitudes.
-
Pronosition 1
.
The ratio of two ratios having the same consequent is the same as the ratio
of their antecedent magnitudes.
That is given any A,B,C, magnitudes of the same kind (A:B):(C:B)::A:C for
if not (A:B):(X:B) is greater (or less) than A:C. Hence if greater some
multiple of A:B, say P:M, exceeds another multiple of C:B, say Q:N, but
the first multiple · of A, say K, does not exceed the second multiple of C,
say L. But since K and P :M are equimul tiples, P :M: :K :B. Similarly
Q:N: :L.:B. Hence K:B exceeds L:B and by Euclid's Proposition 10, K exceeds
L, which contradicts the hypothesis. Therefore, etc.
Similarly (A:B):(A:C)::C:B
Q.E.D.
Proposition
~
The ratio of the ratio compounded of two ratios to either component ratio
is the same as the other component ratio; and if the ratio of one r at i o
to a second ratio is the same as a third ratio, the first is the same as
the ratio compounded of the second and the third. That is given any six
magnitudes A,B,C,D,E,F, such that (A:B comp C:D)::E:F, I say that
(E:F):(A:B)::C:D and (E:F):(C:D)::A:B.
As Euclid demonstrates in Book VT., to any three magnitudes a fourth proportional can be found (provided the ratios of these magnitudes can be
expressed as ratios of straight lines). Hence let A:B::K:L and C:D::L:M,
where K.L,M are straight lines. Then (A:B comp C:D)::(K:L comp L:M)::K:M,
and so K:M: :E:F. By the preceding proposition (K:M:(L:M): :K:L and
(K:M) :(K:L): :L:M. Therefore (E:F) :(C:D): :A:B and (E:F) :(A:B): :'C:D. Again
let (P:Q):(R:S)::T:U then I say that P:Q::(R:S comp T:U). Obviously from
the above if (R :S comp T :U): :V:W then (V:W): (R :S): :T :U, hence
(V:W) :(R:S): :(P:Q) :(R:S) and V:W: :P:Q. Therefore (R:S comp T:U): :P:Q.
Q.E.D.
•
�- 5- .
.The sum of two ratio$ having the same consequent is the same as the ratio
of the sum of the antecedents to the consequent. That is, given any three
magnitudes (of the same kina) A,B,C then (A:B + C:B): :(A+ C) :B.
Since (A:B):(C:B)::A:C then by Euclid 9 s Proposition 18, Book V (which it
is easy to prove for ratios as magnitudes) . (A:B + C:B):(C:B)::(A + C):C and
by the preceding proposition (A:B + C:B):: ((A+ C) :C comp C:B): :(A+C) :B
Q.E.D.
These three propositions in effect define ratio of ratios and addition of
ratios and also redefine compound ratio as . the inverse of ratio of ratios.
That compounding also corresponds in some way to multiplication of numbers
is evident from the next proposition.
Proposition
±
If four ratios are proportional, the ratio compounded of the extreme ratios
is the same as the ratio compounded of the m~an two ratios.
That is: given four ratios A:B, C:D, E:F, G:H such that (A:B):(C:D)::(E:F):
(G:H) I say that (A:B comp G:H)::(C:D comp E:F). Since it is possible to
find ratios the same as the above with either the antecedent or consequent
prescribed, it suffices to prove the follo-wing:
if (A:B):(K:B)::(B:L):(B:M) then (A:B comp. B:M)::(K:B comp B:L)
But this is immediately apparent since (A:B):(K:B)::A:K and (B:L):(B:M)::
M:L, hence A:K::M:L
Alternating according to Euclid 0 s Proposition 16, A:M::K:L. Therefore
since (A:B comp B:M)::A:M and (K:B comp B:L)::K:L (A:B comp B:M)::(K:B compB:L)
Q .E. D.
Ratios and "Real Numbersn
The fourth and last of these propositions closely resembles Proposition 19
from Book VII of the Elements. Someone might well ask, how are ratio and
number related? And the ·startling answer is that ratio is number and number
is ratio, al though in a somewhat larger sense of 99 number" than Euclid was
familiar with. That is, ratios are the same as the nposi ti ve real numbers' 7
of modern mathematical jargon.
All numbers are 77 relations in respect of quantuplicity, as are ratios.
"Threen means nothing other than the relation with respect to quantuplicity
of three things and one thing,* it cannot exist without a unit. (Even for
Euclid "a number is a multitude composed of units.") The distinguishing
characteristic of numbers is that they are relations 'With respect to a
* Used as an adjective, of course, the number attributes this relation to
the noun it modifies.
�- 6 single and non-arbitary unit.
17
An unit is that by virtue of which each of the things that exist is
called one." Things are called one, moreover, by virtue of a relation,
namely ~ relation 1.£ respect £.!: quantuplicity between ~ thing ~
itself.. Something is called one virtually because it is the same as
itself.
Therefore the unit is in fact the ratio in which antecedents and consequents are the same. Euclidean numbers, i.e., integers, are multiples*
of this unique ratio, or equivalently by our previous hypothesis, the
rati,o s of multiples of any magnitude to the magnitude itself.
Besides the integers and the unit, the real numbers include the so-called
0
rationaP~ and "irrational" numbers.
The former, as their name implies,
are ratios, distinguished from the latter by the comrnensurability of
antecedent with consequent. The '9irrationalsn, (in the modern sense of
the term) are also ratios, but ratios with incommensurable antecedents
and consequents. Although neither rational nor irrational numbers are
multiples of the unit, they do relate to it quantuplicatively since the
ratio of any real number (i.e., ratio) to the unit is the same as itself.
For example, (A:B):(C:C)::(A:B):(B:B) since obviously C:C::B:B. And
(A:B):(B:B)::A:B. Therefore, (A:B):(C:C)::A:B. FUrthermore it can be
proved that ratios as real numbers, ill 121£ show an isomorphism with the
points of a line, that they are continuous, and that they are distributed
copiously among the integers.
If Euclid had not chosen the word 0 greater" to describe one class of ratios
not the same as a given ratio, and implicitly the word "less" to describe
the other class, if instead of greater and less he had chosen to call
them light and heavy, masculine and feminine, hot and cold ratios, these
conclusions would be inconsistent ~dth Euclid 9 s thought. But he did
choose that word. Therefore it is consistent.
Q.E.D.
* something can be multiplied without reference to number simply by adding
to itself.
�- 7FOR
HOUGt~TAGANDIE
Charles G. Bell
Even the Romans in the decadence
That heaped the fallen world i:Ni th monuments
Of their gloom, and when the bitterness of sex surprised them,
Loved it, sought it, prized it.
And from fabulous shade of the Dark Ages,
Out of crypts and cloisters, rise nameless voices
Avowed monks on their knees inclining
To the dear socket of a girl 0 s inturning.
Our own forbears, sanctimonious Puritans,
Warmed beds with bundling; staid Victorian
Dames, under bustles of silence, veiled the same fesses,
Smooth, indented, thighs spread for caressing.
Body, naked, cloven, supple, swaying
Here while the great cloud waits in abeyance
At the sun's horizon, shall we not mate and slu.mber,
Our foldings wreathed:on the leaves of Indian Summer?
�- 8 - .
THE NEW FALL
Charles G, Bell
17 Triste, triste is the fall, the sad fall,
With wind and mist and leaves that fall."
(Victor Hugo, who was, alas,
The principal poet produced in France.)
While we, in a culminance of gold -Tulip and oak, sassafras, ash,
With wine and scarlet of dogwood and gum,
And the filligree of creeper and thorn -We, stripped to the skin, in rivers of sun,
On .the hilltop stand, and cry the love
Of these twined selves and earth that moves
To the waste of winter by a turning road.
W swear the rapture of this new world
e
Is the sun°s seizure on flesh of the fall.
�- 9 ..
ON THE SHORE OF BIRTH
Charles G. Bell
I wake from a cruel dream:
Odysseus, brandishing the blade
At the threshold of sleep,
Drives back the spirits
From the pool of blood,
Seeking the prophet.
I, clawing through dark
To the spilled sacrament
And wine of force,
Tear sleep with my cry:
"Odysseus, stern guard,
Put back the sword;
I am he; let my tongue
Blossom in speech. 01
I wake, my mouth filled
1Ni th the salt reek of blood.
�- 10 -
~
nrNDMQN
I
�- 11 -
THE GNOMON:
A NOTE ON THE "KNOWER"
Eva Brann
I.
II.
III.
IV.
V.
VI.
VII.
Shadows as Images: the Astronomical Gnomon
Images as Tools: the Geometrical Gnomon
Tools as '7Knowers": the Ari thmological Gnomon
THE SUNDIAL AND THE ORIGIN OF CONICS
THE SUNDIAL OF VITRUVIUS
Notes
(Correction§ to AN ANATOMY OF ORBITS, April Collegian]
The gnomon,rival in interest to the canon (Collegian, Suppl., November 1962),
appears thrice in the mathematical texts of the freshman year: in the fall
in Euclid (II, Def. 2) as a geometric shape, in the winter in Nicomachus
(I, 9) as a numerical scheme and in the spring in Ptolemy (II, 5) as an
astronomical deyice. "What do its forms have in common and why is it called
Uthe knower" ( 0 '!"
wv
' from 'f \.'I v ~ en< H v., to know)?
wr
I.
Shadows
~
Images:
2
Astronomical Gnomon
"Proper people usually take their shadow
along when they go into the sunH.
Chamisso, Peter Schlemihl
It is among the wonderful facets of the visibie world that every solid body
under the sun casts a shadow. To be exact, there are two sorts of bodily
shadow, which Leonardo da Vinci, whQ was fascinated by . this appearance,
called "primary 71 and naerivative".1; The first belongs to the body itself
and is a consequence of the curious fact that bodies, in their opacity, stand
in their own light, just as they hide the larger part of themselves from
sight (whence the eye and the sun are often compared; in optics this leads
to the notion of visual rays -- cf. Euclid, Optics, D~fs. ).• , Therefore their
surface, or as the Greeks said, their ~'apparencyH ( E\fLc\'o..v £ .LCA..
)2J
always has a bright and a dark side. In the ancient world, which still
lived under one primary source of natural light, this was an overwhelming
fact. Greek pot-painting, for instance, -- a craft humble and popular enough
to permit us (as go classical text ever does) to speak of the predilections
of "the Greeks a-- · testifies to this. Athenian pottery, which was produced
in tremendous volume and sent to the ends of the known earth, used two
basic techniques, the one belonging roughly to the "archaic~' sixth, the
other to the nclassical n fifth century B. c. Archaed)logists speak of them as
"black-figure~'J) and nred-figure" respectively. In the former technique,
the figures of men, boys, horses, armor , girls (listed in descending order
of interest) and other paraphanalia are put in rich black glaze onto the
bright orange ground of the Attic clay. Therefore they appear to be seen
against the light, as schemata, as flat, sharp, black silhouettes, slimmed,
as they would be in nature, by the encroachment of the light around them.
In the later technique the reverse is done -- the figures are "reserved" out
of the black glaze covering of the pot. Therefore they appear as if the sun
were full on them, and, being nourished as it were by light, are generally
larger than the black figures, while the addition of black interior contours
gives them a more substantial look: Leonardo aptly called such body shadows
�- 12 ...
"the expression of body ;~ . Their use w elaborated by Greek painters into
as
a technique called n shadow-painting" ( o- v.. l £A y f o.. ~ (. ~
) , a species
of trompe-1°oeil which makes the image look more natural than nature; it
is often cited by Plato as the .very paradigm of the art of illusion.
(e.g., Republic, 365c, 52JB, 58JB, 586B, 602D).
But the two grandest and most instructive examples of all such shadows
were, as Empedocles taught, the darkness of night, for
11
Earth makes night by standing under the rays . of the sun
>
,,.
r....
,.,
/c;,.,
c tf)
,,
/'
/
( vu V:.TC\ a~ yQ.Lo.. ·nv1crw V\LO"Tyt.vll\ ~o...££0-0'1..
n4)
'-~€:Atov5>),
and those amazing phenomena after which the sun 9I s own circuit was named the
}
'\.
"circle of light failure~' ( £.~A£L"tt1Lv,05 V<VK/\o~) - - the eclipses.
* * *
*
*
However, the sort of shadow relevant to the gnomon is really only the second,
the cast shadow, which the painter, considering it as darkening another body ,
calls 0 derivativen, but which is , taken in itself, a very peculiar kind of
image.
As an image, it is first of all natural, like a reflection (Republic 510E),
and inseparable from its body, being its g 'doppelgaenger ~': O-\kLD. b..n [oTolx "S
as Euripides says, (Andromache, 745). Indeed, the ability to produce a .
shadow is the very sign that a thing is a proper body among othe:r bodies;
it is at once the warrant and the effect of its substantiality.5J Secondly,
shadows are negative images, images by deficiency, in which that which is
visible in surfaces is almost entirely absent, nfor what is seen is color°'
....
'c,
.l
,,..
( 10 yo..e OfQTov
£.oTL ?( f w /-L~
- Aristotle, De Anima 4 18a29 ) •
To this kind of shadow tooJthe first accounts of the cosmos are indebted,
for as soon as failures of light in the heavens were recognized as shadow
phenomena, the outline of the earth could be seen upon the moon, and from
its phases could be inferred its character as
~1 a
night-shining borrowed light, ·wandering about the earth"
tr f.
y~1°" v t:..>-. µ.. c v 6 v ~AA6'f'-OV ~ ~s
<"' u v.., L~°'" ~')
ft.
).
w
1
Parmenides, Fr. 14.
But the most honorable function the cast shadow has ever served was to be
admitted to-t~lace shown. in this diagram of the metaphor for the road to
being ·iXl the Republic ( 507ff.) :
eye
--+
(
thought ---)
shadow
body
(
(
mathematical object
being
sun
<
good.
The properties of shadows which fit them to be the sensible representatives
of mathematical objects are just those described above and developed below:
shadows are schematic consequences of the shapeliness of bodies, preserving
as natural images a certain truth even under deformation: they are the
lightless witnesses of all visibility, more easily consulted about its ways
•
�- 13 than is its dazzling source itself -- and so they are to the eye what
mathematical objects are to thought: the nether aspect of being.
* * *
*
*
*
The third characteristic of the cast shadow, namely that it changes in length
and direction independently of the body which produces it, is that which the
astronomical gnomon particularly exploits. These changes are so fixed and
familiar and so much more easily observed than the course of the sun t~thts~1
(the s\4.y ·'1b<tf is names after the shadow
( o ~ L ct l
its clouds cast -Partrid~e~ Origins) that the reversal of their progress becomes the very
signal of God 0 s special concourse · "Behold, I will bring again the shadow
:
of the degrees, which is gone down in the sun dial of Ahaz, ten degrees
backward. So the su.n returned ten degrees, by which degrees it was gone
down" (Isaiah 38: 8, II Kings 20: 11). The gnomon, by which shadows are
observed, is a thin upright, set up so as to cast a slender, neat shadow,
whose changes with the hours and seasons can be closely w ~t-c\.J.td. A gnomon
may be no~r· more than a stick in the ground, but it can also be the pointer
of a sundial with carefully calibrated base, or even a tall obelisk-like
official monument.6) Such instruments were often called "shadow-viewers 0
( O-V.t08t'\f
Q
).
The first skiothera are said to have ~een set up in Sparta by Anaximander in
the first half of the sixth century.71 One of them seems to have been a
sun clock ( ~ f o v-v. . o\\ce..l.ov) Wf o Xoy £.L ov ) to tell the hours of the day.
It seems fitting enough that the Spartans,
then in the early days of their discipline
with its many public occasions, should
have been the first to want a public
clock. Later on most public places must
have had one; the Athenian market place,
for instance, had a very large public
water clock-sometimes also called ·>
"gnomon" (Athenaeus IT, 42b, but usuallyS)
97
~A f. i' 0 J f Cl.
- - nwater stealer ) .
The name gnomonics came to be applied
by the Greeks and Romans to the flourishing practical art of dialling generall~,
and particularly to· the construction of a great variety of sun clocks (see
Vitruvius_IX, 8), among them some with inclined rather than. upright pointers,
such as the one which may have occasioned the early study of conic sections,
described in IV. below.(lndeed Kepler thought it a fact that gnomonics 77 begot
for us the geometrical doctrine of conic sections -- Eoi tome, p. 20.S.)
But
the first and most ubiquitous gnomon was always a natural one -- man, the
upright creature (Aristotle, ~ 2f Animals 653a31), talking away the
morning as his shadows waned:
These three houres that we have spent,
Walking here, Two shadowe?s went
Along With us, which we our selves produc'd;
But, now the Sunne is just above our head,
We doe . those shadowes tread;
And to brave clearnesse all things are reduc'd.
The theme of the human gnomon will recur.
* *
*
*
*
*
*
�- 14 -
The gnomon in its properly astronomical function depends only on the shadow
at high noon.9) Its construction
is, of course, identical with that
of the sun clock and one fundamental
diagram serves both, as iri V. below.
The principle on which it works is
that of a projective image. The
gnomon°s vital part is therefore its
shadow-casting tip, called by the
Romans its ~'navel'? (umbilicus) .
Because the earth is to the heavenscn~
as a point (Almagest I, 6), this tip~
be taken as the center both of the
rational and of the sensible horizon.
Thereupon the upper half of the small
circle ·drawn about it in the northsouth plane serves as a miniature
m
eridian of the heavens, while the
part toward earth may become a sensible quadrant, measuring the elevation
of the sun. Hence in the gnomon 9 s tip
coincide the center of the world and
a kind of cosmic eye on whose. retina
(the dial) the sun°s motions are projected in reverse (such projections
through the center of a circle or
sphere are r1 cw called "gnomonic " ).
while the gnomon itself, by blocking
the sun°s rays toward the earth, produces the shadow-index distinguished
by us. The interest that the ways of
such travelling markers exited is reflected in the [Aristotelian] Problems
(611a14ff.): "ivby is it that although the sun travels at a regular pace the
increase and decline of shadows are not the same in an equal period of the
time?" (La., why, in the figure of V.} is RC less than CT?); also 912a34ff.-It is:--curious and significant thought t hat within t he Copernican system the
gnomon projects the earth 9 s ow motion onto itself.
n
a. What motion of the sun does the noon shadow given off by the gnomon
follow? Anaximander, when he furnished the Spartans with a sun clock, seems
also to have installed a gnomon 11 to signal solstices and >equinoxes" (Diogenes
/
Laertius, ·II, 1 -- the Greek, more appropriately, says Lcr~~.JA<c...f 1..-- 0.5
-'7 equal days") .10) In our latitudes
the. shadows of the culminating sun
get shorter toward summer, come to
a standstill (solstice) and then
grow longer again, being of the same
length both at spring and autu.~n
equinox. These seasonal changes in
the shadows of the culminating sun
are perfectly familiar even to primitive peoples, who use gnomons as
•
�- 15 agricultural calendars.11)
But if the observations are reflected upon,they
yield the idea of a second solar
motion, independent of that of the
heavens which carry the sun through
its hourly and daily path, namely a
gradual ascent and descent between
the tropics (turning points), taking
place in a direction opposite to that
of the diurnal circuit. The gnomon
shows the total arc of the north-south
motion to be about 11 of the meridianvs
83 parts or c. 47°40°. This is the
eeliptic . . . /, t"'1 its obliquity, the great
dtversifying circle of astronomy.
Although Ptolemy uses two different
· instruments for obtaining the obliquity which he carefully describes (Almagest
I, 12), the various men who were credited with this great discovery, Thales,
Anaximander and Pythagoras in the sixth and Oenopides in the fifth century, 12)
were all associated with the gnomon also (see II. below), and the gnomon
was certainly instrumental to it.
b. But there is yet something more contained in the gnomon's shadows.
If the dates at which they reach their various places are carefully kept, it
is found that the time from spring equinox to summer solstice is 94t days,
but from summer solsti.ce to autumn equinox 92t days (Almagest, III, 4). This
discovery was ~ade by Meton and Euktemon in the latter part of the fifth
century B.c.13; Such an irregularity of the sun°s motion would scarcely
ever, I imagine, have been noticed, had it not been for the gnomon. For
no eye. can directly follow the path of "the· heaven 11 s 2lorious sun that will
not be deep-search 0 d with saucy looks" -- as it may~the planets. Thus the
gnomon brings down the image of an anomaly whichJonce known, becomes a prime
stimulant to the formulation of those rationalizing hypothesGs which were
_
the chief preoccupation of technical astronomy in antiquity (cf. Almagest
III, 3).
~~o~
c. Not only the sun's motion in the heavens but also man's place under
the sun is ·indicatea by the gnomon' s shadow. Vitruvius (IX, 1) says: "It
is due . to divine intelligence and a very great w
onder to all who r efl ect
upon it, that the shadow of a gnomon at the equinox is of one length in Athens,
of another in Al-exandria, of another in Rome •• ·"· Even more impressive
as a direct index of the diversifying effect of the sun's obliquity are the
varying directions of the noon shadows. So remarkable has this fact always
seemed that the habitable zones of the earth are characterized lby the
directions· of their shadows: ~ 'These [the temperate zones] ·are alone habitaple while the regions beyond the tropics · are not, for the shadow would not
fall to the north, while it is known that places become uninhabitable before
the shadows cease altogether or change to the south [i.e., south of the
summer tropic J ·, and the regions beneath the Bear [above the arctic circle}
are uninhabitable because of the coldi1 (Aristotle, Meteorologica, 362b6ff.).
So that according to Aristotle,men can live only in the temperate, 17 heteroscian ':
( f. H.- ~ o- v.. L C?S
- "other-shadowed 0 ) latitudes, while Ptolemy admits
1 parallels down to the equator ( II, 6; see also
also the :'amphiscian ~
Copernicus, II, 6); Kepler also was fascinated by this way of identifying
o
�- 16 people and quotes ~nth relish some
lines by Lucan remarking that the
shadows of Arabs are all sinister in
direction, which he explains in the
way 'bhe figure shows (Epitome, '.P• 205).
In the more accurate determinations
of geography nastronomical and shadowviewing instruments 99 are indispensable
(Ptolemy, Geography II, 1). Ptolemy
OiAi\ s'-"a- explains that while t~e heai'ens turn
c>.ow1 ~o'\-.oabout us ( t\£el~o-\wv V\f'\~S ),
...;1t\.\t. pv-or< so that we easily manage to see a great
I (.ft
part of it, the earth cannot be
Kcr~r
travelled over and surveyed by one or
even several men; one of the obvious
consequences is that to locate themselves on earth 1-ne."' must, strange to say,
take their bearings on the more accessible heavens. In fact, the grid of
our terrestrial maps is still a projection of celestial circles. (The figures
in V. will show ~"'"'~""-~' "\\'f how the length of the equinoctial noon shadow
immediately gives the latitude above the equator.) It follows that each
parallel is associated with a ratio, that of the gnomon°s height to the
equinoctial noon shadow (Almagest II, 6). In order to calculate this ratio
the Pythagorean theorem is necessary, and it ·is perfectly possible that the
gnomon problem invited its solution -- as we will see in III.'· the gnomon
·is first and foremost a Pythagorean affair.
·
1
O'ri£.e
<;i<LOVVl{~n c:. S\VV\'tle...~'•t'{
i!.
VV\c\-trstooJJ
d. And finally the gnomon car1.1,..be used to make large-scale measurements
of size. Diogenes Laertius (I, 27) reports that Thales measured the pyramids
by using himself as a gnomon, "having observed0 when it [the human shadow]
.
is ~qual in size to us 9 ~ ( na~C1..1~ ti~c-o v1~ OTi.. q _,,u.-2v tcro_rf.y£3\ \ ).14)
This story is a good one on several counts, first because the thought of
Thales outdoing the Egyptians, who are supposed to have been the Greeks~
masters in practical geometry, is a
nice one, secondly because it seems
so characteristic that a Greek, coming
from a country where buildings were
built to human scale,15J should apply
this scale to these Egyptian monstrosities, and last, because it is
a literal exemplification of man as
•
------~----'
measure. o\~ o \0r'j~\" .s<:o\t>Eratosthenes
S""CAc\ow o\ 0bdi::.V- =hei~\.ir.
(third-second century B.C.) used the
gnomon to measure the size of the earth itself. The method is as follows:
S is Syene, a city lying under the
summer tropic;
A is Alexandria, under the same
5
meridian but north of Syene,
0 is the center of the earth.
~
I\~
l\
tttaun
/
/
'
\
I
t
0
)
Since the sun is very far awaYJ its
rays strike parallel to each other.
At noon of the summer solstice they
�- 17 -
strike the gnomon at A at angle a, equal to 70030° or one-fiftieth of four
right angles. Arc SA is known to be equal to §,000 stades, angle AOS to
angle a. The whole circumference is therefore equal to 50 x 5, 000 or
25,000 stades = 24,662 miles.
* * *
*
*
*
*
We have looked at the gnomon as producing reflections of daily time, of
celestial motion and of terrestrial extent. Of these works, time-keeping is
the first and greatest. At least Anaximander, the supposed discoverer16) of
the gnomon,must have ascribed to the measurement of time the greatest office
possible. In his one extant fragment17) he makes time the assessor of the
penalty of destruction and the recompense .of return which things owe to
each other for the outrage they have committed by abandoning the common
pool of the boundless to come into being. But if the world 0 s changes occur
n according to the command of time ;; ( Vdl 10. .,-~ v To G XJ 6 vo u
TC:t t..V
) ,
then in keeping time men discover that order.
~
Plutarch explains why men are favorably placedfor time-keeping. In the
eighth Platonic Question (Ch. III), discussing the passage in the Timaeus
which relates how the demiurge sowed souls, 1fsome in the Earth, some in the
moon, some in all the other tools of time" ( ·O' ~yo.. vo._ /(f 6 vov
-42D),
he asks w
hether this means that the earth too revolves, for all the other
"tools of time 11 are planets. His answer is that it is best to think of the
earth as standing still, thus 'wproviding those bodies which revel ve with
risings and settings by which the first measures .of time, night and day,
are defined • • • For the gnomons of clocks also act as tools of time not
by changing positions along with the shadows but by standing still, thereby
imitating the earth's blocking ( -r o £it LIT f o ere> o Ov ) of the sun as
the latter revolves about the former H (There follows the Empedocles
.
passage quoted in I.) Evidently Plutarch interprets the earth's role as a
tool of time to be
complG.mentaq to that of- those parts of the heavenly
clock which 0 have the epithet 'wanderers' 9 ~ and which were made for the
enunciation ( cJ Lo ~Lo-r 6v ) and keeping (
~ v .Ao. v-. ~ v
) of the numbers
of time i1 ( 38C). For tne earth, by nopposing itself to the sun '~ brings
about the first sensible effect, the first reflection, the first measured
measure of time. Thus because it is t he home of shadows , those movi ng
images of time -- just as time itself is · a ~?moving image of the motionless •918)
(J7D5) -- earth becomes a measure-taker, while the planets are measuremakers. Hence it is here on earth that images of the heavenly clockwork
and i~struments for fetching its motions down to earth are made.
II.
Images
~ ~:
~Geometrical
Gnomon
97 truste wel that alle conclusions that
han be founde, or ellys possibly might
be founde in so noble an instrument as
is an Astrelabie ben unknowe parfitly
to eny mortal man in this regioun, as
I suppose."
Chaucer, A Treatise on the
AStrOlabe
This same Anaximander, signifioantly the first writer of a book of the kind
�- 18 -
entitled in later references 110n Nature n ( 1\ ~fl. ~ ~ c.r ~ w 5
),
not
only "invented the gnomon • • • and was the first to draw an outline of land
and sea, but also to build a sphereu ( t. -i('.)~V Ji v,a~ yvwJ.Aovv.... qpw\05 •.•
'
""'
'(\
\ ~
<"f
\.i
. ) \ \.....
,.{)/"'
\
/.
V,O.l 'fV'\'J V~C.l VO.ACt.<70~1 ) 1~£.f~U~:rcov 11\WIO~ t.yfl.4. ft..J c/i.l\AC>.. ~£A\: 0-\0l.Lfc'.AV
V,QTf.0-V....LUV..0-(-Dio.g. Laert. , II, 1-2). These are the basic tools of' the sci enc es of heaven
and earth. They all share an apparently simple, but on reflection very
questionable character -- they are in some way models. By a model I do not
here mean something that may be talkedabout like this: "This is only [!]
a model, the real atom contains nothing of the sort" (Eddington, The Nature
of the Physical hTorld, Ch. IX, speaking of Bohrg s model of the hydrogen
.
atoffi}.'" These instrlimental models are rather to be regarded as true images,
which~ before they are put to use as instruments of observation, can serve
as teaching models, as '1visual aids" for acquainting the student with the
rational structure of the world.
I
"""\
)/
All ancient astronomical instruments that I know of embody some such part
of the universe~~the descendent of Anaximander 0 s sphere, the .astrolabe, whose
construction PtoletnY describes in the Almagest (V, 1), is the most complete
in this respect.19) It coincides basically with the Pythagorean model
presented in the Timaeus (and here tt is of interest to note that Pythagoras
may have been Anaximander 0 s pupil 20 J ).1t consist)
of fixed "colures 11
.
representing hoops of the heavenly container acting as reference meridians
~;+_ . --------·.
and the band of the"other", the
~><-,.
zodiacal circle in whose center
~ ~/ /l
~ '
''\ \."
\
lies the . sun° s path, the ecliptic. 21 )
ll/
-~
The astrolabe, however, while i t
0
omits the axis and the earth wound
5
I/,'/ :J~I . ~
around it" of the Tim}an model'
I \~ v
adds
sliding P?inters
- .
~ ;
and movable mer1d1an and horizon
6
\\~~
~ ~2/"
circles. (Such index circles are
~.::::::::.
. 0 6l"' ¥
•
called •0gnomonic", Kepler, Epitome,
""'-~_!is--~;::i
7
/
p. 134). The whole is therefore
~
~ I / / ./
a skeleton of the cosmos, that
~~ ~/
aspect of the visible world which
'
~
· --_. . -.
it has in the reflective view, in
' \
'gtheory a (,. '3 ~ w f CC\..
, from
_
_
-9 ~ 0.:J f o _)
- ~ "spectatorH);_
,e-/y.r';/
Q
,
/k
J'
1 , . '.
u
/ ~/~/~I
~r
.
\\
J~~"\\
r)
- ~.\;
calibratio~s~
Here · arises an apparently simple-minded question. What need is there of
observation if the best parts of the world are already before us? This
question might elicit from the astronomer a most important fact. The model
which he possesses has, it will turn out, a different origin and a different
standing from the astronomical theory he is working on. He has taken it
over from the physical philosophers, who themselves used only the simplest
t ools to obtain it -- particularly tools like the:· gnomon_, which produce
natural images. The artificial model they have constructed does indeed incorporate all that is knowable of the world ~- its center ~vhich is coincident with the center of refl.ection, its roundness which is the only perfectipn
possible to a moving body, and its orthagonal and oblique principles which
act as sources of regularity and irregularity. However, this latter principle
gives rise to appearances not construable in terms of a fixed and timeless
structure, but only by complex moving diagrams. The astronomer 0 s enterprise,
-l '-"'e ,-e (~c r e ;
consists ~n finding such diagrams as will "save the
�- 19 appearances 11 , that is, as will show their irregularities to be merely
apparent by producing a geometric diagram which will account for them. But
since more than one such diagram can be produced, and since none are entirely
satisfactory, they remain mere hypotheses, quite different in standing from
the model, which simpl~ represents what is and which may therefore serve as
a guiding frame for fixing the aberrant appearances.
Yet even once the usefulness of the instrument is accepted, its very nature
remains a problem. The model,as has just been emphasized, is not a model of
the total world -- it seems to overlook some appearances, in fact most of
them, while it contains all sorts of parts no one has ever seen. It is a
model only of the world 0 s rational structure, of its geometry - but it is
also a sensible artifact, made of Hcircles accurately turned with four
perpendicular surfaces each", and existing in time. Is it not, then, a
copy of some pure model, a timeless paradigm which has been espied beyond
the appearances? Is it not rather the embodiment of the model for the world
than an image 2f the world?
The Timaeus presents a fantasy answering the perplexities of a model-making .
science such as that of the Pythagoreans. It shows that such a sciencecut5 a cros~
overlooks the world as a visible, appearing world and by going always to the
geometry behind it, avoids the only road which can lead to being, that which
confronts the contradictions of appearances as appearances. It shows further
that its principles of account giving lead to a hopeless confounding of
"before" and "after ~'. For wherever the human account is to be embodied in
a mathematical, i.e., rational image, the thing to be accounted for must
itself be an image incorporating a rational paradigm. But this paradigm
arouses the suspicion of having been construed into or placed under the
world by the human inquirer himself -- he may have taken his account of the
world for its being. Hence arises the following circle, in which ever;J
image turns into a model and vice versa:
noetic
natural
man-made
pure.model
- rational model
pure image
rational image
t
i
The Timaeus grandly stops this circle by decree: 71 • • • to which of the
two models ( tt
0.. d ~ ( \( _rc...n\..) did the builder make t\,e copy alike' to that
which is always the same with itself and alike, gr to that which has become?
Certainly, if the world is a masterpiece ( v< o. .A 05
), and the artisan
good, it is clear that he looked to the eternal (29 A) • • • And if this is
so, there is, again, every necessity for the world to be an im~ge of
something. The great thing is for ever;Jthing to begin according to its
natu.ral beginning . ( O.f ~ ~ v ) • Thus concerning the image and its model,
we must bring out distinctly that accounts are like in kind with those very
things which they expound. Accounts of what is stable and strong and belongs
to thought will clearly be stable and incontrovertable • • • whil~ acpounts
of that which images that model, since it is itself an image ( E- L v.. o v o_s ) ,
will be but likely-likenesses ( f~ v.;. 6 T"t 5
) , being like the former only
by similitude'° (29 B-C). 'What we must not forget is that Timaeus has introduced the very account which is to follow as a 70 likely myth 71 ( z:.t Kw)
, r J ~ 05
29 D 2), so that i t is, by the criterion of this passage, an
Ctr
�- 20 -
account of that world which is made in the i1uage of a sensible model -- and
the Timaeus itself turns out to be the likeness of a cosmologist 0 s guandar'(.
One more reflection on the principles underlying the use of instrumental
models: as instruments of observation these ancient tools are of course
deeply and significantly different from those which most captured people 0 s
imagination at the beginning of modern times22J, namely the telescope and
the microscope. For the latter are extensions of sight beyond and below the
range given by nature and take the observer 1£ objects beyond his scope -for instance, in his Starry Message, which announces discoveries made through
the "spy-glass~', all tending to assimilate the nature of the heavens to that
of the sublunar regions, Galileo says: '°It is a very beautiful thing, and
most gratifying to the sight, to behold the body of the moon, distant from
us almost sixty ·earthly radii, as if it were no farther away than two such
measures 97 23); the very name of the treatise, Siderius Nuncius, which has
the alternative interpretation, countenanced by Galileo, of Starry Messenger,
implies that the observer has been to the stars. The astrolabe, on the
other hand, fetches the star to the observer, as the name b.. O-T eu >. ~ f1 o v
o~yCAvov - the ~'star-fetching tool" (Ptolemy1 Geogr. II, 1) implies. Thus,
for instance, in giving instructions on sighting with the instrument, Ptolemy
says: "the star, as if stuck to both surfaces, is sighted on the opposite
side • • • " (V, 1). The rationale of this might be said to be that the star
to be sighted actually becomes part of the astrolabe, being itself, as an
appearance, a mere fore-sight, serving to line up .t he instrument. What is
really observed is not so much an appearance, as a reading on the instrument,
the numerical stuff of a geometric diagram (at least. in theoretical astronomy).
The readings will be accurate because, except in the case of the moon, the
sensible and the rational horizon coincide and thereby make the center of the
sphere a portable little epi-center of the world, which the observer may at
once be at and look at. Kepler, who was deeply interested in the 97 sphaera
materialis 11 (see Note 21), particularly in the reason why it could be used
even .in a heliocentric system, explains its character in just this way. The
material sphere, he says, is an Heffigy of the world, such as our sight
imagines for itself; it is made in such a way that the theory (ratio) of the
prime movement and of movements dependent on it can be demonstrated to the
eye as with an instrumentn, and the earth is the 91home of eyes" (domicilium
oculoru..rn -- Epitome, pp. 101-10 2).
It is my guess that the disc.overer of the gnomon conceived the very earth
itself in the image on an instrument. Anaximander held, and was probably
the first to hold, that the. earth was in equipoise at the center of the world.
Scholars are therefore somewhat embarrassed by his notion that the earth is
cylindrical, lookin~ something .like a column drum of which we inhabit the
upper flat surface2 ) -- it seems so incongruous with his geocentric
spherical model. But could it not be that this cylinder is conceived precisely
in the i 'mage of a gnomonic column, an 71 analemma" (see V. below), the pedestal
of a gnomon? Could _ t not be that Anaximander saw the .e arth 0 s shape in the
i
image of that very instrument of observation which had shown him something
of the sun°s circuit?
* * *
*
*
*
*
To say,then, that instruments are rational copies of the world must first of
all mean that they incorporate geometric principles. But it means above
�- 21 -
all that they are constructed. Now the model-making activity is itself · in
want of tools; I mean tools whose function lies inbetween the ntheoric'°
tool,s discussed above arid the mechanical tools which literally do w~rk
( t f'f Cl. ) and therefore give their name to the whole class ( o ~ f o..vU-. ).
These tools must be a kind of embodied geometry -- we might call them
1
demiurgic tools 1' . Of course the Timaean demi urge himself, as a noetic
artisan, has no need of them, since their function is to guide the body and
to aid the senses: they nruleH the human hand so that it is not distracted
by the fits and starts of the body, and they assist the eye in answering
the questions ;'is i t straight?i 7 ,v~is it on the level?n, ~ 1 is it upright?:'.
w
The geometry incarnate in such tools is nothing else than Euclidean rulerand-compass geometry, a. because it i .s timeless, eschewing those shapes
·
·
· wh\CY. o.r~
·
.
w:h ose '. produc t ion is mec han1ca1 , 1.e. ,;\ prouuce d by th e mo t•
ion in t•
1me o f
interconnected rigid parts (for instance, it~ is reported that np1ato himself
blamed those • • • who reduced the doubling:the cube to a construction by
~e
'i"'-" l IA~_) l/\.Q l- )'A'\ J( fA.. V l V\ 4-s
means Of instruments and machines; 7
KC<-T~O-\Z~v~s
- Diels I, 429, 9; this is of course precisely the kind
of construction so fascinating to the seventeenth century, whose cultivation
issued in Nev.rton°s theory of fluxions; cf., for instance, Descartes Geometry,
Bk. II); b. because it is''preferential", always working from the special and
more 19 perfect 97 elements, such as the right line, the right angle and the
circle.
Now Proclus comments on Euclid I, 12, the proposition on the1 construction
f the perp~ndicular' and in particular' on its name - V\ v,o. v~ -ros
9
"'{ f CA
V\ '
~the line let fall (as a plumb line) UJ as follOWS:
H Thi S
problem was first investigated by Oenopides [ 5 cent. B. C.J , who thought
it useful for astronomy; he, however, calls the perpendicular, in the
archaic manner, [a line drawn] gnomon-wise ( V-..e>.r0.. ""'(V W/Ao V 0\. ),
because the gnomon is at right angles to the horizon" (Heath I, p. 271). This
Oenopides, who studied the geometric construction of the gnomon, is the
same man to whom the discovery of the obliquity of the ecliptic is most
authentically attributed (see I.a., above). But Proclus has much more to
say about the perpendicular; in fact he almost writes hymns about it.
Commenting on Euclid's Definitions X-XII of right, obtuse and acute angles
he says: "But the Pythagoreans take the solution of that triple distribution
back to principles and do not hesitate to define the causes of those
differences among rectilinear angles. In effect, since there are among the
principles on the one hand those w~ich reside in the finite, causes of limit,
of sameness, of equality • ' •• and"' one. the other hand the principle which
resides in the infinite ••• giving diversity to things, • • • one cause,
arising from the finite, produced the right angle which alone possesses
equality and similarity with every right angle, which . is determined, remains
al ways the same and admits neither increase nor decrease. BuL another cause,
arising from the infinite, which is inferior and of double nature, produces
two angles • • • which have an unlimited tendency to more or less •••• This
is apparently also the reason why the Pythagoreans refer the angles back up
to the pure causes of the divine arrangements • • • , for that which is
right • • • belongs to the gods .• n (Proclus, Commentaires .fil!!:. le Premier Li vre
des Elements d 0 Euclide, ed. Ver Eecke, p. 120.) And again: nThe right angle
is in fact the symbol of unyielding power which is united to equality, limit,
or boundary. It is for this reason that Timaeus calls the circle of the
other, which possesses for the divine soul the ratios of sensible things, also
0
rr
�- 22 -
right; for in our souls the circle is broken into fragments of every sort
and undergoes the various deformations which .result from generation, while in
whole souls it aintains itself intact and stable in the presence of sensible
things 0 (p. 249).
It is clear that the demiurge of the sensible model must gork with a carpenter0 s square, in fact, with the prototype of all carpenter 0s squares. This
tool is the very symbol of the builder 0 s
craft, providing by art those prime shapes
which our sublunar habitat cannot produce
by nature. The Greek word for the carpenter• s square was gnomon • Theognes,
in the mid-sixth century B.C., mentions
it along with two other such tools; he
says that the envoy sent to Delphi to
/
·,
consult the oracle should be yg straighter
than the 1 0 ~ ;v o 5
[ C<?_rnpass 1 , the ctr 0: '5 ~l V)
[ plumb-line 1
and the
'fV w ~ c.,;1 v
Lcarpenter 0 s square] n (Heath I, p. 371 ) • It
is, however, not knovm which application, that to the shadow-casting upright
or to the carpenter's squ.are, was the earlier; the Theognis passage above
appears to be among the earliest uses of the word in a text. I would guess
that the workman°s gnomon came first -- the builder wants to know that posts
are perpendicular and corners square and it is the plumb-line and the
"gnomon" that can tell him. ·
However that may be, the name of the tool was next transferred to the corresponding geometrical shape. For instance,
Aristotle, when he wants.to illustrate
that alteration is different from growth,
says that "the square, when the gnomon is
placed around it, grows blJt does not . ·
al tervr ( Categor':is 15a31 )~-')
Euclid seems
to have been the first to extend the
definition to all parallelograms (I, Def.
J): " • • • let any one whatsoever of the
parallelograms about its diameter with
the two complements be called a gnomo.n".
And last, Heron of Alexandria (Definitions,
58) defines the geometrical gnomon as· any
figure which when added to any figur·e
whatever makes the whole new figure
similar to that to which it is added; and he
goes even further: ·' "In general, a gnomon
is every addition whichj~akes the whole
well-proportioned ( £. u ~ "'( e/.\.A... 0 v ) or
a figure ( (T A\
n•
q r ().
.)
The scholiast, in commenting on Euclidas
definition, explains the existence and the
name of the gnomon thus: "It is to be
noted that the gnomon was discovered by
the geometers for the sake of brevity, but
the name arise.s from an incidental property. For from it the whole is known
�- 23 ( '{ v c-0 ~ ~) ~\C1..t ) - - either that of the whole area or of the remainder,
when the gnomon is either placed about it ( 'IT£ f LT \. i.9 v( T ~ L ) or taken
away. · And in sundials it only serves to make known the actual time 97 (Euclid,
ed. Heiberg, V. pp. 22.5-226). Presumably he means that from the geometric
gnomon one may calculate the number of an area, while from the .upright one
may tell the time. Ibes this do justice to the origin, the name and the
functions of ..the nk.nower'~?
III.
~ ~
7
~Kno'\ilrers":
~
Arithmological Gnomon
Gnomon:
know-man
Florio
The Elizabethan lexicographer 0 s jeu daesprit which is quoted at the head of
this section will prove to be more apt than the scholiast 0 s exegesis, for the
gnomona s name is no accident. (The once popular use of ~'gnomon 11 for
nnose"26) evidently alludes tq a similarly pregnant homonym -- as everyone
knows, it is often the nose that knows.) But how can the gnomon, or any
tool, be said to know?
a. Obviously the gnomon as throwing off a shadow pointer might be said
to know what it points out, while as a carpenter's square it knows the nright"
angle in the same way that a plumb-line knows how to find the perpendicular O.V'ld
a ruler can command the hand. So also,...rules of right conduct are called the
'°plumb7 line of l}fe 1;_ ( o- •~()/A~ (3 \.. o u
) or th~ "gnomon of moralsu
( 'J v vu/Aw v V\ ~ w v
- Diog. Laert. IX, 12). 27 J
b. There is in Greek, as in English, a use of the word in which it is
largely synonymous with the more popular word 9 ~canonP 0 • Iv\ o.. v ~ v
means ·
simply a rod (cf. "canev') used for keeping things in shape; for instance,
the staves bracing a shield are called
V, o.. v 6 v £.. 5
in the Illiad
(XIII, 407). Later it comes to mean a guide line or straight edge such as
is used by masons. Its assumption into the theoretical realm is best exemplified in the monochord, a calibrated sounding board displaying the geometric~l realization of ~ system of inteic,~~1s worked out by compoun?ing the
simplest number ratios, namely thoseAas~the Pythagoreans had discovered,
sounded as consonances when expressed in string lengths. The monochord
could be used theoretically for experimenting and practically for tuning
other instruments. The theory of proportions according to which the canon
was "cut 71 (Sectio Canonis), or any such system of proportions, came to be
itself called a 19 canonf', as for instance, the Canon of Polyciei tus, which
was both the title of that sculptor 0 s book on proportions and the name of
the statue which embo<
!ied them: ?
'Ch11tppus holds beauty to consist in the
proportion not of the elements ••• but of all th~ parts to each other, as
they are set forth in the Canon of Polyclei tus. n28) Thus the word ncanon°
came to designate the codified didactic exoosition of fil2Y_ theo:ry_, much as we
speak of 1'a theoryn or a 1'1body of knowledge 97 as if they were objects. For
instance, in the corpus of Democritus' works a logical canon ( IT'<.
AD"flV....W" '..<...c..vwv
- Diels II, 91, 10) is listed, just as later Aristotle's
logical writings were called the Organon; 9'The Tool 71 • Therein lies, of
course, the whole secret of this usage -- theory is here regarded as an instrument which, when mastered, makes a man expert. This is the use which
Vitruvius has in mind when, reciting the names of the great Greek theoreti~
rt
�- 24 cians, he says that "they left to posterity many things §Qncerning machines
and observational instruments (organicas et gnomicas) 0 • 2 J And this is the
use most agreeable to the moderns -- in the initial book of modern science,
called the~ Organum, theory is explicitly treated as a mental tool:
'! . • It is by instruments and helps that the work is done, which are as
much wanted for the understanding as for the hand. And as the instruments
of the hand either give motion or guide it, so the instruments of the mind
supply either suggestions for the understanding or cautions~ (Bk. I, Aphorism
II -- such books of aphorfms are precisely what the ancients called a
\\gnomo1 ogy'') •
,..
c. The Tables containing the records of readings are usually called
canons, for instance the various catalogues and tables in the Almagest, whence
instruments of observation in generaljinsofar as they yield lists of readings,
are called gnomonic or canonic. In this sense a canon is a handbook of information.
In all these three applications -as index, as theory, or as information, the
gnomon might be said to act as a tool of .knowledge. But how can there be
such tools and what is the manner of their action?
* * *
*
*
*
*
The possibility of the thing depends, it seems to me, on the possibility of
conceiving of reason itself as an instrument or of thoughtas being at work.
The notion that our bodies are tools, either our own or someone else 0 s, seems
natural enough since we can indeed feel oureel ves "pushing ourselves" or
being "handled 17 • And since the '° handiest ~', the most skillful part of our
body, is the hand, inasmuch as it can itself wield tools and also because i t
is our hand that feeds us,all men (except perhaps young men) do think of it
easily as the most : instrumental part of their bodies. But the body possesses
als<j 1 other tools whose very name means •'instrument", namely the 9'organs 0
( o p 'f CA. v t;.__
) of sense.
These seem, usually, to work effortlessly and
to produce nothing new but only to make us aware -- as we suppose in practice,
whatever our theory may be -- of what already is outside us. Among them the
eye seems to bring us the most variegated awareness and from farthest off.
(All these considerations can be found in Aristotle -- proof that they are
natural ; see N
ote 30).
But anyone who has ever thought or "used his mind", particularly if -though the
effort was great- he has found it blunted and undiscerning, finds it natural
to think of it too as an norgan 77 • Usually one of the two chief .bodily organs,
the eye or the hand, is chosen as the model in the image of which the reason
or thought is conceived. The Stoics are the great proponents of the latter
metaphor31) which is always taken more or less literally by those who choose
it .
Consequen 1 \ y · ""\ l things tend to be reduced tQ the tangibly
·
material, so that even sight may become a species of touch, 32) and knowing
itself is understood under the type of 91graspingn -- Zeno, the founder of the
Stoic school, is said to have been in the habit of demonstrating the meaning
of ;1knowingn by showing his open hand and saying, n 'A visual appearance is
of this sort; 0 next he closed his fingers a little and said, 'assent is of thi s
sort', and then he pressed his fingers closely together and said that that
was comprehension -- and from this analogy he gave the name, which it had not
had before, to the thing itself: catalepsis
[v...cx 1 ~ ..X V\ 't'S -c o\"\<e?t] • .... *'
(Cicero, Acacfmica II, 47).
"·
·
�- 25 Now insofar as gnomons are said to make figures ,,hold their shape ( (Jx._~ ,10-C{.. )
by acting as confining straight edges ( v<. et.. v o..; LS ) and directrices
( ~ .J ~ u \ ~ 1 £_5 ) -- this is in fact a second account of the name. given by
the Euclid scholiast (p. 226) -- they may indeed be said to "comprehend"
or "grasp ~ 1 their figure. And by reason of this grasping function they may ',
in turn, be used as the tools by which .reason itself can grasp figures. Some
such commonplace of exegesis ha~ presented itself to several of those who
have been struck by the name.33) And yet it misses the point -- for "gnomon"
does not mean "instrument for knowing" but ;'knower", and first and foremost
the human knower;34)(so, for instance, certain Athenian officials, whose
duty it was to inspect the countryside to see if the law against cutting down
olive trees had been violated,., were called _, 'V' v ~,,,)6\J £.<.) , -"\
Hmen who . are
{. .)
15 ,., , _}_
'"
strict because they know" - 6L CU<.~\ IC:.L) 0..\\0
OU
y vWVO..L - Etymologicum Magnum, p. 236).
* *· *
*
*
*
The Pythagoreans, however, understood their gnomon, the numerical gnomon,
properly -- according to its name. In a passage of the Physics (20Ja10-16)
Aristotle characterizes it, albeit incidentally:
~
" Again, they [the Py)thagoreans] think that the limitless (T6 Rif EL- \ CJ V )
is the even ( -re o.. \ 1 L ov
) • For it, even when it has been enclosed
( LvO.ttoA~~iA.vcJ:t.vo~ and limited by the odd ( eno \OW t\rLf\.\TOU
TT € \~\. v ~ /'Lt~ov
) ,/still brings to the things that are their ii-nclefiniteness ( 1() v ~ n- c;. l -f LCLV
) •
A sign of this is what happens in numbers.
For when gnomons are plac~d .around ( ~ £ f '- 1 '-Ci f. /4 e_ v o v
) ,
the one, the form ( -ro £.'\ cJ 05 ) is one, and without the one ( KCl~
,,
")( w t"' lS )35), i t becomes always other ( i. .\\ o & £ l. "( { 't v f. CJ v o.c ) ..
The main point of the passage is that the principles of "limit '' and ~' limit
less0 reveal themselves in an arithmetical form for the Pythagoreans. For
the successive odd numbers can be added gnomon-wise to the original single
unit, that is to say, they can be
placed around it so as to preserve
-· - - - - - - - -1
the sqnare. On the other hand, if
d, d ... cA. ""'1
successive even numbers ar e p l aced
- ---1 I
about the original two, this cannot
d. oi-. d... d, t
be done gnomon-wise (see Note 35)_,
- - ---i
t
i
and the proportions of the resulting
cA cl..•d- 1 , cJ..l:
I
.
rectangles change with every
addition (although they approach
squareness).
�- 26 Three particular observations must be made about the passage:
a. Aristotle does not explicitly say that the gnomon meant is the square
gnomon, but this is sufficiently clear 1. from the analogy with the geometrical gnomon which is primarily square (see II. above); 2. from Simplicius' commentary, who says!nThe ·Pythagoreans call the odd numbers gnomons
because when they aa:e 'p laced around square [numbers} they preserve the
same shape, just as"'th.e gnomons in geometry 91 (Comm. in Arist. Graec. IX,
p. 457, 1-3) and from Theonvs presentation, who generates the square number
no less than four times; 3. and most important, from the "table of opposites",
the list of contrary principles distinguished by the Pythagoreans, which
) and the "oblong" ( b·.ep 0)A- ( ""t) ends with 17 square~ 7 ( T~Tli 'jWvOV
Metaphysics 986a25).
·
b. Although the square gnomon is clearly the first and most important
(see c.), the arithmological, like the geometrical gnomon was later given
an extended meaning. For it is possible to reproduce ,,triangular' ~ numbers
as well, namely by the addition of rows of numbers increasing by one, a
reproductive addition which is properly speaking a
canon, a straight-edge. The triangular gnomoh may
even be said to have a certain priority (Nicomachus,
II, ?; Theon. p. 37, ?ff.) because it is the image
of the series of natural numbers, because the
triangular number is the first possible kind of plane
number, and because the triangle of four rows, consisting of the beginning one and the first three
gnomons, constitutes the ntetractys", the perfect ten (which contains all the
numbers whose ratios are the consonances36J, which is the very "nature ·of
numberu, and by which the Pythagoreans swore37~. Analogously, pentagonal,38)
hexagonal and all the succeeding numbers can be generated by gnomons, provided
only that the beginning is the unit ,
.
if it is two, nothing can be done to
preserve the shape.
c. Aristotle speaks of the ~. the figure or form of numbers, and we
have mentioned triangular, tetragonal and pentagonal numbers. What are these
shaped or "figurate" numbers? "It is the way ( ~~os
of the Pythagoreans
0 ')'f c-~t-(v
to draw shapes ( O"'>c_'l~o..\
)''says Simplicius (p. 457, 16).
Schematographia was the name later writers gave to the geometrical representation of numbers. This assimilation of numbers to geometrical figures,
still evident in our word "square numbers", is familiar from the Theaetetus .
In order to find one appe11ation for all commensurate numbers Theaetetus
"called square and equiiateral that number which can come about by multiplying
a number by its equal, considerinp it in the image of a square shapen (I~
CT)(ir~ &n£.\.K 0..e>o..v\~S ""\£yo...i-l,..\;)volf.-147E), the rest were to be called
oblong ( IT('o;-,\..~v,'i:.5 Cr)(~YC\. )l'i), and the sides or .ro~ts which could
square these oblongs are incommensurable with thos~e\o;~{ffie square numbers as
lengths but commensurable as areas, i.e., the root of the oblong with the
side numbers 2 and 1, nemely . '/"2, is incommensurable with other numbers as
a side-but the area upon it, namely 2, is com.~ensurable with them. The
crux of this correspondence is that it points to a class of geometric magnitudes for which there are no numerical counterparts, namely the sides which
square the oblongs, the irrationals, which can be made again commensurable
only by the "power:' of the square.
)
0
The Pythagoreans, however, understood their figurate numbers -- although they
�- 27 ranged them under the same · two heads of square and oblong -- in a way basically
different from that of Theaetetus. Pythagorean numbers are first of all
shapely. This appears in the fact that the extended class of the square
includes in principle all regular geometric figures, · while the Thaetetan
scheme, relying primarily on the ~ nature of figures, is confined to
rectangles of varying shape. The square number is the EB":ramount, numb e r-- sh a pe
only because it is al't'ITClys °'gnomonized" by an odd number~ f and i_p therefore
the very "sign that ·odd number is figure-producing ( £ L o o TI o Lo v
) and
limitative ( -rlEf c...""\t:.,rn K bv )" -- Simplicius, p. 456, 16. For in the
square the leading principle of the Pythagoreans, limit, assumes the character
of . the odd41); while the odd, in turn, appears in the square both as its
principie -- as the beginning one, and again in the consequences -- as the
series of odd gnomonic numbers, Where it is present, a number retains its
eidos through all changes of size42)j where the unlimited is at work, rect.::tneJ es
of infinitely many proportions arise.43)
Th•+ .:
u h"' +
•:- r n "' r.• .._ •
~
tu1l.....:; 1: be gai_d f-.() h!"'--V v
_eido__,
s
f'O rlll Or' figure?
It should' fir st of all t be emrJh::\_;.;j _r,;-,cJ that these numbers are int. cn1 l--~~ I · · . f.m
truly prior to their figure: ~ 1 from numbers carne points; from points, lines;
r:om lines' plane figures; from plane figures' solid figures: from so1 i_d
.
figures, sensible bodies."44) It is to this priority of rcd.ng' that the Euclid
scholiast refers when he says that the gevmel,,rlv grmmo n has its name Hby
analogy" ( &, ti 0 _Jv- f. \ C\ ~ <:> f 8..5
) , al though he has already~ just .as .;;orrectly
Observud +..h!l.-b. :i.-b u~ o d.Lo o . 1 V 1;-:;"1 "1 l·;f 1.}1 o<> 50<1111 Pt. CL"iJ (Hni.b crg. f'• 227, 3) •
Y\
l '...-. 1 "l
n. 1
HI).
r
0
0
The figure arises when the units composing the numbers are disposed nonlinearly as points in a plane. This means that there must be at least three
uni ts in the number and so t:the triangle • • • is the most original and
elementary form of plane number" (Nicom. II, 7). One of these units is always
regarded as the beginning of the number and is "potentially a triangle 11
(Nicom. II, 8) or a square,45) etc.; all the following numbers, nwhich
generate ( ~Tt'"O "{l(.. vvD vTct:.5
)46) the triangular, square and polygonal
numbers ~ 1 , , etc. are the gnomons.
The Pythagorean mode seems convincing
enough if one considers that all geometrical figures seem to include in
their determination some reference to number -- as is sh0wn in the name
"tri-angle 99 or "tetra-gon" -- yet the language of the commentators always
tends to give figure the priority. This happens in the very expression
"tetragonal number 11 , which, if the intended priority were to be observed,
should rather be "tri adie figure " . A particularly blatant case is that of
Philolaus (see belo r,.r) who on the one hand speaks of the decaa:ihe Hsource
and leader ~' of all things, and on the other, calls geometry the 11 source and
metropolis ~' of all of mathematics. ( lli.els, I 399, 26; 411 , 11).
Thus the
besetting Pythagorean difficulty concerning priorities (see II. above)
turns up once more in the thesis of the generation of figure by number.
* * *
*
*
*
*
It is the gnomon°s nature, then, to preserve the~· What kind of a thing
is it that can have such an office?
The fragments of Philolaus the
Pythagorean,47) the man with whom Cebes had studied (Phaedo, 61E), can throw
light on this question. The chief of these runs as follows (Diels,I.411,14ff.)
�- 28 r
'' The nature ( c\) u er '-_S / ) of number is to make · things
knowable ( . 'iv w ~ 1..Kc...._) and ts guide and ·to teach a_ yone
n
who is at a loss ( C'. f\ 0 \ ou )"- 'f.. V CJ
) about anything and
does not know something. 1
!or not one among th}ng9 would
)
be clear to anyone~ either-' itself ( n-o.>y .\ . ct uTo
or as it is towards others .( lT f
~AA 0
) , if
number were not, or its being. But .as it is, in fitting
( ~ ejv"- 'fa ~ C,.:)...; ) them to accord With the soul ( V<. 0-T\ avv I
~ u X o.., ·v
) it makes al}- of them knowable ( -y v (A) ~,-CA )
to sens~ - awar_ ness ( CA I. o 0V\. '! 'i:. L ) and conversant
e
( troT o...-yo ~c...
) with ,one an~ther according iQ. the nature
of ~ 0 knower 0 ( K O.\o. '(_VW rcve>S ~ 6 crLv' -Y::48)
making them into /bodies, and distingui·s hing . ( () .X: L ~ w v
)
the ratios ( /\ o yo v S
) of things both unlimited and
limiting -- each apart 0 •
os
Interpretation: nu.mber makes things knowable by its very nature. For
entering into those things which have the form of first principles, the
unlimited and the limiting things, it makes them bodies so that they become
perceptible to sense, and it also gives them their distinctive ratios so
that they can stand in numerical relation with each other. Thus it disposes
things according to the nature of CJ\:. knower, for the knower has a soul
composed of ratios.
The passage is full of allusions to Pythagorean doctrines: 1. limit and the
limitless are the principles of things and are to be regarded as their stuff
(Metaph. 987a13); 2. therefore things are made of numbers, the immediate
consequences of· these principles (987a19); 3. hence numbers constitute sensible
bodies ( 1080b16) ~ 4. The soul is a harmony, i.e., a compound of number
ratios (De Anima 407b27; Timaeus 35ff.); 5. like is known by like (Timaeus
37ff.). ~e other fragments all propose one or the other of these doctrines.
Concerning the last of these
(AgainsLthe Mathematicians,
that the logos distinguishes
since thelogosth~t arises in
(
. ) £.
{
w ~1
\L
v<. ov'
ship ·with her, if it
)
the following passage from Sextus Empiricus
VII, 92) is of interest: ~' The Pythagoreans say
[ is a K ~ L-1 ~ f Lo v] , but not generally,
mathematics is, as Philolaus says, contemplative
an~ seein3 the nature of the wholeJ has a certain kinnatural for like to be known by like. 0
Logos, it appears, had for Philolaus a double aspect -- it distinguishes and
it relates. This is precisely · what the fragment plays on. For number, in
distinguishing the ratios (logoi) of things, makes it possible for the. soul
to discern them and to give accounts (logoi) of them. This is why the
Pythagoreans ??who simply join number with the soul ~·~ call it the ~"discerning
'
~
n
tool of the world-working god" (V,fLru<ov Ko~,ou~'lcu i:)£ou of~a..v0v
Diels I 109, 29). But by making things into bodies it makes them sensible
and therefore available to sense and to the soul. And since the soul is a
system of number ratios, so must the bodies be "conversant" (11fco-<Ayor6'.) ~-;th.
or related to each other, i.e., they must have ratios (logoi) C\ W1on~ each· ·
other. Then they wili form a system of ratios or a harmony .and so tney will
become known to the soul as like to like.
n
It follows: as number makes things to accord with the soul, so i t make s
things according to the gnomon, which Philo la us, 9. u~ c \< to se.e o.. l\ v, e.11\ c.ss.J
�- 29 interprets as the soulas representative in the visible world. For as the
gives an ~ccount of nature so does the gnomon give proportion
( o. v CL A o "{ <- C\.. ) to a shape; , as the soul is the reason for the harmony
of nature; so is the gnomon the source of similarity in figures; · as the soul
takes to its like in world, so does the gnomon fit its figure; as the soul
embraces and binds body, so the gnomon delimits Rnd clasps number;-and so
both the soul and the gnomon ~re ~~~ guardians of €?l8~ , the looks of the
world.49)
·. . .
smy.
continued
Overleaf
�- 30 IV. THE SUNDIAL AND THE ORIGIN OF CONIC SECTIONS
O. NeugebauGr (Proceedings 2.£ the American Philosophical Society, XCII,
1948, pp. 136-138) $hows that the peculiarly restricted way of obtaining
sections in the pre-Apollonian theory of conics (attributed to Menaechmus,
c. 350 B.C., a pupil of Eudoxus) is accounted for if the study of conics
was first suggested through observation of the shifting shadows cast in
the course of a day by the gnomon of a certain type of. sundial.
In the early theory ( 1) only rio-ht circular cones, i.e., cones ·with axes
perpendicular to their (circula~) bases are used, and (2) the cutting plane
is always perpendiculru: to a generating line. The different sections are
then obtained by varying the vertical angle (see opposite page; cf. Collegian ,
October 1963, PP• 36ff.). Both conditions are present in the geometry of
the -- mathematically very convenient -- sundial set out on the opposite
page:
G:
GSO:
~ d:
-¥. ()\ :
GSn:
DIAL:
SfSnSa:
center of rational horizon but also shadow-casting tip of
gnomon GSn;
-- axial triangle of a right cone with vertex G and the circle of the
sun°s daily path as base; ---angle of the sun's declination, i.e., latitude above the equator;
verticle anglesc;f' opposite cones; since the maximum for ~J =23°51 9 ,
-}( cA. = 180°-2 cf is always obtuse;
the gnomon, a generating line of the opposite cone;
a cutting plane perpendicular to the gnomon;
a conic section traced out by the tip of the gnomon's shadow as the
sun progresses; the gnomon°s base itself forms the vertex.
Since the cone in this construction is always obtuse, the section will always
be a hyperbola, but the other sections are easily interpolated.
V. VITRUVIUS 0 SUNDIAL
A mathematical construction of a sundial is called an analemma, literally,
a "pedestal'°. (Ptolemy wrote a whole treatise non the Analemma", his construction is summarized by Neugebauer, ~Exact Sciences 1!1 Antiquity,
sec. 87 w
ith note.)
Vitruvius, the Roman architect, gives such an analemma in his Ten Books on
Architecture (IX, 7). The basic (observed) ratio, from which ~rest o-rthe figure follows, is that of the height of the gnomon to the length of
the equinoctial shadow (5:4 for Annapolis). The numerical latitude can
then be calculated (390N; for the method see Almagest II, 5). Vitruviusv
dial is marked only for the sun°s annual path. ~For construction see
opposite page, overleaf.)
---------
�J ••
Early Conics
and
Sundial
\
-~ ; •.., ~ ·
�Vitruvius 0 Sundial
The parts of the analemrna,in the order of their construction, are:
AB: gnomon
EBIL: meridian in N-S plane
BC: equinoctial shadow
NAG: equinoctial noon ray
GF: 15th part of meridian
LAR: summer solstice ray
KAT: winter solstice ray
FN: equator
GL: summer tropic
HK: winter tropic
N,K,L: culminating sun
PQ: N-S axis
GH: "logotomus"
Circle about D: "menaeus".
!/
/'
I
E1--~~~-->,.--~~~-"ik--~~~~~~~~--t1
Arcs GF and FH, of 24° each, represent the sun's maximum declination
north and south of the equator. Lines drawn from A through the even
di visions of GDH, the diameter of the '°circle of months", cut the base
line in the ratio of the shadows for each month. The semi-circles about
Mand 0 are perpendicular to the sun°s circuit about those same centers
at summer and winter solstice respectively~ they are used in constructing
the hour dials for these seasons. (For the Construction of an hour dial
see Sundials, Circular No. 402 of the Bureau of Standards.)
�- 33 VI.
Notes
General references for the gnomon: The Thirteen Books of Euclid 11 s Elements,
ed. T. L. Heath, Ibver, 1925; W. K. 0:-Guthrie, ~ History 2.f Greek Philosophy,
Cambridge, 1962; G. S. Kirk and J. E. Raven, The Presocratic Philosophers,
Cambridge, 1963; see indices.
.
-
t. The Notebooks 2.f Leonardo da Vinci, ed. MacCurdy, pp. 947-98.5; also
R. Arnheim, Art ~ Visual Perception, pp. 2.56ff.
.
.
.
/
2. the contrary of which is the transparent ( 1ci d.Lu ~ o.v £S ) , according
to Aristotle (~ Anima, 418b1ff) not itself a body but that through which
bodies appear.
3. See J. D. Beazley,
4. ·H. Di.els, Fragmente
~Development
~
of Attic Black-figure, Berkeley, 1951.
Vorsokratiker, 7th ed., I, pp. 331, 20 •
.5. This is the theme of Chamissovs wonderful story of Peter Schlemihl who
sold his shadow to the devil. The general principle that the image makes the
man is held in universal respect in our world, where a person is not cori,s\c~.krcd
to be 11 identified 1' , which means to say, to be the same wi. th himself, until he
can produce a certain paper with his own picture on it. I have noticed a
more innocent version of the same{thing among the modern Greeks, who will
sometimes, at a first meeting, show you photographs of themselves, intending
to prove thereby that they are people of some consequence.
6.
See the picture in Ptolemy,
~
.Q.f. Kings, ed. Halma, p. xliv.
7. The texts on this matter offer certain difficulties(discussed by Kirk
and Raven, pp. 99-103) the solution to which may be that· Anaximander set up
two sciathera, one calibrated for astronomical purposes and another for
telling the hours.
8. See The Athenian Agora, ~Guide, 1962, pp. 108-109. Besides this large
piece of architecture, there has been found also an example of those portable
klepsydrai which were used in Athenian law courts to limit speeches to six
minutes (ibid., p. 164). These pots have been kno"Wn to inspire the envy and
admiration of visiting American senators.
9. The noon shadow seems to be distinguished by primitive people too, who
stay indoors then, unable to bear the uncanny feeling of going about without
a shadow, cf. Arnheim, p. 257.
10. For sun caves, an early form of solstice marker>
pp. 52-54.
11.
see Kirk and Raven,
For instance in Borneo, see! History 2f. Technology, Oxford, 1954, I,
P• 117, Fig. 46.
12. See Heath, Aristarchus, Oxford 1959, pp. 21, 130ff.; Kirk and Raven,
pp. 81, 101, 103. There is some question whether the earlier men actually
discovered the oblique ecliptic or some partial feature like the tropics and
the equinoctial circle.
�- 34 13.
See J. .~ S. E. Dreyer,
!
History of Astronomy, Dover, pp. 93, 106.
14. On the story see Kirk and Raven, pp. 8J-84. The fact that pyramids are
not thin objects actually makes the geometry of ·the situation rather complicated; it is given in T. Dantzig, ~ Bequest .Qf the Greeks, New York 1955,
pp. 52ff.
15. The Parthenon, for instance, (built of course a century and a half after
Thales) is a good example of a human scale applied even to a superhuman
building. For a Greek temple rests on a platform of steps (crepidoma) whose
risers will obviously be felt to bear a relation to the human step (cf. R. D.
Martienssen, 1'.h.2, Idea of Space in~ Architecture, Johannesburg, 1958,
p~ 83).
The Parthenon steps are just twice as high as those of a man, and
for human convenience one intermediate step must be added for each rise.
Its proportions are therefore double the human.
16. a. Herodotus, insisting for some purpose of his own on the practical
nature and the foreign origin of both geometry and astronomy, says that the
Egypt; A.nn d~veJ_opoJ geometry for the purpose of assessing the lands swept
nuay by the Nile, "iuhence it came to Greece, while the Greeks learned both
the gnomon and the polos from the Babylonians=' (II, 109). This seems to
conflict with the reports giving .Anaximander as the discoverer of the gnomon
(cf. Kirk and Raven, pp. 101-102; Kahn, p. 91, n.J). FurthermoreJmost of
Anaximander 0 s inventions have also been ascribed to Thales (Guthrie, p. 74).
It seems scarcely possible to settle the matter except to point out that the
gnomon, the most natural of all tools, was scarcely in need of discovery in
an original sense in any case -- what the sources ought to be read to mean
is that he was among the first to develop it as a theoretical tool, i.e., in
a cosmological context.
b. It . is not kno~m what instrument in particular the polos was; some
identify it with the gnomon (Guthrie, p. 33). ·If it had anything to do with
the gnomon, 'it mo.i ,ho.v.t \oee\' just~~~ ·t•~, fc;( t~tcorresponds to the geometric understanding of "pole~ 7 ; Proclus, for instance, says that if an upright gnomon
is set at the center of a circle its tip will be a pole (Heath, I, p. 185 -actually the gnomon itself i.s a locus of geometric poles, a pole being any
point not in the plane of a circle which is equidistant from all the points
on the circu..mference).
Now the common later meaning of the word is pivot, as in the (Aristotelian J treatise De Hundo: "The whole of the heavens f as I have said; but
there a~e n9cess?.rily .two -.:points which are unmoved, opposj-te one another, just
as in the case of a ball being· turned in the lathe ( -r- D f v lf
) ; they
remain solidly fixed, holding the sphere in its place ( ()1.;vl-:><._0-V-r-ct
),
and the whole burden moves in a circle around them; these points are called
poles. If we think of a straight line joining these two together, which some
call the axis, it ~Qll be a diameter of the cosmos, having the earth at its
ce~ter, and the poles at its extremities;' (J91b).
However, this meaning
misses the original sense of the word, which is 11 something going round 19 , from
"tTeAoyo..L
, .,,go~ 1 • Thus i t is not surprising to find an earlier use
in which polos means nheavens 11 because nit itself goes round and through it
all things gov' (Schol. to Aristophanes, Birds, 179). It is therefore equally
likely that the polos was a spherical model, perhaps Hi th movable parts.
(The pivotal poles become the crucial parts of the first planetary
model to embody a hypothetical account of p\0V'c.tq~1mo.t.ions, that of Eudoxus,
which consisted of numerous homocentric snheres each with different ooles
(see Heath, Aristarchus, Ch. XVI).
L
1-.
t'-"i!. who\e
L.05\.'V\O!i
I·,~
~~~L.'(''1cc.\
C'\v"cA
VV\OY~S
·
CC>V\t-'1V'\UOV.5\';,
'
�- 35 17.
c.
The text:
Kirk and Raven, pp. 117-121. On Anaximander in general see
~Origins of Greek Cosmology, Columbia 1960.
H. Kahn, Anaximander and
;,
>
I
""
18. Translating the pun on
ex - LW v -- ttun:...going" in
c:A L co.v
eterni tyu
>
"
cf. 37fJ7: Lou CJ°' v 0\ '-' wv LC>v
i.L-V-... o vv.-. •
. The pun expresses
the character of time as the source of self-contradiction.
;I
/
;:.
/
19. Ptolemy's astrolabe became what was later known as an '7armillary sphere",
used, at least by the fifteenth century, more for demonstration than for
observation. A picture of it is given in Cornford, Plato 0 s Cosmology,
frontispiece. It is significant that the Neoplatonist Nicholas c;· Cusa was
r
one of the best known designers of such spheres (see I. Hart, the Mechanical
Investigations of Leonardo da Vinci, p. 21; this book contains a brief
survey of simple-astronomical instruments, pp. 19-31.)
1he astrolabe of later times, on the other hand, is a plane instrument,
as was Ptolemy 0 s 11 planisphaerium11 • Neugebauer (The Exact Sciences in Antiquity
pp. 18 5, 219) says that both were based on project ions of the heavens upon a
plane. Such plane instruments as a class are called ntheoricn (Kepler,
Epitome, p. 31).
20.
See Kirk and Raven, p. 100, n. 1.
21. Archimedes says expli.citly that n 'universe 0 is the name given by most
astronomers to the sphere whose cent~e is the centre of the earth and whose
radius is equal to the straight line between the centre of the sun and the
centre of the earth" (The i-Jorks of Archime·fos, ed. Heath, Dover, p. 221 ).
This notion must have been suggested to technical astronomers by the cosmological models,forin th~se. the ecliptic is one of the containing circles.
22. See M. Nicolson, Science and Imagination, Ch. I, "The Telescope and the
Imagination"; Ch. VI, "The Microscope and the English Imaginationu.
Discoveries
24.
cf. Kirk and Raven, p. 1J4.
~
Opinions
2.f Galileo, ed. Drake, Anchor, pp. 27ff.
23.
a+ b
Va2+2ab~b2
-a2
a+b ~ab+b2
gnomon~ ... (2ab+b2)
0
26.
Hence in the arithmetical algorism for
taking the square root the second
subtrahend is still called the gnomon.
The N.O.E.D. can document this usage from the time of Ben Jonson:
• • Her nose, the .r!nomon of Loues diall, that tells you how
the clocke of your heart goes 10
0 •
to Cowper:
~'The emphatic speaker dearly loves to oppose,
In contact inconvenient, nose to nose,
As if the griomo.J2 in his neighbour 0 s phiz,
Touched with the magnet had attracted his".
�- 36 ...
the word gnomon
the former mostly
one curious
those of a
of
sdom
cal and common
of both
with
the
which tell its
Hto judge
The
for
the Freemasons it becomes a
the way we live now that·
It says much
bears the title
books on
28 ..
957
of
cf .. G..
pp .. 248-249
New
Vitruvius I
6 ..
men upon whom nature
memory that they are able
music, and other arts,
pure
Hence
arts because many are the
as tool:
as
980a2J ..
• The analogy
hand, for the hand is a
sense of
~
is like a
intellect a form of forms and
Ch
See for instance
terms of touch ..
for
conceived
Boeckh
9 P•
nos
See
Heath
2
has given a
' pp 542-545
are: v,o,_ ~
In the
see
or
or
·---!--
--
l
~
,,
I
- _[
J._~
The
is
a
be
there may be no
two, or
mnnber
the gnomons wc)uld look as
arranged in the
It is not however,
that gnomons
around
but a
can be
�- 37 when it changes the proportion of t he figure. In its latest and over-extended
such an addition ·c ould be called a gnomon if i t preserved, as do the
gnomons of 2., the numerical relations of the figure, i.e., n(n+1). But this
is surely not a possible function of the original Pythagorean gnomon which
Aristotle and Philolaos mean; even Simplicius still shows some hesitation
about using the word in this way: "And although even numbers are not called
gnomons in the primary sense, because they do not preserve the same form, yet
they may .be added as gnoU},ons to show the unlike in figurate numbers"
( CJ~ Y\ ) -t °' Ta 1 f· O \ ~- 458, 5-7).
--c\
On t _ e other hand it is evj.dently
h
possible to speak of numbers being "pl,.aced around" ( 1H: ~Li l..-$ E.,.,P.- t v o .4
)
as non-gnomons. Therefore V-.:G1.I.. )\<-0r~ must mean that numbers ' which are not
gnomons are placed around the two, which is the first even number, and that the
resulting figure is even, and different with each addition.
36.
cf. Nicomachus II, 26.
37.
cf. Aetius, translated in Kirk and Raven, pp. 230-231.•
J8.
~i
\~
There are alternative ways of ge~eratins the
pentagon, as show'n; see Nicomacbus, Intrgduction
to Arithmet i c (trans. n~ooge), II, 8-11,
especially~· 244, n. 1.
See also Euclid VII, Def. 16, and
39.
Lt .
,•, ~ '
r 1 ~-~~· i.
jj..
!' .S Cotvt-.,,.Ui'-._-("_ (IT J
~
p. 287.t.f.. •
)
40. Galileo, too, felt . the fascination of the tetrasonal gnomon, for he
recognized in it the form of his rllle for free fall. 110.vin_g; 9i ven its geometric proof, Galileo adds ~ corollary in which he formulates the rule
numerically; m
.;Jhile therefore during equal intervals of time the velocities
increase as the natural n~1:11bers, the increments • • • are to each other as
the odd numbers beginning with n.a:nityn (Two New Sciences, Third Day, Th. II,
Cor. 1).
41. which is, in t urn, one of the two elements (
as Aristotle says (Metaph. 986a18).
CT x.__o
..........
l )(
t . i.. C\.
)
of number,
/"1
42. The Euclid scholiast says that "when the gnomon is added the er\v\ LA.o.
grows' while the
£.1' J 0) does not change in quality ( 0 ~) v, b. Ax 0 L o~ ) "
where the former must mean a particular figure of particular size~(Heiberg,
p. 277' 16).
,
43. Aristotle 0 s explanation of the way in which the odd represents the finite
and the even the in~inite has an alternative)given by Si~plicius, p. 455, 20
0
(see Kirk and Raven, pp. 244-245): as the figure
---~·shows, the even can be divided as long as it r emains
even, while the one in the odd blocks divi s ion and
binds the number into a finite atom.
0
•
•
•
.
.
¢>
-
...
Qt
.
44. Alexander as quoted by Cornford, ~ ~ Parmenides, p. 8, ~-~·for
a discussion of Pythagorean number. Passages relevant to this theme are
collected in Kirk and Raven, pp. 242ff.
45.
so the Euclid scholiast , speaking of square gnomons , calls the unit the
�- 38 -
first square number (Heiberg, 226, 8).
,)
46.
)
""'.'
}heon, p. 37, 12; it seems as if with"·
o..rro\f£- vvG.J V\€.)
•••
VW
C>v rt.-) V,o- ;\ 0~ V "\C-\L '1 he Were trying to COmment On the gnomOn 11 S name.
r
47. On Philolaus see Guthrie, pp. 329-333; Kirk and Raven, pp. 307-313. A
large part of E. Frank, ~ ~ fu sogananten . tha oreer is devoted to
proving that all the fragments of Philolaus are spurious esp. pp. 291ff.).
Scholarly literature on the "Philolaic problem 0' exceed reflections on the
content of the fragments bv better than ten to one, roughly. There is, however, an article by Newbold. _ Arch. flir Gesch. der Phil. ( 1906) which disin
cusses the gnomon fragment (pp~ 17'bff:-}"arur-;.hi~Iha:Ve not seen.
48. Diels (as rendered by K. Freeman, Ancilla to the Pre-Socratic;
Philosophens, p. 75) translates: IJ But in fact Number, fitting all things into
the soul through sense-perception, makes them recognizable and comparable
with one another as is provided by the nature of the Gnomon •• ·"· The
11
differences are crucial to the interpretation 1 es~e~1c;,\\i ~ccov-c\•~·~1-t?. for-'\V'\to.,,
11
1
-t\.-\<.
!7.ov\) v\Vlc,\ ''CA..
~or''t~c 11 ~il\C>V'\!\Of\.
•
49. Philolaus applies the word eidos not to th f figure but to the two "proper
forms" ( .>l er\ Cl f(JV\
) of number, the orld and the even! ,, and each of these
has many shapes ( ;vt o f ~ C\..L
) which each thing shows by itself" (Di els I,
408, 10).
VII.
[Corrections to AN ANATOMY OF ORBITS, April Collegian, pp. 1-28.}
p. 8, ii, 1a add: In iv, 3 this is the ~enter of ~ravity.
p. 9, iii, 2, 1. 3: for HgeOllletri(; center"', read o;focll.$".
p. 11, iv, J, 1. 4: for ngeOW\et:rie c.ente.r",~reaci "th~ focqs of the orbits".
The figure for the
~
last two should be --;>
( ~--~H;
__
'-'-...____ f~N S /
'1f{
::.-----
p. 12, diagram: the sun is S
p. 12, vii, 2, 1. 7: 77 eccentrici ty AB=AR 0
;
so also in the diagram, p. 13.
�FEAR
WA.P. OR
AND
There is a
in Thucydides 0
it concerns one of the
move men ..
of fear
Thucydides says that the truest cause of the war
the
grovrth of the
fear necessitated the war
of mutual fear is the
both as a
s for war and a means for peace.
and
have two
us in
discussion
The first of
what fear is.. In
fear is sometimes a virtue
in
the case of fear of God ..
fear is also often
taunts another with
you
men often hesitate to say
What is the emotion that is
such various
And if we succeed in
with the one that is behind
is whether fear, which
war, can ever be the basis for
be, and how is it to be
opposite effects
to deal
second
ssible cause of
ir1l11at
of fear
from the fear which has
above..
T>~.s
Let us begin
them and begin
thereof
a
actions and
, from the
to i~~~~-.~~
Athenian
fear
is
become aware of their
from everyone
are
of a hurt
the future, for i t is the
s is
in the speech of the
are a match for us
another too
for us ..
at once, and
Insomuch
�- 40 unless we oppose them jointly and every nation and city
set to it Url~nimously, tl13y hL~.i overcome us without labor".
Consideration of Athct•.:i. '.3.n action ir.. the :h·'.-,Ere leads t o the concl 1 ~sion
that, if no p r evi.:H~tl~T <:.~ action is tal-rnn, tiwre wili rc,su.1-t, in tbe fllture,
conditions which o.re ha.cmful.
At the time when this conclusion str:.kes someone, wheth8r after thought
or after the rrm.ch shortc1'" pro c .-; s (:if r..:.~1 un ~·:x) 0etsrl C"lgt .J::;:··: ve action by
someone or something el ,'3e, we .:; 2. ~1 .:·: '.)·~' tha,t u. ;;e:i:~ son his Lean stru.:k by
~ .-n os
, thls being th9 word 'Ihucyd::_o:.L:s uses in sr:e:::.king of Spz~:;:~+. . an
fear .9S the c~mse of the w-ar. It is sorm:·t:.!:'ling that is oL:t side the person
involved. W
h9n he has been hit by it one of two things can happen, the
persvn or city involved will follow one of two coursei>.
0
The first of these is blind panic. When, in the Peloponnesian exhortation
before the battle at Naupactus, the soldiers are told that Athenian experience may be useless because ~ 0 fear confoundeth the memory p n5) the hope
expressed is that the Athenians will feel so outnumbered and overwhelmed
that they will consider their skill of lHtle VJ.lue. And so tl:?.3 i ·}·r.: s::'." tJ.nt
factor for success will become chance, which could equ.~ily favor th(nu or
the Peloponnesians.
But if chance is thus so much more powerful th!ln skill, and there is no
attempt made to use skill, the Athenians invo'L ;,red wi~Ll not bs r-:aking
decisions. They will not be trying to und .... rstand what the pw.~~ )•)ses of the
enemy are and dec-i_d-i_ng what their ot-m strategy should be. In short, they
will not be using their reason.
And if they feel th2t the injury they f8 3.~ is completely unavoidable, they
will hope only fo:::· s011!e k 3_riJ of m~:racle ~ t,.r.ic! :_- , 1 ~-~~ :>.e!les by definition are
of all things least subjact to ratio!1:tli t y. .MKi so the opinion of hurt,
together with an opinion, produced by the circumstances involved, that
the hurt is not to be avoided primarily by one 0 s own efforts, can lead
men to panic or despair.
But there is another course that fear can take, and this is the one exhibited
For they are not e,q_sily sub j ect to panic, since
their case is far from a hopeless one. 'I'ney are a po ~.-n :- ful city, \iip·c; 1·:-~me
on land, and possessing powerful confederates. nWherefore, men of L3.cedaemon, decree the war, as becometh the dignity of Sparta.n6) Whether or
not they want this war, they are not panicked by it. This leaves the way
open for rationality.
by the Lacedaemonians.
The first occasion for reasoning is the decision that Athens can be stopped
only by war. Sthenelaidas may have been an irrational demagogue; but even
wise and temperate Archidamn\ls thought a war might be necessary -- vgand
prepare withal for the war~ 1 7) he tells the Lacedaemonians.
And the conduct of and preparation for a war are intensely involved with
reason. The actions of the war are in the future, and the future can be
known only by conjecture based on reasoning analysis of the past and its
analogies to the present. The Spartans will be concerned with causal
�- 41 -
relationships -- what will result from an imn1ediate invasion of Attica, is
it better to wait and attack somewhere else, what should be done to train
a navy?
The whole problem of confederates will also require much thinking. The .
Spartans must decide how best to arouse and hold their own, and also how to
persuade Athenian confederates to revolt. The awareness of separation that
is involved in
jd 05 will make tl.1.crn pay all the mo1·e attention to this
aspect of the war.
ff
And so fear can become rational, and as such is no longer something outside
the person who fears. It is more what is meant by the Greek word 6i ~
and it is, as we have seen very much concerned with the future.
.J'
Thus we have arrived at our second question. Can such a thing as fear be
the basis for a league or for peace? Clearly panic, with its heedless
thoughtless .action and its passivity, can not. But what of rational fear,
what of ~:~)
?
The first difficulty is that anything that is to be the basis of peace must
be very strong. Hobbes says, "In the nature of man we fing)three principle
causes for quarrel -- competition, diffidence, and glory. 17
And these
causes are powerful, for within their categories can be grouped all the
passions, desires, and prejudices that move men to war upon each other. What
makes us think any fear can control them, that it can override desire for
gain and glory? Do not people often act d8~ r ite their fears to obtain a
desired end?
But there are reasons for believing that fear, if great enough, will be even
more powerful than these desires. For while gain and glory are apparent
goods and certainly sought after by men, they are goods that are to be enjoyed in the future. If a man has a dec1.sion to make, and one choice' .may
lead him to gain or glory, these two goods will often come to him some time
in the future. The profits on his business will begin to accumulate at the
end of the week and by the next week he will be enjoying greater luxury; or
perhaps, in the case of glory, he will be honored for his generalship when
he returns to Athens the next year.
Fear, however, is usually more immediate and sure. Men tend not to have the
foresight to fear things far in the future, precisely because fear is concerned with undesirable objects and it is natural not to want to think of
such. The result is that when fear does arrive, the potential hurt may be
very near in time. The choice beh.reen a fairly immediate evil and a good in
the future will often be decided in favor of the former.
And, more importantly, gain can be enjoyed only by living men, and even glory
seems better if one is alive at the same time that he is glorious. In other
words, life is a pre-requisite to either of these goods, and a fear that contained an opinion of hurt to one 0 s life would have necessary priority over the
desire for some gain that, without life, would be worthless. Self-preservation
is not only an old instinct, but it may also be of the first importance in
our actions.
So fear of the right kind and in great enough quantities may be strong enough
�,. ·
- 42 to overrule the other emotions. But what is the right kind of fear? The
Mytelinaeans have spoken of mutual fear. Let us say that I am afraid of you
because you are strong, but you are also afraid of me, for I too am strong.
We agree not to hurt each other, because neither is sure of winning, neither
wants the risk of losing, and neither wants to waste energy and life in wars.
Also, if the two of us combine our strength, we will be that much more sure
against the world. Therefore -- let us have peace.
But there is a great problem in all of this, one which makes this theory always
eventually fail, and this is the factor of changes in power. My C' rr: ·~J C may
fail one year, my slaves may revolt, or my city may suffci' sect· .::. _•
You,
observing this, will judge me eeaker and perha"9s consi r_1 c.=;r :-'. ·!T ~ 2 :-,. - ..,-; 1;. :-·rth the
,.
risk, because the odds have changed. Mutual fe?..r i.s c 1 - ;» :..~ .-•._-.,.._-,_-,L~.:: ·.-. :- .:iu no
longer have a predominant opinion of hurt. And so tGo i~ the peace gone.
1
: ·. ' ..
Mutual fear is not sufficient for the basis of a league. Neither is a fear
that cannot be understood by all. For c:i.n example of th.is let us consider the
Melian dialogue. We col:ld ~; '""'·=' t llA.t w2 b.:-,-l9 the po s·-,·j)_~ i~.i ty h c :"c t.h : .:t t he
Melians are so str1-.:. c.1~ 1._:J ; -:::,c~_._-'. .::i .. . ~ : : •J ~>>~: :'. :t·-;:ss ab ) r (; t ::-~s :~ r/i tuu. ~_, jc·J u~ at they
are no longer bf;iqg ~· ~· .::: .L ~ . y r· : ; ·:-. ·~L•:J,~1 "':.. o rt--i t.:. .~ .'--3 r~ ~·-- C' ~-J!J..:~-i.] f..}~:?: c~' ? .::~ (~ :, -i.- 1 J'. i· henians
.JP,
hoped to have on the m2ss 0s i f E1 ·?-: :~.:-_:_ j L,~ ..-_..~1 c::.~l-j_.,r,,-,:_,:1 t n ~...: l.'. -: ;~:i_-~ '_:;c.J~ ~'./ ~ o t hem.
Let us assume, however, that t k _a · 1. ~: b t, t .n.l8 of ~:. :.~ ~; V;:<.ian 1.e2ders, and that
the fighting power of the Athe1 :i ::! ·1.::; }·; · i c) no-C c .~-i1r :.J·] c.-tcly p ani cked · t h~ra. There
is s ti l.J fc: -sr i.nv0lved here, c--:r1d it i~ fo ar o f ·ct1.-:' ;_: ":'1. equ eV'l s :; ·:; of .Athenian
s
r u.1 ,s- . S· :o "::-J•~ !\ .:: c-~ei '.1 .s-:-.·si::: s nc :.:, or!'_:.y 1..~·1.~--: [-1 '._:;-,o r u.~:.1 0, bl:t c-·~ ~'.°; po 1 ·i.lu 1;:s ~ f o.r V ·.'.0y
h e:. . ·;;~ nc- t>'.:.~· :-~'.-(:.:-: ·c: -~~ , ::~~. /. ~ !1 ~·;:~:.:, n ~1c:~ tl:w ma .:.·cer , r.;::- ·1_::i .J ~ ~"."· t r t:-! ;.; -r,:i..th se vc~ ri ty.
An~! 5 f L.'.:·~~ i>:.::i·,'"-~ ·:. :.: v1 j-, :~~~- 8 ~.~ .• -:,_ ,_·; _d l;a co:ro .:n.:. r.; r- r;::: si·; . ; i :1 -c.:•·:. ,') c c._:_ ~-3 c .f :.hi.s ~ ong
.
:
:
-.
a n·J ·~ Y·;.J ~·:1': ~ '.'0 v:·~-:. 1.~ ~ t, :1 °:.: J:·: :;.J. iC:t l~ l .:~ . ~dt:r:; v:on ~ _ d h ·'.iVG di. f fi c·L•lt:..- - .:1 l e ad'itig a
:
rE: ,-:> i_ o i' -1.1: 0 c~,_ -;·,y ~ :y::. L they had earli -, i: v:-JJ.untci.rily su.r ~ · c tic:er ed.
·t.
But
t li .~tt
~- 2
-!-.·'1~ :~
::1
~
f :·:;:::.
-~.~l e_:. T<·:;-~. :~:.:_;::~\
.•e J
~ i l-:~·
1
:.~-.i.el~ i ~JJ .~:.: r:;· ,; :~.
....
,-:_,.'.-·. .'
:
o·i..l::·:·;_~
f
. :~ .~ ~·
: 1a~ i ,.· ·. 1 .
1
1i"'J:-.: •C'."t.0r:d?
r..,;:;1;.!. ,.!.
c ~-.Ytc, i nl. y
t'.;ey know
i: ·:> ~er..:: f'r ee. i;.1 !:, they
uf l. l·..;:; .:. r rule, n.ot in
;~:_1:·..::::-i·f.::.'."
do t l ~:-~-. ~t~e ~,J i'.:.,'! ~:..i':-r·:': . :. :l·, tt; i'::;I.i.o. ~~. s vv1:_::_J b e , ~: . _".'<:.:..'...J.
term.:-J o f t.r-j ·o :lt\-"~ t:nt r..ight oe pr8sent Ly l ( "' :. :-::1:; b -u.t in t e.r·~JJ.S of pl2-cing
::
one 17 ~ s ·::: U ' j 11 c} 1::: r) ower of people like t h e AU1enians. The Athenici.11 ambassadors s ~1 J, 19 You ~; > ::::. :.:. t.:,:J.-.J3 YC':'Y ab.s t; rd counsel
in deciding to res i..st
u ~.lr:~ ?· :~-!~ ::e-: t~-~ 1}..:i.-J. ,-!~ 1 :-:: ., ;..-01J r11c•.'>:e ~:!" ~ ) nisst ycurseT v es some more di scr c·~ t concl uJ
...
~
'~~ ·,.-•; T'" :J At t;. 2; ~~.rt~!'."'. i".:.l.:·-.=-; i . t r i::· cc~L!.:,J-~ \..;-::.:;n 3. ~"1 f' (.::.k er , s ul::: j i.:· ,u~ .J.ted city ,
r
ar . ~ i ;;::._t\.:::'. t ..'.~ r- 7 r.i ~ .~ 1 :· t, 0 SC 1.~·1 c":.'Y1. :: '~ :~·._;-,:-::.- ;~1 : ·:::: 1·1.~-· ;. C•:'.'' _i_v;,.~~:;;-Lt!. OUS, they may E Ot
re ·::i.1i za a~-:ct l16 l" na:~. icn could lhCl..-J. t he:m in t l1is W~{y ~
8
.
·
And S8 pe1·hnp s t hroughout the dialogue the conversation is blocked by this
Melian fe ar that the Athenians do not understand. And so it is clear that in
any attempt at peace, if fear is used as a means, it must be understa rd able
to all.
Thus our analysis suggests that fear is a powerful enough passion to control
men in the actions that lead to war. As we ha ve seen there is a problem of
determining the proper object of such fear, for it must be fear of something
enduring and must be a fear visible to all. There seem to me to be two
possibilities. One of them is relevci.;it to Tb ._icydides 11 time and later is
:
developed by Hobbes. This is fear ci' the s·t a te. of war. If war plac es men in
a state of nature -- 11 solitary, poor, nasty, brutish, and short''-- · man should
want to avoid the evils that such a state entails.
•
�43 -
In the past, however, war has not involved a state of nature for many individuals. The men who govern countries are often not those who fight in foxholes
(which might be a good rr.odern equivctlent cf what Hobbes had in mind). Large
parts of the population continue to live in civilized society, although the
society may be changed in form by a w
ar.
But now the possibility has appeared, through atomic weapons, of actually
destroying all civilization and perhaps the earth as a suitable place for
life. And this fear seems to fulfill the requirements for a fear that can
lead to peace.
If it sounds too optimistic to place so much hope in fear -- and well it
might -- we must remember that ~Jhere is a large qualification underlying this
thesis. This qualification is sc-.l·;ation and resultant applied rationality.
Even Hobbes says that the laws of na_j_.-..ire are arrived at by reason. If man
knew them without reason, there wolli j never be any state of nature, or at
least not one of the kind that Hobbes de scribes. So a man must be taught,
either by experience or by other m~ ::. ~ t hat war is the greatest of dangers.
But there is something else he m
ust know, that may be even more difficult for
him to learn. This is the fact that all men have some basic needs in common,
and that all men desire many of t he kinds of things he does. If he knows
this -- and on the assumption that other men ~nll be rational -- he can conclude that others have the same dread of war he does. And so he may be free
to follow his aversion to war without the risk of domination by others that
at first seemPd apparent.
I will freely grant that this qualification is very large, and I do not kn-::>·,1
whether it is possible to educate men in such a way. But this theory may be
a road -- a way applicable to both men and nations that avoids the cruelty
of Machiavelli and the need for divine intervention.
*
*
*
*
*
*
NOTES
(All fo~tnotes are references to History Qi Pelooenassian
otherwise noted.)
1)
I: 23
2)
III: 11
3)
Hobbes 0 Leviathan, Part I, Chapter 6, p.
4)
I : 22
5) II: 87
6)
I: 86
7) I: 85
8) Leviathan, Part I, Chapter 13 , p. 106
9)
v:
111
55
~'
unless
�
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co
ST. JOHN'S COLLEGE
SEPT.
1964
�St
tine
s
Grace
Three Poems
moses maimonides
Francis Bacon
964
*
65
�s
these areas
or
di ca
ider these
several s
be
ask
cities ..
tine considers
for
sta
heaven!
reference
can better estimate its over-all
these ques
come
discusses
a
�2
God rul
cities..
ied to
over the
in this sense, the definition cannot
over vice..
and reason rul
be ap
, the soul rul
over an obedient
Because of this
tine modifies
that we can define a
his definition
of love.
a common ob
which is bound
cities vary in
of true
es of
of
11
Thus
upon the
citiness
which their citizens hold in esteem.
cussions of
as a group of
We are
ci tiness
tine's dis-
in
, Rome and Jerusalem..
one historical and the last,
with three
is S
One
What is the
of each as a
It is of great
is a
is the first
which was built
founded to acknowl
with the confusion of
indicate that the ci
this
established in opposition to God
and his a
man s
tion ..
sel
This statement is true in
agree that
the scale of true
failure of the first
of the
citiness
of veneration.
does not necessaril
e of the
the
alternatel
dark and
It is evil in its
ends,
in some sense it represents a manifestation of God s
Providence ..
sees the vastness and power of
some
as
the
the second
is
small
itical.
It
as
He often refers
ike the
, under one
central rule, considered
rule
t would
as will later become evident ..
views of the Roman state..
to
ects
condemn the notion
to God.
Rome is an historical
and
this
and
itself, as one
is true
tine
was eviJ. in its ends
as
it loved were false, and not
be low
to reach God,
a
which resulted in his
• At first
is considered to be an
is the founda-
man ..
ti on from which man launched his
an a
since it
states
tine to be far
and
to the
to that
�3
vastness
states
small
towards the
Roms
al
izes
ends,
supremacy
It is
tual
Jerusalem is a
God s covenant with Abraham
of God
was
tima tel
and will
Jerusalem
will be the one true
, the
will be bo
an
those
interests
a
l have the
these three
definition
true
senses
acknowl
and it
t on the
is
be a
understands the word
commonl
Old Testament allegory
t alone will be a state possess
scale of citiness
It
be the
as the
ect
es of cities
the
can
tine,
considers a
ect
tine s
Hobbesian terms
a commonweal.
bas
There can onl
be a
in the absolute sense of the word, when God is the
is not a true
love and service•
namel
citizens
it is
and
is evil.
Rome is not a true
But what
come to
, and as such
the
its nature as a
the supremacy of one
true
because it too held the
Jerusalem is
ts
s desire for man to
Is it
ills
man s God-crea
this question
creation of man
tima
ive
this assertion?
evidence do we see to
next question.
held
since
terms
revela-
his fall indicate that
first
one considers the Creation
says
s
�4
certainl that he
be a
, but that
and the bond of concord
commended
UI, 21
, in Adam all
Thus in Adam all men were created, and
men fell.
Both alternatives:
beatitude and his
man's
fall, indicate that he was destined to dwell within a
Had man not,
"disobedient use of his free will" fallen,
he would:
pass into the
of the
and obtain, without
the intervention of death a blessed and endless
II, 22
the
indicates tha
Adam and Eve would have
fall taken
the
tined
number of saints, who with them, would dwell in the heavenl
immortally --
for the life of the saints is a social life.
A
further indication of man's civic nature is discussed in connection
with the
ect of peace
says
"How much more
the laws of man's nature
move him to hold
and maintain peace with all
men so far as in him lies, since even wicked men wage
war to maintain peace with all men.
XIX, 12
Peace is man's desired end
this desire can be realized.
earthl
He lives in cities so that
nature.
peace is the
while eternal peace is tha
But in what sense is the
of the
a
It is clear that information about the heavenly
from revelation
and therefore we must
tion of
is
comes solel
upon
tine s
to
, whether literal or all
discover in what sense he thinks the
, is a
of the
of God, the
It is difficult to determine whether the heavenl
more than the
of the
tined,
God and one another in God. 11 (XIX, 1
to have institutions
ike those of
of the social life of this
and Rome?
Is this
tine
�5
a
more
that the life of a wise man must be
could the
of God either take a
attain its
were not a
is meant
UJha
this social life?
We are told of
describes
In its
state the heavenly
peace
faith; and
faith it lives
it refers to the attainment
action towards God and man
IX
In contrast to this statement
9
s Christian
of Plato, and Platonic
social order
but rather
rest
Can
seem
life of eternal beatitude consists
and
Hims el
ineffable sweetness
I
reconcile this Platonic
of
within the heaven!
1
31
with the statements
tine makes
social
over "obedient citizens?
tion
a
and
another
God
of this state-
firs
tion
is clear that
God, the greatest fel
the
e for man.
tion is more
the
How do we unders
of one another in God?"
remark that
tine
ife
It seems that it is
the existence of some sort
there is
this
social
the heavenl
come
The second half
among men.
be
it will come
when God
is there a
?
tine
es
es His obedient citizens
between the
sense
�6
the conditions for the contem-
social life is necessary to
the most
life to flourish
be one where the
situation would
unhindered
life could
for social invol
the
tine would say that within
this is not so.
The eternal reward is intimatel
consists
connected with the social life, even
in the
the
of one
of one another
diction in this because
God which
tells of
It is this
God ..
y
There is no contra-
of God, the supreme
another
suggests that while the
11
life is to be basicall
tive in nature, it will be embodied in the form of a
deemed men, 1
The
ife" of man
earth, because
s
'
be
in so far as it
is
and heavenl
to the "social
i t to exist
of re-
the social life.
, both earthl
lends its el
the
earth
There is a
for
ted
is
s
and not in the immediate manner in which it will
of God,,
in the ultimate
There is the need for
men to live within cities on earth to escape from the Hobbesian
"state of nature ..
s ti tutions..
We cannot do this without the
This "state of na ture
"unnatural
11
is, in real
man' s most
nature he was created to be
state, since in his
a social animal, and dwell
institutions
as such..
The
as
to God's
man will be restored to the
nature, and
assist him to live the social
one another in God ..
11
The
of his
, the institutions of the
will not be necessary
of the
ife
11
, both
y and
, is
rooted in God's Will for man to have a social nature ..
IUl
social nature
among the
In
for his nature as a "social animal.
the heavenl
ultimate!
with its
helps man whose nature has deteriorated as a result
fall
in peace,
and its in-
would say
accord
this, is that God wills man's
"the
His creation ..
and mutual peace
'
11
�es G Bell
Is
the garmen
textured time
Of their
, so entwined
Their very
were one
timeless! y
Breathed
cleft and
e
Seek and
Is it
the falls
ed
come
Be as
dream
The
and years
and self-abuse
memories
than
Less
ts
the
else
�8
EM CORE
Charles G. Bell
Marianne:
I swear, if Eve seduced Adam to eat the fruit,
to what gauds have gone unrecorded
Or Lilith
It was not
of
Of song ..
brow or breast or the dear hoarded
'
and brea
the
t old
UJitness
second
; and when you s
flute
to be
that song
for the secret savor
Your l
Of lost romantic
I
but
'
you so confound me,
wives, loves, whores
To lie in the falls of your
If ever
Off the
end, it is the drowned
Yours forever,
Charles.
Schubert,
�9
Charles C Bell
To climb, that l
resilient,
To take
To
air
all
our arms
, branch over branch, the a
And trail
for the nurture of
centuries
bone of
, terraces of green
to be, to unfold the one
Here, earth marrer, lift the
dream to be life-rooted, l
are:
of your prayer,
that tree.
�-10-
ON INTERCALATION
by
Moses Maimonides
is a very strange thing for it is
to say whether it is
a product of nature or of custom. On the one hand, this seems to be a
treatise on astronomy and yet different peoples have
count from
but
Not
Nonetheless, each is based on
motion of the same
the present treatise was written many years
, it uses
a method known to the Babylonians prior to the rise of the Greek science of
__ I've
in the
order that the
have some notion about that
inherited and
to
is
to say
or not geometry
role in the earlier science. On
, there are no
any such
on
suppose that a man could spend his
the other hand, it is hard
fe recording the motions of the
and searching for patt1rns of reoccurence
on the
in which the
moves.
The
we
in nature but on the
has · ..
foundation not
passages as well:
for each new moon of
the month of
offer a passover
your God, for it was on the
your
you from Egypt. 0
to
and
who
One
the
us are not comeach month
that each new moon start a
time fall during the same
be composed
new month
month
wmich we are
of
days
�a new moon ..
that summer
~ime of the year.
is to so
the
not commensurable
, even though the
each
have
s means that some
and some
others 1
that some
will
more
of the new
the
The
believed to
of
.l..l.IJ.\JlJ.J~U.\.J
text, .I fear that one
translation from a
J.J.O. .
of
wrote
A
Thou
of me -- may the
and in
which thou
thee
6
exertion,
this means
a teacher
any of the ideas
for thee
book alone will not be
for thee since its
the teacher
not be needed, but rather that in a conhim
I mean that in that time it
taach
the names of the terms of that science and the
which are
lead thee on the way ..
will make a
that thou shalt
and
Teach
resume to make
in need of
stead fast in
which are not
from other
But as for thee
the cause of the
but
I be brief
over any
take
place of a
I have not set it as my
of the arts
ifll'hich same
is
it even to one who is
) many other
ch come
was not to
alone.. Now
�is seven.
se
number
the Second
f
s
the
is
know the number of
of the week the
The
se
are
�each
out for thee to be
of the
for thee
hours since
for thee on
of
that from the
with the sun at a
a
time is 29
, 2 hours and
is the time of a lunar
When the
s
is the number
the total
the
account
the 7 years among
the
�4is that the
is
9 years
of the birth of each
we
which totals
s from the
and 793
is
clear that the number of a lunar month is
when thou
the
,
and 876
remainder is
we
have made
year is 13 lunar
when thou
takes the number of a lunar month and
it
3
what
totals from them
be 383 days
hours and 589
when thou
s from this there will remain 5 days
589
The
is 5'
589' Behold It becomes
to thee
that what remains from a lunar month after thou hast
lunar month is 1 12'79J 0 • The remainder of a
the
of an intercalated year is
the
of 9 years
Jhen thou
take the
times and the
the two
7 times
temain 2
6 hours and 595
what remains from the number of days of the
tr acted
I,
write for thee
should be
for thee; for the
art is
we have shown
for thee to
Know that the first year
of the years
birth of
that
The
\1
of
~ the
hours of
hours of the
of
to
an hour
thee from the
from this
�5
mean
matter, but thou
of the fourth
from
to the
of
arrivest at the birth of
in
to our
which
-- and that is the birth of
sions. The
for we added
We
birth of the
lli
we
clear the
know the birth of the
this
one
raise
·whatever remains from the column of
go back to the hours and
whatever
to
a
to the column of
not fill up
write on the
s from whatever totals more
and subtract
When thou hast done accoron the
the birth of the
is after this -- that is
come out for thee to
9 hours and 949
hour. Thus add 2t1 595 to
260, and there
thee the birth of
In the same way do
write for thee the births of 0
to
Teach
arise
in
of a teacher.
out the
in the way which we have
for thee
table. If what came out for thee agrees
in
know that
work is correct and if there comes out to be between the two
them a
of
know that that is a mistake and
answer agrees.
the
of the
of each year.
year of a
is known in the
we have
to the first birth of the years
the birth of
for thee
this
The birth of the
was
Ue added to it
hour
of hours in
form
sions.
\,l]e i'llTote it on the third
the column
the
the 3 hours of the
hour
we
to the 8 hours of the
line
and the total
that, we
with the
and the
knew that the
of the
was
of the
�6
want to
the
the birth
after it
of each
�7see Form
Behold! we
and
so that it is not
made clear and
time
to be
clear from the
become clear to him in the
thus from the
the deed of
out the birth
out the birth of each month goes on
same way
in the same way.. Know that for the wise men the
to the conjunction of the moon and the sun in
motion, and thus thou shalt
it with the
of
Name
the
Know that
look into
my
want, as I
year
be for
become
after the
Deferrable
to
comes out in any of
not be on that
of the
the
and thou must
leans upon it
s
of any month that thou
thee to know on which
New
of that
manners that birth
The rest of them
There are
The First Foundation: v-Jhen the birth of a
comes out for thee to be
4 or
6, New Years of that year is deferred to the
Do not
whatever hours you have, be
few or many.
of what
is like: if the birth comes out for thee to be on
any hour of the day or night , New
of that year
be
if
be
the birth comes out for thee to be on Day
New
of that year
comes out for thee on
6 New Years of that year
5 if the
it
or
.. The
7 Do
are never
as New Years)
But
Day 3 or
5 or
The
is
The
Foundation: vJhen
birth of a year comes out for
which is
for
-- as New Years -- and
An
at half the
more
do not fix
Years
6 hours
what this is
If the
of any
was
is 2 11
and
of that year
J:
was at
less than
even
one
-- for
if the birth was
2 11 1
of
2..
for the rest
of the
for thee to be
2 at 8
hours or
J;
if the
is on
3 at
hours or more
will be
5, because
deferred from 4 to 5. We have
made clear that New
cannot
, when the birth is on Day 5 at 8 hours or more,
same year
be on
7, because it is deferred from
and we have
explained that New Years cannot be on
when the birth is on
at 18 hours or more, New Years of
2 since it is
Day
to
2. The sign of this
is what the wise men of
Memory
(
it
before
noon, it is
afternoon
noon is as
�8
way
�9 ...
Full or
and if there
or
4
3
is on Day 5
there are between them 4
2, the year is
of the
5,
6 , Day 7 and
the
7 and the
there are between them 3 days: Day ?, Day
If the
of which thou dost want to know
is intercalated, do this verv same
) there are between the day upon
is
the day upon which the
there are 5
between them the year is Deficient; if
if 7
, the year is Full The
5~6v
D0 0'F', and
is
the first
an intercalated year is on
? and
the
that
year is
because between the 2 days there
since the
on Nhich the year which comes after the year
want to
know· is fixed, is not
in this count as we made
From what
we have
it
become lucid to
that thou are not
to know
a year is Deficient or Full or
after thou hast
that year and the year
comes
thee all the years of this our cycle in a
and the
Teach
f by it
the form of the
see Form 10 •
Know that whenever
DllF'
year
New
out.
5, if the year
if it
The
Day 3 that year is always
that
is that when New
nor Full, but
but
it is not
it can
or Tuficient as the
which
D and
2' D°
Know that when New
is
it to be Deficient, and
to be
The
in a
is
go back to
make st
to w:ha t we have
and
the
and the
year comes out for thee to be
when New Years
7 or
2 or
it comes out for thee to be
when New Years is
5 and the
thee to be
when the
know that there is a mi
it is found. When thou
New Years and whether the year is Full or
without a doubt the
of each month is known. When the
of each month is
the appointed times are known
the
are kno1,m
a doubt
�of
Of the
��-22-
the month of Nisan of the year which we
is~
918 of the creation (
year)
of
the
of the month of Nisan of
year to be
22 days from the
of the month of Nisan (which was
Day
· came out
1, since there are 22 days between
the
not reach the day of the
as we
We
1
to 22
2; we
reached to Day 3; we added .~3 days to 22 the
day of the
which is Day
Then we knew that the ........_..._..........._
·or
year which is year 4 thousand 918
of the month of
By
subject thou
the month the
of Nisan
be
thou
to know at which
'-'""'-'""" ....... L.•C:..
.i.•..i..;"'o.... ,,
.-..-~~--
in
case
of Nisan is knovm
us at 1 hour
clear
from
when
is not
but
of
fir st hour of'
of the
1
so
��I.
v
��x
�kn owl
of the
e
1
3
2
4
9
3
4
3
5
4
7
3
7
5
6
7
8
1
2
9
1
6
2
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
5
6
5
6
1
2
3
4
6
7
1
2
4
7
1
2
3
5
�1
be seen from what
we
�x
year
a
in an
x
excess over
excess
excess
one
each
year
years
years
excess
e:gcess
excess
years
years.
excess
�30
20b
the
consequence of
, there are
either
months
of
must
making the
this
the name of
have
as
�remembered
not
ris
a
is
s treatises
faceted; as seen
s
neither an ancient
a
s
a
ta
and doctrine
are
all
�32
about the "natural
method of scienti fie invas
'
of the
ti on
reason
proper
the proper end of
and (to name but a few of the many new ideas) the nature
which exist in the world.
to the first
I limit myself
because it seems necessarily
both to the
refutations and to the introduction of the new method:
can talk about
Before one
kn owl
certain methods of
ess, I think, and before one can dismiss
are
(or
false, and before one can reveal the true end
as
and the method to attain that end, and
of
to be true about the
outside of himself, one must show how the
ition of know!
is
In order to
refute the natural human reason,
it; he must
for so
Bacon must re-evaluate
e been so mistaken and unsuccess
in their
He must talk about the
of knowl
interactions exis
between the soul of man and the nature of
, and ultimately he must show how this "commerce" between the
soul of man and the
say
refutation,
in themselves
11
I use Bacon s word;
word, for I think that,
of the
can be effected
When
re-evaluation 11 is my own
his harsh and
ery
----
and that ultimatel
he must
either fall back upon some of its conclusions, use the force of its
rhetoric
order to
new method
or
As I a
~.....__~-
to
a coherent
the
a conclusion
of the
of the success of the
he
of
of this "natural human reason" and its
relation to the world outside of man, I shall refer often to the
the differences and similarities of the two
�The
as
is
e as
for he is a master at
Bacon would
to lead men
be raised is this:
The question
establ
between the
has thrown into confusion all affairs
the divorce of
Preface
their
words ?
(in the mos
that we mus
em before
ps
is not also
I
a
and rational facul
cise
order
it is mos
the
necessary
emics, and
pre-
understand
can decide as
of
Baconian method
I
the true method of
means
first
shows the
Bacon says that man's knowl
false
the candl
of
distorted
men
these secrets
e
and able to
as
is necessa
hers el
because
are too weak
recesses
man s true vocation to
into the
violentl
causes of
"act.
been
wa
and
laws
But until now this has not been
the
em
in most cases,
s
causes
�34
wha tness 11 of
and
ca us
to nature, (that is, for final and formal causes, and for the
answers to questions like, what is
find out
) rather than
to
work; the first are not
the nature of
tell us, rather
man s
unders
The
to the
and which
about the nature of
, is weak, confused
, and prone to abstract too
in
icable to
notions which do not
therefore, are of little, if any
use
man s dominion over nature.
Bacon wishes to restore man to his true
first
des
ce as ruler of Nature
all the false notions and habits which stand in
and then
the way of
man
a method
In certain cases
means of which he can discover the true causes
of the former
however,
cannot des
out that the
these habits but can
has certa
tendencies,
so tha
this insidious action of the mind may be ranked and
Preface, 445 •
His method, then,
with a way of
the
to abstractions;
its
it is a kind of non-
tial (that is
know!
the
exclusion
unders
ex-
is tabulated and retabulated so that after
of all
instances
of the
, the
can at last be allowed to consider the
"affirmative instances
, arrive at a true and useful
further
is a s
can
; Francis Bacon
"it to be for the interest of the
and future
with his
that
should be
He sets as his task the in-
unders
Bk
a "
which "readil
from the Latin
' XCVIII)
means a
Bacon
and
notions which are "false
to stand,
tion of the
a
reconstruction,
to
some sense
stores up
confused, and
and even,
upon the human mind
and accumulates
abstracted
�other
sa
is clear
Pro em
is at once
ristotle, Bacon conceives of a mind
both
and
a
The
an
seems necessary to Bacon s
telian
to have an
upon the mind
~~~
but at the same time has to
the wrong conclusions
Nature, men come up
the fa ct that
other
blame Nature
it necessary to blame the mind
postual te
men
can be active
that Bacon conceives
active in the
it is
wa
t is
concern
is
ways,
doesn
therefore, since ha
or pursue the wrong
want
for he
is described
skill full
it
is another
t
this is a
of
for in a sense 1
makes
colours into actual colours.
unmixed
in this sense of it is
since
J
Bacon
so
t
so that i
eternal,
prepare
be immortal
e Nature herself
have power
We notice that
enables
of
r~ature
the
are
..i.;......_.;...;........-.~.;;;.;_~
direct
into nature than the former
the
�36
than the restitution and
due and
a
of nature.
II
He uses the
of
effect upon the
--~~
fa cul ties of the
mind, to
......_~~-
to the effect which the
mind, and to
axioms will have upon the unders
axioms can
to nature and its
often, to
of
(and, of course, if the
2
te into nature, so can the unders
clear that the mind, as Bacon describes it, does
It is
have an innate
unders
, and what else can the
than
over nature mean but that he is more
hims el
those
, exercis
of natural
means
, become immortal
ultimate power over Nature
even
if he was to conquer, seems very like this
he had
positive state like l
am mainl
Since
of the
interested in the
of the
mind as Bacon describes it, and in the rela
its "activities
from the
and the
of
those which are called the
Idols
the crucial s
its most s
to be
I
the discuss
the Tribe
in his re-evaluation of
It is here that the
the unders
in one
'
Refute the natural human reason"
which
of which Bacon comes
between
instances..
is used
of 1
is said
The unders
like a false mirror, which,
distorts and discolours the nature of
nature in i t ..
The refutation
Bk .. I, XLI
the natural human reason because
Idols
upon a number of
hiddenness
Nature, 2
not
; among them are 1 ) the
not from the
to be discovered
Truth"
itsel
all the Idols
is
the fact that any true knowl
must come from Nature
that there is
its
tion), 3
al
of Nature
the belief
it does
and 4) the belief that man
If man couldn t know, or if there were
��38
sa
wa remember
9
tha
of sense
the senses:
is misled
hindrance and aberration
dullness
Our notions
• •
the immediate
as Hot, Cold, Black, White, do not
even
are sometimes confused
teration of matter and
of one
The senses are the
the sense
mislead us
flux and alanother
cause of all our mistakes;
more subtle than
therefore
statements about
is
famous
nature" are the necessary resul
man s
certa
is to attain
if
kn owl
For all
himself.
senses
0
the
and
of its nature prone
abstractions
to
are
to resolve nature into abstractions is less to our purpose
than to dissect her
(LI
nature a
means of these
arrived at
almost all cases, the remote axioms
relation to
because
from which
are useless, the "middle axioms" are also useless
The Baconian method
ascent"
in contras , "moves in an unbroken chain
immediate
to
final axioms
a
of nature
he has
were derived, and
so tha
its
and
it never loses
way up, then
are ever watered.
of the
back into the
font 11
Thus, says Bacon
his method, he
have
�has thrown
there is
tra
about Bacon s claim tha
his method
these habits
and
case
form abstractions
and Bacon s method can
When the time comes to
an abstraction
land?
is
I
contras
into
between
Bacon seems
as
addresses
is described
himself
the
refutation"
the conclusions
see
a
I
evident:
cause
be
Bacon:
on
inveterate
to
and raise the sciences
have a relation to
or
�, and the
sense
which is in turn divided into
~~··.. ~~-~tive,
mind.
or
and
elements
Sense and intellect are
of sensation or
the interaction between the
the activities of
from
the
and
and
which are outside
Since these
its el
two faculties have "no nature of their own other than that of
a certain
cannot make mistakes when
(III, 4),
are
the
of sense or
of sensual
and
like
are
are the so-called
about which I will sa
little
that which makes a
to be what it is,
I m fa
of an animal or
forms" which are
are
sometimes
of in this
of as
the "essential
that it is
certa
tion:
the
of the definition in the sense
the constitutive
essense is never in error nor is it the assertion of
but
t as while the
of the
can never be in error the belief
seen is a man may be mistaken so too
in the case of
which are without matter. (III, 6
Forms are often identified, both
Aristotle, I think, and
Bacon,
with final and formal causes
is a
this
soul the
forms
of the intellective soul, and
i t is clear that
for the
is
mind is
~mµv~~ible
without sensa
upon
are somehow derived from
which
for stimulation, and these
are the result of sensory stimulntion of the
of sensation is
it.,. (III,
That is,
the mind
upon the
mind is
work when sensation is not
are
intense stimula
up in the memory
and 2
the mind is
, while sensory organs are
�a
for
we can
is
when we are not
mind is
that is
thus al
to outside stimula
can
the
and acted upon
think without
To
of
an
we can think whenever we want to
even if we don t"believe 0
whenever we want to
as
Error is
and we can
a fallacious
characterized as
That is
white as white can never be mistaken
true
as
is the cause
our
this fact
the assertion ..
this kind of assertion or
a role
assertion is false
we have not
the
forms are
of
means of
11
discursive
can be fallacious
this
this action
i t is said
what
sense
is
is universal
5
these
as a
is sa
as well as
where there
(II , 3
is
the
desire
and
reason
has an
�movement with
is never found
but has no effect upon the
statement, and its
mind.
II
But,
the above
ica tions to the
mind is always
, but
either
or wrong
(
Therefore,
may be
an examina
and
tion
the
conclusion is reached that
inasmuch as an animal is
of self movement; it is not
Both
e
and calculative
tian itself
both of which are the
seems to be
ists
sources of error in the soul
this
in
God forbid tha we should
for a pattern of the world
says
is
out a dream of our own
The Plan of the Work,
llie see, then, that for Aristotle the mind
seems to be the one active force
for stimula
upon the senses
i t moves an animal
desires
animal mus
that active
it too is at first
in the soul,
the
is
have an
of the
desires are a result of
tha
ti on
for
which will resul
from an action before he can be "moved" to
to obtain it.
for these activities
and
the soul has no nature of its own other than a
to be acted
p. 451
sense) is
therefore be contrasted
was mentioned earlier
Bacon
certain
Thus:
that the soul is
to the hand; for as
tool of tools, so the mind is the form
sense the forms of sensible
III, 8
That is, the hand uses tools, and the mind uses forms,
that
is made actual
The Forms are those
them and this
is
means of which
that is
ense
�a
cross a
a sense
as
for
tha , while
each other
sake of
and final causes are sometimes
that
forms
both the form and the final cause are that
an animal "strives
, Bacon says
Matter rather than forms should be the
for forms are
of the human mind
those
tified
them tha
of
of
wherein
it is diverted from more solid
are abstractions,
laws
are
such
ther than
Idols
called
the Tribe
one
7 and
the mind s most
its proper
was
That is,
mind works
advancement
he was
itself as
does tend
forms
O, section
is
man s
be made,
as
less
the
• • • idols of
that can be done
�44
insidious
of the mind
(The Plan of the Work" 444-5
, so that
and
It is
of this nature that the mind must be forced ta follow
the "true
the pattern set for it
of induction.
Aristotle
82con seems to be in
the
marked
of
ties of the soul, 11 but I think that it is very clear that
u
he does not blame all error on the
As the
at the
effort is to effect
of this section show, his
a union of the
and
11
cont.err101.a tive"
intellect,
of the
But it seems
that an additional facul
, if such it may be called,
necessary for this union
some
of the soul, that is
able to stand outside both the
and oversee the
and the
Bacon
of both..
no name for this
that he
the
now that I have
and
mind, it remains that I
and as it were in a favorable
before
Bk .. 1
and leveled the floor of
towards what I have to
in the human unders
For I am
the world, such as it is in fact
(Bk
In his
11
refuta tion
used
of the
a
cxx
1,
Idols of the Tribe,
Bacon has both
Aristotle's theories about the soul..
while
which is
mind
, but if it is also
himself can
be
e calls those
in the commerce between
all sensual
llie see
outside of man the active forces
and the soul of man, and says that
ions,
upon those outside
forces, Bacon, al
that we cannot know
Nature without the use of the senses and that the senses are
therefore
when he says that we may be deceived
even about
True
the senses are
at the mercy of
choose to show herself, and
is
the "active mind 11 must
devise
herself
to reveal
If, as
says, the mind is the
form of forms
��46
the
in
the
but insists that "abstract
sensible
viz both
states and affections of sensible
are not in the sensible forms;
which govern the states and affections of sensible
in Nature, but "abs tract
"restless motion,
11
are
of the mind s
and of its eventual restfulness which is the most
destructive state of all.
True,
what actual sensation
is individuals, while what
is universals
II, 5
But if the so-called "universals" are forms or final causes,
the conclusion of this statement
universals
and these are in a sense
(II'
the
is indicative of the truth, but comes no where near
within the soul;
are
divert it from the true
choke it, infect it,
, and the
of the unders
out
to desire these "universals" is one which can be
and
; it cannot be rooted out.
IV
The outs
1
is one which
s new
of the underthis essay, th2t
have
is
innate
about the
innate,
Idols of the Tribe
for it is these which
are the
one of the mind s favorite idols is its
tions
to be subtle
as Bacon calls it.
linked with the fact that the
that all of Bacon s
careful
or that we are
cannot be done away with
can we know where we are
to land at a
about the motive forces in Nature?
as his
t that final moment
us
away from the lists of
That is,
to abstrac-
But this, I think, (
and flatteries, as
, cannot
when it is time to
on an axiom.
to
which
and land
to land,
a truth
How, when the mind cannot in
�are
sure
a
let
and
necessary
e
this.
�48
But if anyone conceive that my Forms too are of a somewhat
abstract nature, because
mix and combine
geneous • • • if anyone, I say, be of this
assured th:' t his mind is held in
gross appearances of
most certain that these
and alien
from each other, agree in
and that the
power of man cannot poss
and freed from the
common course of nature, and
exaulted to new
efficients and new modes of operation,
the revelation
and
of
of this kind.
(Bk .. 2, XVII)
The Aristotelian:
all the
'
and, as it were,
And the destructive (to this examination):
The· more ancient of the Greeks (whose
are lost) . . . .
did not the less follow up their
engage with Nature;
(it seems) that this very question, -- viz. whether
can be known, -- was to be settled not
"Preface", 456)
totelian 11 answer is very interes
in the l
of the
but surel
the
tables
are not
in the way that Bacon s
rhetoric is -- a moment must come when the unders
the forces of persuasion, comes to its
when it is clear that the mind is
But in terms of
s
conclusions,
the
of
extentions of Bacon's
("of this
of the under-
and its intercourse with nature, the last answer to the
question is the most
If we remember that Bacon tells
us often that the true method takes a crooked
s
, unaided
with the senses, then
to
to
(for purposes of •
of ascent,
axioms, then
' as well as
Truth therefore and
are here the very same
and works themselves are of
value as pledges of
than as
to the comforts of life.
(Bk. 1, CXXIV)
y
�we can see tha
a very
on the one hand
is
be
can't be sure of an axioms truth until
i t to the
and see if we can
said we could do, and if
on the other hand, one of the innate
and then
of the mind is to first form an
all other new information so it will seem
that true
may say
then
is not
nature of
the
That is
of the
it is not so much that
are one and the same, but that, for purposes
truth and
, what proves
scientific
.;.;.;.;;;;:~_;;_...;...-;;;._.;;;..;;;.::.~
be called a
true cause,
be useful
since we cannot
to make mistakes
of the
The
our examinations
we are
able
to say that we
This is
govern
about the motions of natural bodies
that if we can re-
this law to natural bodies and effect
a
be
direction
in the
therefore
t is
and util
finds this facul
Truth
in the direction of
are here the
intellective
then we will
same
which knows Truths as such,
all those in
soul
Bacon
most prone to err.
and
t
consequence
and if
is possible
*
1
Roman
2)
c
in
the
we are
will say tha
efforts succeed
*
*
*
Henceforth
will not as a rule be
indicate the number of the
in which the
appears
the case of books other than the ~~of
book will
after the
tion
Preface; 433, Preface; and
I Bk.
CXX
Bacon is interested
IX,
as an
of Nature
�50
To say that calculative mind
to Aristotle s
; the
tion' seams to me to be a
4)
s
one ..
C. F. Bk .. 1, CXX, XCII, CXVI, CXXVI ( 11 ! do not sl
, but govern it" ..
the under-
�Class:
Members of the Gradua
carry
'
with courage and
will be times when
can muster,
all the
which you are about to
new
that
you well and to express
first, to
Permit me
For many of you, I
in restrictive circumstances where the
find
chances
limited
and action seem
you will manage to
these narrows, and to discover
in
exercise of your powers.
a sa
what I should say
, however
f el
moral
ities
I feel
this
situation
evasion.
some
What I shall be
direction of
at all
it is because
to
or
is an intellectual conscience.
find
f a member of a
and learners who live now or who have lived and written or
pass over
true.
t
see a
of its revelations,
as a scroll when
before.
I
silence the
intellectual and social
What is
If I can
said
of
means disconnected.
seems
the age we
years ago,
t ever shone before
intellect
trace the rise of constitutional
steadil bend a
it to trial and execution
see the
t
their rulers into a
and
and the
men and the
men and every bondman and
the rocks of the mountains
fire expose the
miracles, the
the very 'heavens
him sae the restless
, see
�52
immense distances
violence to
, and
in such a fire of
as less salamandrine
could not have endured; and he who viewed Hell without
would fall to the earth
before the terrific
of intellect
which God has scattered broadcast over this whole age. 11
What, one wonders, could Peirce add if he were to return
f ram the A. Lr. C
under
melvin Calvin, a molecular
that the next
in human evolution is the
and
of outer
upon the
be undertaken, because
space; that this s
that it may suit man in the
each
future to
and read
the orbit of the moon; that there may be other
similar
at some millions of other
in the universe; that our view
of life and of man is
of the
of a trivial to
that of a ma
come to this view
entirel
inverted, from
that
, we
cosmic influence; and that,
tal and observational
upon the basis
science and scientific
Peirce s next
reads:
This
's
taken
ery -- clever feats -but this age is that in which
once more from Revelation
the
sun becomes black as sack-cloth of hair, and the moon becomes as blood,
and the stars of heaven fall unto the earth even as a
tree casteth
her
, when she is shaken of a
wind.'
reaction to all this is less bra
than visceral.
man as a frail creature, a reed,
reed, as Pascal says.
Phrases like 'the conquest of space' or
And I
of nature' seem
that there are
ourselves and our machines
I tend to think of
than that of
more
the earth ..
the surface
a bit of the available
and I can accredit ourselves as
modest ways may be able to do
, and in
the earth habitable
toward
the waste of natural resources, the wanton destruction of trees, and
to persons
violence and
our own, and insis
the
called upon to deal, and
barbarism;
on the enforcement of civil and criminal law;
is
of the situations with
our
in the scales
standards in el
and
t fanaticism and
education;
and in other ways which will occur to you or be forced on your and my attention
now and later..
Some of the details are
of human life and
e, but the end is not.
not be the
The
t
e
�53
most
consistent, we must 1
f a
scale
the means
as
universe is
it is drawn
and the stars are as small as dimes
Now
so many voices
of
more every
in such various tones
of sober sensibleness, of threat and
stern realism,
to truth
there is an
dreams
All will agree:
there
axes
hones
, all will
will agree.
is
I
is
reason
conscience
and
can learn it well
discoveries
The course is
a series
a process
is
is a process
schemes, or deductive
lucid for
has any
the
not a surface, one has
earn repea
Some
I
was clear,
s
as
say,
was
�54
realize with a little shock that energy cannot
be localized in space
assumed it could; or as one can
he had somehow
sonnet he had
read in one way
can call
I
and
about, as does a
This
This
there is a
which
of the scholar who
his way
in
, of course,
and it
s love of his shrubs and
the
the
find that a
can be taken in another.
re-examination and reflection can go on for years,
as
•
and the wall.
must dwell
There may be
But let me say a word for the faithful scholar.
It is
with
that can be known about
to know
differential
scholar
about every-
, or to have de-
astronomical tablets, or to have followed the behavior of
bees
detail
the
of ritual and
traced
or Kant till the loci of
has its
, or to have studied Philo JudaeuE
of archaic
are all familiar.
fame; and it has its
satisfactions,
conscience.
could
about matters that anyone
There is a virtue in
s
if he
Such
had the
the
and could take the
time.
Please understand:
unless you want to.
you know.
to become
am not
am
whoever you are,
You cannot know all that
to know some of the
there is not time.
But to
the veil of a
is to
the swindle
will detect the muddle,
Here
direction of the
the inadvertence, when
or
more than
with closed doors, and a
tion.
It is
of exhibits that
t can be
and
to progress
he is
ect matter
of hotmislead
But do not be too harsh on
of science, that
the sake of progress,
been so divided
breadth of
know.
Amidst a
And what if you do enter the
to choose
you will be
detect it
out.
has
It is so that the scholar can
dead, before he has
any
make for progress
or
as a
�ects
progress, we become
side-effects
the
seen in the
can no
God
and
not follow that
But there are
reliabil
a scale
diminish
it does
And
that
could die old and full
life because life underwent
had
believed
confronted with a
advance in ideas,
be tired of life, so that
scholar, as I
say
with melville
hearts
man
life could
him death has los
scholar as
its sense.
described him, cannot answer this
tears and hie aloft to
down
can add
wi
take
the scholar to
•
as
St. John Perse
the
claims
He antedates science.
seer
archaic man
cosmic
rel a
order
of cosmic events
the secret
be sa
in esoteric
of the world.
attested
and so there were
the sacred riddle
it was necessary
This
and
Listen
questions:
I ask
naval
where is
the earth I ask
where is
seed of the stallion
ask
"Whither
moons and the hal
the seasons --
�their desire hasten
Whither in their desire hasten the waters?
them
and
the source of
riddles; you solved them or for-
the ritual riddles were
feited your head.
wisdom to
It was accounted the
a riddle no one
contest among the
Yanaka holds a
could answer.
a thousand cows.
his sacrifical feast, with a
, has the cows driven away for himself before-
certain of
wise
to defeat his
hand, and
The
One of them
unable to answer,
from his trunk and falls into his
loses his head, which
Reverend
cries out
when all are silenced, Ya
Brahmins, if any of you wishes to ask any questions let him do so, or all of
of any of you, or all of
if you like; or let me ask a
if
or kills himself out of
In Greek tradition, the seer Chalcas dies of
His followers attach
, when bested in a riddle contest
themselves to the
Menander in the presence of 500
with
The Venerable
lonians and Greeks and 80 000 Buddhist monks, throws out each of his dilemmas
Find your way of that one, your Ma
with a
here
We are not far from the
fifth
Greece.
is
For the cosmos,
from which
arise.
have to render
For, says Anaximander,
did
But the sacred
of words
vouchsafes the divine decision
word is, but in the first instance it is a gesture
and a
to a
activ
the
I propose that, with
bad
our words, each of us makes a world which he inhabits
is to
tion to
be nonsense, were it not for the fact that it is not
reason it is not may be that we are all
supposes an intention
e
to the ordinance of time
one another and atone for the wrong
Now all this
love and hate
in that same
must
is
the
the furies must be
rule the universal process
of course and
and he
ike the riddle contest
Strife is the father of all
tic
attraction and discord
power
But the word still has aacred,
who knows it, can live his life.
seer and
who booked such fabulous successes
It is hard to say what a
like all
it pre-
Unlike other gestures, its
convention, an idea or universal
�center is
a
the intended
The central
one
mere
same
has lifeless
same
or if it
same
, from one identi
does so
from one context to another
to another
of immutable combinations
mere sound is inanimate
structure
this becomes evident to me if
the
to
f several times
observe it in its starkness; it
that I
, dried-out
dead
The
it is the
for different men.
nevertheless new.
on the other hand, can be called
of memoriGs associated
Like all
it is
ted and
it is
The memory is
when a memory stirs
appears as bizarre
and associa
a storehouse of
I have an
which res
an earlier one
, or a sentence
a
, or consonant
I live
t is
dissonances
works
that
us
human heart
some ultimate
is
says 5 •
is
mysterious
Parse
time
I
an unwarranted
far
tehsad says
ict
make
a
are those
mistake.
olive branch
before all
the wand
in the hands
turn
systems.
master
�58
Here all is
ear
This may be, a mathematician
, because he has created the entire structure himself
fact that, while
It is a curious
discuss their role in terms of
what
mathematicians, in
and truth
do, use words like
But I am more concerned at the moment
el
and
the fact that
method, but its deliberation and
s
mathematical
, can reveal every
orderly demonstrations carry me
How is it situated in the
mathematical
in
certain
another
The domain of mathematical
of which all the
are
each new
When the
of the
has
of other
of these new
sufficient
had their
without
The
are
has an internal life
mathematical
The various elements of mathematical
are indissolubl
which have led to its appearance, and
related to
s
of any one of them returns s
mathematical
and
he may be able to define them in an autonomous way
not fixed once for all.
one another.
The domain is unveiled
accessible.
opens new
to the earlier theories in
to the
to all the processes
e
of
from its
as
succeed in
it from the
and represent it
verifiable
of associations
of
, and
mus
is
in which it first
which borrows from that
a
data,
The
is not before
or structure may lead to the
ects or structures
the data of
the constructions are enchained in itineraries that
one can somehow traverse.
structures.
te
~..::.;::;~..;;;;.;:;.~
in one way
The evidences obtained
of a
in an
or
These constructions
progress
nor
e world with which we can
for instance,
a
cons
how is this
as such in the field -of
immediate rela
lated.
, as on a
ife of consciousness?
ects are not
belong to a .
in an assertion
, each s
We can ask:
fulcrum, round the law of
the
a
ization is
ever more
It must shell out, from a
determinate
•
It must
in the mathematical
as more
structures are
the
�59
conclusion?
t
it all too briefl
was
autonomous
tions, and contain in itsel
would constitute the
a
which would
the
to all further
mathematical
mathematical
and
here be
oeonT"!::'I
tion
elaborated in
that
ti on.
The
be
, but would go
and substitute for it.
the limit-idea of a
silent and full
own proper intell
We are here before
exis
its
the characteristics of
the
and those of
model and
all
discourse
I
means of formalization
y
a total
is unachievable.
various theorems
sta
it has been
detail the
claim that,
are
content of these theorems
the
But I
that
there is
s
more
back
resolute!
to reflect on its role
of formalization, and
one can see the limitation theorems as
believe this view can be
the relation between the
ife
character
the
out
instance
a
infinite and the actual infinite.
is the notion of an
each o
constructive
; the latter is the resul
be
that
to
substitute
There is
tha
be said about their
knowl
tha
heard that such a system cannot be achieved
which can
a
realized
Both
and mathematics construct, and
, as into an exterior
space, the formulae of their achievements
mountains
Both
mathematics, and
their
mathematics of
an incessant
with the world
ways
a
I am
Both a
a
in widel
Where are their roots?
which is not a
as a
seems
most
e
one
conseientious conscience.
to be a
indeed, the
The mind s
its work
What
�is
affairs
the connectedness of a manifold of elements.
The
grasp
eness
is
idea
correctness
tive links
movement is
Whatever is
time
escapes from the immediate coincidence
self with self
into the evanescence of the past.
itself the
There is no moment
of all the others, a
f the
as well as the future and which
itself
dimensions of all
instant involves elements tha
What is
sense
are
these
conscious
pas
mode
Consciousness
the
the future
, is open
There is an
what is not
consciousness
the non-
direction
the
, is
moderation.
s
pas
as
ied
seems so characteristic
past as i t
t
is there
can have sense
it is
an outside
some
has had
constitute itsel
consciousness
roots
, is
its
attunement to
can raise the question
its
, and to pursue
courage
its
�virtues
Let
gesture
this
liked i t
et
back
�
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The Collegian
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�CONTENTS
. .. . .
kbout the Cover •
Preface ,.
•
e
"
•
•
"
•
•
The Origins of Modernity A
•
.
President's lvlessage •
·•
.. ..
.tt.
•
. . . ..
.. .. .
..
.
0
..
•
•
.,
1
..
..
1-
2
•
0
..
3
.4
Lecture • • Norman
Note on The Problem of The Giver and
Thomas Hopper •
.b. Note On the Ineffable ..
k Reply to
• .. • • • Parmeniscus ,, .. .16
Note on the Ineffable n
..
.. Peter
Steiler,
the elder
18
g
Der Schone Gegenstand • • • .. •
ze
.._,c,..n_,__, ....... :
•
von Schvordtner ~ • 20
Owen Sears" " 21
Ivlississippi Homogenized - A short story
Judd DuVall .. • 22
Word ., • • • • • .. • Walter Hinckley .. • •
�- 1 -
editors of ·nThe Colliegian n believe
de
should be
ely connected
academic
•
cover
of
occasions,
has
to
allego
of such
e
some
repeat
eQ),~the·cha
the cover
0
�... z PREFACE
This issue of "The Colliegian" is devoted to articles
content and subject matt-er bare a
that "discourse is significant."
wb0se
to the idea
Since this· will serve as an
introductory issue for a large portion of the community,
th~
editors have asked alumni and friends of the college to submit
articles for publication in it.
Those readers who are familiar
with "The Colliegian n will find this issue to be merely another
in a series of scholarly pul;>:t.t.cations.
encounter "The Colliegiann· for
,
~
.
·'·'
'.,.i
I
first time with this issue
.
will find it, and those which
interest· and edification.
We hope that those who
, to be of continuing
�On April 22, 1963, ground was broken for the new college
at Santa Fe. With the overturning of the first spade
of. dirt
came a revolution,, rviost ordinary colleges expand when their
need for space increases; our college, when faced with such a
need chose to duplicate itself$ Indeed, Santa Fe is something
in the way of a revolution is a pioneer venture
American education~ After much long work and planning I am
happy to report that our dreams have become realitye
The classroom building, student center and dormitory
buildings are fast nearing completion. Like all new college
constructions both here and in Santa Fe, they are earthquake
proof and are equipped with the ultimate in acoustical and
temperature control equipmento In addition, the moat
several of the dormitories will provide the maximum
social
security for the students at largea Approximately 80 students
compose
freshman class at
play a truly unique role in the history of the collegeo On the
one hand they must uphold the trad ion of the students being
allowed the utmost freedom for individuality and self expression,
on the other hand they must not completely alienate the
c
of Santa Fee In the jargon of the college, this feat
can be accomplished by subscribing to the "dialectical interplay
between
and
()n The Director of Admissions
assures
the Santa Fe freshman class is ably e
for
such a
, which
compo
new
the motto
community, will carry
:
VT The books are the teachers" n
They, (the
is , will be on a salary scale similar to that in
The administration
well equipped to
and vital tasko The treasurer - business manager,
member of the operation, has already demon
a
ability to master the manifold facets of
members o
This brings us to the problem of finances. I am
the annual giving campaign to help relieve the College's
somewhat dismal financial situationo My assistant has organized
the giving campaigm into three major phases,
two interphases and six sub-duplicate minor phases. Such organization
is designed, I am told, to distribute the giving among
widest possible base of income during a maximum period of time.
As I complete this message I am preparing to embark upon
a fortnight of
ch will take me to the
corners of
the world. I
to spend most of my time acting in an
advisory capac
to the local school boards in various under c
st'
my
e I remain
to the philosophy and program of the college, both here and in
Santa Fe.
�- 4 ·-
J_,evy
.L
No play Shakespeare wrote
s
en so neglected as
Titus Andronicus, and yet few plays would seem to
more
interesb ·than· Shakespeare's first tragedy; for its t6wering
tragi9 hero, for the richness.of its incident, and fcir the
strength' of . s poetry .. ·· Indeed, there have
en a few men
in every age who have.been fascinated:
the perspectives
Ti·tus op~ns: such diverse !Ilen as Goethe 1 commenting in the .
famous ReplY: to Kb za bue, Alexander· .Pope . his critical Pari Ba thus, and Berthold . Brecht; who s gl"',asp of Shakespeare'sintention: was as profound _as his rejecti.on of
But the·
~cademic
· hava largely avoided
· except .to d¢bate
. among
d
-!llatt
of eniandati.on-;
-fina;Lly'
whether
sp:eare. 0ctua1ly wrot:e it.,
·energy'·erribara:sses
. them·;:•
catagori'es .of literary critI
se:e·m inadequate
.uiff-:Lc.ulti·e s po s
by
seeming prc:ili:f.erar
elaboration - .
idei1t ,, inc:J-udin'g-':·:
mutilation· and rane ,-.
is a br·:i_lliant:=~but
work"" ;: And ;:,Ye:t it:· .-.
C:"C?c}:ible:J:t~nat
'as': Shakespeare ::. s have
had ihte·:Lligibl.€
:.constructing :.th.E?
. .
did_-o· .~ Drobably
have;
made a mistake in measuring the capa-city of Shake:s,pea1rei
of our
s and ours el ve$0
···'-~--' ,_;
·
quited·' ~rid ,;we can no
·-·-~Shake spe~r~'~VJa§·--p:!7imari
'r:~~:j3_·,s · establ1shB$
s
J_~o n gs'"' --Fo. :-the ..
2
gr'o.11p ?. b :f
narning- Romar{ hero\~'-S'~
~SJ1e·s ~ Ho9(;lh-~ ;pl~y,~:~ 1sh ow
.we. seek must 1 finally 1_ be_-- pbJSti,.c~·lo.,
that ·we rnu_st·;:'_h9.rt
setting of the
<I ·- .:..
_; _ e~mine ..
....._ ·. '; ·- ~- :::_j
-· ·, ..
to the group of Ro_man play's, it neveramong them.; · The, other plays' Or."' this group
_ _,,,___ Caesar and Antoriy and Cleona t:i5§" ;.,· a.rf{and collecti veTy"-to-· thest~dy-of th~ ..'..po5~reatness
a q&Ianging :_R.ome, through t,1:J.e exam-,
three. of Rome 1 s greatest men,,
In a .larger sense,
these
Republic .-and_~Empire; ;7<:with . Julius
pos-i tion of the fflan ~wnose.·. gr.eatn.~·~33
:;:>o
ing,made-gr~atness·~mpos
:.. •
.J. • i
•. :.. .
.
• ,'
: ::
.
. .•
.
;
\..)
. j._.
�"the man who became a godo
to this theme?
n
vvnat relation does Titus bear
The difficulty in framing an answer is posed first of all
by the
ct that no Roman; great OT infamous.~ was ever namea.'
Titus Andronicuso Furthermore, the temporal setting of the
play is unclear,, The first scene opens on Saturninus Y and
Bassianus' struggle for the imperial throne" That would seem
to
the date as post~-Caesar, at least" But
1
is based on a question of political principle~
pleads:
wa_s the last
"I am his first-·born son
n
That w re
rial
Bassianus, in his counter
nBut let desert
, Romans :i
speech sets forth a royal principle~ primogeniture~
second a Republican one of
ct
on a basis of merit ~
Republican principle v1ith
roots buried in Aristotle's
definition of c
zenshipe
ect of
s confrontation
Aristotle and Caesa~
s of the only
Shakespearian play named
a :i.wr:.
ent
" is to
place the Empire and the Rr2public before us in a relation that
is not
cal at all.
diale
f'.al
mimetic~
We
must be prepared to follow Sbakespeare
a dialogue,
l..h
. ,,_
1°
or l. f you pre f er, a myL.~ s
lGS re~
1 s myth-~t olling
orically given / to Plato
of which, indeed~ it bears some slight touches~
this dialectical tension
s ~een csL li
appears a..
III
The role Titus
to play is suggest
our
contact with the drama by his very name, obviously derived
from the Greek: aner, andros:; ho<:·
indeed
appears
from a magnificent defeat of the Goths:. Further,
his entry onto the stage is prepared for by a speech of the
Iviarcy:s who says he is surnamed Pius')
s n is
notoriously
epithet belonging to Aeneas; Titus recall~
the founding of Romec This theme is further developed in
1 daughter, whose name~ I.avi.nia:i is that of Aeneas•
hard-won bride; through the sacrifice of Alarbus the Goth,
whose name recalls Alba Longs; also from
~ , and in a
speech of Titus 1 son. Lucius: the sacrifice of Alarb1:s is
to be "ad manu fratein
an appeal to the old worship of the
gods.
further:
tus 1 own
t
ch,
of
himself:
�- 6 -
, and careless of thine own n
(italics added)
which is an essentially kristotelian definition of the
of
• Titus is presented to us as a great-souled
man.
An adequate measure of his greatness.
, however 2 on.ly
to be found in that moment in which he is offered.the imperial
crown by the Tribunes of the people. In this moment~he shows
himself to be greater than Rome 1 s greatest heroes.. For from
among all of them Shakespeare has shown us ust two who. could
claim divine honors: Coriolanus and Julius
e·saro But for
Coriolanus, wooing the people stood between himself and ac
the essentially divine honors he deserved, and he could not do
it; he would not bridge the ineluctable distance tha.t. remained
for him between the giver and the given. But Titus' greatness
was such. that he did not -need to~woo fickle:masses. Caesar had
scruples-about the people, and indeed achieved a substance
by that of
, but could not
s
honor that should
accompanie·d:~
.
most divine Romans ev.er to li.ve~:,
.. · histprical Rome ... Only the story of: a· Roman who is
·of the gods, or perhaps .even greater than--the pagan.Lgi:>'ds: of
can relate.
death of. the ·pagan· gods, and~; the~
ianity.
·-
his
most complete paradigm of Roman
less a tragedy. Why does
of
.great-souled man
be given· to?.. I think not~·
is threatened by Saturn~nus: .: :
s
, would thou were shipp'·d to
the crown to Saturninus
in part
atta
legal - Saturninus deserves the crown by primogeniture;
son of an
king - but
part
is
s
to
show
that inspite of the insult,, .TDitus' ·highest
:virtue as. a Roman
that of. being a~·thoroughly decent man;
a. gentleman.. But that is not enough. Titus 'Andronicus ·is
a play
the tragedy that.lies unspoken in.the pages
of· the
Only when philosophers are"
•• and
not a
sopher.
·
·
to
of. Titus'
i.s
swift.~
In
la. vinia to SaturninuS' for hiS' s. hrid e,
Bassianus, who claims her-a.s his
warrning· by Ma.rtius:. "suum cuique is
second use of Latin
the play)
Ti·tus.
son
guarding the escape of: thG) lovers.
Titus cannot understand the impossibility of bridging the
�distance between the origins
Rome
s decadence,, :ndeed
as a gentleman, he must be unwilling to face decadence for what
it is, so he kills his own son, in an attempt to achieve polit
cal good beyond Roman justice
which is in fact in contradiction to it
Saturninus marries Tamora, the Goth, who entered
the state as a captive of Tituso
The sequence of events flowing from Titus' re
or
inability to make honor serve philosophy for the political
good is relentless: it reaches a terrible and awesome climax
for Titus and for Rome - and inde , as we shall see, for us in his decision
bet
to cut off his hand~ his sword hand,
that the lives of two of his sons might be spared by Saturninus~
He does so,
that we might
fully alive to the weight and
majesty of the issuts involved, he does so on stage, before our
eyes, only to
his dead hand returned to him with the heads
of his sonsG The climax of the tragedy of Rome or the
ct
anc
ical
ct ice,
by
trick of a barbarian - indeed a Moorish courtier - at the
Roman court"
The
c
e of both
and the Imperial Rome
which could not contain his Republican virtue is inevitable;
the only survivors of the final ka ta strophe~ in which Titus 7
Lavinia, Saturninus, his barbarian queen, and her two Gothic
sons go to their deaths, are Martius - whose "suum cui
n is
for us Roman law> - and two characters whose irnniense import···
ance
es precisely in their being strangers to Rome0 Of
e
, we
now only to remark that
form
s-peare gives the
stroph0 is in harmony with the theme it
closes:
having Titus slit the throats of the men who raped
and mutilated his daughter, and serve them as a casserole to
monstrous mother, and in concluding the play in a universal
slaughter Shakespeare brings us back to the world of keschyilius'
before J--.thene 's court replac
vengeance
el is come full circlen
his greatness as a playwright as well as that as a man
of political wisdom that puts all this on stage: the sight of
the 6ishonored Lavinia) holding between her handless stumps of
arms the basin
o which pours the blood of her pitiless
enemies must be unforgetablen
So ends the man of courage ( manliness). Inevitably during
the course of this tragic kine s, we wonder if the hero's
name is as ironically revealing as his seconde Titus is
the anglicized form of the Greek word Htithosn which in turn
is an obscure form of"tifuthasos# ( Cp" Liddel & Scott, 9th ed,... )
which bears the meaning rrtameG, domesticated .. 71 This word,,
interestingly enough, is used by Plato in the
and
of the statesman, the true statesmanc Titus is
an
ironical name - its obscurity is Shakespeare Ts device to keep
�-- 8 -
audience's eye on the action,, But it inevitably has
echoes for us. Some measure of the care Shakespere has us
constructing and writing his myth can be seen in a metaphorical
extension of the theme of tithaseia~ Just as the Greek word
is opposed to the word agrios (wild), so i2 the language of the
play, "When wild beasts are used in the j_magry, the panther or
tiger almost always ironically take the place of the lion;
the lion is the classical creature most like the hero, but the
panther is merely wild.· The irony is carried even further:
when a lion is finallyt used, it is used by Lavinia vainly
pleading with Tamora, the empress; to stop the rape by her
sons: she refers to a lion moved with pitya
IV
of T tus, up to the paripateia, occupies
second, or central act of the three, is
three acts.
the rape of Lavinia,,
must look at. this act
concerned
of Rome from the other dialectical pole,
which shows the
of
decadence, before rai
the -question of the
survivors of the tragedy ·-· that is, Shakespeare's
characters of
.of
world .
·rape is performed during a hunt by Demetrius and
sons of Tamora. They begiri the fii"st scene by ~confess
great love for Ia vinia, until Aaron, Tam©ra 7 s Moorish lover
proposes
rape to them,. In order that we not loose s
the significance of their passion, Shakespeare·· has first
Demetrius, ca
Lavinia
dai.nty doe, 11 :
we hunt not·' t'le; with horBe nor hound,
But hope to pluck a d~~nty doe to ground.~
as
a
so
the doe. It comes from Book
i& and is the
second creature mentioned
the hunt sequence during which
.Dido.
begin their ,liason,, Th~ first beast named is
the .goat, famous for its amor0.us procliv:Lt.y;:,""' During
hunt
in Titus, Tamora is said to be a n1acivlous Gothe. a · For the
Elizabethians Goat and Goth:were phonetically the-same;
(Cf. As You Like It,
iii 6·-9) __,,.As an astut~.E?::·_$tudent of
Shakespeare has· obs_erved: "They were sol.ely of
s
and their
ions were almost totally political or
erotic;" Demetrius· and Chiron were captives of Rome, and hence
apolitical.
were in this sense, then,-nGoths"o Further,
there is
other place in. Shakespe:are where a lover
Demetrius
a s.earch for his love: during a hunt,
that is
Night Dream,, That Demetrius was an
athenian,
part in a festival celebrating the
founding
seus~
The later Demetrius, captive
of Rome, seeks
_,_end, reveQg.e ;, the revenge of uprooting
the foundation of Rome, in the· pet·son of Lavinia,, But his
o
�- 9 revenge goes further; he cuts out her tongue and cuts off her
handso Rome is not only to loose a clear conception of its
origin, but it is to be cut off from logos, a fitting revenge
on the part of captive Athense
These events occupy the first and last of three scenese
The central scene shows the murder of Lavinia's husband Bassianus,
his being thrown into a pit, and the falling into the pit of
two of Titus' sons Martius and Quintus (who are to be blamed
for the murder)e1 The imagry in this scene is most striking~
especially that concerning the pito It is called a "subtile
hole,n an "unhallowed and blood-stained hole," a "den,n a
ndetested dark blood drinking pit," a "fell devouring receptacle;,
and there are references to nthe entrails of this pit," "the
swallowing womb of this deep pit." Further the two young men
the
, and
can't see. Here
become drowsy
central scene of the aentral act of the only three acts
Shakespeare wrote explicitly dealing with the collapse of the
ancient world within the context of political theory, we are
clearly shown that the source of that collapse is to be under~
stood in terms derived from a confrontation of the cave section
of the Republic with the passages of the Timaeus discussing the
Receptacleo Only by recovering the Shakespeariam teaching on
the relation of the Timaeus as a whole to the Republic as a
whole could we answer the theoretical questions raised by the
first half of the playc But at least we can observe that in the
crucial scene there is no mention of the Godso
v
There are in all eight quotations, or near quotations,
from Scripture
the play, their order in Titus corresponding
with one exception, to their order in Scriptureo Of these
four are from the Old Testament, four from the New, and
of
those from the Old Testament are spoken by Titus. His sequence
begins with his lamentation over the coming execution of his
sons in III,i, and before he gives up his hand; he quotes from
-n
Genesis IV, 11~ It has a double conclusion in Act IV: I Kings
with a coupled use of classical authors: first Horace's famous
"Intiger vitae e1oc etcn in which he defies the power of the
l~oor Aaron, (ineo of Eastern Religion, as we shall see) followed
by a misquote from the Aeneid which rejects the possibility
Divine justicen We are beginning to explore a new dialectical
tensiono The r8solution of this tension as regards Titus is
found in the Arrow Scene of hCt IV and its sequel, containing
these last quotations, it is the most difficult single scene of
the playo . This scene.which .occurs just e-;r~_ the first
quotatiori:of Rornans in IV, i; -.plays on the names of all the
classical gods" further it"is 'the only scene in the play in
which a clown appears, and Shakespeare's clowns always bear
metaphysical or cosmological importance, as they are the only
characters
Shakespeare who invariably raise questions
'
. ,/
�conce
whole.
sta
Twelfth Night
Touchstone
You
both of whom are ref erred to
significantly
the course of the play - cp. Titus
i
with
ii
8
and TA
111 110
AYL III iii
:the sequel ·.to the ..H.rrow scene the c
is hung by
sighifying the dE;ath of pagen religion; his last words are
on
Virgin:
' Lady, n i.e. by our lady.
quotatiotj.s from_
New 'Testament, mo·sfly from
are spoken
.H.aron t-he _Moor, the nvillian" of the
Aaron is
an Egyptian n,ame.;- was the
performed the ,~miracles before
Pharoah, accompanied Moses on the Exodus, -and built the
gold. Lest we hesita~e in identifying the Aaron -pf .the Books
of 1v1os-es ·
e
· of
in the f.irst act when·
-·, _ Shakespeare Inakes
-·..;..; 23.) ---~"But ,.A,ar?n
·\.,u,;.1.i'-..k.;"-'!.Y-
'
.
.da
o~bj
Aaron's
Tamara by
.view,- iri
rgplies:
,· -and an
the Roman
on the subject
-·
s
'
�do some
execution?
, madam, these are no venereal
signs~n
the medium of the
t quotation shows what
ed the bond between
re
- haron's eyes. They have
Dante and Beatrice, and are held together by theology"
~m~k ~s us
poss
of using erotic
e a structure both po~tic and
eological~
••
Further evidence of the irrelevance
is objection
coula easi
be found in connection with an investigation of
.aaron 's mistress Tamora.
is a shame that t
does not
permit us to discuss Tamara; Shakespeare's development '.)f her
is most interesting, especially in the light of the accusat
of ant s
ism raised on gr~unds supposedly found in the
Merchant of Venice. Let it suffice for present purposes to
observe simply that the imagry connected with Tamora is rarely
c ssi
; and
several t
s compared
s, a
en not of Gaul but of
Her name reca
two great
s - the classical one amrnoros meaning portionless, and the
New Testament ammos - sand. Tamora, by the way, is fully
aware of
sues at stake
her role
the action~
the
e scene, at the moment
the framing of Titus' sons
murder of Bassianus, she refers to the ?fcomplot of this
ss tragedy.
an historical moment, she realizes the
orical question involvede It has been asked how
can consider the events to be tragic, since in fact she has
I
her s
ion at this instant is
We must mow take a slightly closer look at the sequence of
the
Testament.
, from Romans
, is spoken by
Roman Marcus who attributes to Titus
'swords : nvengence is mine; I
repay
He is mistaken, as we have seen but his
a context of
ctical contrast needed for
of
playo This contrast is further developed when
Chiron the Gre
ironically quotes from Romans XIII 9-10
ecting ch~rity for lust (IV
43 )~ Then the whole
cter of the use of the quotations changes; the last two are
spoken by Aaron and are not the least ironical. This is
accomplished
a sudden change in Aaron ts relation to
Chiron and Demetrius, and indeed to the whole action,, Vilhat
causes this sudden shift in perspective, which takes place
lines? haron is presented with his infant son - his
born son
he
It is this son who is one of the two
ipal
of the close of the play. The effect on
Aaron is elec
; he quotes from the words of Jesus,
only
such quote
play. To protect his son, he kills
s
nurse, forsakes Tamora, t eking Chiron and Demetrius, and
flies to the Goths when he is captured by Titus' son
,
who is leading a
c army against Romen He betrays Tamara,
�, Demetrius and
as
,
to
son.
betrayal is to Lusius an act
uncovers for him unsuspe
commits his first and
honest act
he makes the last
quot&tion, a
different reference to charity.
Shakespeare's perspective on the infant
whose birth
we see.that of modernity
self is suggested in at lea
two ways:
, the baby never cries, secondly,
Shakespeare's use
source material.- A mid-eighte
century chapbook has
en found (
a
copy) which
contains a version of the Titus story
the scholars
have agreed represents the only known source from which
Sha.kespeare may
drawn elements
his play. Now
the story as related by the shapbook, the infant is discovered by
emperor and the court, and when a
cerning·its.paternity, Tamara attributes
not -yo
states
that
was "conceived
force of Imagination. n
·about
chapbook suggests
n
a
the
support
�- 13
~·
Secondly, Bassanius :_n
only has a narr_e re ca
that of Bassian:) in the~
Ven1-ce ~ but
a g0lden ring, which
e pit 'into
is thrown. Ths them0
is commerece
symbolized by
ssianors
siano
is married to Portia,
undervalued to Cato rs Portia no
One entire scone of Titus is devoted to comparing Bassianus 1
Lavinia to Cato's Portia.
virtues
displays. Perhaps this can ' d cuss
quest
period. The issue at
is the unity of the Shakespeaean
corpus, in which most scholars are concerned only to cU scove:'.'."
evelilipment of Shakespeae Ts th:)ught" Tf That
is
revealed in one supremely synoptic play
Andronicus~
the imp era ti ve task of Poli ti cal
sophy to rec :Y1Je.r
tea
only
the possib
e~ception of
to understand ancient political
antl to bring the anc
mo rn worlds
o
ion. Thank you,,
�- I4 -
NOTE ON
PROBLEM --- GIVER
OF THE
-
GI\7EN
Thomas Hopper
In our existance as reasonable and social. beings, our
understanding is constantly confronted with pairs of _semi-mystical
interrelated contraries: freedom and necessity, being and non
being and the likeo Corresponding anomalitic· dicotornies present
themselves~ which, while equally dark, concern not contraries~
but correlative complimentar;r elements, such as lover and
beloved, being and becomingo A member of_ this latter group that.
holds considerable promise for conceptual enrichment, and,
surprisingly; one that has been butscantly and negligently persued:
is the problem of the: giver and the giveno Though endemic in
Western literature and theosophism~ this substantive paradox
has recieved only evanescent philosophical analysis o Our presen:l:r
hope is not to fully resolve this fundamental' anomaly, but
simply to bring the interest and labour of the acq;ciemic commun:Lty
to bear on ito
We turn first to the giver .....the very nexux of the problem,,
The act and being of the giver denote.-s.. an absolute . (if principly
symbolic) desire for aesthetic transu~·stantial unificationo
This habitus of the giver is an image of the apodictic manipulati-ve
power of the envir·onmental contingencies by which we are bound(J
The fundamental sensual manifold of the giver - his Weltverhaft.hej tentails a true correlative principle of his beingo Our original
03tensive duality is revealed as a transcendental trichotomy of
The given, on the other hand, being rather a conceptual
schematization; can be understood only as an underlying
concatination of inductive inferencese It reflects an atemporal
ized epitome 0f sacramental actualization~ and thus,
eritivly, a tautalogically absolute antithesis of inductive
of
same symbolical
vvhere the giver constitutes the agent j the given forms an element
of co-extensive subconscious regcneratione
The problem of the giver and the given is therefore seen to
be a representative modal antinomy characteristic of the devisive
interplay which continually undermines the formalized uni versali -';:,~r
of our thcmght and action o Its paradigm is the substratum of
bifurcation demarking a semi-convergent disparity
of the phenomenalistic expiation of our society.
The
ectronic primacy granted to this side of the
argument in the face of its character as a ubiquitous
symbiotic aggregate should be t.al\:en_ only as a polymorphous
cognative norm0' The oviparous regulative coherence of the
entire qualified field serves to admonish us of its conposite
�- I5 -
permian
this not he forgotten.
Although this explication has by no means exhausted the
problem in hand, it successfully delimit s a fruitful realm for
further topical synthesis, and sets out the pronominal framework
within which such
stigations
be
out.
1
�16
1
,,,
'
��- · 18 -
A
- REPLY
TO "A NOTE ON THE INEFFABLE"
-
~
~~
~
~-
Peter Steiler the elder
Editor's Note: As soon as Parmeniscus had complete~
his Note,~passed it about an~nymo~sly amo~g a
select circle of friends. Imagine his surprise,
when~ one morning, several days lat~r, h~ discovered
on his desk in a hand remarkably like his own, .the
following r~ply. Who had written it?. The only clue
was the name with which it had been signed: Peter
Steiler the elder. A hasty check through several
German encyclopedias revealed no such historical
personage. Then he observed that his own copy of
The Complete Sherlock Holmes (Sir Arthur Conon Doyle,
Doubleday and Company, New York, 1953; preface by
Christopher Morley) had been left open to the facing
pages 544 and 545; and that someone had underlined
in red crayon, the following words: "You know !!!Z,
powers, ~dear Watson, and yet, at ~ end of three
months I was forced to confess that I had at last
~ §11 antagonist who was ~ inteileetual 8Quar.- Ml.
h?rror. §-.1 his crimes ~ lost in !!!Y. adr:iiration at
~ skill."
The identity of Peter Steiler the elder
was soon tracked down; although the relevance of the
name to the following reply remains, perhaps, obscure.
Was he, in fact, a henchman of Moriarty? And further,
woul.d it follow from that fact that he was an Ancient or a Modern? The reader, like the editor, will
doubtless find the problem a source of endJ.ess fascination.
/
/
/
/
To be sure, Parmeniscus, employing a chaste rhetorical form
appropriate to his chosen theme, conveys a certain notion of the
ineffable (although it is not clear that he und e r s tands all the
problems involved). However, his stubborn distance from the
flummery of the Strauss school seems at one or two points to
break down: I refer in particular to his footnote five, whose
textural reference (Critias, 123 As) implies either a compromise
with the popular view (paragraph 3 in particular points to a
direct contradiction), or an error whose essential nature must
perhaps be left· unmentioned (Dielskranz, Parmenides, B, 25).
(Unless its presence in such an elegant position implies that it
plays a dramatic - ironic, mimetic- role in the economy of his
paper, and ironic refutatory role, as a kind of sentry standing
to warn the wary away from the thorny, vast deserts of falsehood,
silently shooting refutation of the silent contradiction between
footnote five and paragraph three.) The question for the careful
reader must be, which branch - which horn of the di-lemma - is
intended to give way: footnote five or paragraph three? The lie
in the street may sing a tune supplied by the lie in the soul.
�- 19
~·
It
be true that an explicit refutation of an
author, a scholar of the
of Parmeniscus, whose hint
us
how much more, then,
made explicit,
to a pleasure of illegitimate thought as dazzling
as
irmnoral, would
ourselves
immoral - a boy's
display of unchaste
the elms; that we,
our refutations, must sidle up, hurt, and withdraw, hoping the
reader
understand and follow; pursuing the part of a
superior man.
Such a suggestion would not have seemed strange
to
; although even so just a scholar as Harold
Cherniss (Aristotle's Criticism of the
Socratic
)
find the suggestion ludicrous-~-However
may be, one
certainly_free to propose a
counter-c
cism to my criticism in paragraph one; one
I say, to propose a counter-c
icism to
icism
paragraph one.
certainly, Parmeniscus does not overlook the
poss
ies of the crucial addition of Biblical to Classi
thought
delineating the character of the synthesis,
recognized
later in Germany, but effected unconsciously if one can guess the quality of their silence - by the s
century philosophers in their most fundamental thought..
Indeed,
any consideration of Parmeniscus 1 theme cannot overlook the
overwhelming importance of the more or less conscious
chment
to the Augustinean principle of deficient reason.
any rate,
Parmeniscus refers not only to the very Greek meanings
ssed
emnestra Agamemnon,
83-G63 ) ,
also to the
explic
statement of the Divine name in Exodus (which he
rightly associates with Plato's assertion that a good man should
mind his own business).. vvhether or not these considera:tions
are decisive, the thoughtful reader must decide for
;
or perhaps .Parmeniscus
desire to take up
cudgels of
r to
e us
�20
~
"'
SCHONE GEGENSTAND
Obwohl du suchest die ganze erde rund,
Du kannst nicht finden, entwerder mit Gehirn oder
Ein ding so re , so gut, so gut, so vo
Als sieser hierstehend schoner Gegenstand.
frohes Kind, obgleich
ig,
erbrust sauft sehr
ig,
lacht, und schme
et
er so
,
, zu tragen
nett,
Schnee zu
zu
v'ogeln
,
am Magen,
's etwas schoneres? ••• Ach, wer kann dass fragen?
vie ich machen Lieder ganz ohne verstand;
ma
den schonen Gegenstand.
von
'
'··
-.,.
�COL LEGNO
od €.
't:....
\31, vdd
L.:;
Oh
e~ble logos, on lliind's anvil unendingly pounds,
Forged. The ~epheste~n fireirks singing, seen in ~l~to's C2ve.
OT~ET
Trees hunc;ry, demc.ndinc;
Our,.nos' mate, the c;re2.t mother, the c;iver of life,
Her bret:.'.st flmiinc c:,bund::.nt.
,rbore
temJ)les - c;reen tinsilled colurm.s touching'
strcachinc; u1·-r:.r;.1rd
Yet touching, i.-:i th tress refulr:;ent choirs
, ihere the s:,reet birds sine ~:ncl inhc..bi t,
Ldoring :rtolemy's shell.
T'..ri t
Tit bri t
So rudely f orc d
Terue
Fruitfully ch2ste one, cloud burden's close friend,
Fully e:::cpressinc; Spirits urmtterable end.
~ ens are mdde by fools
~,!hat ore of tiraber cc:.n
:[or The '
like me,
ins-oire .: .. chilles shield?
is j eo.lous.
Translated by
Ouen Sears
�- 22 -·
(dig we must)
Judd DuVall
I
; Vinegar,., " e
I was a young man, and lived all alone,,.,o
Was
delta, or just the
those wonderful summer mornings
's
car
, to
your nose J
one
wear s
Grandpa Ts clothes J
we
n
Honkers weren
hard to
you knew where to
Clayfeet
knew~ He would hobble
would hear his familiar li t·cle voice, squeakecstasy: n
e·-it~
Wall~ y 1 all, cruddle
't got one~eo
would all stop,
of
malerial stench, and trip o
through
through the maze of rusting hulks
the
familiar voice~ We would find him,
hood of a '36 Cadillac, or t28 Delages
red-neck son-of-a-bitch, whut y 7 all got at
of hammering would stop and slowly his
bald head
ear, and he
ce us
a look of pride and cast in his le
in his hand was the prize; the rare honker
we
stare at it with a feeling of envy-mixed
admira tio:m:., three parts to two
n\Nlla ts it say.? Bill,
1" He would shyly hand it to Big Ralph Snopes, who
fJ·
says, Delco-Remy 1 Dearborn, Michigan,
Number SN 26733 7., n
"Delco-Remyi ? gosh~H
balck pressed steel~ Probably made on a
automatic forge, from Pittsburgh Steel Co •.
sheet, catalogue # T 1427 l/S, carbon steel,
open hearth blast furnace method, perfected
's boys
1903~
Iron from Michigan,
Monongehe , dovm the Alleghany,
Cret chpe e ()
�... 23 -
Then Old Grandpa Tdzous would come running. nHey
get outs there you kids . n Big Ralph Snopes and I would
a car over on him, and off we'd bun to the echoes
of his muffled screams0 HJi.rghh:- .h.rghh,, o .. ,., "I say on
potatoe, twc potatoe, three potatoe, foura
It was May aga , and we were liging on the old Hog
Bottom .H.iver.., Or was it May? Or were we living? From 01J.r
ncaven which had neither entrance nor window, one couldn 1 t
tell~
But "Btill it was"
What certainty is present
What mist must, what galant phalanx,
Who then?
Oh incarnate cow"
When, .. ",., rwhen? .
~lgae
and I ( that wasn 7 t her name, but what is a name
to a fact?) were ever~present then in those days'.} It was
a life of continual breakfast,., Bottomless orange juice in a
sea of coddled eggs; punctuated by the Great Toaster, the
sounds of Being Bakingo Our conversations are what I
remember best - our talk was the synbol of our Great Tran.s·~
formation, our leap into the eternal Pablum, inevitably
self,. but otherwise unutterably other(\.:HHarold ?"
Self:- nli.lgae, my dear?H
Other;: nHaroldJ. n
: nEh, what is... , m'love ?n
Other:- YTQoddamit, Harold, will you put that book down ,_
how many times do I have to tell you - no Hegel
at the tableJn
Self:- n H.11 o Salt, pili ease , darling n
IDther: TT There. n
Self: nwhere ?n
Other: ttBy your elbow, you clod~n
Self: HThanks
Other: nHave you paid the gas bill ?n
Self: ttHm, no thanks: dearest n
Other: HWretched fool of a no good writer, you two bit
protagonisti rr11 give you a no thanks c n n The
gas bill, Haro , did you pay it?"
Self: HQas bill,
, yes; always, alwayse Marmalade, butter_··~. "·
Other~ Did you get that story back from n Philosophical Week~:_y 1'
{'j
�- . 24 -
.,,
:tA(3 . 9_
p.e
. wq_ere ~
,3e1~: "Su~;;~h!i?Patir-
.Yo.-µ '.re the Vel t .Gei-s.t and I'm a
· • ·. . :
;
.•·. ·. . .• ·.
.
.
,O the·r : nyou know; the or,i~ -w.:i._t7 the . picture S ·• "
h
Self:'· ., ,-. Oh yes~ - 'Some"man from the Post Office was he.re
about that"
,, ,.. ,. . _
Other: "You couldn't sell water to a chinese laundry, you
fink ••• n
Eternally, now her b.ody ,; arbhing across the . great oviduct
"
of time, the "no passing" zone of the heart, wti.er.~ , tru.cks
keep right ..and the ._
shoulders a~e soft. The ~.a-splyilt · m11'lenium, the · hi-test new deal •••• those eyebrows~ Elysien
Field.s, ripe for plucking. Oh Algae ., Algae,, 1 ·t~me '· is., . o
s
sl·i F:pery.• ·• •. .
·
. ,·.. ·: ·._ :,:_.~, '. "'t.·' . ' . :~
.
'.'.'"t. .:"' ~;. " . ~\\
·was · it:· the delta, or just the usual stink.- • .; • ., ·:·: .... ·.·:..•
Vinegar, b.ir, F.arth, Fire •• .- ••
~-- ·
III
l~lrs. Strudel had run her _shop with an i · on hand for.
r
twe·r ity years~ · Hard .as nails Strudel, her -.fai thf_ l u '·broken
and": cowe·ripg customers. cfalled her. · - -In the "hard...:bitte:n
.. -thi'rties, hard . as nails Strudel had._ learned to be as hard
'"as ::th:ey COI1)8· "In .tho se days,, whe- a· turnip-· could turn the
n .
tide ·from bread to the streets, Selma .-had· le-arned · h:er .:trade.
She ·was.' the. fir . t woman to: carry a ~ .. dard in "the ,: I'~G.G.w~ :·
s
Mun. Enip': + w. "
{International · Green -Groc:ers, Worker..s ',:_·IvIUrii'cipal
Employers and Writers CocSperati ve. ) and in ·a ·group ,kri~ as
hard headed, she was the hardest of' ·the lo:t.-. ShEL w.~·s- ..:·s o ·hard that when the cry "to the barric?tdes P' wa's h~arp, ·-= •·
she would app ea r a t the h ea d of. h e r : local, carry·ipg~ .her :still
remembered signs which read "I~G~.G-.W.Mun .. ·Emp. · + w. Cbop·n Hate
Di~ty · CapiY,alist .Imperialist ~Jar-Mo~g~rs n . .·And· · 1:].er war cries
still brought shudders of delight to those old ' enougb- to.
..
remember those hard living days.. : "Let -em·. ~at turnips ·pr ~: she
would scream, and the faithful w:mld answer ,·~!You ,· tell _em; Selma,
you 're the voice of the I. G.G. W. Mun. ~p + W; ·Goop. ~Arid the
people too:" Some intellectual . pa·r ty' liner :woul<l ·-9-dd'. ..... · - .
.\.
,
Selma's dream then --w~: s- to have· a ·shop ?.f her :·C?: n·, ·-:, ;·
0
preferably in a poor imigrint pa,rt ·of -the · ci~Y.• ,t. -. T;h~~e: · · ~p.·e
couJ-d ble;;d .the .c .ultu.~ally depri_ved thro:ugh tjJg_;rr- ~ prf c"e·s -, ··
shoddy merchand~ ·se, . anq , other~: : me'a:ris. : Srre · w?s ; stire that this
would b€~ 't he "be.s.:t . r way.. to . sl:iow'.'.the :po:or Q:i: ty; ~~' ·furx;.in;e:r: !~
·
r
s
the need for §oci~lism .a nd. a •. Workers: Baradise:• . •-· she. . couTd then
. - recruit these lic.'e ·' ,i nfes.t :e.d. peopl'e' . who couldn 'r t _ ven"'
'e
re'ad
�-
25 ""
English, into her front orginization, the L,SsF.,B . , F.
B. Ms + W+ Dem Assoc~ ( International Scheme for Brotherhood, Folksinging, Bread for the lviasses and World Harmony
Ethnic Democratic .b.ssociation L. The dues, of course,· would
be suitably high •
.h.nd her plans came to fruition - a small ray of shnshine
in a hard life. Through the clever manipulations of the
anchovy market during the war, she had been able to make a
small profit of ~328,223"'43 which after heavy expenses ( such
as support for her aging mother - a roof over her head in
lobby of an apartment house Selma had purchased, and a blanket
had set her up in businessa She would even help her brother
Dave, and his motherless brood of sixteens After
, he was
made a stock clerk, and she called him comradG
was twenty years ago, and of course, times
changes. As she grew older, her idea sm waned, and cir~
cumstances forced her to become crass. How could she have
k~ for example, that the slum
she had set up shop
would become fashionable and rival Sutton Place as a residence
for the young elite, advertising executives, young homemakers,
British secretaries, and, in short, the entire New York
Times Political Ferment and Fashion Arcytypes~ She was
forced gradually to raise her prices ever higher in the
e of the rising demand for her products. Where in the
past her Rutubegas had been the most expensive on the
Eastern Seaboard, she was now forced to stock such staples
as chocolate covered ants ( for which her brother Dave had
developed a fondness, forced to it by his ever-present
hunger - she didn't object to the cost so much - it was
deducted from his salary when possible, but he greeted
the customers
sticky fingers)~ Beluga cavyiar cat
food,
beansi etc~ She tried to keep abreast polold le S3f .B, F. S~ Bq +
Ho E
c
had given
for the Yo+lVlc11..R .. F.+R of F in
( Young
and Middle .aged Republican Fascists fo:r Resto:ration of
edom and 1v1onarchy in 11.merica
ID
)
But this had succeeded so well that she was forced
to give up her leadership, and the organization was now just
another enclave of the John Birch Societyo
One day, as Selma was ruminating over a can of Filberts
Deluxe Crystalized Cockroaches, Comrad Dave rushed over.
"God'
feet are killing me e"
"So
else is
n
"Well
I c
sit down once in a while .. ., on
-nLook, is that
you rushed over for,"
"No - we
a ca
from some guy.n
"So, we
n
"This guy wants a hundred Rutebagas, qu
�«se~lma,
d~
how do you do that·?n.
nno what. Comrad Dave?" ..
"Blanch
that..
makes me
nListen, crumb, you know where
wasn't
me J ?·
Jd ·
Rutabega's?
haven ~t
B~F.S.B.M.+W~H.E. Dem. ~Assoc.
b .·
"I dunno. He just called and said.to have
.Y
this afternoon. He··said he.'d pick em up!!! n
nr don't
. the smell of thise f~
''I. don't· either - why don .'t you close
pan .of ·~ -·
cry~talized cockroaches - they make me blanch."
are w·e gbing to get· a hundred. Rut<3.bagas.
.
the
ernoon =it's already three thirty.
" Shall T
the A.+P ?"
. .
yo& deserve s
een
,-there s some guy snooping around· ~h~
got up and. we·nt to the ,strang·er, who, had deep
thin li~s,· a
and peppe~
, and a pear
squint. :
..... __
ttya lookiri f\)r son18thin ..near s;lghte.d: strang~r
a
·
. ·suspiciously.
L · :~ < . .·
•.. , . ;·, ..· .
n~cuse me·,
I call:ed about
Rut?-"bega n
"But it isn
· o'
yet,."
eyed stranger was undismayed.
"l'll:wait · n he said crypti
'!I ':rn used., to~ waiting.
'
's
f! :.:
hawk eyes
great cyc:les.
be -my_
!
1
,.
_
If .J.).r_
'
you'
he
~tabegas.
took out a
· and ·:-s
of.
to I"eaQ:." .i. ,
, we·:ain't.g~t·no .Rutabegas,,.f il-:ts
stranger looked
•
Jewish
n;
saiq •.
- hero of .the-:_L.G.Q-.-Vi[.Mun.
near
have a
nails
not
n
Selma blushed.
s that's me, n she said ..
ttThe same Selma Strudel who .headed
.the. I. S.
B .1v1.+
H • Dem :As9oc .:.?-" ·.:: :. ·
"None o
, n, she r-ep.lied huskily. _
got up ~rtd took
"'Get
shouted.
behind tqe- cases ·
virgin olive
instant Kummel,. appeared a dozen men
seized he~.
handcuffed
"Selma Strudel, I arre
Drug Administration.
..... ~---~--.
you in the name· of
ed
• B F S.
They
Food
'
�- 27 -
cried, as she struggled
"For the penny bubble gum schemeJ This
up.
Your br·Jther Dave tipped us off•"
n But it's a free country .... I can put a political
message in a gum package.n
"Yes, but you can't adulterate bubblegum
s, " she_.said, as they carried her o
Hvfuy 1 why
�-
28 ·-
· '.~\Talter Hinckley
Forms and Functions
Structure Systems
Things
Despite ~he unceasing interest which this series of
correspondence has provoked, the editors of the
Colliegian request that the conversation be terminat
with this Final Word. It should be noted, in passing,
that there is a point beyond which discourse is no
longer significante
I have already caught wind of carping about
e College
community to the effect that this, the eleventh contribution to
stimulating public discussion may be, to speak colloquially,
stomping a dead horse, especially, it is said, in view of the
ct that the original lecture which occasioned all these
ctions or challenges •• ~ more than one review •.• restat
s,
counter-challenges and elaborations of ..... positions"1. could
have been heard by several of the classes who will read
s
present issue of the Eolliegian; a difficulty which is
compounded
the
that the refreshingly semi-extemporaneous
and indeed rather fetchingly rambling delivery of the lecturer
combined with the normal malfunction of both microphones and
student assistant technicians prevented the making of either
a satisfactory mimeograph reproduction or sonic-tape-rec
·2.
I
to issue my own counter-challenge to these my negativist
s by presuming to quote yet once more
the memorable
editorial of the January, 1964 Colliegian where our Editcr,
sing
on a September, 1963 editorial was perhaps
merely picking
an idea I heard long ago expressed casually
e , the bea tn~k s:a
;
former sophomore.
--:~as· an eloquent ·reply to ·possible detractors:
, that I venture t6 quote these· forthright words8
. ··
"In the following weeks students and Tutors will be
ed t~ contribute reflections or challenges
concerning future lectureso' On occasion more than
one review of the same lecture will be published for
··purposes of comparison and controversy.. Lecturers
will be
ed to submit restatements, counterchallenges and elaborations of their positions. The
record of such debates will be, I think, of value
n
l. Vide
2. How serious and lamentable this happenstance is might well
be shown by
article.
�I wonder i.f J.t wj 11 ~01 r1•s,c::i hJ c ~,n. 1, 1,nQo '>....-1~;--, 1~.;·.
onl
managed to catch a refracted beam of it through the rnedJum ~f
these pages to sense the white heat of the j_ntellectual
·
sustenance which consumed us on that memorable winter ':ve:::,_-~
No doubt the somewhat puzzling yet suggestive nature of the
title: Form and Feeling
ThingSystems_, with its
suggestion of that breadth and catholicity of inquisition which
is one of the hallmarks of the Sto John's College Spirit
together with the hasty and indeed somewhat mysterious onset of
the lecturer who, as some of you will no doubt recall, was
recommended on short notice by Dick "Pee-Ween Schutz, the former
lacross star and noted old-program alumnus, as a last minute
suestitute for Fra De Scudery 1 s eagerly awaited lecture on
Thomas Aquinas' little known tract: Contra _Isidorus,, Arriving
thus under the most trying conditions the lecturer succeeded in
leaving the entire College community with the tmpression of an
intellect
is a challenge to fathomo It would be super~
fluous to adduce any more evidence of this than the very fact
that here I am (to carry on the metaphor) casting my lead
where my fellow-students have sounded before me, and hoping that
at last my line may sink to the very depthsc
Let me then (to use the appropriate figure) plunge right in
by boldly stating my opinion that the whole controversy which
has raged around the question of the proper interpretation of
the numerous arcane diagrams which the lecturer scrawled on
blackboard with such energy and grace1 is a veritable redherring
our stream of thought"' In
ct; while I do not
to put myself unreservedly in the boat of those who follow
Mr .. Riesinger (Colliegian, May, 1962) in regarding them as in
effect (for in spite of the ingenious elaboration of this
position by I11iiss Swootj.t in the October, 1963 Colliegian this
is what the
argument boils down to) nsirnply a delightful
eu d'esprit", still the uninterested observer can scarcely
resist the temptation to describe effors such as
~
bohn s
admittedly clever and even brilliant readings (Colliegian,
December, 1961) as cases of misplaced ingenuityc Indeed: it
will hardly be denied in regard to this particular ~~~§_~ celebre
i'hat even if the elaborate diagrams with which l'flr., Birnbohn
attempted to illustrate his essay at an interpretation based 011
the neo-depth-pschoiconography of Kraft-Ebbings Rorshach, and
Schweetzer had not come through the mimeographing and proofreading process in such a confusing and inaccurate state as to
make intellegent perusal well-nigh impossible; his final
conclusions must inevitably lead to reflections about the
1. The question of why, in fact, the lecturer seemed to be
having such a constant struggle with the chalk and indeed with
the blackboard as a whole, a struggle which was, of ·~Jurse:
only intensified by the brevity and tangled nature of the patentthroat-microphone-supporter cord, may be explained later in my
text·.
�lecturer's early experiences and present fantasies
·that ba
academic modesty which our
, among
things, exist to enforceo No more, by
by,
I wish to countenance the superficially hostile but
actually quite similar line of research initiated by Mr. -DuVall
(Colliegian, March, 196J) and the miscellaneous group
tutors
who side with him. No o'ne appreciates more than I do the
serious significance of the mathematical analogues which lurked
behind the lecturer's
successful attempt t6 avoid
rigorous mathematical demonstrations or in fact any clear
reference to mathematics at all, still his attempt purely £!!. the
basis of ~ topological consideration of the chalk-trails as they
appeared on the_ surface of the blackboard, his attempt I say, to
see those diagrams as a startling if u ~timately unsuccess:ful
attempt at a.linear projection of Hilbert space must, in the
la
analysis, seem misguided.
No doubt closer to the heart of.the matter but st
a balancing ~iew are the inspired guesses of
, Iviarch, '1962) based on her sensit
researches in
Cabbala and Hermes '
side of
be admitted, however, that
'
though
must also-be
~~··u~·~~u~' refulgently cryptic prose
s not
succeeded
concealing her meaning, the same cannot
statement or counter-challe_nge (I hardly know
lecturer in regard to Miss Simpkins'
Colliegian
ed in :May, 1962 e Indeed
such it be,
the lecturer's pos
since when all is said and
cruc
point as to whether an
the Dean did in point of fact
progress"
, I ·should be sorry)·
any or
lead the reader to cohTusemy
the
ivist position -as'.sumed by
,
,
he . . . . . . ~~. . . . .
rather substantial portions of the lecture
conceived claptrap." Indeeq ::C think
our lecturer well knew what he was{about.
all.
with this hope that I wish to-proceed
now, as
, on a new and freshening tack and to con rather
than destruct if I may permit myself a small Germanic-ism)"
Let us begin by taking up the central concept of nin.G.:i.e Frage
se ,n which, though it tended to appear somewhat mysteriously
at various crucial po
s in the lecture, seemed, as over the
years one
cted on
s fertile applications, to have never
been adequately defined. Here I must state that what I may
safely (the author having left the college in the interim) call
the naive
empt
• Refquart to explicate this concept
the November, 1962 Colliegian flounders quite simply on a
�- 31 --
misapprehension of the lecturer 1 s use of the German language<')
• Ref~uart, having been obviously misled by the fragmentary
character of an outdated Junior language Program (a little
knowledge
a dangerous thing) has simply taken nin die Frage
se n
s most pedestrian sense of rtin-question being"
whereas the significant tone
the lecturer enunciated
the phrase in fact brought its meaning much closer to that of the
American. usage of "questionableJt or as our British cousins might
say} rtnot bloody likely=- n Thus, if I may be clever for a
momentj
• Refquart's own article is not only formally in
question as
Hamlet's great query (later brilliantly refo
ed
by Heidegger and others) ttse
oder nicht sein,
ss is hier
die FrageJ n But also in the most profound sense in die Frage _,
strange, queer and questionable to the core~
Similar philological acumen will, I be
e, serve to
not
the relat
insignificant note of
s but
more importantly the thesis which Miss Winstome argues with the
same show of reasoning in
October, 1963 Colliegian to the
effect that the lecturer must be a right-wing existentialisto
her argument to
e
rests, as
the parallel case
of rlefquart, on a verbalistic confusion. This confusion
must be admitted was hardly confined to Miss Winstome and can
only be explained as a function of the excrable state of the
public-address-oral-amplification-system that evening compounded
with the fact that certain components of the central climatic
control center
the New Building which had been irritat
t the previous summer, had unaccountably and unnece
begun to refunction with a deafening whine. But to make a long
short the ubiquitous word "binkTT or Hbincn or Hbenkn
Miss Winstome quite plausibly interprets as the lecturer's
Austro-Lithuanian equivalent of our own present participial
phrase
ing" is in fact the untranslatable Transylvanian
dialect
word which can be transcribed from its original
runic characters as something like TTbaaing . . This word, or
rather concept is, as I just stated, strictly speaking
untranslatable, but it may perhaps be roughly rendered as
"stupid malevolencen. Thus, to take a typical example, where
Miss Winstome takes the oft-recurring phrase 11 de benk uff tingsn
to mean the being of things, that is their inmost irreducible
essential existence, the lecturer actually intended the only
vaguely related concept of the "drattednessn or ncussednessn
of things, i.e~, that quasi-demonic quality in some
ordinary thing which leads us with a powerful and appropriate
folk impulse from the Ur-consciousness of the race to say
dratl or even damn that thing!
In fact, of course, this seemingly minor point leads me
to what I might want to call my ace or trump carda For it was
while engulfed in a pleasant e"vening 's recreation disposing of
this specious thesis of Miss Winstome's that the encouraging
words of our Editor quoted above flashed through my mind and I
�-32•
·.
/
'
•••
'
·-'
i
'.
,1. .
;
•
•• • • ', J
• ' •
I
.. • •
t·
. :. ·:
'
•~•
I
•\
•',~~!..; ~ ~ ~
:.;' .. . . _~":~ , :
· · ·c· nceivea· not - mer~.ly ·t,he;·, opp.brt~~t'Y. :. b1J~ ;· ~.~e· ~·~i~¥-r · dlity ::.o!~:;
o
~hartng · with -the·_ -Co_'lege at - larg.e··~:.~h.~ ;, ~nsig!,l. ~.: tn~ t fir:$(;. ·.c~me
l
,. - to·.: me o·n that -.cri:sp w-int\~r night ·: qf t _;iat.::-~-~.~t_µre so' ' jhar.:i;y-,'_ J:~ars
!
- ago _- ~ not · existentialismf. of cours:~ . , but .r -~ _ s?-s,~_rn.~ :~a.~j~smf ~ ·; It
was-- easy for me to _se- t ·h1s:: a.t onc.e._ though I scar_cely,~ ~.xpect e
that-- many . of my . re- ,.ders will. ,_
a
$ee the p~:dnt . .. -~esist·e·nt1a!i9m,
_ though - perhaps . past its: he,y~O.-~y in . the intelleQtual demt~~onde
.: ·· of 'the ' contin: nt' has; _only .J ust begup; .to reach ' our shores.·,: in
e
' -a : systematic( and distort.e d. form•< Th9ugh .it has . been ;ri· ld to be a
e
.scandalous or even -~_: amorphous do~_tri:ne by . s~~e phi~osophic.ally
vested interest.,s 1 ,- i .t s le~ .~'ing . _id~aj~ .-:_9-re _ ba?icly striking -,·and
simple' centering' as the'• lecturers title implied' in the 'f orm
. . _ and feeling ~of thing strUC;_tur~ . sy-ste:ms ,::. an:d_
)_:capa ble of; ; profound
" over~simplif:'icat.'ion , in 'the.' : me;mq;c9-h1,_ f;ormu;Lation of Ventre:
:
e
"Les choses -sont . c:ontre nou.s:.__,,.
·
· -· · · .
·
·
i.
1
•
'
~
•
is -
,. .
.,_ -- , · ·: ."Thirigs are aga- ·n·st us. n This
i
the · nearest Engli.sh·
.translation-. I can -find for . the basic. . concept - o.f r.e~;°ist'ent~·alism,
- he · grim .but : enthralling philoso.phy . now . identi£:ie.~ w~i~h t . bl~
t
~ ·bespectacl. d, betrousered ,:. Pierr.~ .-Marie · Vent~e•' . In .~;r~p.sf~rring
e
.
the dynamic of philosophy from J:n<;lP .to a worl4: .o.f . _h.ostJ~~- :'thi•gs,
.:- ; · _- - Ve~tre has achieved: a mp.Jar :reYQl.u ti.on . .9,f .. :._thought, to.< ~bJ9h he
::.. - imself gave . th~ name "resis,tent i~alism." : ~tymylogically _. thing~
h
- (~) ·.resist · (res·ister )- marl (.homrne., underst,_
ood ). Vent.~e . make~
-- · ,.. · a complete -'br_ ak with traditional philosop}).e
iGal methods.•
Except for ··his German precursors Freidegg .· ~nd. HeidansiE?c~e,r,
all prev:iotis great thinkers from ·: the Iliadic~ to ... Harry · ~EJµerson
Fosdick ·: have allowed ..at .least . some legitima~y-_~ to hµmari . ~:tiought
and - effort. Some:· like Hegel or _the middle. .- Plato, : go.e~ . :$9,, far
as ·to ma.ke ·rnan 's .thought the supreme reality". _In "th~ · .. :. _;
resistentialist -cosmology, which is now. ·the -. iritellectu9l _-_ rage of
Paris, . however, ·· Ventre .. offers us _a grand vis ion of the. Un ·~ verse
as One Thing .. _ the Ultimate Thing '. (Derni~r.e Chose). And it i ~
against us.
_
Thus to · those witb :·the · le~st tin;ture of phtlo~~phi~al
acumen, the conclusion to .which one is drawn by the _
for.ce of
-my argument is inescapable. ·: One . needs onlj".."tO- :realize that
: what the left wing German Moslem· resistentialist .Von_ Horlacher
·--· says about the Sitz- im- leben or:·Life Seat which i,mder the _
conventions of a formal lecture can easily be seen as a ·"
~ii~z-~-Gerangnis or - Stuck sec:t car: provide the. basis o_f· ca,
brilliantly sub-verbal rhetoric_: which -a clever lect.urfir ·•9C3.n
turn to the discomforture and enlightenment of his captive
audience. :. Of course the entire mis-en: scene of · that memorable
evening was not a mere chance adjunctto the lecturers_ basic
point but contained oh the contrary, the J .iteral burde1l~> oJ the
speakers message. Every .- detail of that · unforg.e t:table nJn_ tye
�- 33 ....
sev~~n minutes1 , the way in which the gutteral rasp and maddening
manerisms of the professor's voice somehow always succeeded in
preventing one from nodding off into that blissful reverie to
which the lulling siren-voices of the circulating fans
constantly invited one; the hot white glare of the lights
(the dimming mechanism had failed ) on empty wood, pink seats,
and bar.e conc;cete reminding some of happier if dimmer days in
the Great Hall; the constant futile att
s, conceived in
desperate boredom and abandoned in infuriated confusion, to
make any correlation between those unintelligible chalk-scrawls
and the speciously intelligible flow of the discourse, the
monotonous choreography of all the shiftings of position
possible between the barriers of those narrow wooden arms;.
the agonizingly slow revolutions of the second hand as th~
argument (if there really was an argument) seemed to be
to an ineluctable finis, only to rise like a misbegotten
phoenix from its own dusty ashes and proceed
its own weary
way; above all the torturing but constantly recurring reflection
(a typical Sitz-im-Gef~ngnis react
that one had after
intended to cut this ill-omened bore - all these, I say, and a
dozen other subtile influences too numerous to count were
a quasi-diabolical ingenuity brought to bear at once until to.the
insightfull thinker the revelation came with
the shock value
of a genuine resistentialist epiphany s choses sont contre
moil. And from here but a short though significant leap beyond
the bonds of st::lfhood to embrace ones yawning, nodding, thumbends; even in a mad
of charity and
embracing the very arch enemy cturer himself - seeing
suddenly as
a true light,
muddle-headed,
he somehow shared ones own horror
the slowly d
quite ample sheaf of manuscript which
before him ~
the revelation is complete almost incommunicable essencr;
of genuine resistentialism is
suddeness brought
be noticed
here as e
altogether
to the unfortunate exchanges which occurred in
that period after the lecture
elf\ which befitting
traditional name, (especially
the dead watches of the nightn
when all but the most pugnacious of the questioners had followed
the example
ch the Dean set earlier
the evening by leaving
a huff) profoundly
Frage
�Modernity, Norman Levy, p.6, 1. 33
1.
for: nbut
larger part
wi
to show Saturninus
that in spite of the insult, Titus 1 highest
as a Roman is that of being a thoroughly decent man;
a gentleman .. "
read: nbut in larger part it
his wish to show Saturninus
that
spite of the insult, he likes him ..
highest virtue as a Roman is that of being a
thoroughly decent man; a gentleman."
2. Col Legno,
anslated from the German by Owen Sears,
p .. 21, 1. 6
for: UpOUildS II
read: "pounded"
3. Half-baked: :Mississippi Homogenized, by Jud DuVall p .. 28
1 .. 35
for:
read:
11
he took out a pocket of The Philosophy of
n
pocket bo
Histor~u
The Philosophy
Concerning Small
The editors
to apologize for the numerous errors
appeared
the diagram on page 32 of the article.
note
following corrections regarding it:
1. All triple primes should be double primes;
primes should be single primes; etc.
e
2 .. The line labled. D'E' iF'E should be cut in mean and
extreme ratio at point Q, rather than in subduplicate
ratio at point P·as the diagram indicates.
3.
ar solid K' Lrl' NOP, because of the changes
correction 2 .. of this eratum, must be rotated
upon its semi-minor axis 29° so that QT 1 ( which according to correction 1 .. is now qT') will coincide
with line G'H' 1 (now corrected to line gH').
�
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�65
68
65
is
Textbook
*
�A QUESTION OF CERTAINTY
John Merritt
Honorable Mention
Junior Essay
Prologue
Montaigne summed up the state of knowledge in 1580, with the publication
of his second volume of essays; everything is
un~ertain.
The doubtfulness
of what Aristotle wrote is only augmented by each commentator and confusion is compounded so that the hundredth commentator leaves truth more
obfuscated and arcane .for the hundred-and-first.
Montaigne's solution
to this problem is unique ·-- perhaps untenable.
Since there is in the
outside world no certain knowledge, let us not sorrow or despair, but
rather, like the tortoise, withdraw into ourselves and study our nature,
study ourselves.
But his own remarks on the inconstancy of our actions
leaves him resting on a none-too-soft pillow of doubt; if there is no
knowledge, let us not bother ourselves by trying ·to add to the anarchy.
Let us instead take what comfort we can in this Heracliteen world, and if
our kidney stones should bother us, we may pleasantly write
· them.
essa~a
about
All this may have its roots in the nature of the world, but certainly
some cause for Montaigne's observation can be found in the critical
spirit of _
the fourteenth-century philosophers, notably William Ockham.
This Franciscan logician concerned himself mainly with epistemology -studied the very structure of cl assical metaphys i cs .
Summa
as Aquinas or Duns
Dominican schools
Scotusj~is.influence
was
Though he l eft no
dominant~-
even
i~
and for the three hundred · years during which his
criticism was the philosopher's principal tool, · arguments which :once
seemed uibrant and
now to drop still-born from the mouths
viril~ _ seemed
of the old masters; what was . demonstrable was. quick! y turned to -.merely
probable.
"In all
argum~nt ,"
Ockham observes, "something will be : -
accepted which is either doubtful or· taken qn _aith .. "
f
three centuries
philo.sop~ers
out the truth of Ockham
-
agreement.
Now, the
and theologians seemed determined to..•bear
is statement,
.
2)
. .
~-
seemed
For the next
for the dialectic -- and .t he dis.
interminable~
.
supr~me . i~ony ot~urred
in 1633, with the condemnation of Galileo
�2
by the Inquisition.
A board of theologians, themselves in the throes of
doubt (as Ockham and Montaigne had before remarked) condemned Galileo,
who had founded certainty with the science of nature.
from one point of
view, the establishment of a consistent, orthodox system of metaphysics
which would allow for the development of certain truth in the sciences,
and also be acceptable to the doctors of the Sorbonne is the well-nigh
insuperable task of Descartes.
I
In the midst of all the uncertainty of the theologians and the doubt
raised by Montaigne, Descartes proceeds to discover certainty.
The
proper way is to begin at the beginning, where all is dimly shadowed
forth -- with doubt.
Although his father and his daughter had died
during the writing of the Meditations, Descartes, with admirable _philosophic
fortitude, announces in the first paragraph of his book that he has
banished all care from his mind and is happily agitated by no passions.
He is, therefore, in the perfect state to prosecute his endeavor
erection of a car.ta in foundation for the sciences.
the
-~
To this end he observes
that reason teaches him to withhold assent no less carefully from what
is uncertain than from what is evidently false; the process of dialectic
is not good enough for him.
dialectical, premisses.
He must start from demonstrative, not
The reason for this is clearly seen in the first
metaphor in the book -- "When the foundation is undermined," he says,
"the superstructure will collapse of itself."
The delicate forms of
dialectic will simply never do, for they are always hanging in the air;
3
Descartes must build a building. )
Let us now see what he
do~bts,
and what are his reasons for so doing.
The natural reply to such a bold endeavor as Descartes' is "you must be
a lunatic! no one in a normal frame of mind can doubt what you doubt;
some unnatural humour has plagued your brain."
It is indeed amazing that
anyone should have so wondered about the outcome of the book that he
completed it -- that . i t was not utterly forgotten instead,. .9f~·-t'he cornerstone of a great revolt.
..•
~· ....
Certainly Descartes must shdfu us cause.
To
begin, his sen_es ·have been known to deceive him, and since a wise man
s
does not entirely trust what has once -led him into error, he therefore
denies all knowledge . contingent on sense expfrienca -- including the
fact that he has a body.
For Descartes is not a . body; he is by nature
�3
a being seeking certainty~· and ". since he must acknowledge that : he has experienced noth-ing · in waking life which can· be distinguished ·from the. life
experience in a dream, he is compelled to admit that· all nf his . senseknowledge, and even the experience whence it is derived, may be a dream,
and has no nece~~ary r~lation t6 t~uth ·-- perhaps is radically other than
truth.
The only knowledge he possesses that comes not fra·m the sens·e s
comes only- it seems,from the mind--mathematical knowledge.
,
Certainly
this is not doubtful.· But, Descartes observes, there is an old idea in
the mind that.thaie i~ a God, an a1l~powerfu1 being.
What if this being
were not b.e~evoient, but evil, and played some complicated game with
Descartes, deceiving him ·at every turn, m king him think he perceived a
·a
truth clearly, when in truth he saw as in a .glass dark1y4 ) __ ~aw nothing
qut . ,falsity everywhere he turned, and. under the aspect of truth;?
·Indeed,
it is the more probable that this gr~at Deceiver exists~ since withbut
the least consideration of this omnipotent monster, Descartes has, and
with reason, come to doubt even that he has a body.
If ·he could be
de6eived about that, surely he might be deceived in thinking
th~t
the
-
.
th~orams of p~re ~a~hematics wer~ wholly and incontrovertibli tiue.
So
Descartes, who sat at the feet of rriontaigne (who taught doubt); i~ now
--
master; he teaches with doubt.
"
Committed to a doubt deeper than Montai~n~'s, Descartes mtist either ~find
certainty or live in a world far worse tha~ his teache~ 1 s; · ~s to d~~bt
required activity in the first place, to continue on the way to knowledge
requires even more.
His mind is hurled into an abyss of uncertainty&)
at the end of t~e first Medit~~i6n, and he propose~ to remain there ~or
the remainder of the day' les·t" -the old' habit of believing his senses·
should return and prevent ~is finding certainty.
One need read only the
first page .of the first Meditation in order lo see . that something v~ry
new is about to unfold, to
chall~nge
inquiry ·into what is meant by the
search after truth,
On the second day~ ' De~cartes pro~os~s to find a firmament to cl~av~ the
deep _
sea in which he finds . himself immersed.
. . ever"ything which can
if there be any.
He
has proposed to ·doubt
be . doubted; 'now. he mu·s·t find the limits to doubt'
The firmament which he proposes to find,
::plication) to .c reate, he likens to
~r~himedes'
or
(by im-
point in the se.cond
�4
metaphor of the meditation.
Archimedes has asked for but one fixed and
unmovable point in order that he be able to move the earth.
Descartes
no~
This point
seeks.
Mastery of doubt seems to follow directly from asking the question ''do
I exist?" since to answer this in the negative is plainly impossible,
and if not contrary to logic, certainly contrary to nature.
"I do not
exist" cannot be true, since that would mean that the subject of the proposition did not exist, and if there be no subject, or no term or terms
for the proposition to relate, there can be no proposition.
Plainly
and certainly, however, it can be answered in the affirmative, for even
if Descartes be utterly deceived by the great deceiver, yet can he not
fail to exist, for surely someone must be deceived.
Certainly the great
deceiver has already lost his battle; for if we were always deceived, we
would never know it, nor be allowed to think of Descartes' method.
The~e
is little analysis that can be performed on Descartes' Archimedean point
of a strictly logical sort, though some psychological analysis is possible-in fact, necessary.
Logical inquiry is hampered by the membership of
that proposition in the class of immediate inferences; it simply is true.
Mindful of the need of extricating himself from his wholly
and unnatural position
6
uncomforta~le
~ and as quickly as possible, Descartes finds
his Archimedean point in the fact of his existence; if he thinks or
experiences, doubts or in any way acts, necessarily he exists.
The
question that must now be raised is of the meaning of "I exist",if I lack
utterly a body.
It is clear that the cogito expresses a truth independent
of the idea of body, but we must ask what it means to exist
which Descartes nowhere answers.
that belong to him.
a question
Rather he discusses those experiences
He is a substance, a substance devoid of any of the
characteristics of body, and in which inhere at least the properties, or
powers, of doubt, conception, assertion, denial, and will; a substance,
moreover, which experiences imaginative pictures and what (for want of
a better term) we call sense perception.
That Descartes possesses all
these characteristics he cannot deny, even if he claims that he has no
body whatever.
But in order to further understand his ego, Descartes
directs his efforts (in what seems like definition ignotum per ignotius)
to the analysis of body.
Everything we know by that mode of consciousness called sense perception
�5
is not known by taste, touch, smell, sight, or hearing.
Nor yet is it
known by the imaginative faculty; only by a purely mental, or . intel+ectual
inspection is anything known.
To show this, Descartes chooses as an
example a piece of wax, which we are naturally inclined to think known by
the five senses
perhaps by them only.
it shows itself chimerical
fleeing.
~ot
Yet, placed down by the fire,
sends our weak knowledge (itself a chimera)
one of the properties we recognized the wax to have by
sense did it have essentially, or in nature, since each of these properties
has disappeared, and the melted wax possesses an entirely new set of
sensibly known properties.
Was the wax then known by the imaginative
power -- our capacity to mentally form pictures of extension, change,
flexibility, and so on?
capable of
~assing
Of course not.
The piece of wax is entirely
through an infinity of stages that my imagination in
its finitude could never comprehend.
How, then, is the wax known?
nature of the wax must be known only by some purely mental
The
inspe~tion
its perception is not by sight or touch; or even imagination, nor was it
ever so, though formerly Descartes took it to be so, _ when his knowledge
was imperfect and confused.
Now, however, he knows the nature of the
wax clearly and di$tinctly.
It is difficult to imagine a conversation
between Descartes and one who asked if the wax were known, or one who
claimed that he did not perceive extension by the sense of mental or
conceptual inspection, but by the sense organs.
Hard it is to know an
uncertain world.
Now, what light does this throw on the nature of Descartes' mind?
Descartes
now claims he knows himself -- he means his mind -- far more clearly and
distinctly than the piece of wax.
For clearly, when he judges that the
wax exish, and sees this .c learly, the result which follows is that he
exists, and exists as a mind, as a being who knows by inspectio.
A
fortiori, I suppose he would say, the mind is c1early known, since extension is clearly known, ·and the consciousness is that which knows.
It
is interesting indeed that the nature of extension .is mentioned before
the nature of mind -- in fact, the nature of mind does not explicitly
appear until .the last Meditation, in which material things are discussed.
One may also note that although Descartes claims mind to be better known
than body in general, yet the only property of the mind that Descartes
explicitly mentions is
existence~ ·
Betw~en
the lines, lies the
the fundamental criterion of the mind·; inspectio -- activity.
unw~ittan,
�6
Creating his universe entirely anew,
Desc~rtes
has first found a point in
the middle of his vast sea, by virtue of which he intends to push himself
to dry land, the groundwork of the third day. This earth-moving point;
is
the new center of consciousness_!/understood not in the passive sense of
the ancients, but in an active, free, and masterful way.
The way of
Bacon -- to torture and force nature to yield her secrets to man, to
teach man the language in which she wrote tha world, appears to be here
opened.
What was once the power of the gods is now man's.
The ego-centric
universe cannot be understood in the obvious pejorative sense, for the
sense of ego is now that of ordering force, active intellect, and this
is a faculty shared in by all men.
To follow Descartes through the
Meditations is to become one with Descartes; whatever is accidental to
both writer and reader disappears beneath the power and unity, the
community of intellect.
This point, the existence of active intellect,
.
.
constitutes the separation of extension and intellect, and is . more and
more clearly shown by reference to the clarity with which the nature of
extension is perceived.
III
Entering now on a quest which has the starting point (the existence of
mind), Descartes next investigates, as the proper order requires, what
is meant by the conscious being; he will try to grow by degrees more
familiar with himself.
To his opening question, "how is it so certainly
known that I exist?" Descartes replies that he clearly and distinctly
perceives it, and lays it down as a general rule, as one of the properties
of his mind , that whatever he clearly and distinctly perceives is true .
All truth, insofar as it is just that, must have some common characteristic
perceivable by men.
We must ask what this is.
Descartes knows one thing
certainly, that when he thinks, or experiences anything whatever, even
though that idea be materially false, he must exist.
He knows that he
possesses the capacities of doubt, conception, volition , asser t ion , and
denial because he exercises these powers.
act.
It is Descartes' nature to
These actions imply a subject in which they inhere -- namely
Descartes, and the nature of this implication seems to show that what
7
acts or has power exists ). ; this simply because it cannot be otherwise.
No farther into the proposition can .we go.
The evidence for ·the im-
plication is not any formal rule, and thus stands unique in this book.
�7
It is evident for one reason
that it is clear and distinct.
rule of clarity and distinctness is the only rule which
~an
Since this
be extracted
from the only truth which Descartes knows, then it must be the defining
characteristic of truth; all other truths, if there be any, must possess
that characteristic, too -- that it admits of being very clearly and
distinctly perceived.
Therefore Descartes asserts the generalization of
his rule.
Doubt, like the man-eating tiger, must return, for Descartes had only
begun his arduous journey because he found the recognized truths uncertain.
many
Before careful examination of his beliefs, Descartes believed
thing~
he can no longer hold; they no longer appear clear and dis-
tinct, though once they did.
..
Why did he arr?
Because he merely thought
he perceived such things as extension and mathematical theorems clearly
and distinctly, and was deceived by attending to his ideas with insufficient care.
Perhaps, in fact, there is a great deceiver who made
all those beliefs he formerly held appear true, though they
w~re
false.
Although he thought them to be true because he had a natural inclination
.
.
to do so, he perceived them not by the light of nature, but confusedly
only.
Thia supposition is sufficient to explain how Descartes was be-
fore deceived.
But before he can further push his knowledge, he must
inquire whether an all-powerful being exists, and whether it is within
the limits of that being's power to
deceiv~.
To this end he proceeds
methodically to classify all his thoughts, beliefs, feelings, and impressions, that he may see in which of these truth and falsity do
properly inhere.
Obloquy must indeed follow from the failure to show that God exists,
sine~
willy-nilly on that failure follows the closure of knowledge.
This
can be avoided if we observe the states of Descartes' consciousness,
his ideas.
These ideas are such as to borrow their being . fro_ Descartes'
m
consciousness, since an idea cannot be grasped clearly
consciousness perceives it.
unle~s
These ideas comprise variously imaginative
pictures of objects,_ volitions, emotions, and judgments..
speaking, nothing in the _ima. ination can be false, since
g
exists independent
~f perc~ption
true that it is . imagined.
.
.
.
the
wh~ther
it
is wholly besi9e the point; it remains
Similarly for .volitions or
. ,
..
'
Now, formally
'
emot~ons.
The
only species of cognitions in which truth or falsity may formally inhere are thus judgements; to these Descartes must now turn and discover
�8
that by virtue of which he falls into error.
Unnatur~lness
is the essence of falsehood, since the mechanism by which
falsehood occurs is the substitution of spontaneous inclination for the
light of nature.
for that inclination and the light are both "natural,"
and therefore the mind assumes that because there is a connection of
ideas, the same connection exists between the subjects of those ideas.
The implication could only be valid if the ideas were clearly and distinctly grasped, and
gra~ped
as existing.
been laid down before the next step.
The necessary precaution has
Among Descartes' ideas is the
idea of God.
The proof Descartes now offers is a proof for the existence of a
benev~
olent deity from the necessity of a first efficient cause -- a proof
ancient and honorable indeed.
But it acquires in Descartes' hands
certain changes which are essentially ramifications of certain previously
discussed Cartesian notions.
Descartes has already observed that he has
various sorts of ideas, and that of these ideas, some represent a
greater amount of reality than others~
Thus the idea of a subs~ance
has a greater amount of representative reality than the idea of an
attribute, and what represents most reality is the idea of God.
Now,
Descartes argues, the efficient cause of an idea must have at least as
much reality as the effect.
Only a being with the actual perfections
represented by the idea could have caused such an idea, and therefore
God exists.
Earlier versions of this proof had depended, at least ostensibly, on
the existence of material things, which everyone had naturally taken
for granted.
Descartes has eliminated this supposition from his
version of the proof by showing that even if nothing should exist but
his own mind, one of the aspects of that mind is the idea of God, and
that idea must have an ePficient cause.
This cause could be God, or
sensible objects, or some subject of intermediate reality, perhaps an
angel.
That the cause cannot be material beings is clear, since the
idea of God is of an infinite, omnipotent, benevolent being, possessing
characteristics which manifestly cannot inhere in extended ·being.
Nor
could it have come from. his parents or an angel; it would have had to
be in them, and since further they are not by nature necessary beings,
�9
it is impossible that they should have the idea of themselves.
Nor
can there be an infinity of causes, and therefore the idea was ultimately
caused by God, and placed ·in the consciousness to serve as a sign that
man was created in the · image and likeness of his creator.
Removal of the distinction between conservation and production with
.
.
. respect to eff,icient cause destroyed what difficulties
migh~
by controvei;.s y between a Scotist and a follower of Ockham.
observes that the act by which God
creat~d
be raised
Descartes
the world is not conceptually
distinguishable from the act by which he preserves it in being.
This
also means that there is no intermediate cause between man and God.
Man is completely dependent on God for his very being, in the same
way that the idea of God is not only . p~oduced, but conserved immediately
· by God.
The idea of God cannot be
·produced, by a
b~ing
conserved~
any more than it :can be
of less reality than Him.
There is nothing be-
tween Descartes and God.
To the objection that this idea of God could have come from himself,
Descartes has merely to point out his contingency.
There is nothing
in him which necessitates even his existence, and his lack of perfect
kn~wledge sur~ly
exis~ed
marks him as a
in him potentially.
crea~ed
being -- even if all perfections
Descartes considers, too, the objection
that , th~ idea of God could have come from several partial causes, and
re~~ct~
.it on the ground that such a conceptual grab-bag could never
give rise to the clear idea of the unicity of God.
In general, although
by nature the certainty of Descartes• proof is questionable, it can be
made satisfactory by the
el~boratio~
of certain
s~holastic
?istinctions,
with which Descartes never bothers -- and with good reason.
.
'.
.
Out of the abyss of doubt and uncertainty, Descartes has now emerged
as it seems, victorieus.
him of
wit~out
certa~n
He had need of a benevolent deity to ' assure
truths the certainty of which would be questionable
a proof that such a being existed.
He found this proof in an
old proof, manufactured anew from certain principles clear and evident
to Descartes.
First, in looking fer an efficient cause of the idea
of God, he searches out, as it were, the efficient cause of himself,
.
.
for the idea of God is a mode of his own c6nsciousness.
there cannot be, for God, any distinction between
Se~ondly,
corise~vation
and
�10
production; not only is God the first efficient cause of the idea of
God, but also the immediate efficient cause of Descartes' own mind, and
even, in some sense, a formal cause.
Thirdly, what seems to be a clear-
cut distinction in Descartes' writings, the distinction between the
actually and potentially infinite, becomes furry at the edges.
The
only difference between God and man is that the one is actually infinite,
while the other is potentially so.
But the mind is potentially infinitl3 ,
and in soma sense has a hold on the actual infinite; the idea of God is
a mode or aspect of Descartes' own being.
IV
Unless he possessed knowledge of a benevolent deity to insure that he
is undeceived, Descartes would have had to remain in ·doubt.
But doubt,
essentially an active process, cannot remain as it is (Montaigne, for
Descartes, must have been the supreme enigma), and therefore must either
push forward to knowledge or disintegrate totally and be forgotten.
But,
under Descartes' mastery, doubt has slowly been gnawing away at the
nature of ·things, leading first to the existence of the self as pure
intellect, and then to the existence of God, whose goodness prevents
his · potency to deceive.
In the fourth Meditation, Descartes reflects
on what he has done, and observes that there is little truth indeed in
our perceptions or corporeal objects, though much can be known about
the human mind, and so much more about God, who conserves Descartes
at every moment.
From the finite to the infinite is manifestly the
direction of our knowledge.
Contemplating his experiences on the past
three days, Descartes desires to move to the knowledge of other things,
and to this end, he again examines the nature of judgment.
To judge is a gift of God, and since God is good, He could not have
given man a faculty the right use of which could lead the mind astray.
But if this is true, how could man conceivably go wrong?
Descartes
has a very simple, and venerable, answer to this -- the .idea
being.
of non-
Descartes is ~~apped, as it were, between being and non~being;
error proceeds from non-being.
Since Descartes is
not . ~imsel~
God, and
thus equipped with all perfections, it is very easy to see the possibility
of deception; we must employ our God-given faculty to acquire truth
rightly.
Truth, then, comes from God, and error comes from non-being.
�11
Exceptihg one problem, this seems to be · the perfect explanation of error.
We can frame that problem by observing an obvious expansion of the principle behind God 1 s inability to deceive.
If God is the most perfect
being, then His work must be the most perfect, too, and the existence
of Descartes 1 ability to err argues a lack of . perfection that should be
in him.
Descartes proposes two answers to this problem.
First, he
recognizes the infinity of God, and observes his own finite mind to be
out of all proportion thereto.
He then sees that there are many things
about God which are mysterious indeed, and which will forever remain so,
remarking incidentally that for this reason he desires consideration
of final cause removed from physical inquiry.
Next, since he clearly
and distinctly perceives certain other beings as ideas, and also that
God is capable of creating whatever he clearly and distinctly perceives,
Descartes considers, as Leibniz later does, that creation as a whole
may be indeed perfect, though created individuals when considered in
isolation seem imperfect.
The principle of sufficient reason is a
dangerous principle, applied to God.
Turning now wi~h Descartes to his own case (since his case is our
case) we see that he separateg the
cognition
turn of
~nd
will.
phras~,
since
~ources
of error into two faculties
Error caused by cognition is an admittedly strange
th~
intellect, strictly speaking, cannot err.
Nevertheless, it can be a source of error, since the knowledge of any
being but God is finite, and privation of knowledge leads to error.
Will, however, is fully as infinite and perfect as the will of God.
The will of the soul, that is, its impetus to act, is Descartes' mark
of God's authorship, as before the idea of God had been characterized.
It remains, however, to discover whence error originates, for the will
is perfect in kind, and so also is the understanding, finite though
it be.
The answer is that the will to assert or deny the truth of a
proposition is forever outrunning the ability of the intellect to
judge correctly.
The infinite keeps drawing the finite on
-~
even
beyond its c'a pacity.
Luckily, however, we have discovered the method of not erring. as the
outcome of discovering how we
err.~)_
We_ must not. allow. the will to
carry the intellect away . with . it, but must curb it so that we. assert
�12
only what we clearly ·and distinctly perceive as true.
And that this is
entirely possible, though strange and difficult, we need only examine
the work of the first three days for abundant proof.
The light of nature
is a powerful tool, but it must be correctly used, for the chief and
greatest perfection of man is this·:
that he might never go wrong.
Now
Descartes has discovered not only the cause of falsity, but a tool for
the
disc~very
of ·truth.
v
Four Meditations have now been completed, concerned with doubt, the .
existence of mind, with the nature of co.n sciousness, God, and with
the manner of acquiring certain truth.
odd, and seems to 'pose as an
four days and the climax to
The heading
o~ _ this
in~erlude
com~ ~-
Meditation
The fifth Meditation is quite
between . the drama of the' past
a calm before the storm, as it were.
~sports
that
~tis
about the nature of
material things and the existence of God, ·though the Meditation seems
at first glance to
~
the nature of material ' things for
a higher
goal
a proof for ·the existence of God, which is ·apparently different in kind
from the proof offs.red in Meditation III.
of the same fact?
The Meditation is
Why propose two cer·tain -proofs
p~imarily
about the nature of
material things -- not the existence of God; the proof .is not essentially
different from .the previous proof, but is a simplification thereof; the
con~lusitins
on which Descartes mainly seizes are different from Meditation
III; the general conclusions of the fifth day are necessary to the
development of the following cay.
Inquiring into the nature of material things in what appears to be the
preliminary part of the Meditation, Descartes asserts that among his
various 'ideas he finds a state which can be called imaginaticin, -.c haracterized by .the formation of mental pictures of extended beings.
For
example, Descartes observes that when he thinks of a triangle, besides
experiencing the purely .mental inspection of that object, he is . aware
of a power within himself to picture such a thing by means of the
. ·:· im~gination.
Imagination can call forth these
picture~
at_ will. ·These
. : imaginative pictures, though they be of no thing that. ever was, can
. .yet ... ,.i~ no way be called. nonentities. ror Descartes clearly and dis.
.
tinctly .perceives that they have their own distirict ~nd unchangeable
�13
natures.
. hese ·natures ·are .nat .fi9ments of· the ·imagination at all, but
T
·quite independent of his thinkiryg of them -- for :various properties can
. be proved .or ·,them-
these ideas,
. ind~pendent
of their ac.t ual existence.
Triangles have by nature three sides, whether I ·choose to imagine them or
not; I am constrained by the light. :. o.f nature to so think.
Now Descartes'
di~covery
that certain properties necessarily inhere in
certain subje~ts independe~t _ the actual existenbe of these subjects
of
leads him to cons~der God's existence once again. God is the subject
in which the attribute of existe~ce nece~sarily . inheres;. . .th~~efo..re, since
.
. .
. ..
.... ..·.-- .. . ., .
·
~e.scartes has an idea of God, _
God exist~.
_ he an'?_~_ent argum~n~-- ~' ::called
T_
."ontological, 0 of passing from the possib~lity . ~o ~h~. nece~si~y of perfaction, is revived again in a new form. Implausible as Descartes•
form of the argument may
b~,
the idea behind the argument
se~~s essentially
..
ample~ - ~ strong 1 ~ersi~n of
..
sound. Descartes, however, chooses not to
the proof in order to show not only the a~alogy to
c~ncerning
.the nature of
ma~_er ial
his first existence proof.
·--
~he
·.
; _
proofs of _
theorems
· things, but also the resemblance to
In the case of both proofs, from the idea
of God, Descartes passes directly to His existence.
In the first proof,
existence is demonstrated by conserving efficient causes; that is, the
idea of God immediately implies His existence. In the second proof,
existence · is ·also ·ahowri ·oy ·immediate ·reference to the · idea. · Descartes
himself elsewhere admits that the first proof is an elaboration of the
second; the exceeding close relationship .between the efficient cause
and the formal cuase for Descartes is thus brought · into a ·strong ·· light •
.
.
Thus, the seeond form of the proof, being essentially a simpler ·version
ot ·the fir$t; has as -its · final cause a somewhat diffe~ent idea.
In diecussing ·;the .outcome· of the proof given in the third Meditation,
~escartes
the mere
says .that on all accounts, the conclusion must be that .from
fact ~ · that
clearly exists.
he exists and :has :an idea of the perfect being, God
But in his discussion of the second -proof , ;he says that
it always comes back to this -- that he is not convinced of anything
excep~ ~ha~ ~~ - elear1y · ·~rid distinctiy p~rceiv~~.
different objectivas· in mind in ·each case.
Descartes h~s ~ery
In the fifth section of the
Discourse an · Method, · De~cartes declares that resting his arguments solely
on the . perfection . of.- God·, .ha· tried . to prove · all the law's · nature that
of ·
might have beeri · doubted; like the fox, .· he ·has·· more methods .. than : 6ne
of achieving a single aim.
�14
To see what Descartes makes of this, we turn to the last part of the
Meditation (which is quite as long as the proof proper), and observe
that he returns to the .nature of truth and of material things.
Truth
depends on two things; potency to admit of clarity and distinctness of
perception, and the light of nature, which, in turn, depends on two
more things -- Descartes' intellect, and his knowledge that the deceiver
does rot exist.
In fact, Descartes asserts that were it not for his
knowledge of God, he would be uncertain of everything else.
He is not
arguing in a circle, for there ·is a distinct difference between what is
immediately clear and evident, and what one remembers to have been clear
and evident; our trouble is weakness of intellect -- we cannot be
actively knowing all the time.
Even the Deceiver could not make false
what Descartes clearly and distinctly perceives, though he could very
easily make us falsely think that we clearly perceived what we did not.
Now, at last, the argument from clarity and distinctness of properties
to necessary inherence in a subject will follow, to open the entire
field of mathematical physics as an exercise of the intellect -- not
of the senses.
VI
After all his difficult preparation, Descartes is prepared to consider
the final cause of his efforts in the sixth and final Meditation.
He
has led us from the distinction -- nay, the utter rift -- between mind
and body; now we approach the existence of material things, the
expl.~nation
of the occurrence of error in sense-perception and doubt,
and an involved discussion of Nature.
In part six of the Discourse on
Method, he claimed that just as the last things are proved by the first,
which are the causes, so also are the first things proved by the last,
which are the affects.
The sixth Meditation is the triumph and justifi-
cation of the unbearable doubt that initiated this struggle into the
opeh air, from the cave into the light of nature .
Tortured long enough by the demands of doubt, Descartes plunges into
the work of the last day with a detached fervour; no moredoea he fea:r
uncertainty, for
his·p~th
is
clea~ •
. His pains are compensated by dis-
tinguishing the mental states of intellection, imagination, and sensa.
~ion;
by considering carefully the properties of these three states,
�15
he may see that sensation implies a being other than himself.
Having laid
down the plan before it is carried out, soma of the drama seems to be
gone, but -if it is, it is ·replaced by something of essentially greater
interest -- explanation.
Descartes' distinguishes again between in-
tellect and imagination, this time .adding to the distinctness of their
functions the distinctness of their dependence on himself.
The power of
imagination is not essential to his nature, to the nature of his mind,
and therefore it is probable that it depends on some other being than
himself for existence.
Descartes now makes the most preposterous state -
ment in the Medi.tatiOns; · he claims that if he were joined intimately to
a body so that he could contemplate it instead of ideas, then he could
readily understand the phenomenon of imagination in that way.
Other considerations must be taken into account before a certain judgment can be reached.
Since the argument from imagination is a merely
probable account of the appearances, we must push our researches into
another mode of consciousness -- sensation.
At this point, as at a
similar point in the Meditation on the existence of God, Descartes
begins an enumeration.
first he considers those objects he took as
real before· the regime of doubt began, then he reviews his reasons for
doubting the capacity of sensation to lead to truth, and finally he
sets out what he may now believe.
Unquestionably the state of mind of Descartes before the opening of
the Meditations was largely determined by his body.
The first of the
so-called sensible objects he had previously held to exist was his
body, the central problem which gave rise to the Meditations.
This
body gave him experiences of pleasure, pain, appetites, emotions,
and sensations tangible, visible, and
a~dible.
that he distinguished and "knew" ·the world.
reason.
It was, in fact, thus
for this he had good
First, he experienced these sensations without, and often
contrary to, his will.
It was further his experience that the mental
state arising from sensation was far more vivid, and, in its own
more distinct than anything given by his power of imagination.
wa~,
The
inference he had made was that the things in 'the world exactly resembled
his ideas.
What cotild be more natural?
·-Tested against that touchstone, doubt, this inference has shown its
�16
base metal~ . Sense experience is indi~tin~ui~hable from what we observe
as the same mental experience in sleep, though in sleep the .subject of
sensation is missing.
Since Descartes , did not know the Author of his
being prior to . the third Meditation, he was also obliged to admit that
there might be some omnipotent ·demo·n dealing failures to all his efforts
· to find truth.
Even the intimate
expe~ienc~
of pain could not shake
his doubt that he had a body, because pain should be felt ·in a limb
only . if . that .limb exists.
But
Descarte~
had known people who had lost
. limbs to complain . of pain in their lost limbs.. Certainly it is possible
that
h~
erred.
But his stance is now different by five days from his
position prior to doubting, and stronger than on any of the preceding
days.
What may we balieve with certainty?
Confirmed in his belief that there is a God· who would not deceive him,
Descartes can now analyze both sides of- this question.
the argument proceeds as
follows~
Roughly speaking,
Because I have a clear and distinct
idea of myself as a conscious being, not an extended being, and also a
clear and distinct idea of extension ·1acking consciousness, it follows
th~t
I am really distinct from my body and
sation is
contra~y
~u~h
co~ld
exist without it.
Sen-
that it causes states of consciousness to arise even
to my will.
Therefore it cannot be that they arise from myself,
but must arise from some substance containing at least a like amount of
reality with the idea as the idea represents.
So mY
idea~
of. extension
must .arise either from corporeal objects or from some higher reality.
To
the end that I might distinguish between these sources of reality, God
has gi ven me no faculty whatever.
He has given me a strong , natural ,
inclination to believe that they arise from actual existing material
~bjects.
And because God cannot have given me any power or . inclination
· the right use of whtch · might:·:_lead me astray, I am constrained to say
that my sense impressions and imaginative powers are related to corporeal
reality.
It may be that corporeal objects are .quite unlike my ideas,
nevertheless, Descartes asserts, their nature must be what I clearly
and distinctly apprehend it to be -- that is, what. ver falls within the
e
subject-matter of 'pure mathematics!
Rhetoric's needs would seem to be now satisfied, for wha·t was to be
proved has been proved; yet half of this last medita.tion rem.a ins .•
. Natura appsars three tim~s as riiten. in the sixth Meditation as in any
�17
of the preceding ones, and provides a clue to the nature of Descartes•
book.
In this Meditation, toq, the use of verbs in the first person
slngular or the use of the personal pronoun ego has markedly decreased,
as · als~ th~
word Deus; natura has taken their place • .
Out of this proof for the existence of corporeal reality, as from the
three previous proofs, has come reflection on the nature of truth and
By
.falsity, this time cast in the contrast between nature and habit.
"my nature" is meant the complex of all that God has given me; by
"nature" is meant the whole Qf creation; by "the light of nature"
is understood the .principle by which truth is grasped by men.
Now,
the light of nature shows me many things -- that I have a body, that
by means of that . body certain sense impressions of corporeal objects
come to my mind, that these extended beings exist, and so forth.
It
is by the light of nature that I know my nature as a conscious being,
as an
ext~nded
being, and as a compound of those two natures.
I err _ nature.
by
And yet
Was . it not natural that I took extended things to
be like my ideas?
No.
Habit of inconsiderate judgment we take
a$
a
substitute. for the light of nature, and it was thus that I took extended being to be similar to my ideas.
This habit of ill-considered
judgment is developed by the will overcoming the intellect, a mechanism
explained and overcome in the fourth Meditation.
In considering nature, Descartes runs up against a further problem -,
.what among physical objects should I seek or shun?
These things .seem
to be taught by nature, because our perception of pleasure and pain
gives us our clues.
Vet what is to be done about the man who is sick
dropsy, and has no need of water, yet experiences thirst?
wi~h
In his
first reply to this, Descartes, in an astounding image, likens the human
body to a well-made clock, which. may yet run down and tell the wrong
time.
Clearly the clock obeys . all the "laws of nature" whether it runs
well or ill .
the
~ction
h~althy,
So we have been allowing our will to inadvertantly impede
of our intellect again; it is only with
that the nature 0f the dropsical is corrupted.
·such, the sick man is , quite as
·this
~aspect
~xplanation
is not
~'natural"
sufficient~
to us, the
Conside~ed
as thehealthy man.
There temains a
re~l
as
But even
fault in the
nature of the sick ma.n , since . he desires what is harmful to him. . How
can the divine goodness permit this corrupted nature to deceive us (for
�18
corrupted or no, it is still
nature)~
Repeating again the real distinction between mind and body, Descartes
observes that we have two natures,mind and body.
Now in the healthy
state, man's ability to perceive pleasure and pain are obviously
ordered for the best, because when I must take water,
r feel thirst.
This is caused by the intimate association of corporeality and
consciousness.
But nerves, as Descartes claims to have learned from
physiology, operate by pulling in the area of sensation in the body
to a common sensory center fn · the brain, which in some mysterious way
affects the mind, causing it to experience sensation.
But by a
~
metrical example, Descartes shows that that same experience can be
caused quite as well by a pull on the same nerve, though higher or
lower than the original position.
Therefore it is possible, because
of the infirmity of our nature (that is, the nature we possess as a
compound of mind and body) that our nature should deceive us.
We have
not all the perfections of God, however perfect we may be as part of a
world.
And even taken from the ·point of view of the individual, the
mechanism of sense perception is still better ordered than any possible
alternative.
Ending this almost fantastic journey, Descartes returns to the distinction
between the infinity of God, the mystery of his omnipotence and omniscience, his depth and grandeur, and our poor, confused, finite, feeble
understanding.
Remembering the great distance the Christian must feel
between himself and the power of God, he admits that practical needs do
seldom allow us to examine so carefully a situation that we be not deceived, and cautions us to recognize the infirmity of our nature.
In-
deed the rhetoric was not finished.
EPILOGUE
Because of Galileo's condemnation, Descartes suppressed an early treatise
perhaps containing much that is in the Meditations.
It is difficult
to imagine a man convinced of the truth changing his beliefs even for the
sake of the Inquisition; force merely drives the heretic underground.
I therefore made it a rule of thumb that the Meditations was a very
subtle book.
The rule was correct.
Drama is the essence of the
�19
Meditations, and the order in which statements come is variously shocking,
amusing,
baf~ling,
astonishing, and at times, perfectly logical.
IDhy
does the simpler form of the proof for the existence of Go'cl coma·· after
the more complicated version?
To focus attention on
6l~rity
and dis-
tinctness as criteria of truth and also on the nature of material . things.
But .why .ts it there at all?
Preci'sely to take attention away 'from the
astonishing nature of material things.
Csrtainly Newton and the Sorbonne
doctors would read the Meditations differently.
Or why, in the second
Meditation does a general criterion of truth and a proof for the existence
of God follow immediately on the inquiry into the essence of ego?
Examples could be multiplied almost without limit.
Execution of Descartes' task, as of any scheme of grand dimension, requires
discipline and action.
effort is doubt.
The generating force of Descartes• stupendous
It is quite curious that the first collection of
properties Descartes takes as belonging to his nature are doubt, conception, affirmation, denial, and volition.
attribute.
Descartes has not one passive
Wonder is not in his vocabulary; if he knows what it means,
he despises it as the milquetoast's reaction to nature.
If certainty
is to be achieved, doubt must be pre-supposed, accepted, and dismissed
in reasonable and orderly fashion.
Mind for Descartes is in constant
activity, while for the ancients, the intellective faculty was passive,
open to receive the truths of Nature.
Thus that which was formerly
thrown under the intellect for contemplation is now thrown out of the
intellect for its inspection.
Both the quantity and the quality of
knowledge gained under the old aegis appalled De's cartes .
Such · a passionate
seeker after truth was he (for he had to have more and better knowledge),
that instead of founding philosophy, he created philanthropy, theodicy,
and anthromorphism.
Descartes thus commits his own cardinal sin;
before sufficient reflection, he wills that his new subject should be
metaphysics.
Coming to wisdom via doubt means embarking from an odd point -- a
mathematical one.
One of the most fascinating (and elusive) problems
of the Meditations is the ego -- what is it?
Perhaps one might say
that it is that .active, intellective, conscious tool which organizes
the vast fund of natural knowledge; it almost takes the place of God.
But still we must ask in what the being of this mind consists.
Descartes
�20
would, I s4ppose, say that this . is a great ·mystery, just like the being
of God.
Ellipsis is · D scartes 1 best; method of discussing ego.
.e
I have
already pointed · out the at_ange sequence of the third Meditation; while
r
its avowed purpose is study of ego, the criterion of truth and the
It is almost expected.
existence of God pop out as theorems.
are
per~al?s
There
three dozen places in the meditations at which the nature
of mind .is alluded · to elliptically by the dramatic -power of order.
Things, ideas, impressions, truth, God, order are all in soma strange
way related to this strange "I" that is
yo~rs
The "!",. li'ke gootj sense,
days' journey.
and mine after our six
seems· equally shared by
all men.
Of the nature of this self, so little can be said; it is true.
·were we formerly more capable of understanding ourselves?
·. We before understood ourselves as integrated
beings.
Wonderful.
What more can be said?
But
Doubtful.
physico-in~ellective
One problem, or. pseudo-
problem, which the earlier view avoids, Descartes also avoids (by not
· addressing himself to the
proble~):
how are the faculties of sense
perception and imagination possible? .How can two substances utterly
distinct,
h~ving
no properties in common but existence, interact to
produce these phenomena?
How can we know the outside world at all?
To a certain extent, we are
· creat~ng
How can we determine the extent;
it.
To how great an extent?
Descartes invented (or discovered)
what came to be known as the mind-body problem; its ramifications are
many and varied, especially in questions about the foundations of
knowledge.
Though Descartes would probably not admit to many of the
problems found in his work, he has no recourse but to mystery. . .
moving through the same problems under a different as.p act- · another
,
question comes to light.
What has happened to God?
Why are both
Descartes' proofs cast as merely plausible though they wear the mask
of demonstration?
The late scholastic masters could have made
eoormously impressive proofs
principle of sufficient
door,
f~om t~e
~eason
same material.
But the
has slipped into philosophy by the back
Though no_ until· Leibniz will it be operating · af its greatest
t
efficiency, Descar,t,es tacitly assumes it
~o.
prove his- deity benevolerat.
But in scholastic thought one ·principle i~· supreme.- --~ safeguard contingency.
The
ru~~
of .sufficient reason amounts to a denial of that
�21
principle.
Until deservedly kicked back into ignorance, the "philosophers"
will henceforth sit on the footstool of God.
Every rule proposed as universally true must be either self-evident, or
given in experience with a degree of probability approaching certainty.
Whence comes this puzzling rule of clarity and distinctness?
It is de-
rived from an examination of the cogito, but why does a criterion so
dependent on an
indi~idual's
mind ·come out?
If I perceive something
very clearly and very distinctly, and you do not, how can I possibly,convince you that it is true?
If there be no
fo~m
to a truth, about which
I can speak (and can speak because it is exterior to us, or common to us
1
all), then discourse can degenerate to .verbal squabble.
The controversy
between Hobbes and Descartes shows ·this with exquisite clarity; Descartes
will have an idea be one
else.
thing~ ·
and Hobbes must
ha~e
it mean something
And is there a ·difference in the self-evidence of "I exist" and
"God exists"?
Of the unclear · or indistinct ideas
in
the Meditations,
surely principal is the rule of clarity .and distin6tness. :
Go now from this rule, which admittedly has a certain intuitive appeal,
t~
the. nature of physical reality.
The material world can now be known
with .certainty, since the nature of .material things is strictly mathematical.
Clearly a mathematical explanation of the world. has a -greater
clarity and distinctness than one dependent on some notion . of matter or
mass as essential to material things.
With unerring foresight, Descartes
neglects to mention weight once in his description of matter; the problems
that classical mechanics raised qver the nature of mass amply attest to
the recalcitrance of this idea to formalization.
It is . form which brings
forth the clarity of everything from God to writing to matter, that is
the sole nature of things; efficient cause is to become indistinguishable
from formal cause hereafter, and both thus lose their original sense in
the blurring of the borders.
On the nature of things Descartes has imposed a great problem; if my
intellect is an active principle, it must trespass on Nature's own
ground.
Where is the line?
It must be said that ultimately we can
never know the wax, though if God be benevolent, we can know it _exists.
We know only the nature of the wax by a mathemat.ical description of
sense -- phenomena.
Nature has been re-def.ined so as to admit of
�22
ultimately being intelligible, and what the world really is, we no
longer care; we care about ordering the contents of our minds -- no
more.
Perhaps the notions which proceed from this book exceed the
vision of Descartes, though his masterful manner show clearly that he
knew· what he was doing; writing a book about the formal description
of Nature.
Death blows are often dealt by slender needles; Descartes' subtlety,
insufficient to escape the censure of the Church, was yet sufficient to
act as the first rock in the landslide.
Not once going to the trouble
to refute the metaphysics then in vogue, Descartes was never forced to
define his position in an accepted vocabulary; dialectic between the
ancients and the moderns could, and did, stop.
Taking extreme care to
avoid the Inquisition, Descartes by drama, order, metaphors, and
ellipsis put into his book the seeds of a new creation -- a creation
lacking even the quasi-determinate nature of the old order.
Systematically
Descartes destroyed the distinctions between the sensibly known and the
mentally known, matter and form, life and death, actual and potential,
pure and applied, nature and art, intellectual activity and the pursuit
of truth, man and God, and supplied us with a distinction between mind
and body that perhaps cannot be maintained.
Though he reversed the world,
he set it in speed, and though he doubted all, he left us technology; by
the kingdom of Man he replaced the kingdom of God; and if truth be the
final goal of man, or our specific excellence, justice, if man must reign
on earth and wisdom be his only guide, then by his very novelty, his
f aith a nd his failures , he has left us our proper gift , our most
necessary asset, our nobility as man -- the certainty of question.
*
*
*
*
*
*
*
*
*
*
1) The Opus Oxoniense of Duns Scotus constitutes what is fully the equivalent of a Summa, and is certainly the only grand challenger of
Thomas Aquinas' work.
2) cf. Plato, Apology 20d - 23c
3) cf. Genesis II, 1 - 9
4) Paul, I Corinthians 13, 12
5) cf. Genesis I~ i; . also, Genesis 1, 9; 1,14; 1, 26
6) It seems to me an important question whether one can ever get something natural out of what is contrary to nature.
7) cf. Plato, Sophist 247e - 258c
�23
DE LA CRUZ ESPANOLA
Lois Hoffman
I've staggsrGd down
through Old
Mad~id
Drawn to this,
La Plaza
d~
la Cruz Ve1de.
Behold the ancient square,
the rusted fountain,
cluttered with lgoves,
and Spanish soil.
Of its youth, this only
do I know;
That human fleah burned here
And blood ran from the lion's mouth
In sacrificial torrents.
Torrents of ancestral blood,
To drown the soul
With unspeakable horror.
*
*
*
*
*
*
*
*
*
CHILDREN
The first Child
Risa, child of the beautiful smile,
Nymph-like, comforts her broken dell.
The Second Child
I saw him first in the Ibizan moon;
I did not know his kitten had drowned.
"Don't cry, Lila," he said.
The Third Child
The third child greeted me at the gate,
A kiss for either cheek;
She was a Spanish rose that
But being · cut, withered
d~y,
away~ ·
But the number less child, · ·
Born of the infertile plain,
Wandered begging through Ciudad Lineal.
*
�24
PRIZE-WINNING SOLUTION TO THE JUNIOR-SENIOR
MATHEMATIC PROBLEM, June 1964
John Hetland
Theorem: If a tangent to an ellipse meets the major and minor
axes extended in P and Q, the least value of the length PQ equals
the sum of the major and minor semi-axes.
Let there be an ellipse with
center C, major axis KA, and
minor semi-axis BC. At any point
D on AC, erect an ordinate meeting the ellipse in T, and drop
the ordinate . TE to the minor axis.
At T draw a tangent meeting the
major and minor axes extended in
P and Q. Let the length AC be designated as a, BC as b, and CD as d.
=a 2 ;
2
4
a
d2
=
By Apollonius I.37,
CP•d
Similarly,
cQ·cE = b2; co2= _ _ __
b_4
CP
CE
2
KC•CA
TD2 -KD•DA
2 _ b2a 2
b
but by Ap. I.21,
therefore
CQ
-
2
a -d
2
a
•
2
TD
2
= (a+d)(a-d)
= b2__b_2__
a
-
2
2
2
2
•
• (1)
a -d
•
Since
•
Now let d
(
3
) .!
__
= (-a ) 2 ' . where
•
e is any number greater than-b.
(a+b+e)
Thus O <. d
<
a, for
(
( 3 ) 1..
3 )1
a )2
( _a_)2 = (
a.+ -b
a ) = a,
( a+b+e)
(
lim
and
lim
8-?'
Thus, by varying
for all possible
the points A and
same things will
co
(
3
h.
a )2
( a+b+e)
(
= o.
the quantity e within this range, we have provided
positions of the tangent on the arc AB except for
B, where the tangent will not meet both axes. The
be true iri the other quadrants.
�25
Then substituting this value for d in ( 1)'
. 2 2 )1
( 4 .
a b
a (a+b+e2 +
)2
PQ = (
3
3
a )
2
(
a
a
a+b+e )
(
=
.
-
2 2
)
(
b
( a(a+b+e)+ a . 2 ~a+b+e 3 )t
3
2
(
a · +a b+a e-a · )
(
(
a~b+eHa+b+e)
b+e
(
2 .
b ~a+b+e) h2
)
+ b+e
)
.
= ~ · (ab+ae+b2 }(a+b+e) ~· !
( .
b+e
)
(
.
= ( a 2b+2ab2 +~3+a 2e+2abe+b2e+ae2 )) !
(
b+e
(
. 2
. 2
)
'2 .
2
=
( bla +2ab+b )+e(a +2ab+b )+ae
(
b+e
=
(
(
(
~·b-~eHa+b} 2 +ae 2 .)'
)
b+e
2 )
)
)
!
.l.
2
)
..
=
PQ
(
·2 , ae 2) .l.
( (a+b) + -) 2
b+e ) ·
(
:2
e '/
o,
ae
then b+e /
if -b< e <
o,
·then~
If
if
='.o,·
·e
ae
2
b+e
o,
and PQ
>
a+b;
> .o,
and PQ
>
a+b;
2
ae
then· b+e ·=
o,
and PQ
= a+b.
Therefore. the least value of the length PQ is the ~.um of the
major and minor semi-axes, which was to be proved •
· (corallary: the
t~ngent
( . a.3) J..
d
'
~((a+b )~.)
)
., , :
.rl
•
will have its
. .
mini~um
value a+b when
�;:i
26
WHAT IS KNOWLEDGE?
A Plea for the Re-entry of
the Poets into the Republic
David
c.
Dickey
All men desire to know; further, they desire the assurance that they have
discovered the 'truth' in whatever matter they have been investigating.
This formulation immediately raises numerous questions and objections:
"What is 'truth'?" "How do we recognize the truth about anything, if
there is such a thing as 'truth'?" usome men are perfectly content with
the thought that there is no such thing as ascertainable truth, and yet
proceed with the investigation of those things about which relative, or
probable knowledge can be ascertained." and, even more radically, "The
search for 'truth' is a mad undertaking!"
I shall answer none of these
questions at, this time, and, in one sense, I shall answer none of them
at all.
Let us look first at the investigating and un-disillusioned man, the man
who searches for the answers that fue thinks of, however erroneously, as
the truth.
This man will probably call himself a philosopher and pursue
his quarry with a battery of logical tools, methods of observation, and
perhaps finally, dialectic.
None of these seems to explain too much
about the process whereby a man might hope to find out anything about
that which he is investigating.
A man might hope to investigate either things that are without him or
things that are within him.
In the former instance he senses those
things tha\ are without, which is to say that he measures their effect
upon his body in one of five ways.
He knows a little about
a thing as
the light wav,es from its surface alter certain sensitive parts of his
retina.
He knows a little more about it as the particles from its
abraded surface alter the nerves in the mucuous linings of his nose and
mouth.
In fine, it would appear that, at last, he is examining nothing
more than himself.
At the very least he is finding the relationship
between two things, one of them known and the other not.
This is, of
course, what Socrates was warning us about when he spoke of the delusions
of the senses in the Phaedo, and it is perhaps the really frightening
meaning behind the Delphic commandment to "know thyself."
°Know thyself,"
�27
we are told, "for in truth you can know nothing else."
This .is qui ta possibly true, for when ·man examines nature, or - he things
t
that _
are without his body, he must both entangle himself with and separate
himself
f~om,
those things which he is trying to -observe.
The search
for 'truth,' then, must be limited tc)those things that are -within us,
but
here ~ ~gain
we meet the same sort of objection, for it would seem
to be plainly impossible for a man to separate himself,
as
the observed,
from himself, the observer, and thus to determine how the body-soul -that
is a man· works.
To do this he should have, by some device, to stop the
life-process, to see i t in stasis, but this woul_ not be examining life
d
at all.
Even were it
- fruit~ul, , ~uch
a procedure would be· impossible, for
the device of memory, whether written or organic, must be
a faulty one
since words are not omni~~ignificant, nor memory ·- eliable.
r
.'
-
Perhaps if two or more men were to cooperate -- but again, the view is
"
bleak._ man's greatest device for wo·rking with · and cooperating with his fellow man' lang'u age, is not dependable for this task' for it is con:structed upon the very thing which we wish to investigate,- namely the
workings of a body-soul which assigns to a given half-understood feeling
or action a given symbol and then·strives to
ma~ntain
a one-to-one
correspondence between symbol and perception.
The problem of obtaining certain truth is now resolved into two problems,
the problem . of clea.r perception, and the problem of communication~ - We .
b
the suggestion tha_ it is impossible ·for one person
t
have - een:·.laft '.: with _
to see the truth, and that it is impossible for two or more
in the -search for it, since
comm~nicati~n
is not
to
cooperate
acc~rate.
1
Wha.t do we mean by communication? We seem to mean a device -of persuasion )
wher_by the listener is brought to have- in his mind the same thought that
e
w~~
in that of the speaker.
If it were possible, we should desire.it to
-be a form of persuasion that produced in the mind of the listener, a
true thought, though we are not sure that .either mind could have any
•truth' to convey.
If there is an answer to this question, it . may perh~ps lie in the dia2
. lec~ic o_ Plato's Republic ), that fourth part of the divided line,
f
3
that, we are told will. lead us )·"using the hypotheses not as first prin-
�28
ciples, but only as hypotheses" to "the first principle of the whole"
and from there descend again "without the aid of any sensible object
from ideas to ideas, and in ideas she ends."
UJe should like to know,
with Glaucon the route of dialectic, but when he asks, for us, what are
the ways itnd turnings of its path, S.ocrates tells us that he cannot tell
4
us that, though he might perhaps show us something ) 11 like reality."
If the
t~uth
is to be ascertained from hypotheses· used only as hypotheses,
'
then it must be in a fashion independent of the hypothesis tha~ is used.
But it i:s plainly not some logical trick such as that attempted in the
Parmenides, of showing that a conclusion follows both from an hypothesis
and its , contrary•
When Parmenides leads us into like difficulties both
from the assumption of the
.Qr!!!.
and the assumption that there is no .QD.!!.
we are left With the hollow taste of rhetoric and sophistry, not wi~h
5
the knowledge df truth. ) We need something more before we declare that
we have found a route to the truth.
I.
I,
We know in advance that deductive
I
'
'
logic, the logic of the prior analytic can deduce
.!J.Q.
more than its
premisses contain, and we must therefore distrust a priori any logical
process that claims to attain certainty, or even something like the
truth, from a simple hypothesis used as an hypothesis.
UJe, the un-disillusioned, demand something a little more solid on our
plates, at least until we find that there is nothing better available.
But perhaps, if Socrates will not tell us directly what this dialectic
is, the structure of the dialogue itself may contain some clues.
At
the beginning we meet Kephalos, or "head," an old man who, telling us
that he has lived beyond the years of his (}vf-o's
?
and his £.Tit
(}
I
Uf U;\
is now ready to study philosophy without distractions, and ideed is
admirably suited [or this pursuit.
But he is a man who has not' made
anything in life as a money-maker, and he will not do so as a philosopher.
He must leave before the real business of the dialectic begins.
At a
later point in the paper we shall follow him and see to what place he
has gone; for now we stay within, with the men
achieve something.
who~'
apparently,
These are the men of spirit and desire, the
aggravated and the angry, the greedy for the truth, and those who wish
to win
ho~or
by refuting the great Socrates.
And now we see that there is plainly a reason for this, for the two men
6)
�29
of
w~om
Socrates thinks . the most are the utterly impossible and irritating
Thrasymachus, and the honor-greedy Glaucon, a true
Timocrat . w~o
with the best rhetorician in Athens for the praise of . the few.
contests
Neither
of these men desires the truth any more than poor Kephalos, empty-headed,
eager ·man,
y~t th~y ~e~m
to be the men best able to assist Socrates in
his search for · it~ . if i~~eed, that is wh~t they are dtiing. What then is
this Pt.e ces.s . for finding the truth, that it demands such strange qualities
on the" part of its practitioners?
for it, we are told, all of man's
faculties must be trained to the utmost, yet we seem to see little result
from the training in gymnastic and music, grammar, rhetoric and logic,
arithmetic, geometry, solid geometry, and astronomy that we are told is
necessary.
We know that it is, in soma way, from the origin of the word, . either
7
r£~ a "talking-through" or a .. § ~"' - ~ ;O<>S
)' something that is through two ratios or two accounts, perhaps something
sL: -Al:
'
common to t~am. W~ are given a rather poetic image of what it can do in
one part of the Republic 8 ): "It may happen that when the two contemplate
each other and rub against each other, that they will forthwith
s~rike
a light in which justice will shine out and certainly the vision which
is then revealed, we . will fix in our souls."
:
If this is truly dialectic of which he speaks here, then we might guess
at .what he means.
When, in an interesting passage, Thrasymachus .bursts
.upon the scene like an onrushing buli, Socrates uses his very conviction,
his ·
t9vr/> i~ fact, to cause him to blush, and thereafter .something strange seems to have happened to him,' and he has .truly gained
more than any other person in the room in his quest for the truth · concerning
jus~ice,
for, as justice is later defined in.the Republic -- the
·right ordering of the parts of the soul, he seems to develop into a just
u_s
man; perhaps his t3ur-Js
and VC1
have indeed contemplated each
other and seen each other for what they are, and as they rub together,
and assume their just positions we ~ea the light of that fire in his
9
r-eddened face ). Sacra.t ea has won a great .victory in making this sophistic
giver ' of discourses really care whether he finds the truth,
8ur-o5
~nd
riowi with
firmly in the service of his newiy-emancipated vo Cs
he
may proceed justly -in the search for justice. Perhaps, in .this moment
of confusion and shame, brought about by the refutation o·r his hypothesis
his
�-----·--------------------------------------"I
30
as an hypothesis, he has been given a glimpse of
\
To
ov
>'
of the first
principle of the whole, and can thenceforth keep and nurture this plant
which Socrates has engendered in him, achieving, at last, a measure of
truth.
What a beautiful answer this would be! but, of course, even if it works
and ·i s not a glib mis-interpretation, we do not know what it is that ·
makes it work, and we may quite fairly condemn it as "mere mysticism"
if we are unable to determine upon what that mysticism is based, if
indeed it is based on anything.
Why, then, does not this satisfy us?
We surely did not expect to find a
route to truth in logic, for deductive logic is sterile, all very well
for "descending from ideas· to ideas" but useless for getting us to the
first principle of the whole. Inductive logic, the logic of the posterior
analytic is no better10 l., for it depends upon analogy, and the notion
that what has always happened will always continue to do so.
If there
is a route to the truth, it must lie, at least in part, without the way
of logic.
Let us now leave the little-room, and its entombed occupants, and follow
Kephalos.
He has gone without to sacrifice to Bendis, the Thracian
Artemis, a terrible creature who, at a far earlier time had caused the
hounds of Actaeon to turn against their master, who had been changed
into a stag to be torn apart by those creatures in life whom he loved
the most.
She it is who uses those dark, secret chords that run through
all men and animals, uniting them by passions so unspeakable, so base,
that they should certainly not be the concern of Socrates and his
friends within the sheltering walls.
men who have no
tyrannical
6}-~;5
f7/L &vi'"' t '7<..
This place is only safe for old
left to warp, and who pray to have their
returned to them
only for Kephalos, and
perhaps other old men.
But even old men are not immune from the dark forces that even the gods
can only use, not mold.
At a later time old Teiresias, wisest of the
wise, danced with sage and powerful King Kadmos a wild debauched
bachanaal upon the same ground where once Actaeon's shredded corpse bore
witness to the fact that men are not thinking creatures alone. : Eu~{pides
�31
shows us with a
fascinat~d
and a horrified .genius this scene at . the start
of the Bacrihai and we watch ·as it writes its way towards another . scene,
strangely like' but· far more wrenching than that of older days. There is
a ·new god loosed in the land, a god who once more plays the dea.d ly
fascinating tunes to which all men, . will they it or not, must dance.
He is Dionysos come to claim the worship of the land that ,bore him, come
to take possession of the people from whose .dark hatreds he is sprung
as suroly as from his double birth of Zeus.
Nothing stays him, for all the women, closer perhaps to the basic sanguine
tidea, must follow him.
Sven Agave, mother of the doomed King Pentheus
is there, sucking at the fonts of milk that nature throws out to these
her children now returning in their worship to their bestial base.
No
woman can be blamed for what she · does in these rites, for none can resist.
no!
We, the watchers, feel within ourselves these same tides -- but
It is not thinkable.
liver of the examined life.
feel their pull somewhat.
We are like Penthsus, the calm, deliberating
We can resist these things, though we might
"But what if?" we ask ourselves, "What if?"
We strain •twixt wish and duty.
We blush to feel the eagerness, but uie
shall not give in.
Dionysos now approaches us -- Pentheus.
Would he not like to see the
wild women ·disport themselves on the sacred mountain, casting their
anguished bodies over ground where once brave Actaeon lost his. life?
( f"or watching women's mysteries!) He, for. us., wills to resist, but we
know that he cannot. · Off he goes, will he ~- nil! he, the last and
perfe·c t victim of that thing which is within him as much as in the
pitied, loved, and envied Bacchai.
The chorus sings for his destruction,
of ripping him, impio.us male, apart• UJe feel their rage, and though we
know it mad, we .cannot quite resist.· But quickly, as quickly as the
climax of orgasm, the rage subsides, and, gasping, we begin to see
again. .We now barely remember that we had a part in that rage, the rage
against the just .man, the outsider, the .dude; the fink, and we watch,
in washed-out resignation, the slowing .pulse of the play.
In comes Agave,
'
one
.
swif~
gl~dly
I
bearing the head of that great beast which, in
'
motion of nature-given strength, she
truding body.
'
ha~ .
ripped from its in-
She has won great honor and wishes to show her son the
�32
lion's head.
Perhpas we envy her even now her frenzy, but we see the
"real world" coming back, and the little of us that would be Agave is
abhorred with her as she slowly sees • • • that it is her own son's head
that she bears. We look at what has happened, and what happens, and we
see, if we are honest -- and the poet, by his art, has left us little
choice -- that it is all •••
~·
We do not puzzle over the meaning
of the word, but recognize that here it fits.
des.cent from madness is true.
But we see also that the
Thou·gh man may have his base in Bacchic
fren~y ' . he must return to the world of the
AD
ros .
There is something
in him reasonable that, however artificial it may be, re-asserts itself
upon him, or within him.
We see this happen to Agave, and, in measure,
are reassured.
This,
is poetry, and it has achieved something that may have meaning
then~
for us avan within the little room.
But
first~ .
what is poetry?
Let us shy away from the easy
ra~te
of
Aristotle, and· not say simply that poetry is imitation, though we have
seen that it is that.
It is something else as well.
composed and presented to men, it must
communicating.
be
It is plainly not logic.
First, it is
assumed, with the purpose of
There is left the possibility
that it is rhetoric, and therefore to be exchewed, for rhetoric, a
later follower of the Platonic-Aristotelian tradition will tell us, is
that form of persuasion which convinces by an undue and unfair appeal to
7
,,Ct
/
the · <i7Tt. .uuf"'t.,o<. , and it is possible, by a deception.
He further
tells us that, to him, all things in the physical world are subject to
demonstration within logic, either the prior analytic or the posterior,
and that, therefore, when rhetoric convinces of the false, it can , be
refuted by logic though perhaps with difficulty, for men's minds are
often weak.
When it convinces of the true, it is the weaker ·route to
something that could be demonstrated logically, and is therefore to
be shunned .
alternative.
But perhaps we have over looked somethi.n g.
Poetry may appeal to an entirely different· part .of the mind,
and we have seen that it does.
appeal to the
There is another
tJ%,cf s ,
£
Poetry consists in those arguments which
even as logic and rhetoric appeal to the
and
lTL (} vJL/-<
respectively; but this is, in none of these
cases, a simple demarcation, for the soul is not so much divided as zoned,
VD C'S
�33
and the parts are forever and inextricably mixed, which is how we may
,.......,
speak of the
having a desire.
Vou5
We begin now to grasp how it is that poetry qonvinces, for each man,in
examining himself, and presenting the conclusions of his introspection
with the art of the poet, is able through the
audience, and without the use of the ;\;
cros
&vf""rJ5
of his
in its more narrow sense
to convince another man of what he then sees to be true about himself.
Poetry is the artful suggestion of the true.
art convinces, but rather· the combination.
Neither the truth nor the
That thing which is in itself
true to the reader or the watcher of the poem is borne in upon him because
8vr!S
i t is true, and as it is presented to him, through his
the art of the poet.
compel us, without a
, by
Poets convince us, and with the very sensitive,
~6rd
of argument, but they must miraculously lose
their power, or become rhetoricians, if they essay to convince us of the
false.
The power of the combination is so great that Euripides was able
to convince us of those things which we willed not to admit about ourselves, and which he knew from a pitiless, and perhaps
mad~
examination
of himself, to be true.
These things are true, for we feel them, but what is it that makes it
work?
In short, what are the answers to the covey of questions that we
flushed in the first paragraph?
moment.
The first seems easy enough at the
What is truth?
Men have certain things basic to them and comm,on among them, for they are
created of the same stuff, their elements, whether we call them earth,
air, fire and water, or give them a name from organic chemistry with so
many syllables that it would coil four times around this page.
llie
might, in desperate instant, even call them love, honor, hate, lust,
treachery and virtue.
Whatever these things are -- for the moment it
does not matter -- they are common among men.
Upon these are based their
instincts and their weaknesses, .and that peculiar phenomenon recognized
...
by both Euclid and Plato under different names, !'<Jt_Vd,.</
\I
and' vof-~fl-~Vo< /\z_ ovt£s
0
ments that all men of good will must
nature.
11)
-;>/
Z:.VVDLri..£.
• These are the simple state-
accep~,
because of their vary
It is to be noted that these common-.notions can apply, conceding
their origin, only to 'intuitions' and agreements about men and by man.
�34
Though we may well never
~now
what precisely is the substratum
~pon
these notions are based, we can reccggize them, and postulate it.
which
It is
these in large part that normally produce in us that very well-founded
c'o nviction that we may now call truth.
These common notions have a peculiarly
force
negat~ve
12)
, for they force
men, at least men of: good will, to accept them _ ecause they cannot, try
b
as .they will, find an alternative ·that is not repugnant
~o ~hat t~ing
within them which makes them -men, animals, and (18tural bod_ies.
in this
~ sense,
Indeed,
Euclid is a poet • . Some of his definitions are explicit,
following from sense perception; some are arbitrary
explaining _ ~he .
author's own creation, but a few ("A point is that w ich has no part."
_
h
'!An unit is that · by virtue of which each of . the
t~ings
that exist is
·called one."_ do not show us the thing being defined, but lead us by
the poet's art to that point where we must know what the subJect is, for
we cannot think otherwise, and we accept the truth that is implied,
though not demonstrated.
What then is this dialectic of which we made so unsatisfactory an
analysis in the first part of the paper?
is from poetry that it must derive
it~
It is in part poetry, and it
strength.
It is, however, a
particular form of persuasion that has one man, the questioned, as its
intended audience, and is able to work with him far more immediately
than a general poem to a general audience.
the interrogator is this:
The problem that
conf~onts
He wishes to instill a certain truth in
ano~her person, · thoug~ he is not ~et absolutely sure if it is indeed a
trtith.
He k~ows that ~oetic comm~nication will ~how that it is ·a ttuth,
thus helping both parties in the search for
t~uth
principle that he has somehow found in particular.
in
g~neral
and this
This would be all
very· well, but the one t6 be questioned is not ready to listen to any
poetry, so the problem is how to· induce in him a · state of
susceptibility~
If ha · is a man like Glaucon and Thrasymachus, a man who · has a strong
opinion in which he takes pride, in :short, · one that is involved with his
()-o~J5 , the problem may be ·salved.
I
All the interrogator need do
J
I
·is to' iiiduce ·in the question a state of tftlTOfL<:X.
, . a feeling that
he has be~~ refuted in that op~niri~ or theory which he prized so highly.
Then he will be ashained with liis
t!f vrJs 1 ~) and be ready tc;- receive
the knowledge, i f it is true, for since at this moment his
&rJs
is
�35
very briefly -- in complete charge of his soul, only poetic communication
could convince him, and that could only convince him of something true.
To produce this state of
:>
Cl(
/
!Tof L.ol
, the interrogator might at any
time be called upon to use any of the liberal arts including rhetoric
and faulty inferences from analogy:
for the state of
'>
t:l(11
I
of t_,,,<7{
is only necessary that the questioned feel that he is refuted
14
,
it
).
Poetry in its more formal manifestations cannot work this closely with
its audience and so must limit itself, it it is to be successful, to
subjects to which the audience is already susceptible.
When po_ ts do
e
not do this, they automatically limit their real audience to those who
are, either by training or chance, susceptible.
But no matter which
poet we read, if he conveys something to us through his poetry, we will
find that it is compatible with that which we have received from all
other peats, for none can communicate anything but the truth.
There is a certain pleasure connected with the infusion of poetic knowledge, and since this appears to be the only way in which we can achieve
certain truth, we may easily see why it is that man finds learning
enjoyable.
Might it not be possible that a man could receive true
principles from nature as from a poem?
Would this imply a divine Author?
This question presents us with one possible answer to the perplexing
problem of how an individual mind is able, as we have seen, to do something about itself that is true.
But we do not need this suggestion.
Even though the devices of memory and writing are not completely reliable, a man may determine enough concerning himself from them so that
he will be able to present. something that is near en.ough "like reality"
so that those elements of it which are true will be heard by the
audience, and they will have learned.
Poetry is present in many fields of investigation, even in some, such
as
&L~ Lft<itSJ whibh
are thought to be strictly logical; a man may divide
the whole thime and time again to find something that is within him, for
though he knows not where it is, he is there, and ,like the man lost in
the woods, he can guide the
where he is.
hun~ers
to himself, though he has no idea
Just as the hunters in going to the lost man determine his
relation to the outside world, so the process of
~ivision,
guided by
poetic insight, determines as it goes the position of its object in the
15
)
�36
outside world ·of thoughts.
Aristotle, the man who would like to root all knowledge of the physical
war ld in sense pe.r ception, is forced in the fourth book of the Physics
to appeal not to
t~e
senses but to the common notion that all men have
concernin.g a "now" -- tha:t it is the boundary between the "before" and
the "after."
But be that as it may, we have delayed long
. he title to this paper.
t
eno~gh
the
sec~nd
part of
That was:
A PLEA:FOR THE RE-ENTRY
or
THE POETS ·INTO THE REPUBLIC
..
but that plea is ·aver already, the poets, we find, are in command and
always were.
non-existent
They founded the Republic and no argument directed to their
cam~l'
without the walls can dislodge them from the Acropolis.
Plato fears them for the dark forces that they speak of and seem to
manipulate.
He fears the ba6hanaal, and
is made of the same
stL~ff
judge~
rightly that the poet
and talks in the same way•
He feels that these
forces are a danger, and must be eliminated, but· he cannot exclude them,
for it is upon them, and the firm bedrock that they represent, that all
logical thought, dialectic, and the Republic itself, must be built.
The
poet Plato cannot expel himself.
*
*
*
*
*
*
*
*
*
*
NOTES
1)
It may seem a little violent to refer to communication as a form of
_
but when one is dealing with the mind of another, trying to
communicat:i f with it, the situation is indeed analogous to the sort of
persuasion whereby man seems to control nature by using her laws against
her.
persu~~io~,
2) There is no reason to suppose that the dialectic of the Republic is
inherently superior to the two other major types of Platonic dialectic,
but it is the only one that promises that it can attain certain, knowable,
first principles.
3)
Republic 511a
4)
Republic 533a
5) In the October Collegian, Mr. Klein suggested th.at the rea$Qn the
dialectic of the Parmenides seems to be so sterile i~ that .the ~artici
pants are not including the possibility of the indeterminate dyad. If
this is the case, then .the entire dialogue, insomuch as _it is logical
in nature does not really b~ar on the possibility of ariivirig ~t . th~
�37
first principle of the whole from hypotheses used as hypoth~ses~ but
rather from a sort of artistic implication. This ~s consonant with
things that will be _brought up later in the paper.
6) . It must · oa gr~nted that there is some anomaly, i using·tha division
of the soul from the Republic in a paper that is' trying to determine
whether the method used to discover truth in the Republic is valid.
However, the division of the soul is accomplished by agreement about
personal : experiences among the vario~s parties in the room. Though
this may not . be f9ol-proof method of investigation, it is at least
a "likely story."
7) Although I do not state in the paper which of these I prefer, it
is of cou·r se clear that r favor the second theory of the origin of the
dialectic • . This tho.e ry ·would fit in admirably with the conclusion that
I draw.
·
8) Republic 434e 5. This is my own translation, though the las~phrase
is borrowed verbatim from the Jowett translation • . I translate r"A~
in two places to get both the. idea of possibility, as with the oytative,
and of immediacy. Instead ·of combininguKOff ou VTES
and Tf1-'j30vTtS
in~o the one word "frictionu .as does Jowett, . have chosen to keep. them
I
separate. The full quotation is:
-~C){~ -rrf.x .,;v' Tfd\f) c(AA~A<:A o .Korro'C'vr£.<... ~~ T\Lgov'TE5--'
a
,l ,
./
.... , ,
/
W<l1T£f ;J<. lTur~ ·t..'~, £~~o(J-L1fci.L ffOL7JQC:'-fl"EV Tr;~
r
6. L """ Lvrrv
in;r ' "'
fh/CJol 1U1CTof1-Lt9-o1...
,
f>~v Z-f ~ ~ J': v o '1't. vl v
ctivr v rrcr.r 11/Z"v o<vToZ.s .
1
t"
9) This proposal is, of course, not altogether serious, but is intended
as an example o·f the difficulty, and perhaps the impossibility.. of trying
to deal with the . dialectic of the Republic in a logical fashion rather
than a poetic one. This does not mean that - th7re is not a fa~ amount
of truth in it, but -I believe that the ffv~ o ~
and vov 5
rubbing
against each other to find their own place6 . is altogether too pat.
10) there .is a certain difficulty in the statefuent here, when we try to
apply ~~at ·has . be~n said about inductiv~ logic to what ·Aristotle hi~self
says in the Posterior Analytics (I 1, 2, 3
II 19) and the Metaphysics
(I 1)~ . Thar~ is implicit behind all of his arguments for building first
principles from serise perception the assumption that n~tute 'is regular
and pre~ictable. Vet · Aristotle himself, in dealing with the pr~blem of
Tv,X_ "1
and T::i. i rc5~d,. T ov . show~· tha.t what we call "chance" or
.".l uckn is o~oL.rJ.. K..(..,t,; v-uµ_,(1Ef7J t<ov. .
· . • tt,e further ~ells
us, : in the metaphysics that 1tliere c'an be no scie.n ce of owf4 t<o\ Ta;
Cv-?-f3z./l71 ko'v. Indee~ in the wide sense in which he ~ses the concept
or c:J'°'v(JL"' ~ v{,/µ.pi.f 7 f<.d v
. in the sixth book of the Metaphysics, (i.e., those/things which are only "sometimes" but not "often")
it very much resembles n..'2rrf~1ov
• Whatever, he concedes that all .~
of these things arise out of coincidence, and that, in the chance convergence of two causal chains a new phenomenon (vis: a rainstorm in the
drought season) may occur. He does not make the next step and conclude
that this new phenomenon might well be the mover of other things, producing, in the end, something new. If he had realized this circumstance
to be a possibility, he would have been forced to abandon the assumption
that nature is predictable, for it is precisely these things that "don't
happen very often" which could render invalid the "first principles"
gained from ~epeated observations.
�38
11)
Republic 348e 9
12) That the common notions have a negative rather than a positive force
is apparent to us when we attempt to deal with th~m. We do not feel
immediately their truth, but rather we find it impossible to contradict
them, to find an "out" from such a proposition as "equals added to equals
have equal sums." We cannot see any other possibility, for if one were
to be larger, which would it be?
13) cf. Republic "• •• is not a soul equally . to be deemed halt and lame
which hates voluntary falsehood and is extremely indignant at herself
and others when they tell lies, but is patient of involuntary falsehood,
and does not mind wallowing like a swinish beast in the mire of ignorance,
and has no shame at being detected? 535e (Jowett translation)
14) We now see the full force of the scene described by Socrates at the
very start of the Republic (328a) where he talks of torch-race on horseback, with horsemen carrying torches and passing them one to another
during the race. This is, in fact, a paradigm of dialectic. The team of
man and horse: yo v.5
and ()uf'--J ~ must cooperate to pass on the flame
that has long ago been discove~ed. It must not go out!
15) This is the same problem as posed in the Meno. How is it that we
are able to recongize the truth of a proposition about which we know
nothing, or thought that we knew nothing? The device used in the Meno
is essentially a poetic one, and we need not suppose that the knowledge
of geometry was planted in the mind of the slave boy by the gods. The
hypothesis, or wrong opinion which is already within the slave boy is ~
enough to give the dialectician a lever with which to manipulate his
1
(J-u~o 5 and make use of the common chord of humanity which binds the
two -- Socrates and slave boy.
Aristotle, as we have seen, also tried to solve the Meno problem
in the first books of the Posterior analytic. Being unable to accept
an "un-natural" (in the modern sense) answer until all the "natural"
s·o 1utions had been exhausted, he first says: "Our own doctrine is that
not all knowledge is demonstrative: on the contrary, ~nowledge of the
immediate premisses is independent of demonstration. (The necessity of
this is obvious; for since we must know the prior premis~es from which
the demonstration is drawn, and since the regress must end in immediate
truths , those truths must be indemonstrable.)
This is an exciting statement, and we wait to see what this immanent
knowledge is. But we find (Posterior Analytics II 19) that is merely the
process of induction from ~epeated observations, a process that we have
already seen to be uncertain.
To this extent we must say that Plato is closer to the truth than
Aristotle, for he recognizes that the principle of learning is within
the learner by virtue .of his humanity.
��FOREWARD
The following manual on the analytic geometry is intended
to present the connective links bet1rreen the conic sections as understood by Apollonius and as they are understood by the moderns.
The manual itself is divided into three sections, an introduction,,
parts I and II. In the Introduction we shall present certain propositions
concerning the conic sections which were either known to the ancients or
which could have appeared from the point of view of the ancients even
though no ancient ever recorded them as far as we know. The proofs in
these sec~tons were taken from:
Pappus D'Alexandrie, f:. eollecti.2!!, Mathematique
trantlated by Paul Ver EEcke, Desclee De Brouwer
et C 8 , Paris, 1933·
(B) Morton, Pierce, "On the Focus of the Conic Sections"
from Ih£ Transactions of ~ Cambridge Philosophical
Society, vol. 3, pp. 185-190.
(C) Newton, Isaac, Mathematical Principles, tr. Florian
Cajori, University of California, 1947.
The second part, which is intended to be read after the first
book of Descartes' Geometrie, will present solutions to various problems
of a similar nature to those dealt with by I:Escartes in the second book.
Most of t.he proofs have been tak9n from:
(A)
Monsieur Guisnee, APPLICATION DE L'ALGEBRE A LA GEOMETRIE,
OU METHODE DE DEMONTRE PAR Lv .ALGEBRE, Les Theoremes
de Geometric, et de resoudre et contruire tous les
Problemes. Chez Quillau, Paris, 17JJ.
In connection wit h these problems it is recommended that the
student refer to Q!l Analytic Geometry by Fermat which appears in English
tran~lation in DRvid Eugene Smitb's ! Source 122.2k in Mathematics (Dover,
.19.59), -vol. ~I, · P• 389. -·
- · The second part of the manual which is intended to be read a~er
the readings from .the second book of D3scartes 1 Geonietrie, concerns itself
with ' the reinterpretation of D3scartes from the standpoint of •
the a priori
coordinate system. The sources were:
( A)
(B)
Charles Smith, !n, Elementary Treatise 2n. Conic
Sections, Macmillan and Co., London, 1904.
Smith, Salkover, and Justice, Analytic Geometry,
John' Wiley and Sons, Inc., London, 1954:
�INTRODUCTION
Prior to the study of Descartes and the modern account of the conic
it will be necessary to consider certain propositions which were
or could have been known to the ancients but do not appear when the subject
is considered from the Apollonian point of view. For this purpose, we
must see what the ancients meant by a Locus.
By the word ~ or place I mean that line or surface all the points
lying on which have some definite property in common.
For example, given the line
AB (fig. 1), I call by the name
Circle that line or place which is
such that if any point C be taken
lying in that pmace and if the lines
AC and BC be draRn, the angle ACB will
be a right angle.
Or again, if CD be dropped
Fig. 1
perpendicular to AB (fgg. 2), I
say that the locus of any point
c_
C such that the perpendicular CD
is equal in square to the rectangle AD, DB, is a circle.
(
I '\!.
A.. k~/ /
__'
Now we must consider the
/\ \
\)
.' \)
following propositions from Pappus.
\
;·
\.
Similarly, propositions 51
-------·--· ../
'
and 52 of the third book of Apollonius
may be restated as loci problems:
Fig. 2
given two points A, B, and the finite
line segment, c, then the place1. in
· which any point Plies such that AP plus BP equal c is an ellipse.
In addition to the Apolloninn problem of the locus with respect to
three and four lines, Pappus was able to present those same loci in terms
of a locus with respect to a line and a point.
sections~
· /!\\
/
- i)
"
The Solid Loci Concerning the Focus and the Directrix*
Book VII
Proposition .238
If the line RS be given in position and the point G be given not
in the same line, then 'if any line QU be drawn perpendicular to RS,
meeting RS at U, and if the ratio QU : Q be given, I say that the
G
point Q lies on one of the solid loci which is a section of a cone.
Pappus proves this proposition by means of the two proceeding
propositions.·
Proposition 236
Let the figure be as before, and let the ratio of QU : QG be that
of equality.
I say that Q lies on a parabola.
~at .. GV drawn perpendicular to RS and
QN perpendicular to av.
Now since
· NV= QG
and
GQt= QN2+ ID 2
*
Pappus d'
Alexandrie,
U C6llection MMthematique, P• 793
�-2-
and
QU·= NV,
Tfuerefore
N1J2 = QN2 + NG2
Now let VG be bisected at the point A and
such that
NN' = NG.
But since
VG,_ VN' + GN2 = VN2
and
QW~ + m~2 = VN2
Therefore
VG, VN' = QN2 •
But
VN' = VG - GN'
and
VG = 2 AG
also
GN; = 2 GN
Therefore
VN' = 2AG - 2GN
or
VN' = 2AN.
But
QN2 = VG~ VN'
Therefore
QN2 = 2AN, VG
or
QN2 = AN, 2VG.
Therefore Q lies on a parabola having
AG as diameter and 2 VG as parameter.
let N' be taken on NV
--,
,..i rt
"I
u-------- -/i\ !
----
r/
/ j
1
\
1
·
1
\ \ I
l \
I \
I
I \
I
\~
V j-----~~-~r--~c~
.-: , i
N A:
Q.
Fig. 3
E: _
D;
It should be stated that Pappus, himself, by no means considers
what we have just given to be a method for finding the parabola. On the
contrary, the above proof is followed by a sy~thetic proof in which he
finds the line P which is the parameter of the proposed section, and then
arrives at the figure itself by an appeal to Proposition 52 of Book I of
Apollonius. In later times this property of the conic becomes a defining
property and there is no longer any need to return to the cone in order
to discover the plac4 on which such points lie. One might say that the
place becomes defined as the collection of all such points. Once the
appeal to Apollonius is dropped, one is faced with the following problem.
How do you know that the collection of all the points having these
properties compose a continuous line? Perhaps the collection has holes
or is merely a cloud. It is at this time that continuity becomes a
problem. From Pappus' point of view, however, the line still has a being
of its own, and hence it is irrelevant even to raise tae problem of
continuity.
Pappus continues as follows:
The synthesis of the place may thus be accomplished i n the fol lowing
manner.
Let the points V and G be given and let the (given) ratio be that
of equal magnitude to an equal magnitude. Let us cut the line VG into
two equal parts at the point A, and let the line P be double the length
of the line VG. Now since the line A&, which is terminated at the point
A, is given in position, and the line _ is given in length, then about the
P
axis AG we may describe a parabola AH of such a nature that if one takes
a point Q on it and drops a perpendicular QN to the line AG, then the
rectangle formed by the lines P and AN will be equal to the square on
the line QN. (Apollonius, Book I, prop. 52) I say that the line QH is
a part of that parabola.
Let NN' be taken off equal to N~. Now since VG is double of the
line GA and GN' is double the line GN, it follows that the line VN' is
also the double of the line AN. Consequently the rectangle contained
by the straight lines GV and VN' is equa 1 to twice the rectangle contained
by the straight . lines· VG and AN. That is to say, to the ·square on QN.
�l
I
-JNow let us add the square on the line ~N! ~hich is equ~1 to the square
on the line NG; it follows that the square , on the line ·'VN is equal to
the square on the line QN plus the square 9n the ~ine NG. Consequently,
the line ADH constitutes the (required) place.
Proposition·237
Again let the figure be as before. I say that if the ratio· Qil : QG
is greater than the ratio of equa1 ity, then Q lies on an ellipse, but if
sess than equality, it lies on an hyperbola.
Since
GQ2 = QN 2 + GN2
QU .= NV
and
NV2 : QN2 + GN2
:: QU2
GQ 2
Now take N1 such that
· · · NN°·2 : GN 2 : :. QU2 : GQ 2 •
2
2
Therefore
NV : QN2 + GN :: NN' 2 : GN 2 :: QU2 : GQ 2
2
2
2
Therefore
NV 2 - NN°·2 QN2 + GN - GN 2 : : QU : 00
or
NV2 - NN'2
i!Let
NK
Therefore
KV, N'V
Therefore ·
. (1)
Now
QN2 :: QU2 GQ2.
= NN'
2
NN'
KV, N' V ·: QN2 : :
=VN2 -
Qu2
NK : NG :: QU : GQ.
And since we have already considered
the case in which QU equals GQ, let
us now consider the other cases.
Case I
Let
UQ be larger than GQ
Since
NK:NG::QU:GQ
Therefore
and
(2) ·KG:NG::QU-GQ:GQ
Now take A' on VG in such a way that
VG:GA': :KG:GN.
Therefore VG+GK:A'G+GN::KG:GN
or
VK:A'N::KG:GN.
And take A on VG in such a way that
VG:GA: :N'G:GN
s
Fig. 4
Case II
be larger than QU
NG:NK: :GQ :QU
NG:GK: :GQ :GQ-QU
KG:QN: :GQ-QU:GQ
GQ
VG-GK:A'~-GN::KG:GN
Therefore
·vG-GN' : AG-GN: :·GN' : GN
or ·
VN' :AN: :GN' :GN.
�Hcnco
�l
-4a-
to tho plane AQP, and that the striight lino OS which lies in tho former
plane is porpondicular to tho common section AA' of tho two plane, OS
is perpendicular to ·the plane AQP?. Therefore, if a sphere be described
from the centre. 0 with tho radius OS or 03, it will touch the plane AQP
in the point s. Join iJE, and let 13DE be the circular s.oction: passing
through BE; join VP, and let it cut tho circle DDE in D, and join OD.
Thon because tho triangles VOD, VOB have two sides of tho one equal to
two sides of the other, each to oa~h, and tho included angles OVD, OVB
equal to one another, the. bases OD, OD arc likcWiso equal, and tho angle
VDO is equal to tho angle VBO, that is, to a right angle. Therefore, if
a sphere be described from tho centre 0 with the radius OS or OB,~tho
point D will be in tho spherical surface, and every other point of tho line
VP will be without.it, and tho same may be. shown with regard to every
other slant side of the conG : therG fore tho sphere.. so · de scribed will
touch the surface of the cone .in tho circle BDE.
Lot tho lines DE' AA'. (produced if necessary) . moot one another in
tho point X, and tho planes i3DE, AQi::> in the lino RX. Then, because RX
· is common section ·o r .two plane~, each of which is perpendicular to the
· plane VAA'.3, RX is perpendicular to AX. From P draw PR ponpondicular to
·Rx, and therefore parallel to AA' or AX; and through V draw V.F parallel to
AA' or PR to meet ED (produced if necessary) in F, and join FD, DR. Then,
because FD and DR arc parts of tho same common section (Viz., tho connnon
section of the plane BDE with tho plano of the parallels VF, ·PR), i'ffi is
a straight line.
Lastly, ~oin SP.
Now, tho section of the sphere made by tho plane VPS is a circle;
and tho straight lino VP touches this circle in tho point D, because it
lies mn tho. same plane with it, and moots it in that point oril.y; and for
the like reason PS touches it in tho point S; therefore PD is oqual to PS.
Again, because tho triangles PDR, VDF arc similar, PD is to PR as
VD to VF; but ~D is equal to V13, and it has boon .shmm that PD is equal
· to PS; therefore PS is to PR as VlJ to VF, that is, in a constant ratio.
ihorcforo, etc. Q.E.D.
..
It need scarcely be added that bhe poino S thus found is tho focus
.
.
and RX tho directrix of the conic section.
If tho plane of tho conic section be not parallel to a slant side of
the cone, that is, if the section be an ellipse or an hyperbola, a second
sphere may be inscribed in tho lower scbmcnt of the cone (soc fig. 5a) or
in the vertical cone (sec fig. ~:e), which shall touch tho plane AQP in ~
a second point S', and tho··honical surface in a second circle, with regarld
to which tho same property obtains. For to this tho foregoing demonstration is equally applicable. the letters with dashes being substituted
ofr others, each for each. Thus wo arrive at tho other focus and tho
other directrix, and in those cases it is easy to perceive that AS is
equal to A'S', and AX to A'X'. Tho next proposition will show how
readily tho inscribing of those two spheres leads to tho simple properties
by which tho ellipse and hyperbola arc usually defined.
Proposition II
If a right cone bo cut by a plane which is not parallel to a slant
side; and if two spheres be inscribed, as in the last proposition, touching
the plane in two points Sand S', and tho conical surface in two circles
DDE and b1 D'E'; tho sum or tho difference of the distances S~ and S'P'
of any point Pin the conic section from tho points Sand S', shall be
always the same; tho sum in the case of tho ellipse, and the difference in
that of tho hyperbola.
����l
.. 7PROPOSITION :r1
Problem
Given J, K, L, M, and N, no . three . f which are in the same straight
,
it be required to construct the conic section passing through
the given points. Let it have been done.
And first let JN be parallel to
KM. Let A bisect JN so that JA
equals A~ and . B bisect KM so that
KB equals BM. Therefore the line
AB is given in position. Let it
cut the figure at G and E: thus
EG is a diameter. Let LZ be drawn
parallel to A.B meeting the figure
at z. Let KZ meet JN at P; NZ meet
GE at R; LZ meet JN at C; and ll~
meet JN at H.
Since the points
J, K, L, M, N, A, and Bare given,
then H and C are also given.
But
ZC:CP: :ZD:DK
line~ l:et:~
and
LC:CH::LD:DM
therefore
ZC,CL:PC,CH::ZD,IlL:KD,Jlv1
and
ZC,CL:JC,CN::ZD,DL:KD,IM
(cf. Apoll. III:l?)
But since C, H, J and N are given, P is also given. And since L, C, and
Let ZN meet GE at R and JL meet GE
at s. Therefore R and S are given. And by the same reasoning as above,
RA,AS = EA,AG.
But R, A, and S are given. Therefore RA,AS is given. Therefore;FA,AG
is given, and by the same reasoning EB,BG is also given. Th~refore as
will be shown, E and G are given. Therefore the diameter EG is given.
But
GA,AE:.AJ.~2::GE:the parameter.
Therefore both the diameter and the parameter are given and so the
section may be constructed. (Apoll. !:52-59)
Q.E.F.
K and P are given, Z is also given.
Lemma I 2
It remains to be shown that if the rectangles GA, AE and GB,BE are
given; and if the points A and B are given, then the points G and E are
also given.
Let
AB,BW = GB,BE
and
BA,AY = GA,AE
Therefore
WB:BG::EB:BA
and .
BW:WG: :BE:EA.
1
Pappus, Book VIII,
Prep.
Xii!. ·
2 ~·• Book VllI, Prop. XIV.
�-8But
BA :AE:, :GA :AY
Wherefore
BE:EA: :GY :YA.
Thus
BW:WG: :GY :YA
w
B
G-
A-
BW,AY = WG,GY.
Fig. 7
But since the points B,W,A, and Y are given, G is also ·given.
same reasoning, E can also be found to be given.
f
'v'
I
and=
By the
Q.E.F.
PROPOSITION IIJ
Problem
Again, let the points J, K,
L, M, and N no three of which are
on the same straight line, be
given, and let none of the lines
joining them be parallel, and let
it be required to construct the
conic section passing through the
given points.
Let it have been done, and let KN
and JM be joined, and let them
intersect at the point T. And through the point L let LT.n1 be parallel to
JM, meeting KN at U, and the figure at ~~
Now
NU,UK:LU,UW::NT,TK:MT,TJ (cf. Apoll. III:l7)
But the points J, K, M, and N are given, the ratio
NT,TK:MT,TJ
is also given. and since the lines KN and LW are
point U is given.
Therefore
NU,UK is also given.
There fore
in position, the
give~
LU, m~ is given.
Thus the point Wis given, and by the method given in the first part of
the proof, one can find the conic section passing through the points
.J, W,L,M, and N and it will also go through the point K.
Q.E.F.
PROPOSITION III4
Problem
It now remains to find the axis of the figure, given a pair of conjugate
diameters.
Let AB and CD be the given conjugate diameters, and let them intersect at
center E. And if they are not equal, let CD be the greater.
' 12i2.• , Book VIII, .Prop. IlV, . chap. 16
4
....
·-
12i2.. , chapter 17
�-9Therefore E bisects AB and CD.
Now if AB Gilt let rp bisect Angle AEC, and OP is the axis; but if not,
through .the point A·let the line GH be drawn par.aJ..lel to CD; and on the
line AB, take the point ·F such that
..-~···- ·-- -- · · · · ····<,
- DE2 .
·
,/,.
.
... ·
,
EA AF '·
And let EF be .bisected at K.
· / .
·
-~·-.. . ·s·-And since CD is greater than· AB
/
c_ // :. .· ··· ---·--\--; -·--·->-~
1
K will fall between A and F. Now
/ . --. --....._
\j
/
~
let the line KL be erected perH '··- ~:.:_ -·· ---·---·- Of~- -- .. . ~_\_ -~ :
pendicular to AF meeting GH at the \
---..__ _.._
\
i
..•. ·• /) - -. · - ~~-- - ·-· --) P
•
-----I .
I ?
. point L.
.
- ·.:. .."'-._ I /
,!
-- ··
Now with radiu~ LE, let there be
\
, _.~~::·.-_ /,~/ ______./D
_
a circle described about L as
\
/ 1.1
' ---. •. ?A ···
/
t\
;,..
center, and let it cut AL at G and
· / , /"
_ ·,·r
,..
H. Next, let the lines EH and EG
'·.
.·
be drawn, and from the point A let
·
Fi~. /9 .
the perpendic~ar AM and .AN be dropped, and take··-D ·--arra P on EH such that
EO = EP 2 = GE,EN.
·
And take the points 2 and R on E such that
ER2 = ES = GE,EN.
Therefore OP and RS will be the axes. (cf. Apo~l. !:37)
Q.E.F.
=
.
.
•'
1
¥ ._ _·_ _
·- _
'\
I
/
t·
Pappus has just shown that if five points be given it is possible
to construct the conic figure passing through the five points. We, of
course, have only shown the case in which that figure turns out to be an
ellipse. The other proofs, however, are very much the same thirig.
I also say that if five lines be given one can find the conic
section which is tangent to the five lines.
The proof is taken from
Newton and will require several lemmas.
�But
: :BD:AC
=
DG
=
F
is
matter
I say
:BG.
�-11- .
Therefore
and
or
PF:AP: :GQ :BG
AP :BG: :PF :GQ: :FO:OG:
AP :BG: :AF:BQ.
LEMMA
:AF:~
.
Q• . E. D.
rrr3
It four sides of a pai:-allelogram indefinitely produced touch any
conic .section, and are ~ut by a fifth tangent : I say, that, taking 'those
segments of. any two coterminous sides that. terminate in opposite ang'1i,es
of the parallelogram, either segment is to the side from which ,it is cut'
off as that part of the other coterminous side which is intercepted between the point of contact and the third side is to the other segment.
Let the four sides~ ML, IK, KL, MI of the parallelogram MLIK touch
the , conic section in A, B, C, D; and let the fifth tangent FQ cut those
sides or the segments KH, MF of the sides KL, ML: I say that, that
f-··-··--·· ---- ---- -· ,_ 0\ .._..:, __ ~..1:',-~:---- ·-·---.--- ·- :;L
--·
__
·,
ME:MI ::.: BK :KQ,
I ../ ··
\.
and
For~
·:v /~-·
,,
KH:KL ::: AM:MF
~
by the preceding lemma,
ME: EI:..: AJ.'1
I
I
\ .\... //~. .
'
I
;
..,
'·'\
I
\
I
/
I
/
I
,l/'
!•
ME:MI ~-: BK:f:Q.
-~
.
...-/ /"' -. '\.
c
or BK :BQ,
and, by addition,
. (\
_//
I
"-
"'·,
. ~
,. ,
----- :~-- ---- ~--- ··/'!<
-·-·
~ ',_
B
/ .
. "\......
KH:HL:: BK or AM:AF,
Also
/
I
I
Fig. l .1 H
and by subtf.action,
KH:KL u AM:MF.
Q.E.D.
COROLLARY
r4
Since triangle K is similar to triangle MFE,
QH
QK,ME U
KH,MF~
But since
KH:KL: :AM:MF,
Therefore
QK,ME
= KH,MF = KL,
COROLLARY
AM, which is ·~~ also given.
rr5
Let E•Q• · be a sixth tangent meeting KI at Q' ,· and MI at E'.
Now it was
shown that
ME:MI: :BK :KQ.
Therefore,
ME,K~
= MI,BK • .
) id. Bk. I, Lemma X:X:V. 41d. Bk. I, Lermna· x:x:v. Cor. I. : 5id. Cor. II
�F··:i . ..····· ·'-·-- ·----1:-1.t. __ ····-- -~- -· -··------~-· - - ...· L .
. .,
...."'.
,
,{---···
/
·
-12-
.
..
''··,,
~ .,.
But
Therefore
and
or
Therefore
or
= ME~ KQ'
KQ' = ME,KQ
-/
ME',
KQ 1 :KQ: :ME:ME'
·~·: EE 0
:
/
/
/
,.>1
i
'"···~
/ e,
I '••
/
/
gQ :KQ: :EE' :ME'
.'
\\
;,
F'."l
ME' :MI: :BK :KQ'.
~·:,BK
D
·.I
,-I
c. ·l
'\ .
\
'\,
L -·----n /
:QK :ME 0 •
;
---q:~§ ---_/t<
l-f
"
,.'
~Fig. ~1.2
/H
Therefore if EQ' and QE' be drawn, they will . both be parallel to the
base of the triangle IMK, and the line joini~ their mid-points will
bisect the line AM and the intersection will be the center of the
ellipse.
_
LEMMA IV6
Given a line, and a point not on the line, find a line parallel to
the first line and which will be tangent to any conic section which has
the given point as center, and to which the given line is tangent.
Let BF be the given line, and 0 the giv~n point.
Now through the point 0 let any line MON b~ drawn meeting FB at N.
And let
ON=OM.
I say that if a line KL be drawn through Mparallel to BF, it will be
tangent to any conic having 0 as center, and to which BF is tangent.
r ./-------~ -a.
·
Let there be such a conic,
and let it be tangent to BF
at T and let OT meet KL at s.
Now since
N
. /
/
sr--/--~ T
OM= ON
Therefore
I
SO:OT: :OM:ON
and
/_,.
/
OS = OT.
I\
/
!\.r
' j/' ',..,_
)., ; '
•
And therefore KL is tangent to the section.
-.....
I
/
..... -. ... _
L
..
/
/
I
- - - .. ,..
Fig. l J
Q.~.D.
PROBLEM?
To describe a conic that is tangent to five straight lines given
in position.
Let the given straight lines be ABG, BCF, G- 8D, FDE, ahd EA. TAke M and N
on · AF and BE such that
AM= MF
and :
BN = NE.
And let MN be drawn
Therefore MN passes through the center of the section.
(Lemma III, Cor. II)
6 Newton, Principia, edited and with commentary by Thomas Le Seur and
Francisci Jacquier, T. T. et J. Tegg, London, MDCCCXXXIII, p. 180, note b.
7
~ewton, op. cit., tr. Cajori, Proposition XXVII, Problem XIX.
�-13-
-.,
Fig.
Again·,~. take
J
.
...__
4
P ::af.a Q on- B:O!_,'a.nd GF such that
BP= PD
And
FQ = QG,
.and let PQ be drawn; and let it intersect MN at o.
·And since the center is also on PQ, 0 is the center of the section. Let
the line LK be drawn parallel to BF which will be .tangent to any conic
section which has 0 as center, andis tangent to BE, (Lemma IV) and let
it meet EF at K and CD at L.
·
Now let CK and LF be joined, and let them be produced to meet in ·R.
Now if 0 and R be joined and the line be pr~duced meeting BF at H, H
will be on the section. · (Cf. Lemma III, Cor. II) If .in this way the
other four points throughwhich the section passes and the section may
be found by the method of Pappus given before.
In addition to these proofs, we .s hall include Newton's .proof of the
five-line locus theorem because of its elegance.
THEOREM8
To find a point P from which if four right lines PQ, PR, PS, PT
are drati-m to as many other right lines AB, CO, AC, BD, given by_ position,
each to each at given angles, the rectangle PQ,PR, under any two of the
lines drawn, shall be to the rectang~ePS,PT, under the other two, in a
given ratio.
Suppose the lines AB, CD, to which the two .right lines PW, PR,
containing one of the rectangles, are drawn to meet two other lines,
given by position, in the points A, B, C, D. From one of those, as A,
draw any right line AH, in which you would find the point P.
e Ne-wt.on, ~·, Lemma XIX.
�-14-
7
Let this cut the
opposite lines BD~. CD, in H
and I; and, because all the
angles of the figure are
given, the ratio of PQ to
PA, and PA to PS, and therefore
of PQ to PS, will also be given.
This ratio taken as a divisor
of the given ratio of PQ, PR to PS,
PT, gives the ratio of PR to PT;
and multiplying the given ratios
of PI to PR, and PT to PH, the
ratio of PI to PH, and therefore
the point P, will be given.
Q.E.I.
.--
- \1-
·--
-~
- F
.
)
Fig. , .)
Corollary I
Hence also a tangent may be drawn to any point D of the locus of
all points P. For the chord PD, where the points P and D meet, that is,
where AH is drawn through the point D, becomes a tangent. In which case
the ultimate ratio of the evanescent lines IP and PH will be found as
before. Therefore drawn CF parallel to AD, meeting BD in F, and cut it
in E in the same ultimate ratio, then DE w~ll be the tangent; because CF
and the evanescent IH are parallel, and similarly cut in E and P.
Corollary II
Hence also the locus of all the points may be determined. Through
any of the A, B, C, D, as A, draw AE touching the locus, and through any
other point B, parallel to the tangent, draw BF. ~eeting the locus in F;
and find the point F by this Lemma. Bisect BF in G and, draw!bng .the
indefinite line AG, this will be the
A\ r-=
position of the diameter to which
,
\
BG and FG are drdinates. Let
· c
~\
this AG meet the locus in H, and
AH will be its diameter or latus
/
"
~
transversum, to whic~ the latus ·
I
\,«
rectum will be as BG to AG,GH.
~·
. If AG nowhere meets the locus, the
/
/ c.,-\
line AH being infinite, the locus
~
. /
\
will be a parabola; and· its latus
/" /
rectum corresponding to the diameter
\ v '
\
will be BG2/AG. But if it does meet
.. /4 - · - - - - - - - it anywhere, the locus will be an
\ _
hyperbola, when the points A and H
' e
Fig. /h
are placed on the same side of the
.
point G; and an ellipse, if the point G fall between the A and H~ unless,
perhaps, the angle AGB is a right angle, and at the same time BG equal
to the rectangle GA,§H, in which case the locus will be a circle.
t
And so we have given in this Corollary a solution of that famous
Problem of the ancients concerning four lines, begun by Euclid, and carri ed
on by Apollonius; and this not an analytical calculus but a geometrical
composition, such as the required.
· ·
�
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�TABLE OF CONTENTS
What is the "Nothing" in Much Ado About
Nothing? •
• • • •
• • • • Leon Rottner, '65.
• 1
• • Veronica Soul, '66.
• 12
"Thomas Mann the musician": Lecture by
Victor Zuckercandl. A Review by • • • • • • R. A. Licht, '65.
.16
Lisa Grey •• · • • • •
Chasing Chaucer • • • • • • • • • • • • • • • • • • Toni Katz, '66.
Comment on Robert Goldwin's Lectu~g~orable mention Sophomore Essay
nsome Theological Implications of
• Alfreda Veratti •
Locke's Chapter 'Of Property•.
.31
...
3rd Part of Textbook on .Analytic Geometry
* *
*
.51
. . .Robert Sacks, Tutor.
.31
* * * * * * *
...
.Susan Roberts
• Sally Rutzky
John Falencki
Art Editor • • •
• • Daniel Sherman
Faculty Advisor • • • • • • • • Eva Brann
Cover. • • • • • •
• .Paul Ollswang
Editor •
Assistant Editors.
mr.
Sacks' article which was to have appeared in this issue will be
distributed on Wednesday, March 3rd.
�- 1 -
WHAT IS . THE "NOTHING" IN MUCH ADO ABOUT NOTHING?
Leon Rottner
Woven together in the plot of Much Ado About Nothing are three separate
stories.
First:
what ·seems to be the underlying
story~
the romance of
,·
Claudio and Hero.
Second:
the romance of Benedick and Beatrice, which
seems at first to be applied over the first story like embroidery in rich
colors on a rather dull
ground~
Third:
the impossible activities of a
fantastic constable and his watchman, which are endowed with such an
extraordinary character as to give them an entirely special place in
the play.
For some the weaving
~ill
never seem complete.
Whenever one of the three
stories is unfolding on the stage, it will seem to be diverting attention
from the other two.
At its worst, it will seem to be three plays, the
actors of which are each in turn making their separate appeals for our
enjoyment and applause.
rrom this point of view, the wickedly jolly mood Beatrice and Benedick
put us in from the moment the play begins almost thoroughly eclipses
the prettier lyric romance of Claudio and Hero; they make Claudio and
Hero seem unreal.
Somehow, the utter incompetence of Dogberry transports
us on waves 6f laughter far
two.
fro~
the misfortune that overtakes these
The fact that Benedick never
their distinct functions.
me~ts
Dogberry seems to emphasize
The turbulence of Benedick's romance stands
out sharply against the almost uninteresting sedateness of Claudio and
Hero's.
When misfortune overtakes Hero, Dogberry descends from some-
where to save us from too serious an evening.
The audience . comes pre-
pared for an evening of enjoyment, and Benedick, Beatrice and Dogberry
strive to keep it such,
They are sufficient in themselves.
The only
justification for the story of Claudio and Hero is that the brilliant
colors of
th~
other two stories are enhanced by comparison.
*
*
*
*
*
*
I have been describing a· po int of view I
*
don~
*
*
t share.
thing, it has been a popular view for centuries.
*
Why?
For one
For another, ·Don Pedro
seems to a c:remarkable extent to characterize this : view on the stage.
�- 2 -
Like us, he is, on the.whole, ~oo sophisticated to take seriously the
. lyric romari'ce of Claudio and Hero.
Don Pedro treats Claudio's awkward
beginning gestures as a lover as dispensable:
"Thou wilt be like a lover presently,·
.And tire the ·hearer with a book of words. ,"
(I, i 308-9)
That C_audio . shquld ·Want to express more than his desire is unthinkable:
l
· "W.hat need the bridge much broader than the flood?"
(.Ibid. :318)
We remember that Don Pedro's plot t _ make Benedick .'fall in love• is
o
designed to fill an
~therwise
uneventful and rather ·boring gap between
the betrothal and the wedding-day.
opinion of Benedick.
The plot itself is based on a low
The trick wouldn't really be funny otherwise.
Since we laugh so hard at Benedick throughout the first three act·s , I
thfnk we ~hare Don Pedro's opinion about him:
"from thf:l. crown of· his head to the sole of his foot, he is
all mirth."
"(III, i i 8-9)
In short, Benedick ~s no more than clown.
If we take · seatrice's
dis~
dain for· him at face va.lue, .the. hilarity of the jest is in forcing
like poles of a magnet together . and ·being amused to see them spring ·
violently apart.
Bu .~
this phenomenon . is accompanied by fireworks,
·making it an even more diverting one.
Don Pedro says·:
"I will undertake • • • , to bring Signior Benedick. and
the lady Bea tr ice into a mountain of affect.ton the one
with· the othei-~"
(II, i 379-82)
It will be even funnier if they are constrained to remain together;
_
then the fireworks would begin:
· "I would fain have it a match."
(Ibid. 382-83)
That would be an endless source of amusement, but even if not a match:
"The sport will be when they hold one an o_ inion of another's
p
dotage, and . no such matter. That's the scene I would see,
which will be merely a dumbshow."
(II, iii 223-26)
The power of Beatrice's remark at . ·the masked ball is its a.lament of
truth:
"Why·,· (Baned ic:k) is the Prince's jester • • •
"
(II, i 142)
�- 3 -
Surely Oen .Padro is dismey-ed to find that his plot has been ell ho
succes~ful when . Be nedick challenges Claud lo for the love of Beatrice.
1
Don Pedr~ · m~st think .. that not ~nly is _Benedi?k the jester but also
Just as some of us, Don ·Pedro would .
the _genuine fool at· 'this· point.
have laughed if .he ha~rd · Beatrice ask Benedick to:
"Kill Claudio";
(IV, i 291)
for his view of ·Benedick's determination to carry out her command
would seem to follow that reactioo naturally:
". • • for the love of Bea tr ice: (he.) hath challenged · thee. · • •
Wtiat a. p.~a~ty thing man is; when he goes fn his d.oubl.s.t and
hose, ·anti leaves off his wit."
(Vi. i 19B-2n3)
That is ·; what a pretty state i.if affairs when a _man goes forth in ·the·
fo~l
world playing the
(iri this
commands of his beloved.
c~se) by
following the senseless·
In fact, I feel sure. that if we examine· our
reactions throughout most, if not all, of the play, we will find that
they coincide with those of Don Pedro.
I would like t6 put this another
way-. ·.I · wonder if. Don Pedro is not an ' image cf the greatest part of
the audience.
Perhaps, as _
that would imply, the audience has been
made prince and attempts, as Orm Pedro does, · to rule all that goes on
in the play, Dogberry and Friar Francie except,e d.
We remark that at
the same time Don Pedro remains aloof and uninvolved in the activity
he seems to have initiated.
At th~ end, in fact, Don Pedr" is; ' in
o
effect, back to where he was before the play began, confronting his
malevolent bastard brother.
Perhaps once again Don John
~ill
find
himself:
"
. . . trusted with a muzzle, and enfranchised , with a33-34)
"
(I iii
clog.
I conclude that Shakespeare seems on the one hand to flatter the
' judgment of the audience by giving it so pr9minent a place in the
affairs of
promin~nt
th~ characters~
on
the other hand, however, since that
place doesn't do the audience much good, and affairs seem
t6 take their own merry course, Shakespeare doesn't seem to · ba approving
of the audience's desires and hence its position in the play is more
revealing about the audience
*
If this is true, then
*
*
flattering.
tha~
·*
*
*
to . hol6Do~ Ped~o's
,. . ·
*
*
*
*
point of . view is merely to
�- 4 -
share the blindness of a character in the play.
As such, this point of
view is in no sense a revelation about the structure of the rest of the
play.
What is the nature of his subjects and their relation to one
another which the Prince does not perceive?
Moreover, if he is correct
about their character in the beginning, what is the change that occurs
in that character which he misses even up to the end of the play.
for the beginning of an answer to that question let us return to the
question about the title that everyone asks sooner or later:
What is
the "Nothing" in Much Ado About Nothing?
There seem to be four immediate answers that is, four answers that stand
out.
These four may not be the only ones, but since they are immediate,
let us begin to investigate them first.
Three of the answers correspond
to the three stories mentioned above:
1)
"Hero • • • is disloyal."
2)
"· •• you told me today that your niece Beatrice was in
+9~e with Signior Benedick?"
(II, iii 91-93)
3)
The content . of Dogberry' s sel"'_+qnr.es., the significance of the
words he ut tars.
~·
. ···"
(III, i i 107)
..
These three are located for the most part in the first three acts of the
play, or may be said to be characteristic of the first half of the play.
The fourth "Nothing" is characteristic of the second half:
4)
11
Let her awhile be secretly kept in,
And publish it, that she is dead indeed."
(IV, i 205-06)
It consists of two parts, the pretense that she is dead and:
4a)
my brother hath a daughter,
Almost the copy of my child that's dead,
And she alone is heir to both of us."
n •••
For a "Nothing 0
,
(V, i 298-3Dn)
the first succeeds · in causing a remarkable amount of
real misery. · Is this not owing to the readiness of both Claudio and
Don Pedro to believe what they see?
In Claudio's own words:
"If I see anything tonight, why I should not marry her
tomorrow • . _ • I will shame her."
(I II, ii
126-28)
While it is true that Borachio:
II
• most like a liberal vill~an,
confessed the vile encounters they have had
a thousand times in secret",.
(IV, i 93-95)
�- 5 -
I believe that the greatest blow was dealt when Don John fulfilled his
promise of bringing them to see her disloyalty.
The rest of the testi-
mony could only reinforce their astonishment at having seen it actually
happen.
As far
a~
Claudio and Don Pedro are concerned, Hero dies as a
result of the shame brought on her in the church, and Claudio's life is
endangered by Benedick's challenge.
This revolution in fortunes is
made possible because Claudio took for real what was only the · semblance
of reality, and thereby felt justified in voiding his promise to marry
Hero.
The weight of the promise for Claudio is not a very heavy one.
Of course, Hero's disloyalty is a fiction, whereas Claudio's disloyalty
to his own .promise and all those to whom it was made is, unfortunately,
quite real.
The case of the second "Nothing" presents an interesting ·variation upon
the theme we have begun to develop in the case of Claudio!
Benedick, too,
obliges his deceivers; but he believes that what they say is true:
"This can be no trick.
The conference was sadly borne."
(II, iii 228-29)
It cannot be denied that Beatrice and Benedick are drawn to one another,
the beginning· of the play leaves us in no doubt about this.
There are
even indications that they have been courting some time before the play
What is significant is that their courtship has brought Beatrice,
begins~
at least, a great deal of pain:
"Indeed • • • he lent (his heart to) me aw.hile, and I gave him
use for it -- a double heart for his single one. marry once
before _he won it of ma, with false dice, therefore your Gra9~
may well say that I have lost it."
(II, i287-91)
Beatrice•s · auffering stems, then, from Benedick's fickleness:
he is a
.lover who only lends his heart; and from Benedick's clevernesQ he is a
double-dealer ·in love.
Benedick, in short, is a famous breaker of
promises.
He is
braggart.
Claudio, though a newcomer to the art of breaking promises and
introduc~d
to us in the beginning as a notorious
though he is convinced that what he has seen gives him a right to break
his promise, seems t6 be in
· th~
same predicament as Benedick.
there is no way to distinguish their failings.
As yet,
Were it not for the
dreadful consequences of his mistake, Claudio might be excused as being
�- 6 -
new to the affairs of love; it might be argued that. inexperience is what
leads him to the timeless
beloved.
m~s~ake
of the lover:
to fail in a vow to his
The consequences of Benedick's miscohception are not slight either.
there is
~
If
chance that he and Beatrice could successfully spend their
lives together, he seems to be letti~g it ·slip alarmingly in the time
between the deception in the garden and the church scene. From the
moment the · three deceivers leav·e and he comes out from the arbor it is
clear that nothing any.one could say w uld undeceive him; words have gained
_
o
a supreme · power over Benedick. · Beatri9e. appears with the darkest looks
.perhaps in the whole pla.y and Benedick finds in her biting words a
"l
double-meaning to belie her looks.
After this Benedick only moves to
aggravate the old problem, to the. renewal
of empty promises. He puts
on the paraphernalia of love in earnest:
poetry and wild costume.
the church
Until
he does everything to increase the distance between
scene~
himself and Beatrice.
Dogbe.rry 1 ~ santences, the third "Nothing," present us with what seems to
be an inversion of the
to
c~nvey
them.
p~oblem
of · the two lovers;
thou~h
his words manage
no meaning whatsoever, we are aware that something is behind
Dogbe~ry stu~bles
upon the truth behind the
appea~an6e
disloyalty, yet he is unable to convey it in words to
should know about it.
of Hero's
th~ peopl~
who
For some reason we, in the audience, ·can sense the
substance lurking somewhere in the nothing of his wo·r ds.
discourse achieves a monumental insignificance.
Still, his
This ie th.e · oppos · te of
the predicament Claudio and Benedick are in. 'Their predicament is that
they la-ck substance in the·ir conceptions, yet manage to_ pr. duce sube
stantial consequences from them. They are. eloquent on the subject of
nothing, Dogberry ineloquent on · the subject of. so.m ething. The truth
vanishes once it
he msets.
g~ts
int6 Dogberry's hands, as do most of the criminals
He manages. to
mak~
complete contradicitions out of tether
by onl~ shifting the, word order or applying ihe wrong
key word. He thus · becomes unconventional to. an extreme
ordina~y s~ntences,
prefix to
~agree, ~o
world.
a
mtich so that he seems at times to
.:
head • . There is no
~.
· Coh~ention
pos~ibility
of
simply
M~ve
dropped down
cannot · ~enatrate .
dacei~ing · him,
fro~
another
Dogbetry's
for there is some sense
�- 7 in which hta does not listen a,nd doe.a no.t 19.Q.!i.
Benedick and ..·c1audio
cie'monstrate that a willingness to listen and look is essential to being
deceived.
Only he can deceive himself, as he does• . far instance, in
thinking himself to be rif such vast importance.
Thia is the problem of
Benedick- and Claudio turned completely inside~ou·t~. Their obvious:· problem,
in any case, . is that others are ·trying to d~~eive th~~ and ~u~ce~di~g
in doing so.
The stories seemed before to be only loosely interwoven by the plot.
They
. had a certain, superficial . dependence upon one another.; each ga~e . the other
some obvious reason for moving the way it did.
Now· ~ however, · a definite
..st.ructure appears where each of the three is' involved iri 'commenting upon
rach i~ in a different s~tuation re~
the situation of the other two.
The · play has begun a ·complex invest{~ation
garding the power of seeming.
of that power; it has undertaken to· make Much Ado About Nothing.
*
*
*
*
*
*
An essential feature of the first three acts is the consistency with
which the e.r .r or of sight· is associated with Claudio 'and that of hearing
·w ith Benedick.
They are both singleminded in their misunderstandings. and
this indicates a certain incompleteness in their
char~cters.
Cl~udio's
mistake turns out to be the key to Benedick's conversion in the second
half of . the play; it is the occasion for Beatrice's request.
=~
sequences of.
Benedick'~ chall~nge
The con-
is, in turn, to force Claudio to honor
·. a . promis~ even when the · act that it implies is deeply . ~e~ugnant to him.
I:
I
Benedick and Claudio co~ld !:>e described .as ~. being in· the possession of an
exclusive v .trtua
signal. fa.Hing:
A man of dee.d s
~hat is at once ·:their . signal ' excellence and their
Claudio is a man . of deeds and Benedick a man of. words.
wi~,.l.
tend, I .th,l.nk, to give a greater· weight to what: he
actually sees other men doing.
Just as
h~ ~ expects
ta .be judged by his
appearance of valor or ability, he expects this to be
~n
equally valid
standard by which ·to ·judge other .men ...., Claudio . fell in love w'ith Haro
.
at first sight. Actually there is no n~ed bf · courtship for him. Shortly
'
after
see~np
'
her he says: .
"Is she not a modest young lady?"
·ex-,
"In mine eye, she is the sweetest lady
~hat I ever looked on~"- :
(Ibid. 1 B9-90)
i 1s6)
�- 8 -
Moreover, Benedick at the same time formulates precisely his problem:
(when asked whether he has noted the Lady Hero):
"I n.o.ted_ her not, but I .1 ~nl<ert on her."
Claudio links
noting ~ and-lOoking
(Ibid. 165)
-- Benedick leaves them separate.
Judging by Benedick's readiness to ·b elieve what he hears in the garden it
seems he links noting and hR::it'ina, whereas Claudio, I th.ink, wou.ld leave _
them separate, to judge by his response to Don John's accusation.
Claudio also concludes that Don Pedro is wooing Hero for himself at the
masked ball, totally on the basis of appearance,
Seeming achieves such
power over him by the time he reaches the church that even Hero's
blush is for him a further accusation.
would serve to undeceive him.
Nothing he could
.§!!!.
j r~or.e_n_~ _
at that moment
It is, on the other hand, purely the effect
of words which lays Benedick so low between the garden and the church.
Benedick, as a braggart and a breaker of promises, need not be a cynic.
He is
ready to impute the best intentions to men:
"This can be no trick, the conference was sadly borne.u
(II, iii 228-29)
Braggarts,
contrar~
to cynics, are known to be very easily
live in a kind of fantasy world where there are no deeds.
duped~
. They
They have a
kind of childlike innocence about fantasy which finally leads them to
have a difficult time judging between reality and fantasy.
What is most
important, however, is that they are not capable of consciously deceiving
others; Benedick ' s words give an accurate account of him, just as deeds
do of Claudio.
Benedick does not harbor secret motives in his heart.
cannot but reveal what he thinks inhhis words.
He
This make.s him a poor
actor and incapable of any real suspicion about the motives of those he
overhears.
This is the knowledge Don Pedro has of Benedick which makes
his ruse in the garden so successful.
"(Benedick) hath a heart as sound as a bell, and
his tongue is the clapper, for .what his heart
thinks, his tongue speaks."
(II I, ii.i 12-14)
By trusting that others are the same, Benedick's heart is reached by
their false words.
Benedick has done good service in the wars, according to the messenger,
�- g -
but:
"(Claudio) hath borne himself beyond the orom:i.se of his age,
doing in the figure of a lamb, the feats of a lion." (I, i 13-15)
In war, his actions belied the mildne·s s of his face and his age, revealing
the state of his heart.
seeing in
press in
hi~
face ·
words~
th~
But in
lo~e
he is grateful to Don Pedro for
grief of his heart which he feels he cannot ex-
Claudio is a timid lover because he lacks a command of
words to express the feelings of his heart • . With great relief he accepts
openheartedly Don Pedro's rather cold formulation of the problem:
"How sweetly you do minister to love,
Who know love's .. grief by his complexion."
(Ibid • .314-15)
The link between Claudio and Benedick is the promise.
Each stands on
either side of it, the one in the reaim of words and . the other in the
realm of· deeds.
W~
must say that Benedick's
-~re
word~meaningless,
because
~
they view promises as a boundary beyond which he .does not ve.nture into the
world of deeds.
Promises always cause Benedick to rebound into the world
of words, for him promises do not imply deeds.
Benedick's words are
supremely reflective words, words that endlessly recoil back upon themselves.
Claudio faces the promise from the other side, that of deeds.
No promise is inviolab~e fo~ . Claudio, because ho promise properly preceeds
the deed in importance'·
p'r om'ise, the one
tci the deed.
standable:
~s
~.oth
men are blind to the importance of the
implying the deed, · the other as being inviolably prior
Claudio's friendship with -aehedick
i~
perfectly under-
Benedick satisfies Claudio's assumption ·that words have nothing
to do with deeds.
Claudio is content with 'the judgment that Benedick is
one kin~ 6f man and he is a~other, with nothing whatsoe~er in common;
but we can see how intimately they are related through their mutual
blindne~s
to the value of promises.
* *
*
*
*
Are the problems these one-sided
we laugh t at ·them?
*
na~ures·
*
*
*
*
must face less serious because
It sea.ms to me · that we· may be· laughing at their mis,:
fortune without realizing it.
We can be sure much Ad6
a comedy during the first half
m~inly
Oogberry.
Abo~~ · Nothing
is
because we cannot"help laughing at
Something assures us when we laugh so hard that things cannot
�- 10 -
turn out to be seriously amiss.
It is strange, nevertheless, to realize
that we are in fact laughing at misfortune.
We have been discussing the first half of the play in terms of a threefold development of the theme of
11
Nothing".
power over Dogberry, who can neither speak
Nothingness has a great
I!.Q!_
act; over Claudio, who
can only act; and over Benedick, who can only speak.
The guiles of Don
John and Don Pedro would not, perhaps, have the effects that they do if
the two lovers were whole men, capable of speaking and acting.
As it
is, they are brought to err because of their one-sidedness.
The church scene is the culmination of the errors:
a wreck of fortunes.
It is also the beginning of a transformation in the characters of Claudio
and Benedick.
It is characterized by the astonishing fourth "Nothing" of
the Friar's counterplot. The friar's : counterplot is the beginning of an
answer to the challenge proposed by such misfortune; How will life go on
from this point?
At the end of the scene we find Benedick making a solemn
promise to Beatrice:
(IV, i 335)
"Enough, I am engaged; I will challenge him."
By Beatrice's closeness to Hero and her deep sorrow over Hero's misfortune, Benedick is drawn to the promise that separates him
a
Claudio
and ultimately ta the deed, the challenge and the duel, which plants him
firmly in Claudio's world.
The faith in Beatrice implied by his pro-
fessions of love to Beatrice must now be manifested in an act.
also that he must ask Beatrice what that act i s to be .
He sees
The a nswer is a s
shocking as it possibly could be, but in fact a natural one for a woman
with the strength of Beatrice to make.
This is a rude awakening for the
man of words; Benedick',has become committed to defend the honor of
Leonato's family by killing his best friend.
By seriously vowing to
undertake this deed, deeply repugnant to him, he becomes capable of the
insight which above all else betokens his transformation.
By crossing
the barrier of the promise, Benedick will become worthy of Beatrice.
a
· c~rtain
point the flow of words must simply cease and the deeds they
imply must begin:
"Peace, I will stop your mouth (with a kiss)."
(V, iv 99)
Claudio must struggle also to cross the barrier of the promise into
At
�- 11 -
Benedick's world.
The irony of his declamation against seeming in the
church marks the beginning of a period of turning for him.
of turning enas with his vow to marry Antonio's daughter.
.
.
counterplo~
This period
The friar's
.
now· coma~ into play, for .it provides the necessary basis for
another, wiser beginning ··fo·r those two people who are truly in love.
Hero is exonerated · ba_ck~tage in .front of Leonat_ and'.. Antonio.
o
sult, the counterplot acquires a" .p articular form:
As a re-
Claudio is made to
1 ··
give his promise to ~rry, · unseen, . Antoni.a ' s _
daught.e r.
exori~r~tion
'died,' what · good w6uld the
Had Hero never
hatie done? · Cla~dib would have
been overwhelmed . with s~ama·and this Would have prevented. ~ reunion.
form of the ·counter plot revea'l s a · sophist"icatlon in the
f"ri~r,
The
Leonato
and Antonio which· we : mi_ ht .profitably c~. mpare wi~h ~he ' sophistication of
g
Leon~t~ : and Antonio help Cl~udio to become wor~hy of Hero
Don Pedro.
..,
\
by helping him t,Q accept her back
~ga.in
upon
faith~ .
. 1· .-
Benedick's challenge fo· ·tlaudio. is a beautiful rfrome.n t where· each is brought
·,:
.. '
face to face with his problem simultaneously.
Benedick must look to the
deed and Claudio must ·accept the .challenge and be· true · to ··his word.
both men, the challenge . is a ·mean ground
and the tempering
betwe~n ~n . unt~mpered
for
character
in~ights~
· ·.1
'
A skillful weaving of their destinies served to relieve the singlemindadness
of Claudio an-d BaM·~·di~k . in the second half of the play. · ~a ginning as
opposites, the course of their fortunes has bound
tham . t~g$ther
in a
mutual discovery of the need for the other's virt~~. ·
Dogberry, however 1 blunders
on~
The .way
in which he persistently obscures
the truth and turns it into nonsense ir the .essential
errors made by the
~n
compounding the
His blundering is as important in making the
others~
church scene inevitable as is Claudio~s -wiilingness to believe What he hears.
But, in the second half; 'Dogberry should ,come into a new relation with the
fictions.
While hiding t~e truth for the rlght ampunt of time was essential
to the success of D~~ Johri's plot, r~vealing it at.th~ . right time is
essential to the Friar;s.
Sexton does.
Dogberry
Dogberry, however, does not reveal it, the
con~inues .
he will ever cease .doing so.
as· be.fore, and there is· .no reason to believe
His conf.us.i on is within and a change in cir-
cumstances could never reinedy his
problem~
There is no hope of a cure
for complete self-deception, and though he may not seem to resemble Don
Pedro in any other respect, he may well resemble in this.
�Veronica Soul
When once in ·April Leena passeq . from .four
fiye, a crayon portrait filled her page.
l darkened window and' ·a sad-faced girl•
A row of broken letters joined to form
Her sister's name. A border grew from groups
Of countless heads. Embodied in her strong
Thick strokes were things that Leepa saw and knew
About her older sister. Hard to say.
Her name: was Lisa Grey. Her· hair grew short
And brown• Her eyes soft. blue. And blue the mark.
Up.o n her brow where once a marble step
Was· quick to bruise. An accidtmt.· · Then came
The sullen visits to the questioning ·men •.
She answered nothing. Frequent trips to bring
An end to her· ·s trange ·n ervousne·ss and tears.
A crayon picture of a person's fears.
Afraid· or crowds and darkness. "still outside
This vrl.ndow", Lisa ·thought almost aloud·, ·
"The streets ·are full of crowds and darkness. Dark
As twenty Aprils past when i w:as_ born. . _
If Lisa ceased to lie in sleep she to'o ·- .
Could see. · The times together are · so few.
Things done with her no more in memory.
Like watching people in the rain. We've failed ·
To find a joy in sharin~ - s~ngle joys."
~o
!
These . three square .city blocks of mansions, worn
From warmth, are cold remains of elegant
Society. The families :were .gone . .... ., .,
Age marked the decorative homes .adorned
With railing Weighed by heavy iron trim
And mounted by the weary wind-blown vanes
"That" spun and sharply pointed east· to s.ea • .
.Ttie- r-µsting . oo.ck , and arrow lay atop . . . .
The attic roof. ·Apartment D, fourth floor.
Lisa's ·hidden place, on· e hiding place.
c
They, had :not yielded to the endless taunts
And invitations of the wind. · At · le.a st ·
Sinct:l·: century had turned. On breaking free
~rom· one last jerking spin .the cock has been
Le~ breathless. Then the arrowhead refused
To budge. · The. wind like people traveleq on
To leave . a house and :r.igid v~e b~hind.
Mere lay the oldest · district--Davenport•s . .
.~ast end. Alone it ~ad es~aped the bold
And wrecking blows of shrieking new mac·hines
Which, crudely pampered by the coarse-voiced crews,
�_13_
Crawled powdered with ·raw plaster dust. "Prese'r ve
The Davenport our fathers' fathers '·built.
Restore." That outcry here was nevt;r ·heard
Nor ever; cried. A coastal.· area
In growth transplants its history from land ·
To printed page. Victorian · facade
Was gingerbread that tempts the eyes to sate
Themselves • . Some dared to see. those outcast things
As living structures with a need for men.
For love. They called themselves minority.
The city natives, brick and glass enclosed,
Had · weeded out all but· !the three tall blocks .
Of tall wild grass that sheltered weather birds
Unmoved. And Lisa. Loved. Unmoved. Unheard.
Soft gaze of ieena's slowly moved along
The iron lace ~ence and she began to count
The rails. "•••'teen. eight~en, nineteen. twenty. Years.
For twenty years. As of today we have .
Been sisters twenty ye~s. So long a time
Was needed to admit that she fought not
To love he~ sister. Hatred? Envy? Both
Or one the cause? Confusion caused that TNar.
'With every April I would imitate ·
Her image less, as it grew-old and lost.
Then I had found my private way of life,
No longer living in her ·ways. Why should
The . act of growing up, my·:.. grow:i.ng up,
i!eve caused her such distress? Not mine, but slow
Self-growth made her dissatisfied. A strong
Impatience. Wanting to accomplish all
Beyond the given means. A strength that wounds.
9 If you could learn to live with time .
present moment, Lisa ••• • This I once
Hoped helplessly. Victoria is dead
I know. Her era is not mine. But I
Know too that Lisa lives a world away. ·
Victori~ .air hangs over her.. Not just
Pretending but belief. A world away.
In
To watch the wetness Leena pressed her face
Against th~ window pane to darkening rain.
Gray eyes met pigeon feathers gray amidst
The falling rain. "There stands a ·bird not gray,
But black. A bird of iron upon this roof. ·
From violent winds no ruffled wings, no eyes
That glare. Sealed off and smothered under paint
Like tar. Unmovi.ng. blind. And Lisa needs
That freedom too--to move~ to see• Alone.
Warm breath sets steam upon cool rain-glazed glass.
�-14-
When moisture fades, a wanton feather's found
At rest. Self-plastered to the pane. Outspread
The weathered strands of purple cutting wide
The gray. For Lisa this would be a gift
So prized. A pigeon feather shed today
On Davenport. A simple gift. Rare match
for Lisa's stuffed and balding bird. With grace
He moults beneath a handblown dome. The last
Of acquisitions from the cellar depths
Unearthed by one frail aunt. Decor designed
To clutter rooms, like Lisa's. Haven for
Lost trifles. Things rejected since nineteen0-four by all but aged maide~ folk,
Collectors of chipped porceline, tin cups,
Thin saucers without mates. Soma long-stemmed weeds,
Dried autumn flowers, made their residence
In garish · vases sad with tinted bows
And china roses spotted with decay.
The peeling walls of bone and navy stripes
Bore mezzotints thick-framed and photographs
most primitive of children, servants, or
Whole families of stern-faced men. Stark-eyed,
Completely foreign to the girl who hung
Them last. 'Twas Lisa. All had lived and died
Before her mother had been born. Green fringed,
The weight curtains trapped protectively
The dusty gloom from city cleansing air
And restless April rain that whips the town.
"The past that moves for Lisa doesn't move . ·
For me, nor do I want it to. It's true
Past children were rhyme chanters in the raih.
New children match the newness of their rhymes
And newness of the rain. Ula· still speak words
In English, 'though what's "proper" vacillates .
When Lisa cares enough for these few facts
That people speak, that under pelting drops
The child's ri~e is performed. When she cares more
for timeless acts, than for an age of kings
Gone pale? Vic.toria, dead ·q ueen, must die.
"Once long ago the town faced death to give
The city life. This part is Davenport
The town and not the city--now. This thought
Is Lisa's too. But dates and years do not
Concern me here as I try to connect
The happenings of two girls' lives to find
Out why two sisters were afraid to know
The other, by the other to be known.
With knowledge rides the strength to heal or hurt.
�Yet knowing is not solely that strength's source.
No fear today, nor is . my coming ·brave.
Afraid and h:urt, . I' ·chose to run when hands
Began to tear a photograph, a pose
Of Leena, child of six. 'When she began
To cry, confused because an endless chain
Of children's images remains untorn
And whole. And I still lived. ~ pain unknown.
· To heal a wound from love, once love is lost-A task as f\111 of doubts -as seeking· faith~
Qnce gone • . Perhaps not lost, but almost dark."
As
Leen~
looked across the room, she moved
An outstretched -hand to finger petals, one
By one. A single opened flower spread ·
Its odor. of rust-colored life. · Timepiece,
Wax-violet enframed and mute in dust.
wax coated silenc- . First insert the key,
e
Then deftly turn. Note well the day is not
Victorian. . Mark not those . hours. Know there
. l: t~me fpr this the present day alone. A dim
Reflection from worn looking glass. · A smile
Surrounded by long straw-blond hair unbound.
Worn brown her leathern shoe with loosened strap.
The faded image speaks of freedom, bared
Simplicity.- Both Li-sa, cock, . released
In wind. Ma.de .free to see, to spin. Alone.
"A life, a smile made double in a glass.
Reflection ·o f the past-•a toyqpx trick
Forgotten since long blindness met.its end.
·Itr absence -of four seasons k?pt the pace
Of Lisa's passage, flight .through orie lost age.
A_ s_ster, . distant all the ,days of spring
i
Through growing years, grew unafraid of dark.
My birthday marks a . birth· encomp~ssed by
M
ore than a day. And Lisa is her n~'Tle. "
..
~.;
' ·.
�-~!HOMAS MANN THE MUSICIAN:
Lecture by Victor Zu.ckercandl
A REVIEW
· R. A. Licht •65
Music. in ·the works of Thomas Mann is important• How important?
There are two prime considerations in the criticism of Mr.
Zuckercandl' s · exciting and intriguing lecture:
his philosophy,
9.nd his understanding of· Thomas Ma.nn's:w0rk in the light of that
philosophy., The end of this lectUPe ·:· a.s 3 not simply an analysis,
w
nor even really an interpretation or Marin tha musician.
the intent or the lectu:re was an attempt to
Rather,
the sig...
nific.a nce, the apparently universal significance, of. Mann the Poet.
~ake c~ear
'
'
Which is not to say that analysis .and interpretation did not have
a central place in the lecture.
Although music is manifestly important in ·many of Mann's works,
especially in the larger novels (Buddenbrookfi, ·Magic Mountain,
k•
Faustus) 1 t would not be ·a: mistake to place him in the category of
"culture
~ovel:ists;.
'
Ca
categ~ry
..
which .I irivent ?for the present
purpose), thereby putting music in a secondary, or supporting role
in his work.
For whatever importance we would like to attach to
Mann's statement that he is fundamentally a musician, or to the
quite plausible claim that music in his work is represented as
the·~
highest art, it nevertheless remains true that he was a prose
novelist, and that as a "culture novelist" music is important as
!h2.
German art.
"'The triad world of the Ring•, my diary confesses,
'is at bottom 1T\Y musical homeland.• However, I added:
'And yet at the piano I never tire of the Tristan chord'"
(Story of a Novel, p.95, Knopf, 1965)
�_,.,_
I say 'the German art' because of its central place in his
·l.ife and in .German 'culture• in general.
But equally important, music
1:s 'the German art' ·b ecause of .Mann's feeling that German poetry•
(and possibly• language) are inferior:
"It l\-S.s J· cob Burkhardt who said of Voltaire: 'In him
a
nationalism became poetic, even mythie*' I ~should like to
· see 'the German writer who could produce such a sentence.
Switzerland is the country in which the most . gloriously
· un-German ·things are said in German. That is why I love it .. "
(Ibid. P• 85)
...
Even the great Goethe, Mann's mentor in literature is not immune.
Mann points out in the above passage (p. 84) that st. Bouve did not
rank him among the "very greatest", and that Goethe would probably
' '·
.
have concurred, since he, " ••• regar~ed Shakespeare as ••• far above
,· ·;
himself."
And this "inferiority" of German poetry we. might interpret
as a theme continuously played in Mann's work under the guise of
the German artist as ·'alien• to: German life.
.
We see this in the
c.ontrast between ·the warm, fecund, vegetating
Me~iterannean
-~
bourg~oi.s,
·sterile
and the
...¢..o l_ and constricted north which is the 'geod
. graphy' of the artist•·s soul.
There is something · inadequate about
It is
·· · literature to express the depths· ·o r the German artist's soul.
.
.
.
music, ·Hthe voice of ultimate darkness" as Mr. Zuekercandl so aptly
puts it, which. is.· the art at which Germaiis excel.
Music, in this
·sense, becomes pritnary only as part of a culture •syndrome'.
Culture ~
and tradition;. :.psycholo~i,
~hilosopey
and politics; change
as illness, decay, spirituaJ. growth; national differences: " art and
life .in the particular German sense; these are the •matter• of Mann's
work.
His artist is not merely inspired by the muee, he is striken
and torn inside, ·he is the finest flowering of decay (Hanno Buddenbrooks,· Adrian Leverkuhn, and , perhaps Gustav Aschenbach).
In him
. south and.. north, art and life continually war. 'If the · artist is
�.l&~ .
perhaps Mann's .most fertile theme, it is as German artist in a
qerm~n culture that t.he tales are told~ · 'The 'antagonism of
life, the lurkin~ presence . of death, is "·s et ·in
art and
a particular
and
necessary locale.
~ole
If Mann has .a
ciate, :
.view of :man i'.t is very difficult to enun-
anq .neces.~~ly :· so,
·· culture, which
me~s . bound
'
.
since for him man ls bound up inside his
up inside his own consciousness, and
consciousness is very much a child -:· of culture in t:Us view:.
.
.
.
~
To seek
. the : timeless in consciousness, that is, a knowledge ap?19t from culture,
is to seek death, for the origin and meaning of knowledge, if we are
··· to · believe Mann• s exegesis of the 'myth' of the Fall, is that first
.
.
.
ant.a gonism, or separation of consciousness from phenomena which resulted
from
the awful knowledge.
"But the expression 'good and evil' (in reference to the
Tree of ·Knowledge n. b.) is a recognj.zed and admitted gloss
upon the text, and what we are really dealing with is
knowledge which has·as its consequence not the ability to
distinguish between good and evil, but rather .death itself••• "
(Joseph & His Brothers, P. 27, Knopf, 1960)
In this sense,_·then, mans ca· t.orp• s illness is the rebirth and
·
s
evolution of his- c_onsciousness. ·His contact with (and discovery in
himself of) illness,- decay and death frees him ·rrom his 'culture' to
the extent. that . he. was·, literally, 'above it'. and as a consequence
all his experiences were deepened and thus revealed a new reality
(or . fullness) quite apart from the conventions 'down below•·.
These
experie;nces seem .• archetypal•· in Magic Mountain' {or perhaps chthonic),
but are, with the usual profound irony
o·r
this author, deeply
conventionql.
It is
n~t.
surprising,. then, ... that the . artist is ·a central figure
i? Mann's_ work • . The
l
~tist · has (and represents .in the works) this
h~ightened. consciousness through his .contact with ·illness· --
�physical as well as cultural.
a great artist:
A .gre~t -work of art should be about
Faust should ·have been a musician.
The involuted and ironic character of Mann's work disturbs
many
of
his admirers, for there is something, perhaps, aesthetically unpleasing
Srbout it, · something, perhaps, fraudulent.
Part · or· Mr. Zuckercandl's implicit thesis is that Mann the Poet
transcends Mann the "cullure novelist".
so_mu9h
in ··th~
This transcendance lies not
universality._of. his >themes (which Mr. Zuckerc:andl does
not, apparently, wholly agre~ with) but ~ather in the centralness of
his vision (a convient ter.n for poetic .understanding and which Mr.
Zuckercandl does not use) as a. Poet. Mann's greatness lies in his
use of music, · and his understanding of its intrinsic relation to, and
its oneness ·-with poetry. Mann, in effect, rediscovered the unity of
tonos and logos.
wor~,
To see this we must put aside the content of Mann's
p'\.l.t a.side Mann the culture novelist, and concentrate on Mann
the musician.
This, is in many ways, · a difficu;J.t task.
Mr. Zuckercandl .suggested that a history might be.written of tonos
and logos: .
"It wuld be about as long as the history of man himself
and could .probably t _ach us .a lot about man, the history of
e
his mind., his : consciousness."
Let us consider the outlines of .this history as a ki_d of propaen
deutic to the meaning of the
lecture~
The first epoch of this history· is the most revealing since it is
a "prehistory" and thus
embodie~
.the ·author's most basic opinions.
This is _ "primitive state in which language is something between speech
a
and song, where separating the two is impossible even in thought." The
demonstration 0£ the here postulated unity is another matter.
shall discuss the possibility later.
We
�The next epoch is the origins of civilization as commonly understood:
The Greeks and the Hebrews. In the Greeks we have a separation of
tonos and logos where speech is used apart from music but where the
contrary is not true.
The unity of speech and music remained in, or
rather as, poetry.
" ••• it seems there was at this epoch no poetry without music
as if words needed tones to achieve 'the aim of poetry."
The next phase, of Hmomentuous development• is characterized as
poetic language learning to do without melody. ' But even in this
further separation music remained as
liturgy of the Christian chm'ch."
appeared:
melody without words.
"an
indispens~ble element in the
Here the element of the later crisis
This crisis, locally familiar,
occurred in the 17th Century. · lfPure instrumental'O IDUSiC was the
darkness tha rationalists seem to have inspired.
· connection is
real~
is questionable.
(Whether this
It is crucial that arguments can
and have been made about -European music following its own inexorable
evolution to the present
di~mal
state of affairs.
If music was
interpreted as the language of the passions, rather than as a rational
being, and music has lived on this belief, then it must· be asked
1
whether music is not ::peculiarly susceptible to thi's :·Ut;>.derstanding).
From this crisis, according to the history, music emerged as (i.e.
accepte·d as) the la.riguage· of (dark and irrational) passions.
"The language of tones is now· defined as the language of
passion, in contrast to the language of words as that of
reason."
From this history.three important ideas emerge:
The fundamental
and original unity : of speech and music which understands music to be
a language, but apparently only fully intelligible as such, when
unified with the language of words · Qlthough intelligible also in
�-~. its own right).
Secondly, the latter-day ignorance of this (not
wholly without enlightenment, ho'Viever).
Thirdly, a radical view of
art (i. e. as concerns linguistic art) of which, we shall see, Mann
is made to speak.
Implicit in this argument is the equal (and
unified) status of word and tone as regards reason, and, in the
extension of the argument, the idea that music is fundamentally
rational (and that means as first considered in its .right relat.ion to
logos.)
Certainly this is a rather sparse history, but its impli-
cations are strikfung and somewhat puzzling.
But we will go fUrther
into this in the sequel.
The last stage in this history is, of
Mann.
As historical
course~
the age of Thomas
figure Mann represents the return to the true
relation of tonos and logos, and this in spite of his ironic acceptance of music as the voice of darkness.
As poet Mann is significant
because he thought of himself as a musician and, according to Mr.
Zuckercandl, attempted to return via logos to the original unity:
".•.his mastery of the word combined with an extraordinary
sympathy with music made him the first one to achieve something like a true integration of music and language. He
succeeded in making music itself -- not just the feelings and
ideas it arouses, nor its pS"JChological consequences -- the
musical phenomenon itself in its full and concrete r eality
an essential part of works or the li tarary art. n
In considering this history as Mr. Zuckercandl presents it, we
must try to tmderstand its most striking feature, that is,. the philosophy
which underlies it.
If Thomas Mann "succeeded in making music itself''
in his literary works, what is this "music itself ••• in its full and
concrete reali ty 90 that
~t
may be revealed in, or through, the word?
The lecture· attempted to answer this question simultaneously with the
demonstration of the thesis in Mann's work.
Music in Mann is divided by the lecturer into the following scheme:
�-J, .
~.~ ·~.
,·
a) "Music as construction, as a formc;U principle to .be followed."
b) . "Music ' as a .Subject' a:s a eymbol to be interpreted."
c) "Music as a reality to be created or recreated."
The first is represented in
· ~s
w()rk .. (and Mr. Zuckercandl uses
Tonio Kroger as examp~eJ p:r;-ima;rily in the form of .the (Wagnerian)
'.
leit-motif,
Wagner's.
the
o~
which hi.s use :is almost as complete and complex as was
This repetitive thematic structure works at all levels of
narrativ~ bo~h
identifying character, and most importantly, acting
to unify the work through the very repetition of the motif through
changed circumstances:
"Repetition here expresses change under the guise of sameness,
the working of ·the time fl.ow -- which is the very substance
of the tonal art."
Through the use of th,e leit-motif, and its consequent 'musiclike'
effects, the story may be
it seems,
o~y
on
~aid
t~e . ~evel
to . 'work' like a piece of music, but,
.of an?-logy.
is a "formal principal t9 be . followed~'.
It is in this sense that music
In Tonio Creger :
'° ••.•the words which close the first chapter are exactly repeated at the end of .the story to · form its last sentence•••
the en9 ret'\.irning to the beginning on a higher level of
significanqe: · this ·is the -. exact1definition of the spiral
movement, the foremost.principle of all Western music ••• "
.The case for music as a formal principle of story structure is
well made in the lecture., b.u t since . this use of music is only analogous
we must look further for the "music .itself".
'
-
The second level, of.music ."as.a- symbol' to be interpreted", is
well known in Mann's .yv:ork and
~s contsi~tently
anything else, Music is a symbol .of Death.
this (with the
. .
moqific~tion
.
.
in
rr.
Mr~
throughout.
More than
Zuckercandl accepts
Faustus that it '- symbolizes the
theological cause of _d~ath) one. ~spects, as ·the ap~theosi:s of a
conv~ntional v~ew
of_ ~~sic .held. since . the 17th century·• ·As I noted in
�the introduction,. this aspect of Mann's work, although discussed
at some length in the lecture, does not seem to Mr. Zuckercandl to
be fundamental unless understood within the context of the wider
significance of the use of music.
{It should also be noted that most
'literary' criticism of Mann's use of music would not go further than
this level.)
7fThis whole philosophy of music, it is not Thomru; Mann° s
intention, he merely continues and climaxes a long line of
intellectuar.tradition ••• it is certainly not on the basis of
his philosophy of music that Mann's work will be ultimately
judged. These novels are works of the poetic art."
N
ow, this is very curious. On the one hand, in his analysis of the
role of music as a symbol of death, Mr. Zuckercandl understands it
as a central theme,
in Faustus, and around which, he
c~nating
would probably agree, revolves Mann's philosophic and political
thought.
But on the other hand, the existence of yet another level,
'deeper' than the others, has implicit within it the claim that the
end of Faustus as a · work of art is about the·majsing of the work of
art, i.e. the end is in the act.
a work "of the poetic
Since the work is to be judged as
art", what music represents, that is Mann's
central opinions, is not the basis of our judgement.
In a sense,
although his vision of Art is profound, it would appear that he is
not entirely responsible for his opinions.
experience' is involved here.
A theory of 'poetic
This theory is very difficult to
enunciate, and, I believe, is the most puzzling and least effective
part of ·the lecture.
We shall return to it, but shall here confine
our remarks to more superficial _
difficulties before examining the
third level of Mann's use of music.
There are two paradoxes evident in the view that considers· . a
novelist (or poet) apart from his opinions.
The most immediate is
�the problem of how we understand the words and events and whether
the poet's manipulation of our imagination preceeds_ (and precludes)
understanding in favor of
'expe~encing'.
ThHf is the problem of
rhetoric in its most insidious _
form -- the freedom of. the readers' .·
critical ability is suspended.
In terms of rheto+iq, then, the poet
may be considered apart from his opinion ~ being judged on the
basis of the success. of _his technique.
.All poets have opinions, 'hut ··
great artists are so . because of their use and understanding of the art .
This is, in part r·think, _what ~. Zuckercandl is saying, but·
itself.
in addit;on he wishes to sa.y_ . something about poetry itself that is
more universal than mere' ·t echnical considerations. _
But this leads
to the sec?nd paradox ·which is :a part of the first.
Mr. Zuckercandl seems to be · an. arch-Romantic • . The
And this is that
~ry
is no longer
Love and/or teath but Logos, no )..onger Feeling but Poetic Experience.
.
.
· Can, it be, that rejecting the connection of music and passion, he
•
:'
secretly
ag~ees
••
I
with Mann about .the Artist· and Art?
Is it possible
. that the view that poetry· itself, which transcends the poet and ·h is
work, is a view that considers rhetorical form· more important than
· meaningfyl content?
This. view seems to derive from the concern for
style and rhetoric which is part and parcel o( any 'doctrine' · of
the· passions.
"There is .only one thir-ig that will bring· a poetic work to
lasting life; the poe_ ' s power to c:reate reality ·rrom
t
words. ~ • a world which has the. .full stature . ·Of. reality without
,. existing· physi-caUy.~.A poetic work moves the reader to the
·extent that .he can ekperience whatever it contains as real."
With respect to Dr. Faustus: -·
·"music must become· an· almost .tangible presence., a dominating
.force, an overwhelming reality. The author's ·task therefore,
was pothing less than ·.to . create in words that which surpasses
all words: · ·music."
�course, in
\;1.l.j:=,&.&..l...&...l.,...,Cl.,UV
s
use
on
nor
, in
I
the
the
is
it may be
in or
the work of
a
must
a
or
between
my
naive
or
�seems
means
sense
a
oneness
sense
is
one
is
occurence
as
I
s
I
in
�_27_
sense of the most intelligible in. itself) human experience.. We seem
to have lost, through the vicissitudes of history, our naive sense
· of the world which embodied this experience.
Mann,then, returns to a unified view of the whole that is uniquely
the province of a (great) art.
How did he accomplish this?
Unfor-
tunately, the account given in the lecture is not completely satisPerhaps the vision emb,odied in Dr. Faustus .might exclude
factory.
the pessibility of description in tenns of mere significance and
concept.
For, is it not true that, according to the thesis, the poetic
experience
er
the work is beyond the discursive description of it:
it is the thing itself, mere analysis must fall short.
And this
might be so not only for Thomas Mann, but for the poetic experience
in general.
But to return to Mann's expression of the above thesis in
Faustus:
Mann's problem was to
transfer~
tone into· word.
1?£..
This is
somewhat the reverse both of Kerenyi's position (which· was to understand word as tone) and the lecturer's
9
history'.
The missing premise,
of course, has something to do with our changed experience of these
things.
But we should not forget the end of history where Mann stood
and the consequent adversity to be overcome.
Our end of history
where tonos and logos· are separated in art, and thus .. in experience,
is an epoch which lacks a synthesis -- Mann, through logos,had to
effect this synthesis.
This he accomplished through his threefold
("dial·e ctical") use of music.
But as to how the synthesis occurs:
"the creation of music as a poetic gestalt ... with the transformation
of tone gestalt into word
gestalt'~ ;it
is merely stated that this
happens, and we are offered analogies designed to convince us of the
· plausi b.i li ty of the thesis :
�as
are
a
use
use as a
�as
more or
of the
to
waimE~r"
s
.:.;::..~;:;:;.;:;:::~,
as, a voice
some
our concern
con-
as
common
�s
a
use
on
�I:
mere
it was
as
are
of the two
for a
desire for her creates the
whose outcome
of
s
arises because
a..1..c:..11.Lv·1.i.
have taken an
swore to
in
further one
breaks
is further
Theseus, has
is
prays to the god of war for
who
marries her, prays to the
from
the
for the
to..
However an
s
�be
•
·~
~ '
.
But
'
are
to be
are
been
.
the
,,
both
to see
more •
•
to be
in
of
pursue
to
�to
goes
as a
see
for two years.
works in the
him to the
He
grows
of
own
by
courage are
desire,
one s act
is the same.
same
from
are each
two
Theseus
cause.
him
that each
knows and
meant to
• .Had
is
the
provided a
For
is
have
to
for
But the concern is
not
for a
enter the
as
men
.
a
a
casts
each
to
to Mars for
essence, they each
namely,
is
because
, in
for the same
enunciation of the terms of
�to
announces
no one there
s
s
as
to
as
�and won the duel, is able on his deathaed to say ·these last words
.
.
.
.
.
to Emily: ~'].(know of none/So worihy to be loved as .. Palamon/ •.• • And
if you . ever ~hould be??me a wife,fForget not P~lamon, the noble man.''
.
.
The plot·, moving in the serious realms or lwe, war, and brotherhood, is now resolved.
Not with a sense of "Aha!
Virtue is rewarded,
evil punished," but with a tearful funeral for well-loved Arci te.
Part II: Narrati v~ Style in
The Knight's Tale
The opening narrative or~ Knight's~ describes a situation
which is reminiscent of
Sqphocles~
tragedy, Antigone.
As ·T heseus
is victoriously returning from a qattle, his procession is stopped
by wailing, supplian women.
They mourn for their dead husbands, and
cry out against Creon, King of Thebes, because he has refused their
kight to religious burial.
upon the ground.
Their husbarlds' bodie$ lie heaped
Tnts situation, which allowed SBphocles to·illus-
trate man's tragic condition, is re$_ lved by CHaucer with
o
~i.illmost
contrived swiftness, as though succinctly to set. an aura about his
tale.
For in one fell swoop Theseus declares vengeance on Creon,
holds up the processio. , goes to ·Thebes, slays Creon "manfully",
n
and. proceeds to "deal with' all the - land as he thought best."
Immediately. at the
. onset~ .
Chaucer' shows man to be capable Of "Sig-
. nifi'cant action without ·deliberation over the forces of the universe.
This short tale within·· a' tale: is ··an expressi.~n .of Chau.'cer-, s co~
ception of man's purpose . oh e·a rth.
Nankind is here to live, not
to be -'. puhished, not· tested~ but to" act and react.
�By examining the emphasis that Cchaucer puts on the successions and
emotions of life, one realizes he does not understand their tribulations
and ambiguities to be insufferab~e nor even indicative of man's cleavage
from the divine.
..
This lack of despair and didacticism suggests that
Chaucer sees around him a perplexing· yet acceptable humanity.
One indication is his method
~o"f 'trami ti'on.
Chaucer hops from g grave
event to a festive one at a pace so quick and nonchalant that he prevents his readers and characters from dwelling on man's troubles.
amples exist throughout the entire
t~le.
He even de-emphasizes
Ex-
k~y
parts of the plot such as the two duels and Arcite's death.
The first duel teases the reader by hinting that the rivalry will be
resolved by either Arcite's or Palamon's death.
switches the concern.
However, Chaucer blithely
"Up to their ankles fought they in their blood/
And leaving them thus fighting fast and fell/Forthwith of Theseus I now
tell. ••• "
The reader is given neither time nor sufficientc\iescription
to contemplate the monstrosities of war.
Furthermore such an unbelievable
image of meri in ankledeep blood is so far from experience that its
impact is slight.
At
an even more climactic point, Chaucer changes the reader's focus.
Arcite and Palamon's official duel is given a detailed build-up by full
description of the construction of the amphitheatre and individual
prayers.
In fact the tale so far leads up to the outcome of this extra-
vagant duel.
Chaucer dramatically describes the fight to create tension
and then suddenly inserts, HAt times lli.ke Theseus orders them to rest,/
to eat a bite and drink what each_ likes best", after whihh the fight con..,
tinuss.
�-3'A final example.4: oomes from a particularly emotional. part of the
tale, following directly upon the description of Arcite on his
deathbed, who was "yet alive and some words said,/Crying and
calling
a~er
Emilyi"
Chauder writes, "Duke Theseus, with all his
company,/Is come again to Athens, his cit,~/With joyous heart. and
great festivity."
This abrupt fransition serves to de-emphasize the horror being described.
Th~s
is not say Chaucer disregarded war and death.
By
depicting situations alongside one another, he communicates his view
of them.
As he explains about the Athenians' festivity after
Arcite' s fall, they were sad ·.for Arcite, but "He would not cast a
blight upon them all."
His method of transition serves to relate
his belief in the inevitable procession of life.
When it is sad,
it is sad, but not forever, and not for everyone.
An exam:ination of the components of this ;inevitable succession of
events and emotions provides additional clues to Chaucer's attitude.
The tale is oonstrup.ted on "fi!le conflicts nesulting from l ove , war ,
competition,
promise-making~
As has been shovm, Chaucer does not in-
tend ·t o dictate a specific conduct proper to each.
to evaluate the worth of life's components.
destructive?
1~or
does he want
Is war evil?
Is rivalry
In avoida· ce of such an evaluation of the inevitable
n
components, Chaucer l!Dnimizes their quantity.
�a
one
existence
woman
an
nor
�_,,_
bloodshe~;
and neitherdoes he ascribe ignobility to man's incon-
sistency. · Should we therefore conclude that these conditions all
result from the love that man feels for a woman?
Does this seem to
be the key to their acceptance and justification?
portrayed as a particular virtue worthy of req-ard.
No.
Love is ntt
It is described
as a universal force driving men towards acquisition of its object.
From what has already been put forth, love is necessarily regarded
as a force.
We have seen its power·::-. through its effects on Arci te
and Palamon..
They denounce .their oath, defy Theseus, risk their
lives, and when totally frustrated, wish for death.
Ibes their
power result ft.om their own specific characteristics?
Is it a
spiritual virtue had only by certain men? ·. What caused Arci te' s
and Palamon' s powerful love?
All we are told is that they see &lily
in a garden, yards below their prison tower.
results from mere sight or a beautiful maiden.
know~
nothing of their love.
Their vigorous pursuit
All the while Emily
This is hardly a relationship evolving
from each one's spiritual character.
This hollowness definitely
detracts from the individuality or their love.
Love is f'urther separated from the particularity of the lover .JWben
etauder describes the altar of Venus:
"Lo all these folks were
causht in her snare/ ••• Here let suffice examples one or two/Though
I might give a thousand more· to you. "
Chaucer fur ther attribut es
love to the thousands when he describes the duel:
"You know right
well that every knight/Who loves the ladies fair and keeps his mightf
WoUld wish of all things to be present there/To fight for some
fair lady." This i 's
no~.great
deed which
i
« Arc:ite and Palamon are
�. -4. t
invo~ ved
in, most people would want. to join in. . Nor
i~c
~s.
this duel a
leveling event reconciling Arcite &ld Palamon.
It
o~dina:ry
Love• s.~ incentive is not
event, but. one whic;h -is sought after.
.
not only an·
an indiv:t!iual virtue; .it ts a universal · force.
ey._·means of irong, Chaucer indicates more· of his attitude towards love.
He
points out that'° although love seeks beauty, the force itself does not
mainifest ifself beautii'ully.
self is frustrated.
. the duel • .~rcite
chastity and
se~
We
beg~
It not only leads to deatruction but itsuch irony in the prayer .sequenoe before
_ ars for &f4ly, then
M
arterwards.P~amon
begs
Diana~for
her
also begs Venus for Emily. · This is
abhorr~nce
almost funny. · . Emily.' s
.~ly
of men nearly makes · Arci te' s and
Palm.non's. extravaga.n,t.pursuit a farce •
.-
This ironic situation is significant as 1t shows the manifestations or
· love, . the almighty motivatory, to be imperfect or,· at . least, unbalanced.
That love has its complications and inconsistencies tvcfunther illustrated by Chaucer's inter~ersed : phrases su~h as "0 Cupido (love) !
.
.
-
"
'
That know' st not charity (love) •"
.
So far ·love is po~tr ayed as a frus-
.
trating, inconsistent yet all-powertul force.
~·· "
These effects on man
are ·cl.early defined on the paintings .of the altar of Venus.. There we
see
.:th~t altho~gh
she
h~r~elf
is beautiful, ·man, in her ·-grasp, is not.
· He is un'!\tlfilled and tormented.
"On the altar·one might see,./Wro':J,ght
. on the . wall and piteous · to behold, /The ·broken slumbers ·'a:nd sighing
cold, . T;he sacr~d tears and lamenting . dire/The fierce throbbing of
str~~g. desire/That a1J love's ~ervant~ in this li~e ~ndure9 •• n
This
·. description is a summation o,f' what we have noticed about love in his
tale·.·. . Love ·is a. force working ou:tside of men; the pain it .brings is
�s
as an
on
occureences
s
among
s
as
an
of
s
no more
occurrence
is
men
says
is
�a
grave,
a
not a means
.
"
s
not
He
man.
We
a.Bswers
an
seems to
comes
..
of
men
a
�length of days" to call thier own.
or
the nature of Jupiter the
Creator, Chaucer belives that "High was his intent, Well knew he
why/And what thereof he meBBt."
It is no wonder that Chaucer accepts
man for he has faith that Jupiter conducts him through life.
The
nature of Chaucer's universe is somewhat like a machine insofar as
its separate parts are in gear with one another.
a unit.
The mechanism is
Distinction between Heaven and Earth does not imply break-
age, but difference in function.
We have learned that neither
repait nor lubrication is needed.
illlat· form does this distinction take on in the Knight's Tale?
On earth we see Arcite and Emily and Palamon involved in a strenuous
conflict.
Each has separate desires, each feels entitled to ful-
fillment.
This clash is mediated by the "Righteous Lord and judge",
Theseus, Duke of Athens.
Because his human judgment cannot discern
which knight is more worthy, he only sets up conditions for Jupiter's
order to take
over~
This action exemplifies Theseus• supposition
that the knights must work out this rivalry by themselves.
He
rests assured that the outcome will be handled from above.
Theseus'
position is to establish a formal, glorious set of conditions which
are proper for the fulfillment of Jupmter's
sbhem~.
_The amphi-
theatre, altars, and forces are all enormous, for Theseus understood
the duel to entail the end of a man's life.
Moving up into the everlasting parts of the machine, we see almost
an exact replica of the situation on Earth.
For in Heaven a most
similar clash exists between Mars, Diana, and Venus.
light passionately for their desires.
Like men, they
Had Chaucer meant to show
�_"4_
Arcit- . and ·P-alarnon and: Emily's confiict as wrong, he certainly .would not
e
have duplicated in in Heaven.
Theseus.
Saturn mediates in a way similar to
He acknowledges the will of each god to be of equal
~tgnifi~d.nce.
He appeases each .by telling each ·that his desires will be granted.
We
are told that both Saturn and Theseus are sapient from experience and
age.- We :s ense this ourselves, for
potential
or ·each
Satur~
aeems to already know the
wish will -" be actualized; it is only a matter of time.
Neither Saturn:more Theuseus create thei. r subject's desting.
a specified function.
Jupiter's or.der.
the King."
Theirs is to make a path for Fortune to manifest
For "Who causes this procession of life but Jupiter
Fortune then is that Vlhich brings about or actualizes
Jupiter's scheme.
war
They have
"For certainly our wishes and our fears/Whether of
or:· peace~ hate or love,/ All, all are ruled by that Foresight ab0ve."
Chaucer understrad the order of the universe to incorporate con.t'lict
and unity and to operate by means of di vision of power in the manner
illustrated below.
Jupiter
(Prime Mover and First Ca.use, Administrator c£ Order)
Fortune
'Manifestation of Jupiter's creation)
Sature
(Reconciler of conflicting forces)
Mars, Venus,
Diana
(Forces, Complexities)
Theseus
(Mediator)
Arcite,
(Creatures)
Emily,. Palamon ·
In this we do· not see a breakage in need of repatr.
operating. on different but Unified levels.
combined with the handing down of his
of acceptance and inevitability.
We see a mechanism
The omnipotence of Jupiter
scheme~
accounts for Chaucer's tone
�- ·J:¥>
Part IV:- Inferences from Chaucer's
Attitude.
How can we gain personally from identifying Chaucer's cosmology?
One would suspect that because he recognizes the inescapable throes
of Fortune, Chaucer
~arm::>t
recommend a mode of' conduct.
submit himself -and humanity as ineffectual.
He must
Thus far we have realized
he does not promote a morality whose dictates can be ascribed to
any situation.
Life is too ambiguous to allow for such a system-
atised conduct.
We have also observed that neither does he view
man's life as futile nor tragic.
characters to be
effective~
Furthermore we have· recognized his
Though they perceive the force of
Fortune, none of them resigns his individuality to Fortune's power.
Chaucer must then recommend something between a
an irresponsible attitude towards living.
systemat~d
and
If we look again at his
·c haracters' regard for their lives, we begin to see Chaucer's recommendation.
Looking at Theseus in particular we can learn
Chaucer's lesson.
To believe. man lives on Earth in his natural state, that is in the
way it was intended by Juplter, is to accept the entirety of life.
After all it is accepted by Heaven
whi~h
neither instructs nor puni-
shes, but only brings about life's procession.
Chaucer not only
identifies the people in his tale. he also accepts each and every
one as composing the sum of humanity.
What Chaucer is telling his characters and reader to do is accept,
endure, indulge, and whenever possible, enjoy.
In the beginning
of the tale seeds for this instruction are planted in Arcite's
�•' _ 4-6-
words which are
d~signed
to comfort Palamon.
"For god's love show some
patience as I do, •• /Fortune has given this adversity/Some evil disposition or aspec. , /Of Saturn did our horoscope affect ••• /But as the stars
t
.
.
'
-
stood when· we two were born;/We must endure it; that, in brief, if plain."
---..
Arcite again voices Chaucer's attitude .When he is totally disappointed
kfter being freed from prison. HAlas!
Why is it men so much complain/
. Of what .Great God or Fortune may ordairi, /Wnen better is the gift in
any gui~e,/Than
men mat.,-often for themselves dmvise?"
This statement
reveals that some men recognize that Fortune ordains and ·does so with
what Chaucer calls 'the goodly chain of Lovett, and yet they are not
prohibited by it.
to
strite~
The consequences of an attempt to
~efy
Fortune lead
Arcite .here admits that even if .one's fortune is difficult
to endure, it· is at least less dift.i.cult than the result of man's
attempt to rebel against his fortune.
with the same concept.
For Theseus,
Theseus speaks about endurance
whO"ti~ is
said to be wise, tells his
people that ''Then is it wisdom, as it seems to me/To make a virtue of
necessity./ ••• Wnoso would balk at aught, he does folly,/And thus rebels
against his potency." This implies that man is effectual when, and
only klen, he lives in accordance with hth fate.
Palamon even in his despair, senses that his imprisonment is appropriate
to his fortune.
He knows it so well that he can jolte
He says to himself in prison alone,
We fare as he that's drunken as a mouse
A drunk man .knows .. right well· he has a house,
But he knows not th~right was thither;
A drunk is sure to slip and slither_
And certainly, in this world so fare we;
. We ..furiously p~sue felicity, .
Yet we go wrong often before we die.
a little
about it.
�-41If he had overheard himself Pala.nm would remark, "True, but not
tragig, we· can understarxi it."
Wise Theseus propounds the same regard for life• s
parade~
he accepts it because he sees it as resulting from Jupiter.
However,
~'And,
therefore, of R:t.s Wisdom's Providence,/things and all progressions,/
If they'd endure it must be by · successions ••• " .Palamon realizes the
blatant need for endurance, but unlike Theseus, he does not perceive
or attribute a reason to it.
While Chaucer's doctrine recommends acceptance and endurance, it
also prometes enjoyment.
chauueJn"himself often. delights in his
characters and he specifically tells them to enjoy themselves.
For example, Emily prays to Diana" for chastity and Diana' s answer
implies that Emily should find relief and pleasure in the knowledge
of her fortune.
"lt' daughter
~ ~ heaviness./Among the high ...
go~s~ it has been affirmed, ••• /That you shall be the wife of one of
those who bear for you so many cares and woes."
Emily's prayer is not answered.
By requesting purity and shunning
men's colllliany Emily does not accept Earth's life.
She suspects
such a prayer can not be answered, and asks, as a second choice,
for the man who- desires her most.
It '-is the fulfillment of this
request that Diana says should make Emily leave her heaviness and
enjoy.
Through Theseus' speech at the end of the tale Caucar makes it
· · quite clear that enjoyment is a direct consequence of his attitude.
..-~ J.~.
�--For after Theseus propoundsr the:··relationship of men to the divine, he
concludes, ttc~Wh.at may I prove by this long argument/Save that we all
~----
~
12, merriment."
It is clearly recommended to, and often realized by, the people in
Chaucer's tale that the proper way to regard life is with acceptance,
enduran~e
and enjoyment.
The only possible conduct in the· mortal maze
is bravely to face each eventuality as it comes along.
Yet Chaucer depicts Theseus as having more than the ability to make a
virtue of Necessity.
What is it that distinguishes . and elevates Theseus?
He is the only person referred to as wise.
"The greater was there none
beneath the sun." What constitues his distinct wisdom?
We have already seen him cope bravely with conditions of grave importance,
and by this that he had faith in himself as a man on Earth.
accepted and endured his position as King.
that distinguishes him.
Yes, he
It is something above
th~
If we note his action and deliberation in the
forest with Arcite, Palamon, _Emily and his wife, we see Theseus to evaluate situations in terms of universal principles.
Al though Arci te and P,alamon have defied him he does not punish them.
At
one moment he kas about to slay them, but hei·refrained because he realized their defiance resulted from their love.
He put aside his personal
anger and excused them because their cause was love.
love as the authority:
Theseus r ecognizes
"The God of love, ah Benedicta !/How miglW and
how great i lord is he!/Against his might may stand no obstacles/ ••• And
see how for the sake of God &ho sits above, see how they bleed."
His
�_i.J-9_
reaction to their defiance of him is not one of revenge, but of
very deep understanding.
Theseus perceives the situation as if
he were vieWi.ng ti f'rom one of the forest's trees.
Theseus knows
they are twri men caught in the bond which Saturn used to hold the
eleme~ts
together.
His knowledge does not· stop here.
Sensing his own position as well
· as evecysme else's he admonishes himself for his initial. desire to
kill the two.
"Fie upon a lord that will have no mercy/But act as
a lion, both in word and deed,/To those repentant and in rear . and ~ ~e,d,/
••• That lord must surely in discretion lack/Who is such cases, can
no
distinctio~
Jnake •••• " Theseus' mercy entaiis an· acceptance of
Arcite and Palamon as distinct from himself, and a recognition of
each one's wort.h as a part of humanity'.
'
.
Theseus is · capable of seeing the parts and the whole.
There are
all types of men and yet under the power of love there is .no . transgrct rion.
And although the civil order permits him to subject them
to punishment he understand their defiance in terms of more than
Theseus the
K~ng.
This perspective not only· makes him a "noble Lord and DJ.ke," it
also gives him opportunity to enjoy his position • . He can note the
same irony created by Emily's desires as Chaucer's readers.
And he
does so, exclaiming, "This i . yet .the best jest of them all.•• Theseus
s
is the. oily
p~rs~n
.in the
pleasure of laughter. ·
Knight's~
who ever .indulges in the
�Though Theseus accepts, endures, and enjoys, he does yet more.
Though
he judges with the experience of age, his elevation yet rests in something more important.
Theseus' crowning nobility result! from the
fact that he has faith in the ultimate order of things.
The recognitions of his conduct in the forest ·scene exemplifies his
faith on many instances already discussed,
of Love as
ai;i
For instance, his recognition
authority, and his realization of an ability to cope with
the ambiguitjes of life's complexities.
The prime example of his faith is that he does not, although his position
allows him to, resolve Arcite and Palamon's conflict by choosing between
the two.
Because he has faith that things worM themselves out in accor-
dance with the decrees of Fortune ruled by Jupiter's love, he merely
sets up conditions for the resomution of
th~ir
rivalry.
"I put you both
in this decree,/That each of you shall learn his destin'J/As it is cast;
and hear now, in what wise/The work of Fate shall speak through my
devices."
Had Theseus not had faith in the ultimate ordering of life's successions ,
he would have judged the situation according to his social and civil
principles •. Eut
to
Chaucer.. the c· ownihg nbMli ty .-as exentpiified -by ·~!.rhesetls
r
is to go beyond these forms of social and civil order to a perception of
the Order beyond life's chaos.
If Palamon is in any way the better it is because he prayed for the end
(Emily) while Arcite prayed for the means (victory). And if one needs
assurance that Theseus benefited . from his wisdom, let it be known that
he was never once in despair and was continually honored.
�_51_
ColTllllent on Robert Goldwin's Lecture:
Some Theological Implications of
Locke's Chapter "~ Property"
Alfreda Verratti •66
The main purpose of the lectuee, as I see
i~,
was to extract
fttom the hhapter ?Jlf 1Property" Locke's true.thinking on man's
relationship to God, Mr. Goldwin's thesis being that on the surface
Locke frames his argument with true Christian piety, but beneath
this lies a completely unarthodox, unchristian, and essentially unreligious doctrine.
A summary of the first part of the lecture is as follows:
In the beginning of Locke's chapter"6X Property" Locke
"presents
a picuure 2! s.._world well-stocked with provisions for men who are
themselves
~
Their eeason
2!
equipped-!2z.
~ ~
~
commands
grace--to make good use
£! ~·
way i2.· t~e enjoyment
~ ~ ~
~ ~ ~ §.2. richly provided." However, upon a closer:scrutiny
this concept of God's ben&ficience is "replete
difficulties which cannot pass unremarked !!2E.
without beccmmngttransformed
~!.quite
~puzzles
~
and
close examination
different teaching. '
(All quotations from Mr. Goldwi.n's lecture are underlined.)
Mr. Goldwin then proce.eqs to . show that in effect this gift of
God is worthless, for by Locke's own statement •irt is labor then
which puts the greatest part of the value upon land , wi.thout which
it would scarcely be worth .anything."
lecture with
"~
must conclude
Locke's argument i2_ speak g!
~
earned k£. men,
~
~
He ends this section of his
ll i.[
~
iU, keeping
things worth having
~given by ~·"
!§.
~
having
This. is the first of the
�.difficulties which Mr. GOldwin-.· find.a in understa:<ing what .~L3ckedn
means by ffGod's bounty"•
The seoond difficulty is brought about by Locke's argument against
a universal common.
Locke says, "was it robbery thus (for the man who
•
I•
•
'
has gathered apples) to assume to himself what belonged to all in
common?
·· ..
.
Ir such a consent as that was neces.s ary, man had starved, not-
withstanding the plenty God had"'
gi.ven"him."
"Th~s," says . Mt. Goldwin,
"~ 'plentyi ...2! ~original condition i.! 2! such ! kind th~t · !!!!!!
could 2,2. very badly
2!! !,! they
~ not avoid certai~ mistaken notions
of their relations with one another."
--- ----- - - ---
The third difficulty grow$ out of the form of Locke's statements.
Each time he mentions
a comm.and
·
or God, he immediately shows that this
·· command is consfstent:. Wi,th reason.
Thus Mr. Goldwin conclud~s;
~l~. 2.! hi§. account~ -.~ 1! consistent
!.a making
God's command, - one way 2!: another, supernuous,
~
way 2£.. another,
~
"!2.
every 'mention
2!
.fil 2! GOd' s gifts,
~~"
In the following pages ~f his lecture he addresses .himself again to
the' "question
2! ·God's gift·· ~ ~ world
1g_
!ll ~ankind· 1!l co~on."
hom Locke's text he dra~s the · followi~i t . o ; cci~clusions. · (l) That
w
the world was not, in. ract, giv~ri· to mankind in common, but . Was given
' to those Who are industrious and rat. onal, thus 't he rest of mankind
i
receive· nothing · at
ali, and
(2) "Men~~ their ·i"abor,...!ti, ~thought,
·are .the source · of plenty ·and the , means of increase.
The prospect for
increase depends upon man'~ liberation from the .belief that G~d is his
great bene·faotor. ··This -is, !- · believe~ · Locke's answer to ·the question,
who · gave .~wha·(to man?· ··Men gave the· worild to th~selves, primarily by
understanding 't he .inadeq~aci·es of their natuta.J?::condition ' and the
remedies for them."
�.Ji3.•
Before I continue the sunmuary or Mr. Goldwi.n's lecture I should
like to raise several objections to the preceding.
It certainly
cannot be denied that Locke considers man as the source of human
achievement.
of nature
The raw materials
must be molded to fit
man's meeds, ·and · to man must go the credit and the gratitude for
the molding.
Why ·then does Locke mention God at all, eepecialfy sn
relation to the abundance of .His
gi~ts, an~
especially wt:ien he shews
quite clearly that· the gift, as given, must be cultivat·ed by the
.
.
labor of man i'n order to bring out its worth? Mr. Goldwin' s claim
is that Locke, by doing this, is repudiating the concept ·of God
as benefactor ·or man.
It seems to me that there is ·a much simpler
explanation for Locke's mention of God.
In the· context of the entire Second Treatise, Locke's concept of
'
,.
property is that which allows him to avoid a Hobbesfim type or
tyranny.
If it can be shown
t~a~
prorr:;rty is a concept existing
before the.Tormation or the state, th6n it becomes the duty of the
state to protect this property.
For Hobbes, property is posterior
to the conception of the .state and is distributed by the power of
the 'sovereign.
Since it is the right of the sovere5.gn · to .distribute,
so it is ·the right of the· sovereign to redistribute, thus leaving
man with no property but his life and no means of sustinence except
the tdll. of the sovereignu. It is i.n o~der to avoid this subjection
of mah to the will of the soyereign that Locke institutes his concept
...
..
,• .
of property·, prior to the .conception of the state.
· Let .us for .the moment. assume that Locke is " sincere· Christian
a
with
a belief· in . God, . ~atev~r
the .fo~IO:;·of that .belief'. . An atheist
·might ·have formUl.ated .the situation tn respect
foliowing way:
. ... ·
·,. _
.,
.·
~r
property in the
�The world is there.
No one has given anything to anybody, therefore
everyone is as free as anyone else to take what he will for his needs.
Locke however says:
God gave the world to ;everyone, therefore anyone
is as free as anyone else to take what he will for his needs.
l.Thus
he makes it clear that no one can claim a "divine right• to property.
It ls against the tyranny of man over man mantled under the guise of
divine requisition that Locke is aiming his concept of property.
But, perhaps there is some hidden meaning in his mentioning of God's
"bounty" and subsequently showing that this bounty requires the labor of
the Hindustrious and rational" in .order to make it worthwhile.
This
understanding of the relationship of man's ·.talents to God's gifts is
not at all alien to Christian thought. ·In the parable of the talents
in Matthew 25:14, the gifts of God are given to
men~
to be increased by
their industry and wisdom, not to be buried out of fear or sloth.
It
is in fact to tho:se who do not lab'or to increase the gifts of God that
the doors of Heaven are barred.
Thus, Locke, in making it necessary
for men to increase the bounty of God is in no way deviating from the
Scripture which for him contains the essence of
Gospels and the Apostles.
~hristianity,
the
In his ' "Essay on Religious Tolerance'! he
says, "Now nothing il'i . wership or discipline can be necessary to . .
Christian
communio~
but what Christ our legislatoD, or the apostles by
inspiration of the Holy Sprit:·. have commanded in express words.
(This
statement alone would be enough to make Locke a blasphemous heretic-e:gpecially to Pope Leo XIII.)
I believe that Locke is addressing himself in this chapter to the
"question
.
£!
~
gave
~ ~
!th2m.•" as
Mr. Goldwin has said, but the
. .
problem is not whether God is the donor or man is the donor, but whether
�-·~
any man has a paJ.ticular diivine property right; and the answer is
no.
In the second section of his lecture Mr. Goldwin further evolves
what ·he considers to be Locke's true teaching, by pointing o u.t-·the
inevitable inconsistencmes which result from understanding Locke's
references to God and Biblical as representing an orthodox Christian
viewpoint.
Before considering Mr. Gola*in's argument, I would like
first to give a brief account of Locke's rel:gious thought as revealed
in his other writings.
By doing this I believe it can be shown
that the difficulties which Y.LI". _Goldwin finds in Locke's use of
Biblical texts are brought about by an attempt to impose upon Locke
an orthodox view of Ci..hristianity--and more specifically, a Catholic
view of ..·Christianity--a view which Locke certainly did not hold.
·
FirEt of all, as Mr. Goldwin pointed out in his lecture, Locke
makev a clear and absolute distinction between the function of _
religion and the function of civil society in his "First Letter
Concerning Toleration."
He says!
! :-esteem it above all things necessary to distinguish exactly
.
the business of civil government from that of religion and to settle
the just bounctthat lie between the one and the other. If this be
not done, there can be no end put to the contraversies that will be
always arising betwee~ those that. have, or at least pretend to have,
on the one side, a concernment for the interest of men's souls, and
on the other side, a care of the commonwealtp.
The commonwealth seems to me to be a society of men constituted
only for the procuring, preserving, and advancing of their own civil
interests.
Civil inter ests I call life, liber ty, health, and indolency of
body; and the possession of outward things such as money, lands.,
houses, furniture and the like. _::'! (Ericyclopedia Britannica ed. P. J)
•••••••••••••••••••••••••••
Let us now consider What a church is. A church then I take to be
a voluntary society of men joining bhemselves together 0£ their own
accord in order to the public worshipping of God in such a manner as
they judge acceptable to him and effectual to the salvation of their
souls. (p. 4)
�-56But it is unfair to Locke to simply state the separation he proposes
without giving due consideration to his reasons for doing so.
His
reasons are, as he states them: ·
First, because the care · or souls is· not committed to the civil magistrate, any more than to other men. It is not committed unto hi~ I say,
by God; because it appears not that God has ever given any such authority
to one man over another as to compel anyone to his religion. Nor can
any such power be vested in the magistrate by the consent of the people ,
because n·o man ca.P so far abandon the care of his own salvation as
blindly to leave to the choice of any other, whether prince or subject,
to prescribe to him what faith or worBhip he sh'all embrace. For no man
can, if he would, conform his faith to the dictates of another. All
the -life and power of . true~feligion consitts in the inward and full
persuasion of the mind; and faith is not faith without believing. What.
ever profession we make, to whatever outward worship we conform, if we
are not fully satisfied ih our own mind that the one is true and the
other well pleasing unto God, such profession and such practice, far
from being any furtherance, are· indeed great obstacles to our salvation.
For in this manner, instead .of expiating other sins by the exercise of
religion, I say, in offering thus unto-God Almighty such a worship as
we esteem' to be displeca.sing unto Him, we add unto the number of our other
sins those also of hypocrisy and contempt of His Divine Majesty.
, In the second place, the care of souls cannot belong to the civil
magistrate, because his power consists only in o~tward 1orce; but true
and saving religion consists in the inward persuasion of the mind,
without which nothing can be acceptable to God • . ~d such is the nature
of the understanding, that it cannot be compelled to the belief of
anything by outward force. Confiscation of eEtate, imprisonment, torments .
nothing of that nature can have any such efficacy as to make men change
the inward judgment that they have framed of things. (p. J)
It is not
t~at
Locke .excludes ·Christian ethics from civil society,
f or, ·a.a..: he says:
No sect can easily arrive to such · a degree -of madnes's as that it should
think fit to teach, for doctrines of religion, ··such t!lings as manifestly
undermine the foundations of society and are_ therefore, condemned by
,
the judgment of all manking; because their own interest, peace, reputation, everything would be thereby endangered • . (p.. 17)
Thus if the
la~s
of
civi~
society are founded in order to protect the life
and pr0perty of its citizens and ·to engender peace, as Locke insists it
mus~,
there is certainly nothing in the commonwealth which is in con.flict
with his stated .understanding of Christian ethics.
But he could not,
even if he would, propose a state founded ·upon.Christianity.
For if he
�-.57did, he would be simply setting another precedent for the type of
civil society he most ardently wished to avoid--that in which religion
was no longer
left~
to the private eonscience of its members, but
where it became a perfUnctory obedience to civil authority.
This
to Locke woulcJ. be the most blasphemous form of tyranny, for he
firmly believed that there is true' religion only with the free ·
consent of the believer.
He even vent so far as to say, as I have
quoted above, that no man may give over the duty of deciding his "
religion to anything else than his own
cons~ence.
It is not that Locke would take away from men ..the necessity of
obeying God by separating church and state, not that
he is un;dermining the authority
ot
ih~ . doing~thi~
God, but that this separation
is based up.on his firm belief that a forced adherence to religious
principles does in no way contribute to the true puppose and end
of religion, that is, the salvation of souls.
Men can only attain
salvation by making themselves acceptable· . to God and "true and
saving religion consists in the inward persuasion of the .mind."
(p. 3)
A~5
far as the laws of the state are concerned, since, if they are
founded upon reason4arldtruly directed to the protection of property
and the engendering of peace, they can be in no way contrary to L
Lockevs understanding of &hristian piety, they certainly cannot
hamper the assent to God.
This is all, by its very nat ur e, a
commonwealth can, or should hope to achieve in respect to the religious
life of its citizens.
For
The pricipal consideration~ and that which absolutely determines
this controversy is this: Although the magistrate's opinion in
religion be sound, and th~ · way· that he appoints be truly Evangelical,
�-5&
yet, if I be not thoroughly persuaded therof ·in rrzy" own mind, there will
be no safety for me in following it. No way whatsoever that I shhll
.walk in against the'dictates of my conscience will ever bring me to the
mansions of the blessed. I may grow~rrich lgy an art that I take not
.delight in; I may .be cured· of some disease by ·remedies that I have not
faith in; but I cannot be saved by a religion that I distrust and by a
. worship that I abhor. rt · ~is in vain for an ·unbeliever to take up the
outward show of another man's profession. Faith only and inward sincer:. ity ar.e the things that procure acceptance with God. The most likely
and most approved remedy can have no effect upon the patient, if his
stoma~h reject it·~as soon as taken; and you will in vain cram a medicine
down a sick man's throat, which his particular constitution will be sure
- to :turn to poison. In a·:wora, whatsoever may be doubtful in relgion,
~~t hhis at least is certain, that no religion which I beli·eve.Lito br. not
true · can be either· true or profitable unto ~me. In vain, therefore, do
princes compel their subjects to come into their Church communion, under
pretence of saving their souls. If they believe, they will come of
their own accord, if they believe not, their coming will nothing avail~
them. · .How great soever, in fine, may be the pretence of good-will and
charity, and concern for the salvation of men's souls, men cannot be
· forced .to be saved whether they will or no. And therefore, when all is
done, they must be left to their own consciences. (p • . 10)
Locke also gives another reason for the strict separation of church
and state.
He says:
It may be said: "What if a Church be idolatrous, is that also to Jbe
tolerated by the magistrate?" I answer: What power can be given to the
magistrate for the suppression of an idolatrous Chruch, which may not
in time and place be made use of to the ruin of an orthodox one? For it
must· be remembered that the civil power is the same everywhere, and the
religion of every prince is orthodox to himself•• ~Ir, · therefore, such a
power be granted unto the civil magistrate in spirituals as that at
Geneva, for example, he may extirpate, by Violence and blood, the
religion whtch is there reputed idolatrous , by the same rule another
magistrate, in · some meignboring country, may oppress the reformed religion and, in India, the Christian •••• If (the civil power) be once
permitted to introduce anything into religion by the means of laws and
penalties, there can be no bounds put to it; but it will in the same
manner be· lawful to al&er ·everything, according to that rule of truth
which the magistrate has framed unto himself. (p • . 13)
and in another place: .
Just and moderate governments are . ev~rywhere quiet, everywhere safe; but
oppression raises·-ferments and ·makes· men struggle to cast off an uneasy
and tyrannical yoke. I know that seditions are very frequently raised
upon pretence of religion, but it is as true that religious subjects
are frequently ill treated and live miserably. Believe me, the stirs· ~
that .are . made proceed not from any . peculiar temper ·of this or that ChurCh
-or religious socie·ty, :but from 'the c·ommo.n 'd.i sppsitlon of .~l mankind, who
�-.5,_
when they groan under any heavy burthen endeavour naturally to
shake off the yoke.. that galls their neck. (p. 19)
Thus we . see that Locke's separation of church and state is
founded upon two things· (1) his own Ul?l.tBrstand.1?1g Of the true
scope
·or
religion and (2) his b~lief that ~once the.: state is allowed
'
to ·determine which.
, ,'.
•
reli_g~ons
•
I
may or mat not··be
and unrest .must inevitably follow.
tol~rate~
But, ·it may be
is a perfeatly acceptable reason for ·r eligious
'
'
persecution
if there
ar~ued,
namely
tol~rance,
that lack of it.leads to faction and ·war, was not Locke's first
reason superfluous, a mere duplication for what could be explained
in completely secular terms?
Such a qilestion, I believe, must
remain unresolved until it can be proved conclusively that Locke
did not truly believe in the resurrection of the body • . For unless
this be done, there can be no certainty in doubting the sincerity
of Locke's references to the purpose and the true application of
religion.
With ·the above in mind, namely, Locke's own open unequivocal and
completely unambiguous .statement for the necessity pf the separation
of the churbh and state and his reasons for making this separation,
I would like to examine the argument .of _
the second part of Mr. Goldwin's
· lecture.
He first cites Locke's reference to I fim.vi.17, "God has given
1
us all things richly. is the voice of rea· on confirmed by inspiration."
s
His contention is that Locke's use of this passage and the ·'meaning
intended by Paul are at odds with each other.
The
pas~age
from
Paul reads, "Charge them &hat are rich in this world,_. that they be
not high-minded · nor trust in uncertain riches, but in tJ:le living
,
92.9.• !!12. giveth
l!§.
richly
!!!. things
!g, en ioy~
That they do good,
�-6o..
.... .
that they be rich
cate.
~n
good works, ready to distribute, willing to communi-
Laying up in store for themselves a good foundation against the
time to come, that they may lay hold on eternal life."
Mr. Gold.win, "ignores~ reference
i2.
'~ ~
iQ.
"Locke," says
~0 • ~
ll!.2.
with wh&ch Locke is concerned is this life, not eternal life; and the
riches he speaks of are the . riches of this life, the riches measured
by money, not the riches of good works."
Locke ·"certainly is concerned
with the riches of this world, for after all
p~litics
is concerned only
with this world; however, in this passage Paul also is referring to
· the riches of this world.
worldly things must
t~e
Paul's charge is that those who are rich in
care to be also rich in good woris, a sentiment
to which Locke would subscribe, insofar as it involves the salvation
of the soul.
However, the riches which God gave refers in this passage
to the riches of the world, as it does ;in Locke 0 s use of it.
The second thing which Mr. Goldwin does is to compare Locke's property
teachiptt;dth that of Pope Lao XIII in his_ papal encyclicle.
"E-0pe Leo's discussion of property is superfici.ailil.y similar to
Locke's and essentially the opposite. Leo asserts that all men are equal,
for example, and also extenctthe meaning of property beyond possessions
to life and liberty, as Locke does, but even farther, to include the
soul. H&re we see how much Locke's argmment differs from an orthodox
Christian position, by his omission of reference to the soul •••• Locke is
concerned with prosperity in this life; he is completely silent on any
considerations common to Christian discourses on property; the immortality of the soul, life a~er death, and eternal salvation or damnation •
•••• Locke argues, by his silence in his book on political society and
by his extended discussion of these matters in his other work·s, that God
and religion are of no consequence in the origin or workings of civil
society."
Locke is certainly saying this, but as in the passages which I
quoted above, he said ii openly and clearly.
· his true meaning -µ.nder the
guise<.~
There was no need to mask
of mis-used quotations.
Furthermore,
�the most cursorv
readin~ .
or ·t he
-Letter· Concerni'nf'.' · Tolerati.on
would certainly lead one.to believe that his political thinking
would differ from that·
of a member
: Er. Goldwin himseif
go~s
on to
of. the Catholic cle7~·
~quote
several of
from .the Lett.e r, some of which I have giyen ·above·.
th~se
passages
He draws from
them the inevitable conclusion that:
"Locke meant to exclude .consideration of religion~ and God
completely from political discussion. His teaching is not an argu:·ment for the banning of religion or its exclusion from the lives
· of the citizens, .b ut it is ap argument for the exclusion, 'the
total exclusion, of Christianity or any other religion from any
·participation in political power."
·
With this in mind, there is certainly no reason to expect Locke to
make any mention
wha~soever
of the soul. its salvation, or eternal
_
life in this political treatise.
It is ohly when the attempt is
made to place upo.n Locke the obligation of· co rt hod ox Christianity
th.a t the
th~ological
problems arise in the chapter "Cf·Property".
Otherwise it reads as
~elationship
perf~ctly
consistent with ·his position ' on the
of church . nd state.
a
For as Locke states,-· again in the
Letter:
There is absolutely no, such thing under the Gospel as a Christian
Commonwealth. There are, ·indeed .many ·cities and kingdoms , that have
embraced the fai ~h of Christ.• but they have retained their ancient
form of Government, with "which the law of Christ hath not at all
meddled. He, indeed hath taught men qow. by faith and good works
they may obtain eternal life; but he instituted no commonwealth.
He prescribed unto his followers no new and peculiar form .o f government, nor put he the sword mnto any magistrate~ hand with commission
to ;make use of it in forcing men·:·.to forsake their former religion
and receive his. (p. 14)
·
In the third section
of his
lecture Mr. Goldwin summarizes his
'arguments and draws his general conclusions.
from Locke. "one from
the ·~
Treatise:
He quotes two passages
�"He has so !Visible a claim to us as His workmanship that one--of
the ordinary appellations of God in Scripture ~is 'God our Maker9 and
°the Lord our Maker• •••• He is King because he is~indeed maker of us all •• "
and another from the Second Treatise:
••.••• men being all the workmanship of one omnipotent and infinitely
wise Maker--all the servants~of one sovereign master, sent into the
world by his order, and about his business--they are his property whose
workmanship they are ••••
and concludes :
In the contlict between these passages and the cclaim that man is
his own master I believe we see the ultimate problem to which Locke
was addressing himself in his teaching of property: Is man· God's
property or is he his own proprietor? •••• Locke's property teaching is
nothing less than this, an accouo.tt of God's attempt to provide for man
compared to man's attempt to provioe for himself•·with God found wanting.
This audacious, shocking, and blasphemous theme is the foundation of
Locke's property teaching.
I~
have attempted here to demonstrate that this is not the case.
that Locke's property teaching was for him, the necessary prerequisite
for a free society; free, not from the tyranny of
tyranny of other men.
God · ~ut
from the
If he would free man from religious tyranny, it
was not the tyranny of God himself, but the tyranny of those who would
use religion as a road to t"ivil power and pervert what was for him 'hhe
true.111eaning of religion--the inner conviction and ascent .to God, a
conviction not be forced by political power.
It cannot be denied that Locke's political treatise is .not in accord
with the pl>litic).1 .c onceptions of the old Christian&.
It is also a short
and easily made step between Locke's property teaching and the complete
denial of the necessity of God's existence.
However, I believe it ts
unfair to Locke and in fact simply false to say that this was the true,
albeit. hidden, message ,. of his writings.
For I have tried to show here
that, when read in the light of his theological works, Locke's chapter
on property need not be
vie~···as;.beingt•reRlete ~th
puzzles
~
�even
on
a
not
of
�
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�TABLE OF CONTENTS
• David Jones, Tutor
1
Tentative Investigations Concerning Kant's Doctrine
of the Imagination with Special Reference to the
Transcendental Deduction •
• David Lachterman, '65
• 20
.Charles Bell, Tutor
• 52
James Gilbert, Tutor
• 56
An Introduction to the Problems of Justice
• Laurence Berns, Tutor
• 57
Notes on an Experimental Program in Dance-Drama
• Georgia Cushman
• 70
Two Poems •
• 77
Value and Critetia in Art.
four Poems.
•
f
•
•
"'
•
Note on the Portfolio ,
• Richard Cox, Tutor
Absences
• 79
Textbook of Analytic Geometry (Cont'd.) •
*
*
*
Editor.
Assistant Editors •
Art Editor
Faculty Adv is or.
*
*
*
.Robert Sacks, Tutor
*
*
*
*
• Susan Roberts
• John Falencki
Sally Rutzky
.Daniel Sherman
Eva Brann
• 48
�VALUE AND CRITERIA IN ART
Dav id. C .~Jonas
"Now, just as one Who is deluded as to the amount of his
material we.alth is confuted by arithmetic~, which states its
exact amount, so ho who nourishes delusions as to the wealth
of his own tl'l:oughts and imagos · is brouglilt oa:ck to reality, ·.
when he is obliged to cross the Pons Asinorum of expression.
Let us say to tho former, count; to tho latter~ speak; or,
here is a pencil, draw, express yourself."
Benedetto Croce, Aesthetic
.I
The working assurt?piion ~f this paper is that all judgments of value entail
a set of evaluati~ely neutral criteria; and that these criteria in turn
exhaust.ively determine whether the given object is to b.e j':1dg~d gC?o~,
bad, or indifferent.
etc.", where A, B,
C,
That is, "X is good" entails "X is A, B, C •••
etc. arc characteristics, dispositions, contextual
relationships1 or what· have you, that ~ght belong to either good or bad
things -- depending on one's system of values.
ho~vcr,
Given a set of values,
anything that is A, B, C •.•• etc. must therefore be judged
to be good.
This assumption requires ·a great deal of explanation and
qualification, which I have tried to . supply
elset_Vher~,
but I · believe
it is initially plausible.
It is at least evident that ·value judgments must be by and largo con-
·sistent.
When WO judge:· something t · be good or bad1
o
-
t-ro
must at loast
be able to judge other thirigs which are. ~n the appropriate ways like
, ·
it, similarly good or.. bad.
,/
'
In most cases, we Will in actual fact
.
.
proceed to do just that. · ·m ·that is meant .by .saying· We
.
!l2££.~ot
· fc)llow thi~ pro.c edure, ·is that in evaluative matters we are always f:ree
to
change our minds. · · If we 'now proceed to ask what "consistency" in
· value judgments is, the only possible answer, so far as I can see, 1.s
that it is descriptive, evaluatively neutral consi.stoncy.
For it
�~2-
cannot merely be a matter of our applying "good'1 only to those things
· ~ judge to be good; since if that were the ca.so, we could apply "good"
.
.
.
ju~t
as the.spirit
~oved
us, and still be perfectly consistent.
Finally,
i~ "aonai-atont." does mean. "dcscri'ptively . consistent"' "it follows· that
f~r .any .gi von: appli~ation of "good", there must be a corresponding
recognizable set of .descriptive criteria.
It does not follow that wo
will ·always be able to say precisely what tho criteria are; for even in
non-evaluative matters we can handle criteria complo~ beyond any possibility
<6f complete enumeration~
Nor does it follow there will not be borderlinQ
cases"; or' .areas of criteria that are vae~c or open-textured.
·. does ·follow that thcro will: E£ criteria;
and
But it
if -we are reasonably
'assured of that fac~, we may continue With the .confidence that the object
of investigation at least exists -- must exist.
With sufficient care,
then, we should be able to discover and lay out,· in general outline if
not in detail, tho cri~eriological. structure of judgments of value in art.
II
I ·will begin w.i.th a short outline of my thesis, and continue imperceptibly
into the details.
My suggestion is that there arc two main streams of
criteria in judging works of art -- the "means" and the "ends" criteria -- ,
th ~t. t hey arc in active competition, and that neither of them adequately
represents tho value: of art
are inadequate, not in a
!£ i21£
as an element of human culture.
They
p~joratiV:e sense, but simply .beca1:1so (I propose)
the primary value of art is not ·in its products -- as, say, tho· p~imary
-
value of manufacturing is in the sum value of its products.
. .
"
~
This
observation is_not m~ant to prejudge the issue of the value of individual
works of art, tho~gh_. I admit I might want to take it down several pogs,
�-Jbut merely to make clear a possible cri teriological distinction that
deserves to be considered.
trr'J central aim.
The making of such distinctions · is in fact
"
Finally, whatever the virtue of the positive account I will give, I
will continually re_.emphasize the importance of pressing for an account
of why a given work of art is good or bad, and in what its value lies •.
The latter question is of the ver;J first relevance, and despite its
obvious intimate connection with the former question, it is one that is
of'ten avoided.
For just as we may learn what distinguishes a good
cheese, or a good wine, from a bad one, so we may learn to tell good
art from bad without learning the point of that evaluative skill.
In
fact, the value of wines and cheeses is pretty well restricted· to the ·
titillation of the pal.a te, whatever their actual · price.
It may be · that
in a sufficiently artificial atmosphere -- wine or cheese tasting as a
hobby or profession, or in the shifting unrealities of the luxury
market -- secondary, contextual. values are supcradded to the natural
criteriological structure.
It may come to be a matter of great .i.mPor•
tance whether a wine :is a good one or not -- and hence, the wine itself
may seem to be an object of great intrinsic worth.
But the most
exhaustive survey of the criteria -- the answers to the question:
Why.
:is this a good/bad wine? -- seems to point inescapably at wines being
no more than something pleasant · to drink, and
for open-hearted conversation.
perhap~
a good lubricant
We may similarly ask:
to what sort of
value do the criteria for good and bad art point?
cations of answers to:
What aro the impli-
Why is this a good work of art? for the questioni
What is .a work of art good for -- in what does its value lie?
take as my exemplar, painting.
I will
�-4III
In theory, the connection qetween the criteria for a good painting and
the "endff of the painting -- what a painting is good ~ -- is
str~ghtforward
By analogy, we could say the criteria
and immediate.
for a good penknife are that it be sharp; hold its edge well; not rust
easily; fit snugly into the fingers; be just small enough for eas-y
pocket carrying; perhaps have two or three blades shaped to the most
common uses; and so on.
These criteria are in a familiar and direct
.
'
.relation with the purpose of a penknife~ which is to be carried about
for minor cutting jobs.
A "good" penknife is simply one that has the
characteristics best suiting it for that end.
From one unfashionable critical vie-wpoint, a similarly utilitarian
criteriological scheme fits neatly onto judgmei;its of good paintings.
We may call this the system of "ends" criteria for paintings·; . and
since here the criteria-end$ relation is direct and obvious, we will
simply indicate a few of the more evident ends -- ulterior purposes
to \fhich paintings are commonly put:
1.
:/
Entertainment; pleasing the beholder.
Granting a suffi-
ciently wide ·range of application for "pleasure", this end of painting
and art generally -- is the m9st
I like" sums up the position.
un~versally
Ind~ed,
recognized.
"I know what
a convincing case may be made for
a 'wholly hedonistic analysis of value in painting, including all the
subsequently listed ••ends'' as mere means to entertainment.
we could say
That is,
a fine genre or historical painting, qr _ penetrating
a
portrait, is a Good Thing not because of its documentary or psychological value (which may be quite small), but because we are pleased by
the manner of the documentation or psychologizing.
�-5Whether this view is ultimately justifiable
to judge.
. ~r not~
I will not attempt
It _s at least a strong contender in common-sense aesthetics,
i
and is usually rejected not so much on the roeri. s of the case, as on
t
.' .' : ~ .< . . .,.:.':.,.~;t~:: . ~. . :- ·..::.
.
. ,
~
:: ~~ :
.,,
the objection that _ seems to
it
cheese, or wino.
..•
dem~an
art -- put it on. the level ·of
I hope to show that if necessary, this consequence
....
might be accepted of individual works of art without affecting a more
enduring · importance and
valu~
j
2.
:Decoration·.
· By
which adheres to art as·· a process.
far the n\lmerically
greater part 0£ .. art has
been conceived· with this · simple · funct"ion ·in mind~
Pots, books, . walls,
clothing; porticos',: utensils· and weapons of all sorts and varieties,
ranging back to the historical _dawn,
are
everywhere · covered with '
decorative painting, or equivalent plastic decoration.
the design of an artifact may
itse~f
(And of course
be partly decorative ·in intent --
as the shape of a pot or temple may be decorative in addition to its
.
.
surface decorations.} A· glance through any home-decorating magazine
·should similarly convince anyone .that the modern paradigm of painting -that is, a studio painting
~-
fills a distinct decorative role, whatever
the intent with which it was originally produced.
The ·intimate cor_mection between the decorative and entertainment "ends•
· ·of· art -. is, I will suppose, fairly obvious.
· there is nq other reason for its existence.
is pleasing;
~coration
It is to .awroximately
this twofold purpose that Plato· thought the artist naturally limited,
.
tho rest being
preten~on,
charlatanism, and
inte~lectual
quackery.
He accurately observes that there is no evidence of the artist's
~aving special · competence
to deal with the 'many subje.c ts he nonetheless
does deal \dth~ · But though .the .artist's theoretic.al knowledge of his
��-7many works of art that ·may 'originally have been purely decorative in
intent are now of equal hi-storical value with written documents and . .
ruins.
It may be that this undeniably important facet or art, though
clearly derivative arid distinct from the question of the intrinsic· value
of works of art, is nonetheless sometimes a contused element in critical
evaluation.
4.
Persuasion.
Here we enter the controversial area of what
the borderline of painting ~ t~
might call "intellectual painting" prose.
we
One· of the commonest and most natural areas of operation under
this general end is social commentary • . .We: might therefore as easily
call this "·judgmental" painting as "persuasive" painting -- those are the
two sides of the coin.
Unfortunately, it docs not seem
po~siblc
to attribute any very deep or
abidi.ng intellectual value to these· sorts of paintings, though at the
..same time they do occupy a unique and distinctive outpost on the 'frontiers
of social criticism.
Briefly, their role is to provide the aphorism,
the encapsulation, the
Esm. -!!!91·
Thoy may be. read and understood at a
glance, from Daumier to Ben Shahn to Herbert Block; from The Horrors
. ..
of War to
~ughters
,
of the American Revolution. ·" Certainly, the artist
who is successful in this .venture must be poss·a ssed of .an accurate and
imaginative judgment, as well as the requisite mechanical ·and technical
skill.
But since" success
iies i.~ the veey abstraction and .simplicity of
the statement, the possibility of -penetrating the · subject in a decisive
.
'
way is correspondingly limite(i.
the reasons for it.
We are given the judgment -- but not
�is
�. -910. · PhilosophiceJ.··
Painters are also sometimes supposed to be
eX:pressing a sense of lifo• : a superior evaluative outlook or "philosophy"
that in some manner is .~rssociated w.i.th a unique temper~merit attributed
to artists.
Both of these final two "ends" are sub-classes of the Persuasive-
There is a certain "tfal.idity in attributing these
fedagogical ends.
abilities to painters -- in some cases -- but until it is otherwise
demonstrated, it seems to be in the very nature of the case that such
.1.·.'
. e_
fforts a.re strictly limi t~d by the judgmental and expressive boundlr ie.s
heretofore mentioned.
I do not claim that ·this list 'of. ends is complete, and no doubt a little
thought would . ·enlarge the list
consid~rably.
All I. ·wish to do is offer
a reminder of the very patent fact that painting does have . number of
a
'
..
.
..
·. . : ·
•
prosaic
purpos~s~
~hose
that
•
I •
' •
may.be accurately expresse,d and evaluated,
and that it is therefore perfectly proper to judge works of art in
accordance with the sorts of purposes for which they may be produced •
. A~ the same time I've
tric~
to indicate the reasons for suspecting that
none qf these ends ar.e the sorts of ends that
activ":lty
o~
wo~d
make painting an
much intrinsic importan?e -- certainly not in comparison
.with ·Western accomplishments in science, medicine, technology, politics,
• .. .
..
.
.
.
'
'
jurispr:udence ~ literature, and perhaps even philosophy.
•
obje_cte_ that
d
pa~ntiX:g
p~c~ology,
Vecy well; begin by distinguishing it from
~
philos.ophy, and theology.
/ ,
the painterT
' .
Wh~t
' :.
is the special contribution of
·,
By what means does he arrive at it?
of his accomplishment?
It may be
4 .
is not that sort of thing .-- that it is, perhaps,
. a. .subjo_ t of the spirl:t.
c.
'
.
.
.
• ·-
Speak.
Wherein is the value
��-11Such criteria may sometimes be quite simple:
I've found what entertains
roe
"It entertains me,
~
entertains most (or the appropriate)
Here we have merely a straight-forward subjective statement
people."
plus a general observation correlating dne'
others.
s own
taste with that of
Arid it is ·quite true that so long as tastes coincide, subjec-
. ·tive reactions and objective classification may lie down ·peaceeilily
"I like it" and "It's good"·are indistinguishable.
together!
But
even' in relatively uncontroversial matters, there quickly comes a juncture
where one' 's personil .t ·a ate and the prevailing taste of one's society
At this parting of .the ways~ it is nothing so simple as our
diverge.
call something (say) "entertaining"'
own reaction that allows us to
but rather the' :accumuiated eXt;erl.ence that "that · sort of thing" will
be found generally entet-tair.iing.
of thing" must refer to marks
In this context, again, "that sort
and
prognostications attaching to the
thing itself, and in turn allowing us to make the prediction that it
.will be found entertaining -- or perhaps,
entertai_ ing.
n
.
;
l
~hat ~t
ought to be found
(St.atistical preference is not the only vector
.
.
'
'
.'
determining whi.c.h .criteria
~
..
.society will adopt in evaluative matters;
but we .cannot go into that matter here.)
..
Once the · necessity for · criteria is recognized in cases :or dissension,
it may be quickiy extended 'to· COVer
taste ' correspo~ds· to one's own:Were not ' s"o~ one ~ould have
reaction was or was ·n ot
'
E.. V3ll
those ·cases· Where the "general"
for' the simple reason :that t if this
no :ineans
of telli~g · Whether one ' s own
a reliabl.e · indicator
i'n a given instance.
That
'
· is. there would be no other· immediately available criteria with which
to compare it.
�-12The "entertairunent" case is the most difficult example from the above .
ends with which to establish this thesis -- simply because it is the
most derivative on subjective reaction.
I will take it that, mutatis
mutandis, there are evidently . first-or.der cr.i teria for deciding whether
somet~ng
is good as decoration, . documentation, social comment, instruc-
tion, science,
etc~
Finally,
~t
should be remarked that even under this
simple analysis, a "good painting" may be one which combines several
of the ends I've suggested.
turn be .criteria for a
As to which
Fulfillment of second-order goa1s may in
thir~-order
second-orde~
judgment that a painting is
criteria are relevant,
~hat
will
~good" •.
jepe~~
on
the context in which the work wa.s produced, and under which it is
judged.
Where the ends of painting are . concerned there can be no
single critical touchstone.
It must also be re-emphasized that within any of the catagories or
cross-catagories of ends, we judge whether ·som~thin.g is a good or bad
work relative to other ·works of the same sort; and that this judgment
may t ·a ke on a slightly different cast from judgnients of the value of
.
those sorts or things taken as a whole.
'
Our earlier example of cheese
and wine was meant to point out .hou the. relative ranking of these .
products may in the right context come to be of much greater interest
than the prior issue of the value
o~
cheeses and wines in general.
I
cannot avo-1.d sugg.e sting that a similarly hypnotic interest in .the
relative ranking of works of art, whether or not under the. gen~ral,.
criteriological
scheme . sugges~ed
above, might. have the like
eff~ct
of
suggesting a greater intrinsic value than the ends themselves warrant .•
�a
a
no
a
is
I
•
it
our
of
turns to a
in
is
way
our
Where.
on
case
are
can
of
is
to
of
can
��-15himself with evaluative . rhetoric, simply because there is no one to
'
9bject .to this common practice in art criticism.
.
. ..
.'
~
.
- ·.;. ·rn this species of criticism, as I have been saying, the criteria
.
, .
of judgment are immediate an~ accurat~ly specifiable.
;·· Y.ll.
Wolfi1.in proceeds
a continuing stock of precisely_
.illustrative- examples. - (Perhaps
it would ·not be an exaggeration to say that ·a . shrewd art cri t 'i c could
give
a roughly accurate
.....
mereiy
.
by.examining
·.
yal~ation
_ .e. amples of some · sorts of painting
of x
two or _three is_o~ated square ··inches· o:t surface.)
. . .
· The ' criteria are, in a word, mechanical; like the criteria in a fruitsorting she·d.
In fairness, we must admit that Wolff'lin is engaged in a historical,
not a critical venture.
Similarly, mechanical criteria are to
extent appropriate in schools of art.
som~
But we have already noticed
that Wolff1.in may 'sometimes forget what he is supposed to be about;
and it may also occur that, in an atmosphere of instruction, technical
ability spills over its original container of contributory value, and
becomes an end in it"self.' This too is understandable; and it is
understandable that the ranks of professional criticism draw .most
heavily: on instructors and historians of art.
This does not prevent
qur .i nnocently asking: · What is tne end, wherein is the value, . of a
well executed ·work ·o f art?
answer to this question.
A reiteration of the criteria, is no .
Until another answer is forthcoming, therefore,
it must appear that a good painting is simply one that has been well
executed -- a show of skill.
; ·.···
'
�-16To conclude this precis, ''means" and "ends" criteria are distinguished
in that the former offer distinct first-order criteria whose
fe~ond-
order orientation is obscure, whereas the latter offer second-order
goals of moderate importance, with the usuaf and unobject.i onable
openness of first-order criteria attaching to such gotls.
I hope that,
between theory and examples, I've succeeded in showing that there is
indeed a sharp dema.,rcatio. between these two ·criteriological systems.
n
There is however a similarity in
this~
that the value they both
attribute is supposed to lie in the work, the painting, itself.
It
may be that the most -distinctive value of painting lies beyond the
scope of that assumption.
. v
One of the principle tenets of theoretical aesthetics is that art is
useless.
This in turn is supposed to imply that art is the "pure
form/ science" of something.· For Kant, it is the pure scien_ e _ judgment:
c of
it is the form of judgment without a (practical) ob~ect qf_.judgment.
_
For Croce, as another example, .it is the pure science .of expression
expr ession not to some communicative or informative purpose,_ but
~imply
for its own sake.
Though it might be argued. whet_ er "judgment"
h
or "expre.ssior:i" is the more appropriate term, both these f>_ ilosop_hers ·
h
seem to be g'e t ting at the sa.11e thing:
and I wish to propose that they
_have fallen into a slight · case of mistaken identity.
First, it has been shown that painting is certainly not, strictly
speaking, "useless•.
To this it might be ·rejoindered that I have
�···show
, is
is
art is a
technical
as well.
Games,
are
and
or
d
actual and achieved
is
even
condition, mathematical
end is in itself
well
formal
I cannot
is, that
restricted
into·
a
arise from
��-19t .o have no "end 0
--
to be spinning its wheels.
criteria appear to be pointing at paintings;
pu-~
The "means" or technical
.t _
his is, .a . confused way
of pointing through·· the painting toward the painter
-..i.
toward painting.
· of course, . the technical criteria also qualify as "ends" criteria in
(
this wayi
a display of technical skill is in itself pleasurable and
diverting to behold.)
s.
A~
to the unanswered question of what sort of .discipline
painting might be -The physical stubbornness . of the material, the direct sensual character
of the
~roblem,
·seem to suppqrt the suggestions of Kant and Croce •
.. Painting is as close as we can come -- and still some distance off
. to the· experience of learning to talk anew, when we already have a
language.
words.)
(Learning a foreign .language is simply learning a new set of
:It is thus the discipline of "expression", if you wish, and if
you use !'expression" to indicate the attempt to transform the silent
flow of_sense directly into articulable, manageable
_form~
discipline of "judgment" in Kant's sense of "judgment":
It is the
the direct,
almost manual grasp of reason· on sense, the fiat of the brain that
i~stigates . mind. ·
~lightly
. we
Both these philosophers see the sa~e thing, from
different angles.
But with these metaphorical suggestions,
must atick to 'our own rule and say that these brief analytic remarks
have reached their boundary.
The rest must be another, later, story.
··, :,
...
�-20
the intricacies
second or
Transcendental
ooscurities
is
course
a
realize
The per-
icance
is essay to the
experience
�-21~ imagination;
~nth~
lations as to
second section, I will present .my tentative specu-
th~ nece~sary
•
•
presence of the
imaginat~on
in the consti•
I
tution of the human mind ?nd .the. implications of this necessity.
.
.
.
.
.
.
.
stages of this
'
. inqui~Y ar~ a~imated
Both
by a desire . to understand the charac-
t . r of the .,-C.o pernican revolution that was meant to take place in the
e
Critique of Pure Reason • .
EXPOSITION
Kant's ·discussion of the function and capacities .of ·the imagination
~s
contained pr-imarily in: the "Transcendental Deduction" · and the ·first
ch~pter
of the Analytic of Principles, the "Schematization of the. Pure
Concepts of ·the Uhders·tanding".
It seems .wise to oegin oy locating these
sections within the total structure of the Critique.
The Critfgue of Pure Reason is a propaedeutib to transcendental philosophy ,:- the complete system of
It is resp6nslble for
all
cla~ifying
1
possible a priori human knowledge .•
the sources and limits of the
ment · of · pure reason, so .as to keep it free from errors.
~mploy
More specif i~
cally, the Critique of Pure Reason as a special science is addressed to
one all-important question:
.
. .2
possiole?
How are a priori synthetic judgments
fhis question d~f ines the central issue in the cr{sis ~t
metaphysics wh{ch Kant's work is intended to resolve, namely, the
determination of the exten't to which the activity of the human mind
inv6lv~s p~inciple~ or con~epts that are aosolutely fndependent at ·
experience .and sense i m
pressions.
The efforts of cer t ai n philosophers
or philosop~fc schoo1s to extend human knowledge beyond ihe \ffeld 6f
experience canoe ev~luated on the str~ngth . of this deter~in~tion~
Kant's· resolution of this er is is has two parts, a demonstration that .
ex~eriehca
itsalf is · made possiole only through the existeMce in the
unda ~ ~tanding
-0f certain pure a priori concepts, and a rastriction . ..
of the employment of these .same concepts to the field of possible
experience.
of
The key word in "Kant's enunciation of the . "general problem
pure ·reason" ' is synthesis.
):
1
2
;
.
Introduction 825, 827; cf. "Architectonic of Pure Reason" 8869, 8873.
Introduction Sec. Vi, 819.
�'tic)
actual demonstration
section
nation
a . crucial
sensible
are
be assumed
�-23-
becomes evident:
Unless some matter is given to
cannot inform any m~tter.
Despite this
necess~~y
mind, the mind·
th~
3
reciprocality,
however~ ·
it is possiole to inves-
tige~e
the modes of comparison and comoination i~ isolation from · ~ny
4
sensiole representations , or, in other words; to determine the rules
which govern the faculty of the understanding in its thinking · any
5
object whatsoever, or, as .. Kant puts it, an object-in-general.. · The
science
or
Transc~nd~ntal
these rules is called the
guished from Logic in general which
aostrac~s
L6gic, as
distin~
from all relations of .
knowledge to its ooject, whether pure or sensiole, in order to consider
the logical form of the connection of any .thoughts.
6
This distinction
implies that Transcendental Logic .still takes into account the · nature
of the objects o~ thought whereas General Logic abstracts from all
"differences in the oojects . to which the understanding may ce
In particular, Transcendental
standing
in~ofar
as they can
Lo~ic
r~late
sense-experience, to objects.
directed .~"
considers the rules of the undera prioti, that is, ·prior to .any
The task of .this
scie~ce
wiil thus oe
to analyze the operations of the understanding in order to discover
how these a priori relations are possiole and whether
elements in all knowledge of sensiole objects.
they · a~~
necessary
Kant's answer will be
that sensiole objects canoe known as objects only if certain a
p~iori
concepts of , the understanding are connected with sensiole intuitions.
Now that we have · dis covered the science which seeks to determiner the ·· ·
possibility and necessity of a priori concepts, it seems proper to
re-examine the general prqolem of pure reason which in effect cireated
the need for such a science:
How are synthetic a priori judgments
possible? ·Thus far I have only defined, in a loose way, one rif the
t13rms o.f this question -- "a priori".
Certainly "synthetic" and
"judgment" require elucidation.
3
4
5
6
874
887
879-80
876.
Cf. Introduction to Logic (tr. T. K. Aooott) p. 2.
�-24It
~eems
to me that there is throughout . the Critique an interplay of
two senses or aspects of the term "synthet_c".
i
Where Kant speaks of
synthetic as opposed to analytic judgments or knowledge he seems to have
in mind primarily the distinctions given in the Introduction (sec. IV,
810-14) between ampliative and . explic~tive judgment~, that is, between
.
'
.
judgments that add to the concept of
t~e
suoject and thdse that simply
extract from the concept of the suoject.
·?
based on the content of the judgments.
This distinction is apparently
(Consequently, mathematics
and natural science are bodies of synthetic -- and, also, a priori -knowledge in this sense.)
The activity that
con~titutes
a synthetic or analytic judgment gives
an additional aspect, an aspect, moreover,
foreground in the Transcendental Analytic.
ara, of
c6~rse,
wh~ch
seems . to -be in the
The activities involved
synthesis and analysis respectively.
a·multiplicity of different
represent~tions
The former .organizes
cohe~e~t
into a
structure
· (I hesitate to say ·" unified" structure at this point); the latter
extracts characteristics common
to a
~ultiplicity
of
~epresentations
to form a concept which ·may ,be used as a predicate_ in a possiole judgment. ·
Judgment in the simplest logical sense is the oringing together of two
concepts for purposes of comparison.
It presents an affirmation or
negation of a connection oetween a suoject-concept and a predicateconcept.
If it is a synthetic judgment it adds to our knowledge of
the suoject-concept; if it is also a priori it does not rely on any
s•nse
~*perience
predicate
a~
out · represents the connection between subject and
necessary, that
is~
as holding .in every possible instance
of the ' representation tif oath concepts.
ter of the 6onnection which
mak~s
It is this necessary charac-
it impossiole for
$UCh
judgments to
be grounded in experience, for the latter can only give us a plurality
of instances in which such a connection is represented.
7
Cf. Prolegomena, Preamole Par. 2, a.
�-25-
I have used the term 'concept' quite freely in the preceeding discussion.
Ka.n t gives an indication of at least one of its mean.i ngs in the Transcendental Aest.h etic. (840):
Now every concept must oe thoug~t as a representation
which is contained in an infinite numoer of different
possible representations (as their common character)
and which therefore contains these under itself ••• s
For example, in the -representation 'red' or 'circular' the understanding
thinks a
comma~
characteristic which might oe applied as a predicate
to an infinite number of particular representations.
Concept, howe0er, is given a
~icher
meaning when Kant asserts that ''all
intuitions, as sensiale, rest on affections (determi~ations of a
receptive, that is, passive faculty), concepts rest on functions.
By
functions I mean the unity of the act of bringing various representations
under one common representation. 119
identified as synthesis.
10
In a later passage this function is
Hence, one would expect that concepts,
which issue from the active faculty of understanding, are intimately
connected with the act of synthesis.
The very word in German -- 'Begriff'
from greiffen, to grasp, to take hold ·of so as to hold together -suggests this connection.
Before confrontlng the Analytic of Concepts, I should like to articulate
briefly the principal questions to which this section is addressed.
Kant has descrioed
~
science, Transcendental Logic, which has as its
mission the investiga-tion of the "origin, the scope, and the oojective
validity" of knowledge of ,oojects through pure acts of thought, that
is, through a priori concepts.
I think that the three questions
inve~tigat~d oy Transcendental Logic can oe interpreted ~s follows:
~h~ origi~, · in . what faculty and by what functions do the~e a priori
concepts arise?; the scope, are a . priori concepts merely involved i n
8
9
Cf. Ideas in General, Sec. 1, Bk 1, Transcendental Dialectic (8376-77).
Both intuition and concept are species of· the. genus representation •
.The former is single and relates immediately to its oaject, the latter
~efers . f6 ..the Object mediately by means of a feature which several
things may have . in common. Intuiti6n a~d 6on6ept are divisions of
~nowledge ~cog~itio) w~ich · i~ oojective perception.
893
1n 8102
�-26-
the iogical forms of thought as revealed in general logic, or are they
related to knowledge of a possiole ooject of sensuous experience?; the
ocjective validity, are these a priori concepts necessarily related to
every object of a possiole sensiole intuition, that is, are these
con~
.cepts conditions of the mind that underlie all thought of an ooject
given in intuition?
Kant's solutions to these questions take us from the Logical functions
of Judgment to the Schematism and it is this course
of
reasoning which
I shall now do my best ,to follow.
The first chapter of the analytic of Concepts is entitled 'The Clue to
the Discovery of all Pure Concepts of the Understanding'. · we might
expect that this chapter will offer an · answer to the question regarding
the 'origin' of pure a priori concepts.
moreover, the word 'all' in
the chapter heading suggests that this search is meant to oe exhaustive,
that it is committed, in other words, to exhioiting in a systematic
fashion all pure a priori concepts.
The 'Clue'
i~
the Taole of Judgments.
The understanding •produces'
concepts; the only use it can make of these concepts is to judge oy
means of them.
Presumaoly, this means that all concepts (oody, say,
or divisible) are potential suojects or predicates of a judgment of
some determinate logical form.
General ·Logic is in a position to
exhioit a complete taoulation of the determinate forms of judgment.
The functions of the understanding which are defined as unifying acts
and on which concepts 'rest' are reduced to functions of unity in
judgmen~ -- fu~ctions which' oring together many representations, in-
cluding representations immediately related to the
its one representation.
obj~ct
to oe thought,
On the strength of this reduction or, better,
this equation, .it is possiole, through Transcendental Logic, to give
an exhaustive list of the a priori concepts of the understanding which
is in a one-to-one correspondence so to speak with the table of the
logical functions of the judgment.
It is necessary to understand why this is ·possiole.
Kant oelieves and
tries to demonstrate in the third section of this first . chapter (8102106), that the analytic unity of a concept in a judgment -- that is,
�-27the unity of a representation (concept) that
comprehen~s . an~
is aostracted
from · variciGs other representations (intuitions) so : as t~ oe p~ service
in.- a· judgnien:t .:._ depends ·on a priori synthetic unity .of the intuitions
to ~hich this analytic concept is m~ant ~o apply~
presuppo~~s ~ynth~sis.
I~ s~ort, . ~nalysis
The synthetic functions of tha understanding
which thus make possiole the analytic functions of judgment are the pure
a priori concepts of the understanding, or, as Kant calls them, the
categories.
The importance of synthesis cannot be ov_er-emphasizt?d; it is, according
to Karit,
is
~t
the basis of all our thinking and without it no
possible~ ·
. '~nowledge'
This discussion of synthesis in section three .is too con-
centrated and difficult to oe more than briefly _sumrna~ized.
The a priori concepts of the understanding =must have some content if
they are to be more than
by General Logic.
th~
forms of thought in
g~ne~al
as studied
This content is provided by the pure a priori mani-
fold of space and time revealed oy the Tran~candental Aesthetic.
Space
and time, besides containing a pure manifold of intuition, are the
conditions of all receptivity; in other words, the representations of
any object can only oe intuited if they are organized in space and
time.
Any mediate representation of an object (conc~pt) ~ill ~e affected
oy the conditions of receptivity; namely; space and time as manifolds
of a priori intuition.
In the chapters on the Schemata and the Prin-
ciples of the Understanding it be~omes apparent that the ~e~ation oetween
the categories as they apply to possiole
sensuo~s
experience . and the
a priori manifold of space and time is much more intimate than this
present section might sugg~st.
In any case, if this manifold is itself
to be known or to · oe represented through a concept which is of a unitary
character, it must be "gone through in a certain way, taken up, and
connected.
.
11
This act I name syrithesis.« ·
Let me try to give here an interpretation in the simplest terms of what
Kant means.
11
If representations of oojects· are to· be
~nalyzed
with a
Synthesis is required by the "spontaneity of our thought". The
possible meaning of this statement ·will occupy .my attention in the
second half of this essay.
�-28vi~w
t9 ?bstracting some common characteristic which can oe predicated
of th,esE3 .r epresentations, these representations must themselves oe
thought
_to_g_e~her ~.
rept_esentatiqns
· '. comoine ,_
that is, the unders_
tanding must be aole to hold various
t~ge.ther
in one: thought oefore it can _
begin to compare,
and~ separate.
What.is more, if several objects are judged to have such a common
characteristic, these oojects must oe given as oojects, that is, the
representation of th$ common characteristic (say, redness) along with
_
representations of different characteristics
position in space relative to
~he
(say_r~ctangularity,
or
viewer) must be thought together,
must be apprehended as necessarily oelonging together in the representation of the object.
Now if this is to oe possible in the case of
empirical intuitions of the appearances of objects, it must be true that
the manifold of· a priori intuition which gives the conditions of all
e~pirical intuition, is similarly organized and synthesized. 12 This
latter synthesis Kant terms pure.
Its purity is said to depend on an
a priori ·s ynthetic unity which "renders the unity of the synthesis of
13
the manifold necessary." ··
Thus a priori synthetic unity gives th_
e
rule or 1aw under which the synthesis of the representations takes
place.
This rule or law, which all analysis presupposes,- is also called
a pure category of the understanding.
The function of the sou1
i• the imagination .
14
from which synthesis 'in general' results
(Since I shall oe concerned with this power or
funqtion in much greater detail later, I will ignpre the puzzling
characterisations which Kant gives of it at this point (8103)).
our knowledge of objects begins, then, when
th~ .
All
manifold of pure intui-
tion (space and time -- and as the . Schematism reveals, t _ e latter
h
especially) is synthesized by the imagination.
Perhaps Kant's meaning
here is simpler than it might at first appear.
If representations
12
13
14
8104.
Cf. also 8121-122.
In the Transcendental Deduction it will oe argued thatttiis necessary
unity makes all . knowleqge of oojects possiole.
I think Ka~t m~an~ by soul -understanding. Cf. 8133 . note, where the
'faculty of apperception' which might reasonaoly be called -soul, is
identified as the understanding.
�.-29-
·(intuitions) of an ooject are given successively in time, for example,
..
.
":
some connection must oe established oetween these v~rious rep~~s~~tations
'
if ·We are to be able to recognize anything aoout their relation to the
ooject and, thus, aoout the ooject itself.
this however means that some
power of._ the mind must bdng together these represent'a .t ibns which as
successive are independent of one another irito a single representation
in which they are interdependent.
.
We have one represeMtation· in one
.
.
.
'
moment of time and a different repr~sentatibn. in the following ~oment;
the imagination must represent these tw'o r .e preseritations as standing ·
together, that ·is, it must produce an image of the first, which is no
longer
pte~ent,
and grasp it (oegreifen) together with the second.
the representations: .so connected .. oelong to
th~
When
a priori manifold of
intuition, the synthesis accomplished oy the imagination is pure.
Yet this pure synthesis does not, according tri
knowledge of the ooject.
K~nt,
oy itself
yi~ld
The synthesis of the imagination must take
place according to rules, or "oe executed according to a common ground of
unity".
The rules and the grounds of unity oy virtue of which the unity
of the synthesis is rendered necessary belorig to the understanding and
are descriced as the pure concepts (Begriffe) of the undeistanding.
To summarize, the necessary factors in all our knowledge of ocjects are
the a priori manifold of intuition (space and time), the synthesis of
this manifold through imagination, and the unity of this synthesis
through · the concepts of the understanding.
It should ce noted that these
are not successive stages in a single act of knowing an object ou-t the
necessary components of any such act.
A detailed examination of the relations oetween these factors forms . the
core of the Tr~nsce~dental Deduction.
Although I shall not ca aole to
offer a .thorough .analysis of this section, I will attempt to discuss the
strategy and results of the Deduction with a view to answering the
qtie~tions
concerning the imagination . pos~d at th~ outset of this essay.
-Kant, in the preface to the
Transc~ndental
Deduction entitled the
Principles of any T~anscendental Deduction, ·distinguishes the question
.
.
.
of .right . (quid ju~is) fro~ the question of fact (quid facti) - a dis.· tinction· that occurs in the usage
of jur i .s ts.
A· transcendental deduction
�-30-
of the pure concepts of the
one which explains oy what
u~dersta~ d ing . is
right a priori concepts can relate to
o~jects
of sensiole intuition.
It ·
is necessary to see the difference ca.tween thi.s form of deduction and
an empirical deduction which tra.ce.s the origin of pure concepts to experience and reflection on experience, the
oy Locke, for example.
shown
~o
s~rt
of deduction prese_
nted
Since the e.mployment .of pure concepts must oe
oe legitimate prior to all experience, the source of its
legitimacy can surely not oe traced to
ooj~cts
of experience.
Kant's strategy in the Transcendental Deduction is to demonstrate that
nothing could p·o ss>
i:bly ~ an ·ocf ject of experience if the understan~ing
did . ·not contain pure a pr·iori ' modes of the organization and synthesis
of intuition in
general~
in short, the categories.
15
I may oe over-
simplifying Kant's procedure here but it nonetheless seems to me that
questions of the possiole and the necessary
and oojects, with which
t~e Transcenden~al
r~lationship
of pure concepts
Logic is concerned, are
answered in a backhanded manner, as it were.
The givenness of objects
is shown to be entirely dependent on the pure concepts, and their a
...
priori employment as rules of synthesis.
To the question, "Can a priori
concepts apply to oojects of experience?" Kant seems to respond, "Can
there be objects of experience without a priori concepts?''
It is with
this understanding of the overall strategy of the Deduction that I under16
.
.
.
t a k a my d iscuss i on o f ·some of .1 t s cen t ra l d cc t rines.
The first half of the
Transcend~ntal
Deduction covers suosection 15-20;
suosection 21 marks a point of division after which another deduction
restricted to the conditions of the manifold in empirical intuition
follow·s ,(sucsections 22-26) • . In the first half, then, Kant is presenting
a proof of the
ooject~ve
validity of the categories in relation to the
manifold in intuition in genaral. 17· The full purpose of the Deduction
15
16
17
On this point see especially B 125-126.
I shail talk primarily of . th~ Deduction given in the · 2nd e~ition. It
seems to me that this version is a trifle clearer and has the virtue
of making the transition from categories to schemata more intelligicle.
This phrase was used previously in the introduction to the Taole of
Categories (B 105); it occurs again in B 145 - in the transitional
~uo-section of the Deduction.
It seems to designate any intuition
that is cased on a receptive faculty end not, for instance on an
intuiti0e understahd!nb ~hich is . ac~ive or spontaneous. This intuition
need not necessarily oe through the forms of space and time as is the
case of all human intuition.(Compare B 43 in the Transcendental
Aesthetic.)
�:.
31~
will only cie realized when the
all
OD jects
11
val~dity
of the categories in respect. to .
of out· -senes II is demonstrated.
Accordin"
gly' thera .· is one ·
proof concerning the genus - intuition-in-general, and
concerning a species of that genus - sensiole or
, I shall
to
a ·second
empiric~l
proof
' intuition.
trying to folloili the course of the first _proof according
st~rt o~
t~~ - ~ectional
divisiohs whi6h·Kant presents •
.The first section ( 15) reconsiders the three factors in any knowl'edge of
an ooject _
(cf. sup~a) . ~ithout . making ·their relation to oojects explicit.
.
(This . explan~tion is ~eser~ed for suosection 17)~
.
·'
~
..
..
The manifold of
re~-
resentations can come to us ih a: sensiole intuition; the comoi~~tibh o~ ·
these representations, or of a mahifold in general (synt~~~is) is · a~ : ~6t
of the understan~ing.
Thus, ~hether the mind represents to i~se1i · a
i
sensible manifold, the pure manifold of space and time.,_ or the manifold
.
'
.
,included . under
div~rse ~oncapts,
the representation of
~he comoin~tioM
of what is given in the manifold . is an .act "executed oy the _suoject itself"
and cannot oe given
~hrough
oojects.
This is a central point
analysis of the operations of the mind:
~ppearances
oojects can only give rise to ·
which exhioit no relationship tb . oMe another
determi-nat.i:ons of the
sens~oility;
in . Kant'~
ou~
are merely
whatever organization is to .be fo_uf?d
among appearances is oestowed upon them by
the
understanding .independently
•
1"
•
of all determinations of the sensioility.
On further consideration,
~he
concept of comoination reveals a third ·
cbm·panent, namely, the unity of the. synthesize~ rna~ifoid. · Kant':~. intention here see ms to oe .. t o stress the fact that~ ~lien : var io~s r e pr esentations
18
. ara put together they a~-~ grasped i~- on~ represenfation ~
. ~ndeed the
very possioility of .combination _is dependen't upon the possibility of a
··unitary ' representation. of the repr_e~antations ·ta be combined.. This conce~t
of unity which is added to the representation· is · not the category of
unity which is grounded in a logical
judg~ent
which itself presupposes
the possioility of comoination; rather, it is the concept .of a qualitative unity.
If we follow Kant's
'this qualitative
~nity
refefen~e
(to para. 12) we find that
..·
is wha_. prevails in . a "play' a . speech' or a story."
t
In .t hese · :i nstances qualitat.ively diverse e~e,_ments :or parts are held together as one th~ough t~~ ~i~gleness of the~e o~ plot ~hat ~un~ throughout the whole.
18
Cf. 8 103
Hence, the manifold which is synthesized contains different
�-32 representations which are nevertheless thought of as oelonging together
in one representation. ·1"
intuitions and in
faculty of
9
· 'The source of t:he qualitative unity, oath in
judgments~
knowledg~,
·makes
pos~i~le
the understanding (as a
as Kant will tell us in
$~ction 17).
This
so~rce
must now oe discovered.
The next suosection can oecome as .6bmplicated and ooscure as any in th~
Critique.
I shall hold on to a very simple-minded understanding of Kant's
essantial meaning and use that as .a key to expalining the main argument •
.
.
The understanding has the power of 'thinking' representations (intuitions
and concepts);~ understanding must necessarily · 'think' all of its
representations if they are to oe .m1!J!t at all.
In Kant's words, "It
. must oe p'ossiole for the l think to accompany al,l ~ representations. 1120
By underlining the personal pronouns I hoped to show what seems to me to
oe the chief point:
Unless every representation is thinkaole, there
could be representations in me which would not oe mine, which is impossible.
The more imposing terminology of sucsequent paragraphs should
not cause one to lose sight of this original assertion.
Now there are representations which can be given prior to thought, namely,
intuitions; the manifold of intuition in a sucject must oe related in
some way to the representation 'I think' which makes the representations
the subject's.
An important obligation of the Deduction is to elucidate
the precise character of this necessary relationship.
21
This spontaneously generated representation is called oy Kant pure or
. -1' ~ · ~-':.r-- appercep ti on; i·t is th a t se lf -consc i ousness wh 1c h mus·t ·.- oe capao l e
,or.i ginal
·
·
:..
of accompanying every other
all consciousness.
22
representat~o~
while remaining identical in
This apperception i~, in ~ddition, unitary; that
is, it is · the representation of one persistent self-consciousness (which
is the ground of the possioility of a priori kMowledge).
Hence we may
speak of the transcendental unity of self-corisciousness.
Its unity is,
moreover, synthetic.
19
20
21
22
It seems to me not inapp~opriate to speculate at this point that Kant
has taken over from L~ionitz .~ the distinguishing mark of true being multiplicity within an absolute unity (monadology, para. 13) - and has
applied it to the ooject of knowledge. Even if this speculation is
mistakenj it remains ~ fact ·that the unity of what · may be known is
for Kant the prime condition of its knowability • .
Including logical ·judgments; for example, 'I think' the predicateconcept 8 belongs to the subject- coni;·e pt .A.
Cf. B 133
Kant probably means here all empirical consciousness. Cp. B 133, or
especially, A 117 note, which is quite illuminating.
�-33.
.
.
.
I imagine Kant's meaning here to oe something such as this:
I must think
· every represe-ntatiori. that is given to me (or p~oduced oy me) as mine; for
.,
· this t.o oe
of~-
possiol~
;.. it is .necessary for me to
one self,. . con.sc:iousness in all my thoughts.
c~ncelive ~f
the identity
If t _ is transcendental
7
~nitY of consciousness. .~i.O_ : not exist, the ~anifold of representations
. that is mine wou1d
~ts,1~ '. haMe · no unity~
have any knowledge ·ot
th~
and consequently I could never
. .
..
connection of appearances
.·
o~
. ·. ·.
.
.
.
23
representations.
Kant h~· s already_ ~aid . that "combination is (or, i.nvo.lv·e~) ·re~r~sen. fation
of t.he _synthetic unity of.. the manifold (given in intuition). 11
tity of the self in ~espe~~ to this mani~old
The iden-
~~ssib1e· bnly . ~hrough
consciousness of . the synthesis or conjoining of d{v~r~~ - repies~nt~tions
in our c,onsciousnes~.
24
is
The remainder of the su.o sect·io· is a discuss ion
n
,'
'I
of .the mutual conditioning of the pure apperception and the - ~ynt~esis of
.
.
2~
the manifold.
.
'
"Synthetic unity of the man if old of iritui tions · (in
general, I think), as gener~ted a priori, is thus · the · g~ou~d bf . the
identity of apperception itself. 11
By . thi~ I don't. think Kant means to
displace the principle of apperception from its supremacy in the sphere
26
of human knowledge; · rather, as he explains in the _
next paragr?ph (8 135),
the ithoroughgoing identity' of self-consciousness cannot
~~
thought,
wi.t hout the synthesis- of the manifold give11 in intuition" - for the 'I
think' is a simple representation and its identity in a multiplicity of
representations can be .itself represented only if someth.,ing non-simple,
0
- 'manifold is given. · Thus, although the synthesis .of the
r
~ pon
manifol~
the a priori unity of . apperception, this unity is, in its
. - p~ndent upon the synthesis for its
~urn,
depends
de-
repr~sentation.
". (
·'
.
••• f ·
.The next subsection (17) ~earns to me the most ~~ucial in this first half
of the Deduction.
.For the first ti~e, the notion of •boject' is clearly
defined and oy means of this de~inition the ·possibility of objective
·- .knowledge is shown to be necessarily related to the
of understanding.
-·--· .
~
¢riori conditions
The first intimation of this discussion · occurred in
_
.. _______
~· A 103 and A . 16. ·
1
.
'
.
24 Kant-· afterwards· amends .this to say ~ : the ·. c~nscio~s~ess : of the possioility
of the synthesis: 8 134
25
Cp~A
117 - · A 118
26 B 135, also B· 133 note
�-34-
··: · .,
the previous subsection.in the phrase
Kant begins oy distinguishing the
0
determinate thought. 1127
~upreme
principle of the possibility
of intuition in relation to sensibility (formal cond.itions of space and
time) from the same principle in relation to the understanding - to wit,
that the manifold of intuition should be subject to the conditions 28 of
29
the synthetic unity of apperception.
Only by oeing subject to this
principle of the unity of consciousness in all representations can
representations oe connected with one another in a single consciousness.
If we think of diverse representations as being given in different times,
for ·example,. then this argument asserts that the identity of consciousness
is the sole ground whereby these representations may oe brought together
into one intuition in which they exhibit connectedness and organization.
Otherwise, each representation would last only as long as it was itself
given in time and the manifold would oe a mere 'rhapsody of appearances'
30
lacking a necessary relation to the subject.
Kant now defines understanding as the faculty of knowledge (it was
previously (B 94) defined as the faculty of judgment and as the faculty
of thought:
that these two are the same has important consequences, .
v ide. subsm::t:io1;1 19) ; knowledge, in turn, is defined as "the determinate
relation of a given representation to an ooject;" finally, an ooject is
"that in the concept of which the manifold of a given intuition is united."
I suspect that in these three lapidary statements Kant has revealed the
essential features of his doctrine of experience.
All knowledge of an
unified object , indeed, the oojectivity of an ooject consists ·in· the
unification of the manifold of representations in the concept "of that
object.
In less
elaborat~
terms, in the concept (mediate representation)
of a ouilding, for instance, the manifold of diverse representations
given in intuition (colour, g~ometrical configurations, et. al.)
united: so as tb form a concept
o~
a
det~rminate
to which these representations are ·related·.
31
is
whole, the building,
Accordingly, to ' know '
27 · Cp. 8 169 "Brief Outline of this Deduction" - the principles (categories) ai~ · the determination of appearances.
28 The plural here forew~~ns . us that these conditions will be the cate·-. · ,
gor ies.
29 Cp. A 108 "Synthetic" as an attribute of apperception refers to the
necessity of a synthesis of representations. (B 135).
30 8 137 and see especially A 121. ·Ths phrase 'rhapsody of perceptions'
occurs in B 195.
31 See especially A 250 - A 253 (in Phenomena and Noumena) on the transcendental object which is the "Correlate of the unity of apperception".
�- 35 -
an object is to recognize that the representaticins given in a .manifold
32
are rel~ted in a ~6hereni (~rid, as Kant later argues, necessa~y . ) way
under a unitary concept.
W~ ·
3.3
have · alr~ady learned that the unification of intuitions can take 'place
only i f the a. pperception is unified in this synthesis.
Hence, the tinity
of apperception must oe the aosolute ground of the valid exercise bf the
undetst~nding
.
'
as the faculty of determinate thought, that is,knowledge.
33
As Kant expresses himself a few lines later, "The synthetic unity of
consciousness is, therefore, an oojective condition of all knowledge.
It is not merely a condition that I myself require in knowing an ooject,
out is a condition under which every intuition must
~tend
in order to
.
b.a come an ob JSC t ' f or. me." 34
We might summarize the preceding exposition oy saying that no ooject of
~ensuous
experience could ever oe an object if it were not suojected to
certain a priori conditions of the understanding which are independent
of experience.
The highest of these conditions is the transcendedtal
unity of consciousness.
Now Kant leads the argument (subsection 19 and 20) right where we might
have expected him to in light of the 'Clue to the Discovery of All Pure
Concepts in the Understanding."
Understanding is the faculty of know-
ledge (of the determinate relation of
representation~
to an ooject); it
is also the faculty of judgment (mediate knowledge of an object through
concepts).
Furthermore we know that ·tha categories correspond to the
'functions of unity in judgments.
Sections
~9
and 20 draw out the funda-
menf~l cons~quence of these relationships.
It is first
n~passary
to estaolish the connection oetween the functions
of judgment and the unity of apperception.
Kant argues that logicians
have failed to determine the character of the relationship that exists
between tha terms of a logical . Judgment; if, however, we examine what is
meant oy the judgment, say, "Bodies are heavy", we find that the copula
· 32
33
34
8 14 1 ; c p • A 12 1 ;.; 12 3 • .
See 8 146 and 8 165; 8 138.
Cp. A 77
�-36refer~
to the
ooject~~e . unity . of
apperception and that the forms of
judgment are so many ways ~f . oringing · cognitions (th~t is, intuitions
and concepts) under the unity of apperception.
I think that Kant is
arguing here that when we predicate 'heaviness' of a 'body' we are
connecting the two representations as suoject and property, in other
·words, we · ~re synthesizing the manifold represented under the concepts
in order to reach the representation of an ooject with which a certain
property is necessarily connected.
This synthesis is, as has been ·
estaolished aoove, possible only through the unity of apperception which
first makes an ooject in general conceivable.
All IDY. ·representations must conform to the condition {or conditions),
as Kant said earlier, "under which alone they can stand together in
one universal self-consciousness. 1135 What are these
conditions~
We
have learned that the function which orings given representations(intuitions and concepts) under ~he unity of apperception is the logical
36
function of judgment.
The manifold given in a single empirical intuition must be determined in accordance with one of the logical
functions of judgment.
However, the categories (pure concepts of the
understanding) are the logical functions of judgment in relation to
the a priori determination of the manifold of
int~ition. 37
''Consequently,
the manifold in a given intuition is necessarily suoject to the categories."
With this; the first half of the Deduction is at an end.
Kant
might claim in its oehalf a fair measure of success.
To understand the necessity of the second half of the
T~anscendental
Deduction, it is necessary to return to the Introductory section,
Principles of Any Transcendental Deduction."
11
The
The proolem which Kant
confronts there and which the second. part of the Deduction is meant to
solve concerns the independence of sensioility and
~nderstanding.
The
pure categories (as concepts of the relation of the manifold. of intuition in general to the synthetic unity of apperception) do not represent the conditions under which oojects which affect our sensioility are
given.
Space and time, as Kant has argued in the Transcendental
Aesthetic, are the pure a priori conditions of any sensible intuition,
35
36
37
B 133
B 142
8 105
�-37app~arances - ,
hence any
if they
ar~
·to oe given to
..
to the a priori forms of in.tuition.
sens~,
must conform
The pu.r e categor ie. . do. not in the
s
least contain.similar conditions and therefore we can at least imagine
that appearances would not stand under the necessary conditions demanded
oy the unity of the pure understanding.
of course,
i~
The function of the Deduction,
to _
show that the appearances as appearances of objects in
the complete sense of-the word must conform to the conditions - of the
transcendental unity of apperception.
Yet how sensioility and under-
standing are, in fact, linked together is a mystery which only an
analysis of the necessary organization of the forms of sensibility (space
and time) in all intuition can unravel.
complete solµtion in the chapter on
~he
The dilemma must await its
Schematism of the Pure Concepts
of the Understanding.
The transitional remarks of subsection twenty-one seem to me to oe of
this form:
we have established that the categories
conf~r ~nity
on the
manifold of a given intuition in general without taking into account the
forms or conditions of sensibility through which this manifold can oe
given; thus, it remains to be proved that the categories can
the conditions of all knowledge of the objects
a particular form of sensioility.
giv~n
to
£!:!!:_
fur~ish
senses through
In short, the ultimate aim of the
Deduction is to demonstrate the necessary presence of the . pure
of the understanding in the constitution of human
experienc~,
~o~cepts
or_ -what
,
is the same, human knowledge of oojects.
The 'faculty' of the mind through which the manifold given in
emp~rical
intuition is brought under the unity of apperc~ption and, thus, under
38
the categories is the imagination.
_Kant's account is perhaps nowhere
more oblique than in the two subsections (24 and 26)
doct~ine
of the imagination; to a large
ext~nt
w~ich pres~~t
the
I have relied upon the
discussion of ~he three-fold synthesis in the ·first edition
(A
~7-A 110)
for an understanding of the basic features of the doctrine; the principal
alteration in the second edition would seem to be the elimination of
the synthesis of .reproduction in imagination.
38
This 'faculty of the' imagination~ which has an empirical and & transcendental role, is never wholly separated from the understanding itself. Cf. especially 8 153 end, and 8 162 note.
�-38-
The pure categories of
t~e
understanding contain only the forms of syn-
thetic unity which must be present in any intuition of the manifold of
· representations if we are to have knowledge of a determinate whole to
whidh these representatives belong.
39
As Kant says, the pure categories
are 'mere forms of thought' which is equivalent to saying that they are
'forms of
judgmen~'
which are not influenced by the mode in which repre-
sentations are .given. · Nevertheleee, ·the Transcendental Aesthetic has
revealed ~hat there are in human sensibility a priori forms of all intuition to which every appearance must conform.
In particular, every
object given to us in intuition must conform to the inner sense which
is or contains the conditions of the determination of the manifold with
40
respect to time.
Now, inasmuch as all empirical intuition must be
subject to the pure intuitions of space and time, and, inasmuch, further,
41
as the pure intuitions of apace and time are intuitions of a manifold,
if it can be shown that this pure manifold must be synthesized in accordance with the categories (in order to make knowledge of objects possible)
it will follow that all empirical intuition is likewise subject to
categories.
This seems to me to be the general form of Kant's argument
in twenty four and twenty six.
The first part of this argument (24) introduces the 'faculty' of imagination and the 'transcendental synthesis of imagination' for the first
time (in the second edition); Kant's main point would appear to be that
42
the pure manifold of time contained in inner sense
and, by extension,
the manifold of space, must be subject to a pure synthesis.
Unfortunately,
Kant does not use the qualification 'pure' in his account of the 'figu ative synthesis',; however, it seems to me absolutely necessary to recall
43
this terminology from the earlier chapter - The Clue to the Discovery if what is being said here is to make sense.
If what I have just argued
is correct, then Kant is saying that the understanding (or the transcendental function of imagination) can impose synthetic unity on the
manifold of time (and space) which would . presumably mean that time is
thought of as 'one time' and space as 'one space' • .
Just as any manifold in any intuition must be agrasped
41
42
43
in one act
This is not said explicitly until section 26, B 160, but is already
implied in the A~sthetic - B 39 (space) and a 47-48 (time).
See 8 154 where this connection is made quite clearly.
8 103
�-39-
of
kno~ledge''
44
.. that is, made, . through synthesis, the object of one in-
tuition, so must the pure manifold of inner sense (tim~); i~ objects
given to intuition are to be though of as in one and . the same . time, be
45
thought (conceived of) according to principles .of synthetic unity,
accord.ing, that ·is, to the transcen.d ental unity ~f apperception. 46
The (pure) synthesis of the manifold of sensible intJitio~ is .entitled
'figurative'; it is distinguished from the
synthe~is
ot the . manifold
of intuition-in-general which is thought in the pure categories - the
synt~esis
presupposed in the purely logical forms of judgment.
This
figurative synthesis is the function or act of the imagination and,
being directed only to the unity of apperception or, better, the rules
that proceed from .the apperception, is the transcendental· synthesis
of imagination.
Kant makes only the briefest statement concerning the nature of the
imagination: .... Imagination is the faculty of repres·e nting· in intuition
an object that is not itself present."
and
quit~
If we remembe.r Kant's ·ear lier
general description of synthesis as a putting
togeth~r
of
representations, the force of the above characterization of the imagination
becom~s,
I
thin~,
evident:
the manifold of
given in iotuition successively - or,
a~
representatio~s
Kant says in
th~
is
first edition,
"each representation, insofar as it is contained in a stingle moment,
can never be anything but absolute unity" - thus, if thes·e representations
are to be combined in any way, the representation given in a previous
moment, and no longer present, must be 'reproduced' and set alongside
the representation given in the present moment.
If the representations
are pure intuitions such as moments of time, the figurative synthesis
determines the form of sense itself, in accordance with the unity of
48
apperception.
The transcendental synthesis of imagination thus links
44
8 103
45
Kant says below that this synthesis is "possible and necessary a
priori" if, I think, there . is to be knowledge of objects • .
46
8 105
47
Cf. B 154-155 for an example of how the figurative synthesis of
time takes place~
48 For, the empirical consciousness that accompanies each successive
representation must be related to ·the necessary unity of ·transcen.dental consciousness, if these representations are to be .thought as
'mine' •'· Cf. A 107 .-
�-40-
together tha understanding as the faculty of apperception and the
49
sensibility aa the . faculty of receptivity.
Before proceeding directly to the last subsection which is entitled
the 'Transcendental Deduction' (26), it seems to me not
to present in
summer~
inappro~riate
fashion the more elaborate exposition of the
elements of experience offered in the first edition.
In a paragraph
deleted in the second edition (A 94) Kant lists the three sources
(capacities or faculties) of the 'soul' which together make experience
possible:
sense, imagination and understanding (as apperception).
Each of these has an empirical and a transcendental use.
The important
point of· the whole D.eduction (in both editions) is, I would think, that
the empirical employment is in each case grounded in or made possible
by the transcendental.
Kant makes this only partially clear in section
26 and the long footnote to 8 160.
Hence it will be useful to exhibit
diagrammatically the relationship between the three faculties and their
two-fold employment.
This diagram can be constructed most clearly if
I give the .empirical use and the transcendental foundation of that use
for each faculty.
.
-
Empirical Use
50
Sense: representation of appearances in perception
A Priori Foundation
a priori form~ of ·pure intuition
(space and time)
.'
Imag~nation:
transcendental synthesis of the
imagination
Apperception: empirical consciousness, recognition of identity of reproduced representations and appearances
(empirical concepts) ·
transcendental unity of apper. caption (categories as rules
of synthesis)
representation of
appearances no longer present in association and
reproduction51
49
8 152; note that here the synthesis of the imagination is spoken of
ai the 'action' or 'effect' . (Wirkung) of the understanding on the
sensibility. This expression emphasizes- the a_ biguity of the 'imagim
nation' - i~ it a separate faculty or is it a mode of the understanding' a operation?
50 . This distinction (the first true elements of the three fold synthesis
(A ~7) is absent from the second edition. In . general, it is the empirical synthesis of - the imagin'ation.
51 This is Kant's termi it refer~ to the section of chapter .one of
Analytic and in particular section 3, 8 102-8 105. Presumably a
correspondence between the distinction of Metaphysical and Transcendental exposition in the Aesthetic is intended.
�-41With this gen~ral framework in mind, we can confront the some~hat obscure
exposition of what is explicitly called the'-· ' Transcendenta~
•'
the results of the Transcendent~l An~lytic to
52
' ,
.
The metaphysical Deduction
has shown the one-to-one cor-
Kant begini by
thi~
point.
respondenc~
Peduc~ion'.
r~viewing
of the . logical functions of judgment and the
cat~gori~s
of
the understanding; the first half of the Transcendental Deduction demonstrated the a priori possibility of the categories as flmodes of knowing
objects of an intuition in general.."
It now remains to be proved that
the categories afford the possibility of knowing whatever objects are given
in
~ intuition~
In this case, our conce.r n is not with the form of
their intuition (this is the work of the · empirical concepts) but with the
laws governing combination of appearances.
It is necessary to remember
here that Kant has already declared (B 134) that "Combination/does not
lie in the objects and cannot be borrowed from them, and so, through perception, first taken up into the understanding."
Our attention is first directed to the fact that in an empirical intuition
the manifold is combined through a synthesis of apprehension whereby per· caption is made possible.
53
This statement 6ecomes more meaningful when
it is compared with the doctrine of apprehension in the first . edition
(A · 99-100; A
-20) •.
There it is stated explicitly that ·this empirical
synthesis :.of apprehension is a function of the imag'ination (considered in
its empfr icai-.·employment); through this synthesis the "single and separate"
54
app~arances given in intuition are combined,
present account.
as is asserted in the
However we already know that appearances are subject
to the a priori conditions of sensible intuition, namely, space and time.
S~ace -
and time, furthermore, are not simply 'forms of sensible intuition'
but ar·e:-represen.tations (intuitions) which contain a manifold.
But,
space and time in which a pure manifold is represented are given as in.
.
.
.
. ions ·o f - a sing l e ob Jee t'5 5 ( an d , h ence, th e man.i f old given un d er th em
t ui t.
is thought as a unity).
52
53
54
55
This immediately suggests
wh~t
we
hav~
.previously
This information is given directly by Kant in A 115,
This is implied, to be sure, later in the note to 8 162.
A 120; the appearances are separate in time, I think.
Kant refers us in the text to the Transcendental Aesth~tic; the
reference . seems to be to 8 39 (space) and 8 47 (time) .•
�-42-
encountered, that the pure
intuition~
of space and time are necessarily
synthesized in accordance with the categories of the understanding. This
synthesis, although strangely enough Kant does not make this clear in
the present passage, is the transcendental function of imagination. 56
from this it surely follows, if we have accepted Kant's argument up to
this point, that the possibility of comb~nation of appearances given in
empirical intuition (and therefore dependent on space and time) .depends
on the a priori synthetic unity of apperception and thus on the ·
categories which ere rules for the combination of the manifold of an .
intuition in general.
All synthesis, therefore, even that which renders
perception possible, is subject to the categories;
and since experience is knowledge by means of
connected perceptions, the categories are conditions
of the possibility of° experience and are therg~ore
valid a priori for all objects of experience.
Kant, in setting out the difficulties involved in a Transcendental
Deduction of the categories suggested' that "objects may, therefore,
appear to us without their being under :the necessity of being related
to the functions of understanding ••• 1158 ; it is no longer permissible to
ent~rtain
this hypothesis, for the very possibility of
'object• as a determinate unity of a manifold of appearances . is grounded
in a priori conditions of the understanding--the synthetic unity of
apperception and the rules whereby the imagination, in its transcendental use, synthesizes the manifold of pure intuition. The right of
pure concepts of the understanding to be employed a priori .. in complete
independence of all experience" is manifested in the impossibility of .
experience itself without them.
Since the preceeding exposition has been long and perhaps overly complex,
I would like to present a brief and abstract summary of the Transcendental Deduction as I have tried to interpret it.
(B 121)
1)
Three factors in knowledge: manifold of intuition,
56
The oblique footnote (to 8 160) refers to the transcendental synthesis
of imagination which space and time as objects presuppose, without
naming it.
57
58
8 161
8 122
�:
-43'•
'
combi_. tion of manifold, synthetic unity of manifo_d;
na
l
there must be a ground of this unity.
(8 131-135) . _ ). This ground is the synthetic unity of pure
2
apperception.
(8 136-138)
3)
An object is the rspresantation of a unified manifold
of appearances and is therefore dependent on unity of
apperception.
(B 141-142) . 4)
The functions of unity in judgement are modes of
bringing concepts thought in the judgement under
the unity of apperception.
(8 143)
5) . .The functions of unity in judgement correspond to
.categories of the
(8 143)
6)
th~
unde~standing.
Therefore, a manifold given in an intuition . in general
is subject to the categories.
(8 150-152)
7)
Time, the a priori form of all our sensible intuition,
must be synthesized in accordance with the unity of
apperception (transcendental synthesis of imagination).
(8 160)
8)
The synthesis of apprehension in empirical intuition
must conform to the a priori forms of sensibility.
(8 -161)
9)
The synthesis of ~pprehension is therefore subject to
the conditions of synthesis of a manifold given in
intuition in general (the categories).
(B 161)
10)
The categories are conditions of the possibility of
experience.
Although the chapter on the Schematism of the Pure Concepts of
Understanding impresses me , as being absolutely crucial to an understanding. of the relationship between the categories and intuition, I
have not been able to work out all" the details that a complete interpretation would demand.
The basic problem which the Schemata are
introduced .to solve seems clear enough; the precise
schema is, · at least to
char~cter
of the
me, mysterious.
We know that all intuitions given under the forms of space and time are
subject to the categories--the proof of this was the main burden of the
Transcendental Deduction.
additional difficulty:
This subjection,
ho~ever,
creates an
How can the pure categories be contained in
�-44-
appearances?
The categories are, as Kant has frequently reiterated,
forms of the necessary combination of the manifold given in any intuition;
es such they are absolutely unlike any empirical intuitions.
f"rom the·
example Kant provides, we gather that he means -that the necessary sequence
of ·caus-e ' and effect thought in the concept of causality can never be
'met with' in any intuition which merely presents a series of appearances.
(This argument, in a sense, depends on a dominant conviction of
the Critique, that 'necessity' can never be given in appearances but
rather comes to
~ppearances
through the workings of the understanding.
In other words, necessity is a requ'irement of the mind, not an appearance of 'things' or objects given in intuition.)
Since, then, the
categories are, in i<an·t ' s words, "quite heterogenous from empirical
intuitions," there ·must be some mediating ground on which category and
intuition can meet.
This meeting-ground is described by Kant as the transcendental schema.
All empirical ·intuitions are, as has been said more than once, subject
9
to the "formal condition of the manifold of inner sense";5 namely, time.
Time itself when it is determined by the transcendental synthesis of
imagination--a process
~~scribed
in the Deduction--is homogenous with
the category which, by way of the unity of apperception, constitutes
the unity of time.
Thus the transcendental determination of time through
rules given to the imagination in the categories will make possible the
application of the categories to the empirical manifold which must
satisfy the conditions of the form of all sensibility.
specific example in order to make this clearer.
concept of causality.,
whi~h ·
Let us take a
As Kant has said, the
posits a necessary sequence, can never be
met with in appearances; however, time itself is so determined by the
figurative synthesis that appearances given in intuition follow one
another in time:
consequently, the imagination can produce a a·chema
of the concept of causality through which the succession of appearances
60
in the empirical manifold is brought under a rule.
This rule is
expressed in the concept and directs the synthesis of imagination in
relation to the pure manifold contained in the intuition of time, and
hence, the empirical manifold which is subject to time.
59
B 177
60
This rule is not formulated until we reach the Principles of Pura
Understanding, it is given in the Second Analogy of Experience q.v.
(B 233-234 in particular).
�-45-
This much seems reasonably clear; however, the character of ' these
necessary schemata is by no means transparent.
th~m
Kant distinguishes
from 'images' (the product of the 'reproductive synthesis of
imagination',) with the .result that the ·schema is not a picture, as it
fig~re · (~.g.,
were, of a concrete intuition or a single detetminate
the number five or an isosceles triangle).
Kant's words,
0
Instead, the schema is, in
the representation of a universal procedure o;f ths
imagination iQ pr_
ovi.ding an image for a concept."
~
describe.s the . schema as
61
were~
"product and, · as it
· Later, · Ka.nt
a moriogram; of pure
The only other mention of monogram that· I
could locate in.the Critigue occurs in the Ideal of
Pu~e A~~son ·
in
I am not certain th~t the attributes of a monogram discussed
passage are applicable to the schema, but they
suggestive.
~re
(B 592);
that
nonetheless
The , monogram is "a. mere set of particular ·qualities, deter-
mined by no assignable rule, and forming rather a blurred sketch drawn
from diverse experiences than a determinate image"; it is, further, a
"modes of possible empirical intuitions".
The difficulty with this passage is that it is apparently considering
the empirical rather than the transcendental schemata.
In the latter
case, the monogram is certainly determined by assignable rules, indeed,
its creation depends on the synthesis of imagination in accordance with
rules given in the categories.
However, inasmuch as Kant uses examples
of empirical concepts (dog -- B 180) to illustrate what he intends by
'schema', it may be valid to think of the 'schema' of an empirical
3
1ncommun1ca lb e s ha d owy image 116 wh ic h is possi bl e on l y
64
. .
...
~
"b · ·
b ecause o f th e a priori sc1.1ema t a ot pure sensi 1 1 1 t y.
concep t as an
0
0
0
0
0
0
II
The heart of Kant's argument is that the categories can only have
'objective validity• if they are schematized.
The schemata are mediating
representations · produced by the synthesis of imagination and are
"nothing but a priori determinations of time in accordance with rules. 1165
61
8 174
62
8 181
63
8 598
64
These are the schemata given in 8 182 - B 184.
65
8 184
�-46-
It is only through this mediation that the pure concepts of the understanding can be given an object and hence be the conditions of all
a priori knowledge of objects.
Without 'objects•, the categories are
the bare logical forms of thought in general and can yield no
determinate
knowledge~
With this my exposition of Kant's doctrine of the imagin3tion as presented in th• Transcendental Deduction is at an end, or perhaps I should
say, has now reached a point where it is possible to explore the significance of the varied and .complex expressions and arguments which I
have reviewed and attempted to interpret in the first section of this ·
paP.er.
Exploration hare will be largely a matter of . ~rying to decide
where emphasis is to be placed; in so doing I hope to answer the
principal question to which this paper is addressed:
Why is the
imagination necessary?
(Continued)
�-47-
EXPLORATION
If I were to choose one theme of the Transcendental Analytic which
might be said ~a be the ~ost consequential, my choice would probably
~e
'synthesis'.
Kant seems to me mqst interested in demonstrating
concepts derived from experience analytically in every case
66
presuppose a synthesis which is prior to all experience.
· If the·
th~t
mind is to be in a position to abstract a ·common characteristic from
several. objects, _these objects must be . held together before . the mind;
yet even before this is possible, the manifold of divsrse representations must be organized and unified so as to yield the representations
67
of a single object.
This implies that successive representations
must be connected. with one another according to rules contained in the
understandi_ g, for appearances !2.Y_ themselves can never exhibit
n
connection.
These rules, Kant argues, are rule·s of the procedure
whereby the form of all sensibility--time--is determined through the
synthesis of the imagination.
The imagination, if it is a separate
facility, might _be called the faculty of synthesis, as the understanding
is the faculty of the rules of synthesis.
Even the ground of the
possibility of any employment of the understanding--the synthetic unity
of apperception--implies in its · very name a corresponding synthesis
of empirical. consciousness and the manifold contained in empirical
consciousness, regardless of the manher in which -the manifold is given
68
to the sensibility.
I would even venture to say that the synthesis
intellectualis which "is thought in the mere category in respect of the
manifold of an intuition in general" is in some sense a synthesis of
69
the imagination although devoid of any empirical content.
In short,
synthesis is the absolutely crucial factor in all knowledge of objects
(experience) and, accordingly, the faculty of
synthe~is--the
imagination--
is indispensible.
66
67
68
69
Again I would argue that this priority is logical and not temporal.
Cf. the· important note to 8 133.
See 8 135 and A 118
For 'synthesis intellectualis' see 8 151: In A 118 it is said
· that 'the transcendent~! unity of the synthesis of imagination is
the pure form of all possible knowledge! · Also in 8 103, synthesis
in general is said to be the "result of the power of imagination."
�-48-
This answer, however, is not entirely satisfactory.
We are faced with
a new question which seeks the source of the indispensability of tha
imagination in the constitution of the human mind:
necessary?
Why is 'synthesis'
Kant, it seems to me, offers indirect answers to this
question on many occasions.
It may have been noted that in my exposi-
tion of the Transcendental Deduction I omitted any mention of several
paragraphs having to do with 'intellectual intuition' and the limits or
~onditions of human underatanding. 70 The clue tn the discovery of the
necessity of the imagination is, I think, contained in those passages
and in the chapter ent_
itled "The Ground of the Distinction of all Objects
in General Into Phenomena and Noumena.'
The representation 'I' or -'I think' which is generated by the selfconsciousness is simple, that is, no manifold is represented in it.
I
can only become conscious of the identity of the self in respect to all
representations if a manifold be given to me through the senses, that is,
through sensible intuition.
consciousness- give a
Our understanding can never through self-
~nifold;
objects come _o us through the
t
sensibility.
An understanding which did, through its own representatio_ , give a manifold would be intuitive. 71 such an understanding
n
"would not require, for the unity of consciousness, a spe.cial act of
synthesis of the manif.old",
72
namely, the transcendental synthesis of
.imagination.
Kant also uses the phrase "intellectual intuition" to signify an
operation through which objects . are presented to the mind immediately,
that is, not .t hrough
Kant
73
insists repeatedly that human beings lack such a mode of intuition.
affe~tions
of a merely receptive faculty.
Thus, the understanding in human beings is 'discursive'.
Although
Kant generally uses this term to mean that the understanding thinks its
objects mediately through concepts, it has, I think, another significance
70
In particular B 135 (end), B 139, ·s 145, B 149. It is noteworthy
that there are no discussions corresponding to these in the first
71
.e dition.
8 135
72
73
8 139
G 8 72, A 249, A 307
�-49-
which is important to the present discussion.
a multiplicity which
m~st
'Discursiveness' implies
be passed through over an
int~rval
of .time.
Kn9wledge, however, demands the unity of a multiplicity of representations. · Hence, the manifold that is given iii time must be .combined.
The
ways in which this manifold 6an be combined must correspond . to the ways
in which time itself, considered as the intuition · of a pure manifold,
can be combined (i.e. the transcendental schemata). ·
The schemata are the products of the imagination--" a blind but
.
74
indispen_ able function of the soul" --and are the grounds of the
s
objective validity, that is, of the relation of the categories to
possible intuitions.
The upshot of these ideas seems to me easily inferred yet rich in
philosop~ic
and historical significance.
The operations of human under-
stan~ing,
if they are to make 'experience' p6ssible~ are inextricable
75
from time.
Dissimilar characteristics of a single object are, for
Kant, given in successive intuitions and consequently must be connected
in an act of synthesis which is governed by the schemata and, ultimately,
the synthetic unity of pure apperception.
The relationships between
appearances are not given in the appearances themselves but are imposed
on them by the
und~rstanding.
In short, the 'categories' are not .
understood or grasped in the perception of objects but rather make
objects of perception possible.
What this amounts to, it seems to me,
is a den i a l of the possibility of vous as it is described by Aristotle
(and, possibly, Plat6).
intuition or perception
Nous is a faculty (dyhamis ) of intellectual
as such it is related to 'intelligibles'
76
as sense-perception is related to 'sensibles'
Nous, when it is in
~nd
act, 'becomes' the object of
.
thought~
77
or, to · render Aristotle's
thought in Kantian language, the understanding is a receptive faculty
and is therefore 'affected' by the intelligible forms which are capable
of affecting it.
For Kant, on the contrary, the understanding imposes
form on the sensible representations; what are, for Aristotle, the
74
B 103
75
76
Kant enjoins us to keep this in mind in A .99.
De Anima, 427 a 18 ff.
Ibid • , 4 31 a 1
77
�-50-
. '.objects.
~_f.
.. kryowledge' are for Kant the conditions of knowledge.
sameness and difference, to
~a~e
~nity,
only the most important relationships,
are 'intellectually perceived' and thus truly known according to
-Aristotle.
Moreover, the intelligible forms are known and judged in an
~indivisible time and by an indivisi~le function of the sou1 178 the
form_percei~ed
is .by its own nature unitary and requires no synthesis
which has its source in the understanding.
Perhaps the differences I am trying to articulate can be best illustrated
by comparing the notion of 'concept' and the notion of 'intelligible
form'.
Concept is, as Kant makes clear, more of a function than an
79
entity in its own right
--it is a 'holding together' of successive
and, it may be, qualitatively different representations.
The
'intelligible form' is the actuality of a thing by virtue of which it
is this one thing and not something else.
(Kant appears to have
neglected the problem of the differences between empirical concepts
and therefore between objects of experience; this neglect may have been
intentional inasmuch as he is talking about the object-in-general and
80
not about particular objects.
The acts of the mind corresponding
to the concept and the 'form' are conceiving, i.e. judging, and 'insight'
or 'intuition' of the intelligible form'.
Through the former we
subsume sensuous representations under logical functions--this is known
as 'thinking an object through concepts; through latter, the understanding, which is in itself potential, becomes the actuality of the
thing perceived.
Without judging the merits of the two accounts, we
can still remark that knowledge, as Kant describes it, is no longer a
relational. term, that is, there . is no knowledge of what is in itself
knowable; but rather knowledge is a mode of relating representations
to objects so as to make experience possible.
To resume and conclude the discussion of the imagination, let me say
that because the understanding exists and acts within time, a gathering
78
79
80
Ibid., 430 b 15 ff. Perhaps this is true only of the intelligible
form of an object, and not of the relational categories. The whole
passage in which this phrase occurs is quite mysterious to me at
present. Nevertheless, it is surely a crucial text for any attempt
at comparing Kant with Aristotle. Cf. alee 426 b 20.
Critique, 8 93-94, B 134 note.
8 128
�a
reversal
statement
14-23
82
3
8 197
�-52-
DOGillOOb AND JUDAS
Charles· G. Bell .
If the dogwood were named snow-maiden --
Being that
pure~
geometric,
fr~gile
One of those Flo- entina prof Hes -r
A dawn-f louier; .
And the Judas -- spilling wine-purple
Buds from trunk and branches -- called
Venetian putana -- so flushed
With noon's orgies:--
Would it seem strange that here
In the one ground and season of the heart
They bloom together?
..
�-53-
Charles
are
�-54-
CAVE Of SOUND
Charles G. Bell
..
of concentration in the American home.
We pitch above ourselves a shelter of densely v·aulted sound
There is a new
p~ace
Put on a re·c ord of Bach, advance the dial,
Boost the vocal and orchestral noise.
...
The study where I sit in the child-crowded house
Becomes a plenum of tone:
Cum Sancto Spiritu
.!!:!. Gloria Dai Patria, Amen.
Cries of children, desperate pleas of wives,
All loves, all obligations, g·o down for the third time.
Who am I to turn lifesaver for any but my own thought's child?
One voice requires my attention
You call it self, I call it God
In either case, space charged with music,
It heaps and furrows under a roof of sound
The cave of silence, the cyclop's.forge:
"Bongo, bongo, bongo, I don't aim to leave the Congo."
D1shes crash in the distance.
How should I wake but for the coming of the lord?
�-55-
Charles G..
also
art is a
so eager
terms to be made conduits
serv
a
a
spr
Slows
There
go
hill
nose
s
sewerage
�-56-
NOTES ON THE PORTfOLIO
James Gilbert
During the school year of 1964-65, I conducted a Life Class in the
St. John's Art Studio on Tuesday evenings until the middle of March.
It was well attended by townspeople and by several St. John's students
and faculty members as well.
The moderate fees more than paid for the
models and art materials supplied, and, together with the Collegian,
I have had six drawings done in the class reproduced for this issue.
In choosing them I naturally have favored the work of people connected
with the Collage and drawings which I . thought would reproduce wall.
I have also tried to give some idea of the very wide variety of talents
represented in this group, which has been the most interesting and
rewarding it hAs ever been
~y
privilege to
coriduct~
The .artists
represented in order of appearance are: Bret fields, Judy Millspaugh,
David Jones, Michael Gessner, Charles Lainb and Kay Holden.
�-~
J
--
�l1 I
l1 fl
1/
1
;;f
I
l ii;;· ('p,.!,~ ~>/
I
I
!
I
,I
~
i
I,/ ) ,
I
I J(,
'
�����-57-
AN INTRODUCTION TO THE PROBLEM OF JUSTICE*
Laurence Berns
I ·am, very gr_
?lteful to the Hillel Foundation for asking me to help plan
and take patt in this series.
But I am a bit troubled oy my assignment,
which _ to provide a general introduction to · the series.
is
of
justic~.
The
qu~stion
ar.ises naturally out of concrete political and social problems,
and mo.s t of the other speakers in the series oegin from such problems.
It may .1:be that like so many so-called introductions this disucssion
·..
should be at the end.
But perhaps not.
Now, I might have tried to
present a oroad historical survey of the many different opinions aoout
justice.
But I thought it would be more useful if I tried to present
a somewhat more thorough account of two or three of the most influential
statem~nts
aoout justice,
what closer
statement~ · w~ich
in my opinion have a some-
to that justice which exists in actual political
r~lation
practice. _. The bulk of my remarks will be about the discussion of
jus~~ce .
in Aristotle's Nichomachean Ethics and Hoooes' Le0iathan, with
some. references to Plato's Republic.
Two of these great writers, Plata and Aristotle, in order to make sure
fhat they are talking aoout that justice which exists in practical
political life oegin their inquiries oy spelling out what is implicit
in most men's common . experience of justice and injustice.
in
th~
Aristotle
fifth cook of his Ethics oegins his discussion of what most
people · mean oy justice with a discussion of what they say aoout injustice.
Complaints about injustice must have always been more
prevalent than praises of justice.
There is probaoly no one here who
has never complained aoout oeing cheated or about oeing graded unfairly
on an examination.
But when one complains aoout injustice or unfairness,
one is speaking aoout the aosence of justice or fairness.
And it seems
to oe reasonaole for reasonaole people to spell out what is implicit in
what they do and say.
Generally speaking the unjust man is blamed as one who creaks the rules
.
.
..
.
. .
or the laws and who always tries to get more than his share of anything
..
good~
so · the just man, if we reason .from his :opposite, would oe he
who always tries to follow the rules' or the laws and is always fair and
* A lecture delivered at the Bnai Brith Hillel Center, University of
Chicago, January 1959, beginning a series of lectures entitled, "On
Justice".
�-58Aristotle'~
equitable.
discussion in book five of his Ethics, I think
it might be shown, is cased upon a careful analysis and development of
these ·two general notions.
But we must be more precise.
We speak aoout just actions, just
men~
and just associations, and these
senses of the ·word are interdepen~ent.
A man is just· ·who performs · just
· actions, out ·sometimes an unjust man performs just ·actions in order to
ouild up the kind of reputation which will allow him to practise injustice on
a larger
scale.
And sometimes an unjust man, say a
SW
indle.r 1
by ~ccident ~oe~ so~ething just; either out of igno~ance, say he was
mistaken aoout prices, or out of force, perhaps plain physical force,
someon~
actually twisting his arm, or a less tangible force, fear of
exposure.
So it is not enough to perform just actions in order to be
a just man.
~ just man wants to perform just actions know~ng fhat they
are just actions.
Justice, when it characterizes a man refers to a
haoit ·or fixed disposition to act justly; and not a blind habit but a
habit of voluntarily, or, Bven more, deliberately choosing to act justly.
Therefore, al though acting justly may as easy, being'· a just man is more
difficult.
man.
of
The same may oe said of acting unjustly and
b~ing
an
~njust
Sometimes a man performs an unjust action, harming someone, because
mistak~n
carried away
ide.ntHy or from ·compulsion again, physical for.c a, . or oaing ·
by
anger · OJ: some other passion which is natural. or naces·s ary
.......-- . _,.
The man who performs the unjust action may be weak, out ha is
to man.
not necessarily unjust.
He is not an ·unjust man if it was not within
his power n.o t to .do the act. · The person who caused his anger may oe
responsible .
Here, with the case of the man who acts unjustly but is
not himself unjust, we approach the theme of many tragedies, think of
Othello and Iago.
..
Where there is injustice there are always unjust actions,
but where there are unjust actions there is riot always injustice • . Injustice, according to . Aristotle, is the ·habit or settled disposition to
want and
del~berately
choose to do unjust actions.
Being such a man
also is not easy, if for no other reason than that it is very dangerous:
again, think of Iago, or perhaps Nazi and Soviet chiefs of the secret
police, or Lear'$ older · daughters.
But it may be that at this point it is no longe·r
poa~ible
to rely only
upon our common sense understanding of ·what just and unjust mean.
I
�-59-
have been usirig the terms as if we understood. _
what they mean.
But the
distinction ·o etween a · kind. of act·ion and. the haoit or state of ch. racter
a
that regu1a·r 1y is"sues ·in that kintj of action, this .distinction applies
to ~11 the virtues~ ·what is ·it th~t makes an ~ction just?
Justice is known as the social virtue.
It is usually spoken of with a
view to . the kind .of association that results from our actions;
we speak aoout justice and
injustic~
Althpughi ~/
.
.
~.
'
with reference to all kinds of
associations and persons, the terms are used primarily with reference
to the political association.
Of such justice, Aristotle tells us, there
are two kinds, distrioutive justice and correct~ve justice.
Distrioutive
justice is·exercised in the.distribution of all those things which can
be divided am9ng those who are ass~ciated in the political community.
Such things.are honor, office
peo~le
(which is what some
power), money, safety and so forth.
today call
The distr ioution is just when there
.
.
is a proportional equality between the merits of the·persons concerned
·and the shares they have ceen allotted.
8, his share sh<;>uld o:e· that 111uch
or
deser~,
l~rger
If person A is better than person
than 8' s
of the persons is measured by the
tion to the common
association·.
good, ~ general
share~
~xtent
welfare, or the
of
And the mer it,
thei~
ov~ra11 ·
bontribu-
goal of the
Let .me illustrate by a homey example, which is not political,
out which will help· confirm the remark made earlier that it is not easy,
not even for a ,criminal, to oe a fully unjust
roooers, preferably oank roboers.
~
definite order ·of distr ioution is
The boss , who orga~ized and · .
worked out oefore the job , is attempted .
enginesred the joo, gets 25% of the take.
greate~t ~isk.
the common endeavor they
away car gets 15%.
g~t
Take a gang of'
In every well-ordered gang, I learn
·from the literature and the movies,
· the · oank take the
man~
The two men who
~ust
go ·inside
In proportion to their contrioution ·to
20% each.
The skilled . driver of the get-
The guard who sits oeside the driver and who opens
the.. car door when_~he , inside men come out gets only 10%, and oesides he
is young ·and
inexp~rience~.
In order for the joo to oe
~ccompli~hed ·
successfully, a certain order or hierarchy of functions, per·sons and
rewards or punishments must oe observed.
On the lowest possiole level,
a certain order of distrioutive justice must exist oetween those engaged
in ~ny · co8perative activity. -As. the boss and . his merit er~ to .the getaway driver and his me~it~ ~o · sh6old the ~sward of · the boss be related to
�-60-
the reward of the driver.
As Achilles is to Agamemnon, so the honor paid
to Achilles should be to the honor paid to Agamemnon.
As Moses surpasses
Aaron, so the honor paid to moses should surpass the honor paid to Aaron.
Perhaps it should be mentioned that generally the Greeks held that the
greatest reward the community could oestow upon a man was rule, or political authority.
Battles and arguments arise when men who are equal are
distrioutad unequal shares.
aoout.
This is what egalitarians complain most
Arguments also arise when men who are unequal are distriouted
equal shares.
This is what the oligarchic and aristocratic parties com-
plain aoout.
for instance, when the oligarchs say, there must be greater
incentives for initiative and enterprise.
To repeat, the merit or desert
of the persons is determined oy the extent of their contribution to the
common goal of the association.
Sound government, then, from this point
of view must be based upon an adequate understanding of the personal
qualities of the citizens.
Every legal and political order (not to speak
of every association) from this point of . view is constituted oy a certain
order of distrioutive justice, or a certain distribution of power [taken
in the broadest sense] among different kinds of persons.
That is to say,
every legal and political order encourages the development of certain
kinds of people and discourages the development of other kinds.
What
Aristotle seems to suggest is that perhaps the ultimate test for determining the worth of any law, legal system, or political order is to be
found in the quality of the people it tends to produce and encourage, and
the quality of those it tends to discourage and eliminate.*
Part of
the reasoning behind this linking of personality or character and politics
goes like this:
Most people usually decide to follow a way of life
oecause they want to oe like those they look up to, and those they look
up to are usually those who are in positions of the greatest responsioility,
political responsioility.
One might say that the overall style of a
society is largely determined by those holding the highest political
off ices.
The idea in Aristotle which expresses the inherent connection
between way of life and political and legal order is the politeia, or
regime, or constitution.
* This would oe a decisive consideration for working out the classical
approach to foreign policy, i.e. for applying this standard of justice
to international relations.
�-61' Aristotle seemed to think that up .to this point he was not saying. any~ery
. thing
controversial, merely making explicit what .almost all men think
. acout justice.
Everyone agrees, he .said, that distrioutions ought to oe
maqe acpording to merit or desert of some sort, that sort. of merit which
contrioutes most to the
~haring
of a good life.
But when they oegin
spelling out what the standard of merit is, controversy arises.
Parti-
sans of democracy say that just oeing an ordinary free citizen entitles
one to a full share in the goods of the community, oligarchs say that
we~lth : ls
the oest title, for the wealthy pay .more taxes and wealth is
·usually a sign of initiative and responsioility.
a~isto6racy · sa~
tr~e
merit.
The partisans of
that personal excellence or virtue is what constitutes
·the
p~rtisans
of virtue, alas, hardly ever have much poli-
tical power. · ·If they become politically effective, it is usually through
some connection with one or oath of the other major factions of political
life • .
Ar~stotle
thought that the sharing of a good life meant the shar-
ing of a virtuous . life.
so,
tho~ght
..
rew~rds
.I',·
. '.
He sided with the adherents of aristocracy, and,
that the best •.society distrioutes its authority, honor and
.
.
.in proportion to each citizen's contribution to the
of
~haring
a life of virtue.
The
othe~
kind of justice Aristotle ·speaks of is corrective justice,
which is concerned with correcting inequities in private transactions.
This kind of justice consists not in proportional equality oetween
par~
sons and shares, out in what· Aristotle calls arithmetic equality.
This
kind of justice pertains to contractual activities like buying and selling, and hiring, and crimes like theft and roooery.
It presupposes
fairly definite notions of property and law, notions set and determined
oy the more fundamental order of distributive justice.
It lsads to ·
such notions as a fair or just price and a just wage as well as the ·
notions which guide criminal proceedlngs.
Justice here consists in sub-
tracting what was gained fairly or unfairly from one party and adding
what was lost to another.
What is suotracted from a culprit should cie
equal to what was lost oy his victim.
decided in an
analogb~s : manner
Criminal proceedings are
oy restoring whatever can
to
oe
be restor~d~
and oy trying to make the severity of . the punishment equal to the badness of .the crime.
�-62-
We ~ight · sum thia u~with the ti~ditio~al definition of justice:
Justice
is a haoit wheraoy a .man rer,ders to each his- due, · and he do&a so Decauae
he wants to~
Neither ~n public a·f fahs nor in .. pr iv ate does he seek to
distrfoute · more of good . ~hings to himself · and :· leaa. to his neighoors,
that iS to ·say, more and less than each d'eserve.
II
·.· But ·few men ha_ ever denied that some justice is necessary for social
ve
life, what
~en
disagree about is the status or the dignity of justice •
.
·Is it as some men ·say that neither the evening star nor morning star
. is as wonderful as justice? Or is . justice something much more humole?
This proolem until more
red~nt
times was
alw~ys
discussed in terms of
whether justice is natura1 or conventional.
from almost the e·a rliest times of Greek philosophy a fundamental distinction was drawn oetween the natural and the artificial or conventional.
The natural is what is primary,
fund~mental
and persistent.
The artificial or conventional is secondary, derivative and transient.
It depends
upo~
voluntary acts of man for its
exi~tence •.
Nature,
·according to the Greek philosophers, partly oecause it determines the
' very frame~ork within which everything else moves is of a h~gher dignity
than art or conventiori. Laws, of course, cecause · t~ey are dependent
upon human en,actrnent · ·a.re conventional • . In fact, the word for oath
legal · and conventional ·is the same in
Gre.~,I< ~
,
when the
Gr~eks
Therefore, to repeat,
.
argue·d aoout the status of . justice it was · generally a
. question of whether
it was : rooted in the nature of
man~
or
~hether
it
was merely conventional.·· · Are man . jus.t .t>Y nature, or are they just
merely .because of the compulsion of the laws?
Aristotle's answer to
the . question is oy no means unamoiguous and has been inter·preted in
, v~ry dif~erent w~y~ by . very competent interpretors. ~e ~vidently
.~ eject~d .
}
\
both
'
extrem~$~
One approach might be as follows:
He seems
~atural
or wholly
.·to say that justice· caMnot .be called either wholly
co~v~nti~nal, out ' d~~ends upon ·a certain co8peration b~tween nature
and convention, or nature and art.
tical.
man .is oy natura social and poli-
That is to say, the impulse to form a political society exists
in all men oy nature.
And the goals of political society are also set
�-63-
But the actual drganization of the men,
oy nature, by human nature.
the formation of the political order, is created oy the government and
by the law, by convention through the ·human arts of legislation and
d
gove'rnment • . ;Justice, then, which would prevail if the political or_ er
were rightly formed, would be dependant upon oath nature and convention; nature providing the impulse and end, and art and convention
supplying the organization and institutions which ordo-r men towards that
end.*
But is man oy nature social?
Should we ·not try to do justice to the
argument for injustice?
At the oeginning of oook two
~f
Plato's Repuolic, two bold young men,
Glaucon and Adeimantus, challenge Socrates to prove that it is truly ·
better to ·oe just than to oe unjust.
In order for the proof to . be
conclusive the oest possiole case for the life of injustice must be
made and refuted.
They make that case and the rest of the Repuolic
constitutes Socrates's reply.
aoout
~here
Both
to look for the ultimate
part~e~
to the argument agree
standa~d
of
goodn~ss.
They look
to what holds true everywhere and always with the same force, which
derives its authority from natural necessity and not from any arbitrary ·
human enactment or opinion.
They search for what is truly in accordance
with the nature of man, what is oy nature good instead of what is good
merely because some man or men say so.
And oy nature, Glaucon says,
ta commit injustice is good out to suffer it is evil.
So what is oest
oy nature would be to oe aole to commit injustice without ever being
punished and without ever suffering from the injustice of others, - pure
pleasure and no pain.
It takes a real man to _
live like that, the
praisers of injustice say.
on a grand scale.
Most men lack the power to commit injustice
Therefore, for most men the evil from suffering
injustice outweighs the good they can get from committing injustice.
The many weak, who lack the power or virtue to do what they would really
like to do, .out of fear and self-interest make a compact with each
other
~either
to commit nor suffer injustice.
This is the qrigin of
* Thus nature provides three of the four causes. But the cause which
most of all dete~mines the ch~racter of the political community is
supplied oy human art and conventibn, hence. the political community
reflects the character of those who govern it and give it its laws .
�-64covenants and law among men, and the commandments of the law are what
they call lawful and just.
Justice, then, is in fact approved only as
a poor, conventional substitute for the life of injustice.
A good man,
a man of spirit, would endeavor to rise aoove the pettiness of a life of
justice.
He would never suoject himself to mere convention, Glaucon
asserts.
But how do we know that What the praisers of injustice say acout human
nature is true?
Glaucon t:Jids us to make a mental experiment:
imagine
both the just and unjust man with complete license and power to do
whatever they want.
the same conduct.
You would then see coth led by natural
~esire
to
As Glaucon puts it, every nature naturally pursues
_
its own se_fish e-dvantage as good.
l
It is only by · the compu.lsion of
convention or law that man are led a·s tray to concern themselves with
oth~rs
_
and pay honor to justice.
tells the following story:
To illustrate his thesis, · G1aucon
a certain shepherd, an ancestor of the Gyges
~hat He~odotus tells aoout~ found a ring which ~nabled him to make
When he turned the s~one to f~e . in~ide of his hand
himself invisiole.
he
be~ame ~nv~s~ble,
when he turned it .outside egain he became visicle.
Glaucon, in a way, asks u~: · what would you do if yo~ had such a ring?
What did the shepherd do?
After testing the power of the ring he
contrived to have himself sent as a messenger to the king.
Once at
court ha seduced the king's wife and with her help killed the king and
seized control of the kingdom.
If there were two such rings, Glaucon
says, and both the just and the unjust man possessed them, there
would be no difference in their behaviour . · The social virtue , just i ce ,
giving each man his due, ie not good in itself, not good by nature.
It is not good by nature because man is not oy nature social.
man is by
nature selfish and grasping.
It is
intetes~ing
to reflect upon how Glaucon goes about finding those
purposes which the great guide,- nature, has set down for man.
It is
as if what is social hides what is natural. · Invisioility removes all
public pressures, all social pressures, and allows you to test whether
an action is good or oad in itself, regardless of what other people
say, think, or do aoout it.
Something which is against nature or
nature bad carries its own punishment
or alcoholism.
alon~ · with
.
~y
itself,. like gluttony
Something -which is oy nature -good carries its own reward
.
' ·
-.
�-65-
along with
or
i~
it~elf,
like health. · What aoout injustice?
getting caught at it cad?
Is it really oad,
And what aoout justice, is _ really
it
goo~, or is it only appearing to oe ju~~ which . is really good?
III
ffiodar ·n thinkers generally have tended to agree more with Glaucon than
with Socrates and Aristotle, and some have tried· to achieve something
of a synthesis of oath views.
One of the most important was Thomas
Hoboes, who lived during the seventeenth century.
Hoooes opposed him-
self to all earlier writers and c·laimed that tie· far the first time had
treat~d
politics and morals scientifically, that is, geometrically.
He had met Galileo
an~
perhaps thought that he
politics- what Galileo was doing for physics.
~imself
.
'
looked
whose
~ould
dri f6r morals and
Hoobes also addressed
fa the problem of the status and content of ' ju~tice.
~o
nature for guidance, out in a different
views he attacked .•
w~y · from
He also
the men
Human oehaviour, -according to Hobbes, is to
be understood primarily in terms of the passions, those forces in man
which, so to speak, push him from behind.
·in
It is not to oe understood
terms of the objects of the passions, those things which could be
thought of as attracting man from in front.
control the passions, just the reverse, for:
for the thoughts do not
"The Thoughts are to the
Desires as Scouts and Sp!as to range aoroad and find the way to the
Thing Desired."
The thoughts are instrumental to the desires and passions.
And, for example, courage, which is discussed oy Plato and Aristotle
as a virtue, is discussed by Hoooes as a passion .
Keeping in mind the
idea of the primacy of passion, how did Hoooes look to nature as a guide
for understanding justice?
We simply infer from our knowledge of the
passions what the condition of mankind would oe when there is no civil
society,
wh~ch,
for Hobbes, means whenever thera is no common power set
over men fo keep ~hem in fear.
However, the idea of the state of nature
is not merely hypothetical, he says.
dti~ing
This is the condition of men
civil war and the condition of kings and sovere~gns relative to
ea.ch other (also the condition in many different #laces of the world he ~~~tion~ America as one). ; How are men-related · to each oth~r in the
·state of nature, acco,rding to .Hobbes?_ --1) oy competi.tio·n which makes
~hem ene~ies with anyone who _desires ·What they desire; ~) by diffidence
or distrust 'which makes men apt to destroy everyone who might endanger
�-66the~selves;
3) .oy vanity or glory which is the desire of men to have
others value them as they value themselves.
of every man
again~t
much like Glaucon's:
every .man.
~eek
aoout all men.
So far Hoooes' position sounds very
Man is not oy nature social, on the contrary,
nature dissociates man.
they are too
ln short, there is a war
But what Glaucon says aoout most men, that
and cowardly to live according to nature, Honoes says
for, according to Hoooes, all men are equal in the
decisive respect, the aoility to kill any other.
Consequently, what is
worst of all in: .t he state of nature is · the "continual fear and danger
of violent· death; And ··t he life of man, [isJ solitary, poor, nasty,
brutish :and · short .• •'
There is nothing ennobling aoout the state of
nature, nature is no longer looked to cy Hoooaa as a direct guide ·to
goodness, out rather as
~hat
indicates to man what he has to run away
from. · We are already in an atmosphere congenial to the thought of the
conquest ·of nature.
In the state of nature, or state of war, there is
no law, no justice or injustice, and no· property beyond mere possession.
The only redeeming thing about the state of nature is the possibility of
getting out of it. fear of death, desire for comfort, and hope to
attain safety and comfort incline men to peace ;, and reason auoservient
to these passions suggests rules for peaceful living together. These
rules Hoobes calls natural laws. In ~sing this name . he admits he is
bowing to traditional usage, the rules are merely theorems or conclusions concerning What conduces to self-preservation.
Corresponding
to the most powerful passion, fear of violent death, ~nd dependent
upon it, is the oasic right of nature, an individual right, the .right ·
to
self-prese~vation.
men enter into society with each ·other for th
sake of their selfish interest in self-preservation and security.
Neither freedom, nor wealth, nor virtue is the goal of a Hoocesian
society, rather it is peace and security.
The first and fundamental
law of nature, Hobbes says, is: · "Seek peace and follow it."
Since in
the state of nature every fear is reasrinabla and n6 action can be
called unjust · or wrong, every fuan had
~
right to
everything~
men can
seek peace only by mutually. laying down this right to all things, and
the seconp law of nature enjoins men to do just that.
laying down .of rights is the
soci~l
t6ntract.
By
~his
This mutual
social contract
or covenant where every man mutually· transfers his right to all things
to the sovereign power, oy ,this social . contract civil society is
�-67-
, constituted.
And · since there
is . ~o
morality in the
~tat~
of nature,
all morality is also derived from the social contract, "there oeing no
· Ooligation on any man, which ar iseth not from some -Act of his own .... "
Civil society; then, and morality are dafinitely artificial or conventional,. aceording "to
Ho6o~s.
But, contrary to the
vi~ws
of all earlier
political thihker~, · this does not lead to any d~pre6iat!on of their
dignity out rather ·enhances it.
depreciation ' of nature~)
(This, of course, goes along with the
Since society is constituted oy contract or
covenant, the · social or political virtue, justice, consists in the performance of covenants, injustice consists in non-performance.
But
covenants are not valid~ according to Hobbes, if there is fear of nonperformance on eithsr side, ·so oef~re it is correct to use the terms
just or unjust there must be some coercive power, the sovereign, which
can compel men equally to perform their covenants.
says, fear is the passion to oe relied upon.
Once again, Hobbes
In order for a contract
to oe valid the sovereign must see to it that the terror of punishment
is greater than any benefit one can expect from breaking the contract.
Under Hoooes' scheme all that is required of a man to oe just is intel. ligent calculation of self interest.
The fact that he acts justly only
under compulsion does not make a man any the less just for Hoooes.
Compared with what it takes to oe a just man, according to the Aristotelian definition, there is a drastic lowering of moral standards or
moral expectations.
For, according to Hobbes, self interest is the
legitimate oasis of all morality.
One other way we might see how these
different conceptions of human nature issue in different recommendations
for the improvement of political practice is oy examining what Hoooes
says aoout distrioutive justice.
Hoobes addresses himself directly to
the Aristotelian idea of distributive justice.
Distrioutive justice,
Hoooes said, properly conceived is the justice of an aro.itrator and this
consists not in distriouting to each in proportion to his merit or .
desert,
o~t
in treating each as equal.
has made men equal.
If so, that
For,
equali~y
Hoobe~ . says, perhap~
ought to: be
Then no difference in personal merit could exist.
m~de
men unequal.
nature
a~knowledged.
Or perhaps nature has
Yet, he says, men will always consider
them~elves
equal and doing so they will enter into conditions of peace only .an
equal terms.
Therefore, for the sake of peace such equality must be
�-68-
admit.tad_ .e ven if it.· does · not truly. exist.• . Thes9 -differences in personal
,
merit which for Aristotelians deter.mine what proportion ,of the community's
goods a man should have, are said by Hobbe.s to be. 1) either non-existent
or 2) irrelevant · fo.r political . conside.r etions.
s~andard.s
:.bY lowering its moral
The Hoboesian position
move.8 far over in the direction of
egalitarianism. _As Hoobes presents his doctrine, his study of the pas. h~s .
sions,
psychology, de,termi!18e tuhat . is the most powerful and most
fund~menta+
pa.ssion, fe.B;r; this passion becomes the Pas is o,f the .funda-
mental right, the right to self preservation, and determines the fundamental PL:J.rpl?se of civil society, peace . and secur it.y.
mental purpose of civil
Aristotelians,
b~ing
And since the funda-
is less amoitious -- no lpngar, . as wj.th
socie~y
concerned with moral improvement -- moral standards
in general, and the standard of justice _in particular, are . lowered • .
Hoooes could claim that his political scheme makes no utopian ethical
demands upon
~en.
Politics .cecomes the _art of devisiqg
~aw~
and insti-
tutions in such a way that men will ce driven by their own self
into becoming good . citi:z;ens.
int~~est
I think Hobbes would have wished that _what
Macaulay said of Francis Bacon could be said of . him, namely, "in order
to
his foundati1;ma, he went down into those parts of .· human nature
l~y
which lie low, out which are not liable .to change; [so] that the fab~ic
he has reared • • • stands with .such immovable strength."
In conclusion I should like to return for a moment to the proolem posed
in Plato's Repuolic.
_ h~d
the
ri~g
You recall that Glaucon's story -- · of the man who
that could make him invisible -- was offered as part of a
refutation of the notion of justice, the notion of justice· implicit in
what most men say aoout justice.
When any man becomes invis'ible and
'
•.
is removed from public
scr~tiny
and fear of public opinion his natore
asserts its~lf and reveals man to be fundamentally selfish, asocial and
unjust.
But, let us reflect, what does the shepherd with the magic ring
do when he gets to the court?
act.
He conspires with
he~
He seduces the queen, definitely a social
to kill the king --
~lso
social.
himself king; a king requires suojects, this too is social
· political.
~nd
He makes
also ·
And furthermore, if man is by nature unjust, does not .injus-
tice on the lar.gest scale, tyranny, require not just a few men, but
wh~le socie~y to ~xploiti
•
a
Ver~ well, Gla~con might answer, out do not
I
'
.
all these so-called social acts serve .anti-social and purely selfish
purposes?
We, or I, cannot carry the deoate any further, except to won-
der about the test of invisibility itself.
Perhaps Glauconta shepherd
�-69-
was the kind .of man that oy nature needed to have others watching him
in order to live well?
Perhaps, if justice is a social or political
virtue, : it must _
exist in the open where man can both see and understand each other's. mutval needs?
. . ·i'
�-70-
NOTES ON AN EXPERIMENTAL PROGRAM IN DANCE-DRAMA
Georgia Cushman
On May 29, 1965, the first performance qf an.experimental . project in
dance-drama will oe given in the Key Auditorium at St. John's.
As a
former student of St. John's, I am especially happy for this opportunity to return to the college, and to share with the St. John's
community an annual essay of sorts.
The first half of the program will present three solo items from the
traditional dance form of southeast India, Bharata Natyam.
The first item, Alarippu, is an aostract devotional piece which is
used to open each Bharata Natyam program.
Though gestures of the hands
are used in Alarippu, they covey no specific meaning.
The music for
this item is a chanting of the rhythmic syllaoles which follow the
pattern of the footwork.
The second item, Jethiswaram, is also a pure dance, designed to show
the technique through chains of steps called korvais, which are
separated from each other by an episode travelling from the front of
the stage to the back.
The music for this Jethiswaram is in the Raga
Vasanta (Spring), and is much like the Lydian mode of Western music;
the tala, Rupaka, has six units in each phrase.
Jethiswaram is not
a song, out exposes the line of the raga oy using the Indian solfege
syllables corresponding to the Western do - re - mi.
The third item uses gestures of tfue hands to tell a story, and falls
into the Aohinaya category of Bharata Natyam.
The song is of a
particular devotional type called Kirtanam, and tells part of the story
of Rama and Sita, the principal characters in the epic of Valmiki.
The
music was written oy the Telegu composer Tyagaraja, who lived in the
18~
century.
The choreography was done by Rukmini Devi, Director of
the Kalakshetra College of fine Arts in Madras, where all of these
dances were prepared over the two-year period of my fuloright grant.
T~e
Kirtanam, called Rara Sita, is in the Raga Hindola-Vasanta (much
like t•e natural minor scale), and is in rupaka tala.
The text is in
Telegu, and is a devotion to Lord Rama, as well as a story of the oirth
�-71-
of
Sit~,
and of how Rama won her as his oride.
The second part of the program will present Part III of a new production
of the Indian epic and dance-drama, Ramayana.
Ramayana is the ear lie st legend of Ind.i a, and dates from sometime during
the period 2,500 BC
~ 6~
century BC.
There is a tremendous gap in know-
ledge of his tor icai de ta ii through this period; 2, 500 BC is the tenta'tiva
date for the excavations at Mohenjodaro, and the
6~
century BC is the
period aoout which the Mahabharata, India's second great epic, tells.
Between the time of Ramayana and Mahabharata, Hindu civilization has
progressed from an area limited to the Ganges Valley, to an India which
has oeen eompletely
expl~red. 1 )
Rama is one of four princes of Ayodhya, sons of Dasaratha.
The birth
of the princes has come aoout through the prayers of the childless
Das~ratha,
who is given a vessel of the sacred pasaayam by .the .gods.
Each of the three queens of Dasaratha drinks from the vessel, and one,
drinking twice, bears twin sons.
Rama, the child of
Kau~aly~,
is re-
garded as an incarnation of the Lord Vishnu, who as Shri Krishna in
the Mahabharata says, "When goodness grows weak, I make myself a body •••
in every age I come back."
The first adventure of Rama as a young man comes when he and his brother,
lakshmana, go to the forest to destroy evil spirits which have disturbed
the meditations of a sage.
On the way · home, Rama and Lakshmana arrive
at the palace of Janaka, who is the foster father of Sita, the . daughter
of the Earth Goddess, Bhumi.
Rama, breaking .the bow of Shiva in a
contest, wins Sita as his bride.
Sometime after the return of Rama and Sita to Ayodhya, the day approaches
for a successor to the throne to be named.
Kaikeyi, the mother of
Bharata, wishes for her own son to be king, and forces Dasaratha to
grant her · an ancient vow of any two things which Kaikeyi wished • .The
first wish is that Bharata will be king; the second, that Rama will be
banished to the forest for fourteen years.
1)
K. M. Panikkar - A Survey of Indian History
�-72-
Rama accepts his banishment with great calm, and finally comes 'to an
agreement with Sita and Lakshmana that they may accompany him into
the forest.
Having built a hut in the forest, Rama, Sita, and lakshmana spend their
days happily, until the moment when Sita is caught with desire for a
golden deer Which has streaked through the forest.
The golden deer is
magic, a decoy of the demon king, Ravana_ to ensnare Sita for him.s elf.
,
No sooner have Rama and Lakshmana gone to capture the deer, than Ravena
approaches Sita, and carries her away in his aerial car to the kingdom
of Lanka •. · ·
The remainder of Ramayana tells of the long search of Rama for Sita, the
assistance of Hanuman, Lord of the Monkeys, and the final success of a
great battle in Lanka in which Ravena is slain and Sita recovered.
This ~to~y of Rama will for~ parts r· and II of this p~oductioM, which
· the compaMy hopes to c6fuplate in twb more
sea~ons.
The third part of Ramayana is one which is not presented in In.di.a, nor
~s ~he
form
story oulined in the many_popular retellings.
this _ epil~gue
The verses which
to . the story exist as a separate body of. poetry
C. C. Rajagopalachari, whose. retelli~g of
Ramayana has been the guide for this production, says of the epilogue:
''I have followed the ~tor~ · af · th~ Prince of Ay6dhya as told oy Valmiki.
There was a legend current among people, I think even before Valmiki's
time, that ··after · recover!ng Siti, ·for fear of .scandal, Rama· sent h~r
away to 'live in . th~ forest. · This pathetic episode ~ust ha~e ~prung
known as the uttara kaanda.
from the sorrow-laden imagination ' of our · women.
It has taken shape as
the uttara kaanda."
· After her banishment;
~hile wand~rin~
Valmiki, Ulho offers· her refuge.
born in the forest.
in the fotast; Sita . meets
th~
poet
Lava, the. son of Rama an·d s·i ta, ._ is
Cl'ne day, when Lava fs a young boy, Valmiki takes
him to the river to b~the; btit-~ava ~l~yfully st~als back t6 Sit~.
In
horror and fear that Lava ·has ·drown~d ,' Valmiki lays out the 'sacred Kusa
grass in ritual form, and from the ~rass ~i~es Kus~, th~ twin ~t - (a~a.
One day, while Valmiki is . walk1ng
~y
the river in -meditation, two krauncha
�-73-
birda appear in flight,
dies from a hunter's
~nd com~
arro~;
to rest near the poet.
As the
f~m~le
curses the hunter, but repents hi~ curse.
The .maie bird
mourns her mate, Valmiki
At this moment, the poet
utters a line of verse .in new metre and style.
A vision of Lord Brahma
appears before Valmiki, saying, ttfrom sorrow springs
v~~~e, ~nd . fro~
·
this hour will you sing the story of Rama and Sita for . the blessing of
the world."
Having composed Ramayana, Valmiki
t~aches
the poem to Lava and
Kusa~
who leave the forest to sing the story throughout the land.
Finally the twins come to Ayodhya, and to the palace of Rama.
amazed to see his children, receives them tenderly.
Rama,
Lava and Kusa
persuade Rama to go with them to the forest and bring Sita back from
exile.
In the forest, Sita refuses to return tti
Ayodhy~,
mother, Bhumi, to take her back to the Earth.
··forest grove and takes
Sit~
returns with his people tp
Bhumi appears in the
Rama ·1eav~~ ' ;the f ors st and
... ,_ .
A~odhya.
·!
This · production of
.away with her.
and prays to her
~am?yan~
. .
.is an experimental one, combfr1ing'.'·elements
of the Graham techniqu.e . with thqse of Bharata Natyam and Indian · dance,:
drama.·
·from· the Graham techn_;que.
co~~s t~~ r: use
of the Chorus Figure, who is
the first character seen ir . P,rt III, and who appears at .. 6ru6ial moments
during this section. · ,
The '. episode of
·, . . .
Valmi~i ~n~ ~he
Krauncha birds utilizes the great leaps
and spatial· dynamic of the Graham technique; this does not · appear in
the story of Ramayana proper, but is a separate legend about the poet.
The "doet of Rama and Sita as they meet in the forest uses not only
Indian .dance . techniques, but . ritual
step~
of the Hindu marriage ceremony.
Throughout Part I II the old rules of the India·n theatre
hav~
.been
followed, which forbid cio~e · personal ~~ritact on the stage, or -running
and leaping on the part of principal female characters.
�-74The most extensive use of Bharata Natyam comes in the section of Valmiki's
telling of the story to (ava ~nd Kusa.
This is done in the hand gestures
peculiar to the South Indian dance arts.
The Indian dance dramas .were
originally out of doors, and
perfor~ed
settings did not involve the elaborate properties known in the Western
theatre.
It was the duty of the performers to create by their actions a
setting convincing to the spectator.
This production has tried to follow
that principle; on the other hand, ·extensive use has been made of Western
lighting .techniques to tie together the episodic quality of the story.
The .designs for the costumes are almost exclusively Indian.
In many
cases the fabiics a~e indian, and the blue ~ide of the spectrum has
been avoided, as seems to be the rule in most Indian dance-dramas.
The two most important areas of combination of the two techniques are
in the music and in ·t he interpretation of the .s tory.•
The music, which ·was composed by Flora Cushman, who is also a former
student of St. John's, is scored for
ments.
~
chamber orchestra of ten instru-
The instruments are all Western, but were carefully selected
for their ability to take on the qualities of some of the Indian instrum~nts.
:In particular, the use. of the flute, English horn, and bassoon
was planned to give these instruments an opportunity to be used as the
.Indian flute, and the South Indian reed instrument, Nageswaram.
The percussion instruments of India can be altered in pitch, to coincide
with the tonic and fifth of the sung ragas.
for this reason, the tympani
was used, rather than any of the Western non-pitched dDums.
The music · itself is tonal' · as is Indian music.
modal writing, and in many cases,
corresp~nds
It makes full use of
exactly to the scale lines
of some of the principal Indian ragas.
In addition to being
moda~,
the lines for the woodwind instruments are
highly ornamented, and are improvisational in quality.
·Indian music
makes much use of improvisation, and the ornamented figures are rarely
written down.
With an orchestra, this ·extreme freedom cannot
ex~st;
�of Part 111 - be
The details of the
Sita in
with
new
Forest - have been
and
s exile of Si ta,
of
are
after Sita s
conviction that the various
which is
s
the
civilized
, and a
Vedas to the
of Nehru;
inward and
as
is
Rama
exc
b
class of
one s
dance-drama group
students
fall
studied
Graham
as classroom
work
been
and
dur
se
rehearsals
s
�-76The students, whose ages range from thirteen to eighteen, are pupils
in the Musicianship classes of the Peabody Conservatory, and several
have danced with the group at the Junior Conservatory Camp, directed
cy Grace Newsom Cushman.
A Note About the Company
The purpose of
th~
bicultural dance-drama experiment is the acquainting
of young. students with the forms of the Indian and American dancedramas, . and with the body of literature and history surrounding them.
From the combination of the Indian tradition and religious dance with
the dynamic qualities of the Graham technlque, it may be possible to
create a series of works comprehensible and meaningful to young people
of both countries, for we hope eventually to have a group of both Indian
and American students.
The characters in any dance-drama are not portrayed without some degree
of involvement.
If this involvement has helped in any way to make it
possible for this performing group and the ones to follow to come to
some understanding that, while the answers may not be the same, the truly
great questions have been shared by all men; then the company will have
acted toward its purpose.
�-77-
ZENO AND THE TORTOISE
If Achilles gives the ·tortoise a start, he must first, as he runs after
it, reach the point from which the tortoise started.
tortoise'
w:tll have progressed
By that time the
a certain distance from its starting
point. · And Achilles must again reach this point before he can overtake
it. But whila he .is doing this the tortoise will have progressed stili
further - and so on ad infinitum.
from Zeno of Elea
by H.D.P. Lee
Achilles learned he could not beat
The Tortoise in the final heat
And cried enraged, "I was absurd
Ever to listen to that bird.
Race the dumb brute yourself," said he,
"And prove your own philosophy."
So Zeno, in his maiden raca,
Without a field to set the pace,
Late starting on a muddy track
Where all his learning held him back,
Amazed himself and men and gods
By winning over heavy odds.
(Only the Tortoise in his box
Had fathomed Zeno's paradox
And in his slow reptilian mind
Remarked the fallacy behind.)
Richard T. Cox.
�-78BISHOP BERKELEY AND THE STONE
"After we came out of the church, we stood talking for some time
together of Bishop . Berk~ley's ingenious sophistry to prove the nonexistence of matter, and that everything in the universe is merely
ideal • • • • I shall never forget the alacrity with which Johnson
· answered,
st~iking
his foot with mighty force against a large stone,
till he rebounded from it, - 'I refute it thus' "
Boswell's Life of Johnson
When Doctor : Jcihn$on . kicked ~ the stone,
He thought that he had overthrown
Berkeley's contention that the real
Inheres in · mind .and is ideal.
He hit .the rock a hearty blow
And snor~e~, "I refute h.im so!"
But Bishop Berkeley, s~ili in mind
Extant and questioning, rejoined,
By murm'ring in the Doctor's ear,
"How did you hit on that idea?"
Richard T. Cox
�s
-- Isaac
�Section VI!Ig On the method of resolving indeterminate
problems of the tirst and second degree . that is to say 9 the
construction of the equations for th~ straight line and the
four curves cf the first order ~ i.e. ~ the circle 9 the parabola 9
the ellipse and the hyperbola.
't ;-··- - -,
I
I
~,
·,-," -
,
',
..t\ 'i .;- ./ '/ . : \.~
A-_____ . : D c. ...
....,..._.
... -~ . -----.....· .........,.~ · -
!
· 1'
./
-i !
' _,...,,.-
~>··.c.
{:'.
'
.
(
\
1-t
-&
;-- "
!
/
I
} j
Fig •. ::i •t
Before continuing ,. it might be wise to sum up in very
general terms what we have established up to this point.
1.
Indeterminate equaticns of the first
degree ~
that is
to say ., equations of two unlmoTtms in which neither of the
unknowns is multiplied either by itself or by the
for
example ~
other ~
as,
ay =bx or . x =Y o determine a locus which is a
straight line.
The origin is the point of intersection of _
two straight lines 7 one of which is the place of all the·
points whiah satisfy the equation and the other a ll of the
points through which lines are drawn, parallel to some given
line and tern1inated by the first line.
~ection
2.
!I
'rhis was done in
Proposition II.
An equation in which one of the unlmot·ms appears in
the second degree :, such as ax = y2 .; is a parabola in which
the m1.knowns have their origin at the summit of the axis.
if
However ~ /there are more than two terms in the equation :i such
as ax
=
y2. +b 9 the origin of the unknowns will no longer be
at the summit of the diameter.
This was done in Section
v~
�=
a
are
was
Se
=1
as
e
se
s
s was
d
me&"'l an
se
or
I mean
e
one
a
�recta11.gle composed of a± x and y ~ a 2 ± ay is the rectangle
composed of a
y and a ~ a2x
±
of a2 + ay/b and
a
± b
±x
and
Y~
± xy
ay ± by
X)
± axy/b
is a rectangle compseed
is a rectangle composed of
etc.
Sometimes , however ; it is necessary to change the terms
before such a reduction is possible.
For
instance~
if the
.
.
term~ · in q_ue·s tion "is a2 . ;.. by ? · which is netther the simple
product of a quantity or a complex rectangle , it will be
· necessary to change the . a2 term into a rectangle one of
whose sides is equal to b.
one obtains be -
c - y and b.
by ~
For example ; let a.2
=
be.
Then
which is the rectangle contained by
The following examples will make the method of
reduction clear. ·
£xamples of the reduction f;f second. cY .:.:ree equations to
two ternis.
Example I
Given the equation
x2 - ax + y 2
= by.
Now since the second gegree terms have the same sighs ? and
each has a coefficient
of
one , it is clear that the locus
1 s a circle; but be.c ause of the first degree terms 1 t is also
clear that the center is not at the origin of the unknoM.1.s.
In order to reduce the -ax term s
Let
z
= ·x
Then -
x
= z + a./2
and
z 2 ...;a2/4 +
or
z2
::. a/2
- a2/4
"\72
cJ
+ y2
= by
- by = 0
�- 5 ·i --·
Now let
u = y
Therefore
y
and
z2
Or
u2
b/2
+ b/2
=u
a,2/4 + u2 - b2/4
(a2 + b2)/4
=
-
= o.
z29
which is the locus of a circle whose center is at the origin
of the unlLnowns u and z 9 and whose radiua[;;;:is V a2 + b£ /2,
Thus we have reduced the given equation to pure equation.
.. .
Q. E. :?.
.
. -
Corollary I
z2 + u 2
Since ·
it follows that
{x
=
(a2 + b 2 )/4
·a/2)2 + {y _ b/2)2
=
(~2
+ b2)/4.
Example Two
Given the equation
x
2
+ bx - 2ax - y 2 = O.
Now since the second degree terms differ in
that this is an hyperbola.
bx - 2ax
sign ~
it is clear
Now in order to reduce the
term ~
=x
let
z
Therefore
x = z
and
z
or
y2 = (-a2 + ab - b2/4) + z2
z2
y2 = (a - b/2)~
or
2
a
+ b/2
b/2 +a
- b 2 /4 + ab - a2 _ y2 = 0
which is the locus of the hyperbola whose center is at the
origin of the unknowns y and z and whose semi-conjugate
diameters are equal to
tb
-a or a -
tb.
Thus we have reduced the given equation to a pure equation.
Q.E.F.
�Example Three
In the equation x 2 - 2xy + by =fi there is a second. term~
2xy ; which dould be considered either as part of the x-term
or as part of the Y-term.
But since there does not appear
any y2 term _. one must associate it with the x2-term.
Therefore ~
in order to reduce the
let
The ref ore
z = x - y
z 2 - y + by
=
2xy-term ~
O
We now have a Y-terms which we may
order to have further reduction.
z2
let'. ·
u
The ref ore
z2
= y2
=y
associat~
with the
.N
in
Since we now have
- by
- b/2
= u2
.:. b 2 /2 ;
which is the equation of an hyperbola having the origin of
the
unkno~ms
z and u as. center.
I , Corollary IV)
(Cf . Section VI ; Proposition
Thus we . have reduced the given equation
to a pure equation.
Corollary I
Since
u2 - z2
= b2/2
it follows that
. ,
(yb/2),2 ~- (x
~
y)2
= b2/2.
Exercises
1.
Show that x 2 - 2xy - a 2 + 2y 2
= O is
the equation of an
ellipse.
2.
Reduce the e_ uation x 2 - xy + a2 - 2y2 = O .and. tell the
q
character of the curve.
J.
What 1s the character t>f the curve x2· - 2xy + a2 + by + y2
�---5"3 -
On the Reduction of Composite Products
Example O:ne
Let the given equation be
ax
by
= a2
Therefore
ax
+ by
Let
a2
= a2
= be
Therefore
ax = be + by
Now let
x = c + y
Therefore
ax
= bz ~
which is the locus of the straight line. ·
Exercises
1.
Show that ax - xy
= by
is the locus of the asymptotoes
of the hyperbola.
<G.Hint~
Bhow that a rectangle contained. by two
unknown lines is equal to a rectangle contained by two
known lines ~ then show that the locus of this equation
is two straight lines which intersect and which may
then be considered. as the asymptotes of an hyperbola.)
2.
Show that
abx
= bey
+ axy gives the locus of the
asymptotes of an hpperbola.
Hint~
J.
Divide both sides of the equation by a.
Show that x2 - ax
is equal to b.
= by
is a parabola whose parameter
Begin by letting z
=x
- a/2.
Also
consider the first example.
4.
Show ·by the same method that x2 + 1 ~ xy
= by2
gives
the loci of the asymptotes of an hyperbola.
S.
Show
that x2 - x.y = ·by2 givew ·the loci of the asymptotes
�..
~::~
'-i -- .
On the Construction of Lines Necessary for Reduction
In order to apply the method of reduction to geometry
it will be necessary to consider the construction of the
following equations~
+ a = x
x
1.
2.
a
x
3.
x
± y
4.
x + ay/b = z
5.
x + y
6.
x
=z
=z
-
±b =z
±c
± ay/b
= z.
Example
The construction of
z
Let
+ a.
-
=x
AH be
&'
a line given in
0 / - -__,__<S----Vk..-,-.. ·
,
position go in~ tl11. ·c ;~-C h the
fixed poi.nt
J~
•
Ll."j t~
n/ ___.____"".-_
~r
l\ G be
A
another line given in position.
Nm·r let
c te baken along the
line AH and. extended through
A. J
Fig. 3 5"
such that
AC
= a.
Now if x be measured along
a + x
AH
them
=z
and thus C will be the origin of the unknown z.
And. if CG !
be drawn parallel to
CG ~
Ag ~
y may be measured along
the point C will also be the origin of the unkno'Wll y.
and.
�.~:.
Exercises
1.
Give the construction for the equatiod,
x - a
GI
= z.
I
Find. the cx1g1n_of the
unknown u if
h-<.,
I
Use Fig.3fo
2.
1Gf
A
A
be the
L.---1'------·· f'0
origin of the unlcnown
y and
y ~ b
= u.
I
Fig. Jto
(Use Fig. 3S from the preceding
example.)
It should now become clear that if A is the origin of the
unlmov·m s x and y some one point can be found. which will ee
the origmn of the unkno-vms z and u.
Example
The construction of z where
a -
X
= z.
Let the construction be the same.
It is clear that if
AD= x
Them
BC
=a
-X.
Example
On the construction of z when
+
z = x - y.
Before solving this problem
it might be wise to point
out its
useful~ess ~
for
instance ; if one has the
equation
x 2 - xy = ab ;i
------- ~
I
J_
;
D'
-----~
Fig. 37
1
'-
-
�- 57,_, ·-
it will be necessary to construct z eqaal to .
x - y/2
or if one is given the composite rectangle x2 .+ xy one must
construct z e·qual to x - y in order to obtain the simple
rectangle xz.
Example
Suppose tl:ien that+.the equation · which is to be reduced
contains an xy-term , and let the fixed point . A be the origin
of the x-ter-.m.
Let x verge toward. G, and let y verge toward
H making any angle GAH with the line AG.
Since the equation
contains an xy-terms we will be forced to introduce u such
u = y +
that
b
On the line AH take C and D on eitherside of A such that
=
AC = AD
Thus 7 if
~r
But i f
y - b
b
-!· , ; ::..: U
=u
then D w:L ll b'3 the orignm of u.
Now if one mu.st
.X
~et
1fi'2~~ uce
+, y =
the equation
Z
any point E be taken on the line AD and. let EF be drawn
parallel to AG9 and let the point B be taken on the line EF
such that
EB
= ill\.
Let the line AB be
dra"V-m.
Now since
BF
arid
AE = BE
then
BF = AE + BF
= BE
+
~F
�.... .7- .
-v
or
In this sense A is not only the origin of the unlmowns y and.
x but it fs also the orig111 of the unlmmrm z as well.
If . on the other
hand. ~
it is necessary to reduce the
Y-term , let the points C and D be taken on the line AH and
let CO and. DP be drawn parallel to FE7 and let them intersect
the line AB at O andP.
Now it is clear that the coordinates
for the point E may be either OB and. BF or AB and BF or PB
and
BF,
Exercises
1.
l-ii\i te the construction for the formula
x - ay/b = z
2.
Urite the construction for the formula
x - y - b
J.
= z.
Write the construction for the formula
x - ay/b - c =
Zo
Problem I
Given the angle GAli to find. the point N within the angle
such that if MP be drawn parallel to
AG ~
PM will be equal to
a .given line segment AB.
G
Analysis
have been solved..
Let the
determined straight lines
AB = a
and the undetermmned. straight
N
M
Suppose the problem to
A
I.
I
I
I
f
;
'I/
.,
p . Q
Fig. 3f
�_
_.._\_
·..,,,,_.
..._
...
_ ; ;_,
line
PM
No·w since
= x.
x =a
the const:ruction is given.
Construction
If a line BM is drawn parallel to
I · say that the line
A.1."i~
BM is the locus of all such points.
Proof
Through any point N on the line BM let the line NQ be
drawn parallel to AG meeting AH at Q.
A:Pid sinee AN is a
parallelogram.
NQ = AB
x = a.
or
c~.
E. F.
Problem I I
Given the angle GAH it is r eguired to find a point £1
within this angle such that if MP be dra"im Jiarallel to GA
(AP + PU)
then
= KL.
Analysis
Suppose the problem to have bean solved.
Let the length
,C
-
l\
. of· the determined. line
KL
=a
Qf.___ \
and the unoeterminecl lines ·
and
=x
PM = y.
Therefore
x + y = a.
I .
AP
or
y = a
-I--
A
k
i'1
!\
I
_;_
_
?
'
L_ _
~
· -· -- - -- ----~-,_
-X .
Big. 3 <f
_ _
H
�-
which is the eqaation
~
. .-c
..J
1-
the straight line . but since it
contains three terms
let
a - x = z.
Therefore ···
y = z.
which gives the construction.
On the lines AH and .A.G cut off the lines AB and
equal to KL and let the line BC be drawn.
AC
I say that all
the points M lying on the line CB satisfy the requirements of
the problem.
Proof
Since
then
a
x
=z
z = BP
where B is the origin of z.
since
J~. B
= l-iC
and
PI-1
= PB
:then
AP
+ PM
Now .
= AP
+ PB = KL
or in algebraic terms .;
x + y = a.
G E. F.
},.
Problem III
Given two parallel lines AH add . BK terminated by the
points A and. B and a line AG which makes with the line .A.H
some angle GAH.
It is required to find some point M within
the angle GBK li9Uch that
if the line MP be drawn through the
point N parallel to Ag meeting BK at Il! 1
in the given ration m
~
n.
I~E
will be to AiP
�.~malysis
Suppose the problem to have been resolv.ed.
determined line
Let the
=a
I'lB
and the undetermined lines
= BE :::
AP
and
x
PM = y.
Therefore
and by the conditions of the
l
I_
J,lroblem
A
y -
Therefore
mx
a~
= ny
x
~~
m
n.
~
Fig. t/-o
- na.
Now since there are no other cond.itions9 the problem is indeterminate~. ai1.d
since none of the unknowns appear in any-
thing greater than the .first d.egree 9 the locus will be a
straight line.
(y - a)/x
Sine~
then
mx
= ny
= m/n
- na
Since we have the problem of a mixed rectangle
let
y - a = z
Therefore .... -
mx = nz 5
which gives the construction.
Construction
Let A be the origin of the
W~{no-wn
X which is
the direction of H and the origin of the
talrnn in the direction of G.
..Y - a
=z
Now
~inoe
unlmo~m
tal~en
in
y which is
�- t; /then B will
ee
the origin of the unlu!own z.
BC = n
Let
and. through the point C let the line CD be drawn parallel to
BG and let
CD = m.
I say thatthe line BDI satisfies the condition of the problem.
Proof
Let N be any point on .the line
parallel to GA meeting BE in
BI ~
and let NQR be drawn
and LE in R.
Ci.
And since BCD
1s similar to BQN
then
BC
or
n
The ref ore
g
g
CD
m
g:
BQ
~
t~
x: z
:~
. mx = na.
But .
z =y - a
Therefore
mx =· ny - na
or
( y - a)
or
AP : EE
rx = m/n
~:
m: n.
Q.E.F.
�
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�TABLE OF CONTENTS
On Memisis •
Victor : Zuckerkandl • • 1
Charles Bell, Tutor •• 21
Three Tower Poems
November Tower
March Snow
Investiture
To Learn the .Reason for Theology
.Pheme Perkins, '66 •• 24
(The Human Person and the Ultimate)
Paysage (Landscape).
Christian Harrison , '64 •• 48
· 1964 Pr{ze FreMch Trahslation The Kettle
Veronica Soul, '66 •• 50
Li~teners
Samuel Kutler, Tutor •• 68
From Euclid to Dedekind.
Conclusion: Textbook on Analytic
Geometry •
*
*
*
Editor.
Assistant Editors
Art Editor.
Faculty Advisor
Cover
*
*
Robert Sacks, Tutor •• 62
*
*
*
*
*
Susan Roberts
Sally Rutzky
John Falencki
Daniel Sherman
Eva Brann
Veronica Soul
Also included with this issue are poems and drawings by Iola
Scofieldr a tutor at St. John's College, Annapolis.
�The editor and staff of the COLLEGIAN for the
academic year 1964-65 wish to take this opportunity
to express their thanks to all the
~embers
of the
student body and faculty who have contributed to
the success of this journal.
�ON MIMESIS
·Lecture given in 1955
by
Victor Zuckerkandl, 1896-1965
The motif of this · lecture - motif in the sense of what set it
is
Ari~totle's
ip.)-
motion -
definition of tragedy as imitation - mimesis - of human
action, and in general of the arts of painting, sculpture, poetry narrative, dramatic, lyric
imitative arts.
This
po~~ry
- music, and dance as mimetic arts, ·
the .group of arts which we today call by the
~s
unfortunate term of fine arts (I am not going to use this term, I shall
call 'them, with Aristotle, the mimetic arts, or briefly, the arts; for
the context of this lecture, then, the arts means the so-called fine arts).
One of them is missing . in Aristotle's list:
architecture; so I will not
refer to architecture either.
All these arts, Aristotle says, are mimesis, imitation.
so to speak different species of the genus imitation.
They represent
The imitative
element is not something secondary, accidental in them; it is their essential quality.
A work of art is what it is, namely, a work of
because .it imitates; . the artist is essentially an imitator.
from a work of art
th~
~rt,
Take .a·way
element of imitation, there will no longet be a
" work of art; deprive the artist of the imitator's skill, he will no longer
be . an artist •
. This theory seems to rest on solid ground, to be in sound agreement with
the facts .
Nobody can
deny ~
for i nstance ,
tha~
eve r y painting , every
sculpture, shows something, represents something, and in this sense imitates that which it shows • . (This is true for non-objective painting too;
the only difference there
i~,
external visual experience but
that the : things shown are not objects of
obje~ts
of the im,agination.)
Every tra-
~-
gedy or comedy re-presents an action, and in this sense
action and the people involved
story, every
lyri~
poem
in
expres~ss
imitate~
the
it; ·every· narrative poem .tells a
some
ide~:
they ·imitate
t~e
story,
·the idea •. It is not as . obvious U)ith music and dance, but Aristotle states,
.
'
...
as Plato. did before him, - and he h~s ; a large following throug~ the ages . that ..rnusic and d. nce exp.r ess, and in this sense imitate, emotions, passions.
a
We can grant all this and immediately move on to the directly opposite
�- 2 -
position:
there is no imitation in the arts.
When Aristotle looked at the
paintings which decorated the walls of Greek houses, what did he see?
and shapes covering a two-dimensional surface.
three-dimensional.
Colors
The things represented are
How can two dimensions imitate three?
By the art of
perspective, we say, which creates an illusion of depth on a surface, and
which the Greeks of course
be seen; they are gone.
knew~
There are no more Greek wallpaintings to
But we know the art of painting of the Greeks from
the vases that have been preserved.
There is no attempt at perspective he re;
everythihg is strictly two-dimensional.
Would Aristotle maintain that a
mediocre wallpainting which makes skillful use of perspective is a better work
of art - because it is a better imitation - than one of those perfect vase
paintings?
When he walked up the great steps leading to the Acropolis and
looked at the Parthenon, what did he see?
Among other things, the long
series of marble reliefs - the remnants of which we still see today -
re~
_esenting the long procession of men and horses at the festival of the goddess
r
Athene.
Men and horses in motion - do the sculptures imitate them?
marble does not move.
change in time?
did he see?
The
How can sculpture, frozen in time, imitate motion,
When Aristotle went ta the theatre to see a tragedy, what
Figures on the stage wearing huge masks.
If they were intent
on imitating human beings, why should they hide the only visible testimony
of their being human, their faces?
When the chorus sang and danced, did they
intend to imitate emotions, say, of mourning, or fear?
these emotions do not dance or sing.
People who experience
Aristotle must have been either very
naive or very unresponsive to the experience of works of art if he could
hold that theory.
How responsive or naive Aristotle was I do not kn ow.
he certainly was not that naive.
these circumstances.
But
We can safely assume th~t he was aware of
Naive in this case is not Aristotle's understanding
of the arts but our understanding of Aristotle, more specifically, our understanding of the meaning of mimesis.
When Aristotle says, the arts are mimesis, he did not mean that they produce
mechanical duplicates, replicas, copies that might be substituted for the
real thing.
When he called the artist an imitator he did not class him with
the man who knows how to bark like a real dog.
He understood mimesis in a
wider sense which might be translated, making of images, imaginative imitation.
Image in this sense is never a mechanical duplicate, it involves a transfer
�-
3 -
into another medium, a sort of translation or transformation.
The painter
transforms three-dimensional things into two-dimensional colored shapes; the
sculptor transforms moving things into unmoving stone, bronze, wood; the poet's
medium, into which he transforms actions, events, characters, are words; the
musician ~ s,
tones; the dancer's gestures.
In the process of transformation
the maker of the image may be led very far away indeed from his model; elimination, condensation on one hand, extension, elaboration on the other, may
produce an image which is anything but a mechanical substitute of its model.
(e.g., Steinberg).
But always will the image be
as representing something.
recognized~
image, that is,
Its very significance rests on the fact that it
is an image, that is, related to that which it represents.
The adequate under-
standing of an image is not plainly to see it, but at the same time to see
through it to its model, to see the relation of image to model.
A ·closer scrutiny of the evidence, however, will show many discrepancies between even this refined mimetic theory of the arts and the observed facts.
(I am not going to review the whole evidence, I merely mention a few points.)
/
first of all, the artist himself is very inadequately described as an imitator,
in any sense of the word.
The young man or woman who decides to become an
artist - we assume that the decision is justified - does not do so out of any
desire to imitate anything - or rather, the one thing he desires, passionately
desires to imitate, is another artist.
The decisive events in a future
painter's life are visits to art galleries, not hikes in the country; the
future dramatist's fate is determined by evenings in the theatre, not by
re ading t he newspapers or wit nessing a m
urder.
Andre Malraux whose Psychology
of Art is the most comprehensive presentation of the visual arts from a nonmimetic viewpoint - it has ·nothing to do with psychology as we understand the
term, it is a philosophy - puts it very pointedly:
ttThe composer loves com-
positions, not nightingales; the painter loves paintings, not
always art that makes the artist, not nature, or life.
sunsets.~
It is
The arts therefore have
no beginning - no more than language - or, in other words, the beginnings of
the arts are mythical.
Before we go on I want to clarify further these concepts, - image, and maker
of images.
The prototype in a way is the Qemiurge in Plato's Timaus, who
fashions the universe as the image of the ideal model.
here.
Where there is· an image there must be a model.
All the essentials are
The maker has his sight
�~
I
- 4 -
set on the model; .he takes his bearings from the model.
rived from the model.
The image is de-
The model is prior to the image, not only in time,
which is obvious - the image can hardly precede the model - but also in.
rank:
the model is more than the image, if in no other respect so because
it is the real thing, the other is 'only an image'.
As Plato puts it at
another place; the image is farther removed from truth than that of which
it is the image.
One . might object that many works of art glorify, idealize
their models, and in this sense have a higher rank than the model:
instance in the case of an idealized portrait.
for
But in this and all similar
cases the actual model is not the real object in front of the artist, but
an idea developed from the contemplation of that object - in the case of a
person, the idea of his unrealized potentialities, or of the idea what this
man should look like in order to look like a great man.
With this understanding of image it seems hard to admit that a work of art
is essentially an image.
In the strictest sense there is no . model.
The role
of the model in the making of a work of art is of the most trivial sort.
This becomes evident when we watch artists at work.
A famous example is
Beethoven's shaping of the melody of the last movement of the Ninth Symphony, the Hymn to Joy.
a few sheets of sketches.
W~
have the
te~timony
of this working process in
If a melody is an image of an emotion, then the
model here would be the emotion of joy.
It is perfectly clear that the
composer is not concerned with joy or any other emotion, but with the relations between :tones; if there is a model he certainly is now working with
his back to it.
Nor is he now engaged in matters of secondary importance,
like the search for the right means to .express an emotion.
He is now
struggling with the essential problem; success or failure of this as a work
of art will not be determined by the finding of the right relation between
tones and an emotional model, but by finding the right relation between tones
and tones.
This corresponds to the fact that when the melody is heard for
the first time in the symphony it makes perfect sense - I still .have yet to
find the person who would find any relation between the melody there and
the emotion of joy.
The
~odel,
if. there is one, is as unimportant to the
understanding of the melody as to its making.
Recently I read a paper which analyzed· the seven different versions of a
famous German poem - successive stages of development from a crude beginning
�- 5 -
to .a finished work of art.
poGm:
Dead Love.
The poet:
Conrad Ferdinand Meyer; the title of the
recog~izable
The model is clearly
from the very beginning:
two people returning from a walk one evening, and realizing that their love
had died, and that they themselves
h~d
killed it.
The whole development has
nothing to do .with the relation to the model - like trying to tell the story
clearer,
th~owing
more light on the relationship between the two, and so on.
It has to do exclusively with rhythm, verse, rhyme, syntax, choice of individual words - choice of words not for the sako of a better relation betwee n
words and story but between words and words.
And again, the development is not
concerned with means, secondary matters; the changes mark the difference between a very poor and a very good poem, that is, with the essence of poetry.
As these changes have nothing to do with the relation of the words to the model,
. the poem cannot essentially be an image.
Even more disturbing is this:
the
story at the end, after all the changes, is no longer exactly the same than it
was .at the beginning; but it is quite clear that
th~ 6h~nges
in the
~oem
were
not adjustments to a changed story; it seems rather the other way, the changes
in the words, rhythms, etc. changed the story.
So if we want to call the poem
an image, it would be the rather extraordinary case of the image changing the
model~
or even of the image making the model.
Or take a tragedy, Hamlet.
it the
sto~y
gone days?
Where is the model of which this is the image?
Shakespeare read?
The chronicle which reported the events of
The vague, uncertain figure, the real Hamlet?
Is
by~
Was Shakespeare's
sight. set on any one of these as the model of which he wanted to make an image?
It is clear that if there is a model of Which Shakespeare's Hamlet is the image,
i~
could only be Shakespeare's Hamlet again - the idea of such a man, such a
character which Shakespeare. formed in his mind and then made the central figure
of his play.
If this is the case, the essential achievement is not the making
of the image but the forming
Df
the
idea~
Shakespeare would be the artist he
is., not because of his capacity to make images but because of his power to produce models.
But is this · a reasoeable account of the process?
figured out the man and then wrote the play about him?
That he f i r s t
I would rather say that
the writing of the play was his way, the only possible way, to figure out the
man.
By
making the image he produced the 'model - if you want to put it in
this paradoxical way. - When Phidias made the statue of .Zeus, what was his
model?
His idea of the ruler of the gods?
Where did he get this idea?
It was
�- 6 -
certainly not a current idea - witness the statues of the preceding generation.
It was an idea generated in his own mind.
sense to me to imagine
image.
th~t
And again ·it does not make
he first figured out his idea and .then
Most likely he did not begin with the idea but With
m~de
a blbck
the
of
material; he then uncovered the idea in the material on which he worked.
If
we call it an image, then the model comes into being together w{th the
image.
Those who saw it did not understand it because they 'knew the model;
they understood the model because they saw the image.
That is, the statue
gave them a new understanding of Zeusi .The image makes
even with painters like the
im~ressionists
th~
model; - Not ·
and their followers who turn
again and again to nature in order, as it seems, to be as close as possible
to their models, is the case as simple as it looks.
studios and go out into
th~
open it is
prima~ily
When they leave their
to effect a break with an
outworn tradition; what they expect from nature .is delivery from the dead
weight of convention.
Nature tells them what not to do - but as to nature
being the model - we have rinly to look over their shoulders and see what
they do, what they mean whan they
nature, maybe.
s~y
'true to nature'.
True to their · own
Otherwise it is .much less a transformation rif the· model
into an image than - and I use once more Malraux' words - the secret
de ~
struction of the model for the benefit of the construction of .the can0as.
I think this is enough to give an idea of the eviden6e contradicting
image theory of the
opposed theory:
The evid&nce in turn supports the diametrically
art~.
the work of art is not an image.
meaningfull, significant.
t~
th~
Still it is important,
The significance of an image lies in · its · relation
something outside itself; the work -0f art, not being an image, has ho
such relation.
Its significance. therefore must lie wholly within itself.
It is a completely autonomous construct, closed within itself, without any
essential relation to anything beyond itself, carrying its full meaning
strictly within itself.
t
q~ote:
(this is Clyve Bell, the protagonist of
this theory; he refers mostly to the visual arts, but the implications are
that the theory extends to all the arts):
'.'~e
who contemplates a work of
art inhabits a world with ·an intense and peculiar sig~ificance all its
own; . that sign_ficance is ' unralated to th.I? significance of life • • • The
i
repr~sentative
element may or may not
b~
harmful; always it is irrelevant.
for to appreciate a work of art we .need bring with us nothing from life,
no knowledge of its ideas and affairs, no familiarity with its emotions •
�- 7 -
for a mome.n t we are shut off from human interests • • • to appreciate a work
·of art we need bring with us nothing but a sense of form and color and a
knowledge of three-dimensional space
• I appreciate music, - a pure art
with a tremendous significance of its own and no relation whatever to the
.
.
significance of life • • • The contemplation of pure form leads to a state
of extraordinary exaltation and complete detachment from the concerns of
life."
To me this seems a theory of despair.
I fail to see how anything completely
detached from the concerns of life - and one of them is the search for truth can be in any way important, significant.
This theory builds a wall around
the arts, isolates them completely from the totality of human experience,
makes of them a world of their own • . It leaves the fundamental question wide
open.
No matter how self-contained a construction the work of art is, tones
related to nothing but tones, colors to colors, words to words, there must
be at least one relation to something which is not tones,
namely me.
wo~ds,
co~ors,
Granted that music is tones related to tones, but their being so
related must be related to me, the listener; otherwise, why should I bother?
The same for the other · arts.
The statement ·about the work of art being
meaningful in itself is no answer; it merely pushes the problem further back,
and
make~
it in a sense ihsoluble.
I understand the force of the argument which pushed the theory in this direction.
The work of art can only be either an image, related to something
outside itself and meaningful
becaus~
of this relation, or not an. image, not
related to anything outside itself and meaningful only within
itsel ~ .
If the
evidence against the image theory gets too strong - as it did - what remains
but·the .other alternative.
At this point we have to recognize that this whole
alternative - image or no image - is phony.
here.
There is no either/or situation
We have not yet fully exhausted the meaning of mimesis.
It is Aristotle himself who sets us on this track.
In a paragraph of his
Metaphysics he uses mimesis in a .very . much different meaning.
the
V~
In Ch. 14 of
book, when he talks about the concept , of quality in reference to
number, he
mention~
not yet read the
composite numbers • . for the
VII~
book of
what composite numbers are.
and solid numbers.
Euclid ~ or . have
The Greeks
ben~fit
of those who have
forgotten it, I have to explain
~istinguished
between linear, plane,
The linear, or one-dimensional number is simply number as
�- 8 -
we think of it, when we imagine the units, so many of them
the
num,be~,
as " ~here
are in
all lined up in one straight line; the plane or .two-dimensional
number is the number
w~
get when one number is multiplied by another number:
so many times so many - like a rectangle contained by .two
or three-dimensional number . adds one more factor:
~ide$;
the solid
so many timas. s_ . many
o
. times so many "'.' like a solid _figure contained by thr.ee sides • . for . instance
24, if considered as so many units, is a linear number; considereJ as 3
times 8 it is a plane number, considered as
number.
3
times 2 times 4, a solid
A number -like 25, 5 times 5, or 31., 9 times 9, ·is called a square
number, for obvious reasons; 27, 3 times 3 times 3, a cube number.
the numbers which are not linear are together called compdsite
Now Aristotle says:
All
nu~bers.
"composite numbers which are not in one dimension
only, but· of which the plane figure and the solid figure are the mimema" the word mimema means the reaul t of mimesis; the Greeks ·have two words for
our one imitation which means both the process of imitating and the result
of that process, the thing which imitates.
It is clear that npne of . the meanings of mimesis we have so . far considered
apply
h~re.
36, and
A square,
so . on~
~or
instance, is not an . image of a
nu~ber
The number is not the model of the square.
like 25,
The· square is
not derived from number, is not meaningful because of its relation to
number.
We do not undersmand a square by recognizing its relation to number.
And the makar of the square so to speak is no image-maker, did not have
·his sight set on any number, did · not make the square as ari image of a
:number.
The square is, was made as, and is understood as
autonomous context of
square
otherwi~e
ge6~et~y.
an · elem~nt
It is even impcissib!e to . understand a
than in the tontext af
· gedmet~y#
the study bf the
and of the plane figure, or the solid figure - involves Only
geometric figures, no
r~ference
meaning a geometric figure has,
iM the
reference~
to anythintj outside of geometry.
thi~
~quare
to
Whatever
meaning is completely contained within
the fig ure as an element of geometry .
On the other hand, there :is over and above th is ·meaning of the geometric
figu~e ·
which we now call its
imm~neHt
meaningi
anothe~,
a transcendent
meaning - and I am using the word ·tianscendent literally, without meta-physical ·c onnotations, that is, going beyond one's limits - The meanings of
all words are transcehdent:
the meaning of apple pie ·ror iMstance is
�- 9 -
transcendent, as the word is something audible, while the things belonging to
it _lie beyond the li~its of · th~ audibie in the edible • . So square, or plane
figure, or solid . figure have, in addition to their imrn~~nt: ,, a transcendent
meaning; a relat"
ion to something which is not figure but number, and this is
the meaning Aristotle refers ta.
the geometric figures as we
This meaning is not
arbitrar~ly
a~bitrarily
assigned to
assign meanings to words or symbols;
the relation ssems to arise from the nature of both geometric figure and
number, arid therefore, when it is called up, it throws a new light on number,
and
reciptoc~lly
also adds to the significance of geometric
f~gures.
I would like to clarify this new meaning of mimesis further, by using a quotation of a more modern thinker.
Pascal writes:
The numbers imitate space. -
Here space does not mean geometric figures but extension, the great receptacle,
that in which all the extended things of the universe have their place.
what sense can number be said to
i~itate spa~e?
Numbers
~re
not images.
In
17
cannot be the image of 17 things as we have no 17 things without first having
17.
Number is _
pure construct, a· construct which knows only ·its own inherent
laws, takes no regard of anything outside; numbers are
numbers, not to something which is not number.
example of an
:tmma~nit.J:w
meaningful order.
p~imarily
related to
Their system is a perfect
S-till we ·all know, are all aware,
that mathematics is not a beautiful game of numbers, that it has over and
above its
imma:r:tef.lit~
a transcendent meaning.
ness of mathematics but to its truthfulness.
I do not refer here to the usefulWhat this transcendent meaning
is is of no concern to the mathematician or to the student of mathematics; in
the making as well as in the understanding of mathematics we are exclusivfJly
concerned with numbers in relation to numbers, not with numbers in relation to
other things.
This does not mean that the transcendent meaning is less impor-
tant; without · it, mathematics would not be what it is, namely, true.
question of that meaning is no longer a · mathematical question.
But the
When the trans-
cendent meaning crystallizes in a philosophical· mind - that of a person or a
generation - as it did · for .instance in that thought of Pascal, then it becomes
clear that the pattern of this meaning is not that of an image.
If it were,
we would have to say that number is the image of the order of universal space.
How could it be this, as the very idea of a universally ordered space is the
outgrowth of our
havin~
numbjrs.
The mimema here is not derived from its
counterpart but reveais~ or almost produces its counterpart.
This is a very
�- 10 -
' disturbin~
as ih
observation,
~rofouMd a~teement
that~
pure construct of the mind discovers itself
with a universal order.
It is as if we were
writing a text and then discovered that we had written a translation.
We can now try to formulate the difference between image and mimema in
this new sense.
The image . has its origin in the model and its signif-
cance in the relation to the model; the mimema has no model.
Its origin
is in its own context - number from number - and its significance is
twofold. · Primarily · it is pure construct.
It is nothing but construct,
determined solely by the inherent logic of the construction, not by any
outside factor.
from _that of
Its transcendent meaning is of an
im~ge!
different type
~ntirely
The relation image-model is a one to one relation -
image of this, not of that - like that between a
~ord
and its meaning, a
sign or symbol and the thing signified or symbolized (and this takes into
account the possibility of one word having different .meanings, etc.).
relation of the mimema to its counterpart must be.
d~fferent,
The
as we see from
what we have said:. the mimema made and understood without any regard to
its counterpart, the mimema revealing or even producing its
and so on (this is like saying to a foreigner:
.sound of
'appl~
countarpa~t,
you listen only well to the
pie' and you will wnderstand what it means).
What precisely
this relation is, is the
prob~em
little, but not answer.
The main thing it seems to .me is to show that such
a problem exists.
which I. will raise and maybe clarify a
We are so caught in the meaning
patter~
symbols that we take this to be the pattern of meaning.
I know this is meaningful though I do
to us.
n~t
of words and
Statements like:
know what it says, .sound foolish
They would not to less positivistic minds.
Socrates did not doubt
that the sentences sppken by his inner voice were meaningful although he
had sometimes a hard time finding out exactly what they meant.
The ancient
world was full of oracles .which were supposed to speak the _truth even though
it was very difficult to understand what they said.
And even today, the
Christian does not doubt that the sentences of the Bible speak the truth,
irrespective whether or not he understands . what they say.
Let us come back to the mimetic arts.
I would now say this:
Aristotle is
right ;in · defini~g painting, sculpture, poetry, music, dance as kinds of
mimesis - provided mimesis.is understood as we do it now.
I would not
flatly say that Aristotle did understand it in this way when he applied it
�- 11 -
to the arts.
But it might have been a marginal possibility in his mind.
After
all, we gathered this meaning of mimesis first from his own use of the term.
We recapitulate.
What have we got? . Two theories.
One asserting that the work
of art is essentially image, significant because of its relation to the model,a
transce~dent
relation.
The other asserts that there is no such essential
relation of a work of art to anything outside itself, and that therefore its
significance lies all within itself, - is immanent,
sibility:
We have now a third pos-
the work of art is mimema as we now understand the term.
of art has both transcendent and immanent meaning.
The work
Primarily it is pure con-
struct, nothing but construct, made and understood without any reference to
anything outside.
This construct has by nature a counterpart outside, and
the relation to the counterpart makes it what it is, a mimema.
the question, - What does it mean?
is a legitimate one.
Accordingly
Namely over and above . the immanent context-
Only we must not forget (as we usually do) that the re-
lation between the work of art and its counterpart, which is in question here,
is not the same and not even similar to that between the image and its model.
The art to which this interpretation most easily and most naturally applies is
of course music.
The element of construction is very much in the foreground
in music, perhaps more so than in any other human activity with the exception
of mathematics.
It comes as close as possible to the idea of a pure construct-
its material, the tones, have relation only to each other, not to any thing
else (the opinion that the tones of music are kinds of idealized sounds of
nature, need not be taken seriously); we express this also by saying that music
is pure form, form without content, or - as this seems to imply empty form that in music form and
cont~nt
are the same.
Music is essentially tones-in-
relation; whatever meaning there is in a tone points to another tone, not to
something which is not tone.
A perfect example of immanent meaning.
Vet we
are also mware that this statement, music is tones-in-relation, is not an adequate or satisfactory answer to the question which the phenomenon of music, its
presence among us, puts to us.
not been
~ccounted
We are aware that in this answer something has
for; in other words, we are aware of the fact that music is
mimesis, of the fact of its mimetic significance.
Not all the threads of
meaning that attach themselves to music coil inwards; some of them lead outwards, and they hold the whole construct in its proper place, as it were, the
place of mimema.
But although without an awareness., however .dim, that there
�- 12 -
are such threads of transcendent meaning there is strictly speaking no musical experience; the
knowledge~
they are, where they lead to, is in no
sense a prerequisite either for the making or the understanding of music.
The question:
What does it mean? referring to the transcendent, not the
immanent . meaning, is no longer a
~usical
question.
The composer does not
ask it, at least never when he writes music, only when he philosophizes,
which he rarely does.
And the study of music, .
~f
it is to lead to an
understanding of the works of the tonal art, is the study of tones-inrelation, of immanent meanings.
Of course the question of the transcendent
meaning is a valid question - a question for philosophy • . But . before even
admitting it as valid we must make sure that it is not asked in a thoughtless way: . What does it mean? - with 'what' I usually ask· for a 'this' or
'that', and so I tacitly introduce the assumption that the relation between
music and its mimetic counterpart is of the same kind, of the same type
as that between a symbol . and a thing, an image and a model,. a word and its
·meaning.
answer.
This way the very asking of the question would prejudge the
The problem is precisely to find out what kind of relation pre-
vails between music and its mimetic counterpart.
You see, from the out-
set we get deep into philosophy; and so we understand why good answers . to
this question do not usually tome frbm musicians but from phil-0sophers.
One of these answers, a fmmotis one, I will now quote, not because I want
to suggest that this is it, but because it helps us to understand the '
nature of the questions.
In his Harmonies of the World Kepler writes:
"The movement of the heavens is nothing but a certain e·v er lasting
polyphony (intelligible, not audible) effected by dissonant
tensions comparable to those syncopations and cadences wherewith
men imitate those natural dissonances, tending towards certain
and prescribed clauses, each involving six terms (like the six
parts of polyphonic music), demonstrating and defining with
these notei the immensity of time. It is therefore not too
astonishing that man,. the ape of his creator, should finally
have found the knowledge of polyphonic song which was unknown
to the ancients, so that in some short part of ari hour, byr means
of an artful harmony of many voices, he might play the ever- ,
lastingness of created time, and thus to some extent taste the
satisfaction of God the Workman with his own works in the sweetest
feeling of delight .which comes from the experience of· music, that
imitation of God."
The word imitation appears here twice.
Certain elements of music, syncopations
�- 13 -
(which then meant a type of dissonance, not a rhythmic irregularity) and cadences, are called imitations of the motion of the stars; and music as a
whole is called an imitation of God - Dei imitatri Musica.
Clearly imitation
stands here· for mimesis, in the sense we try to understand it.
to do with image.
It has nothing
Otherwise the study of composition would have to begin with
Ptolemy or Copernicus.
And no listener, however familiar with astronomy,
has yet - as far as I know - discovered in a polyphonic piece any reference
to the motions of the planets.
Neither is music an image of God; atheists
can be excellent composers, and religious faith is not a prerequisite to the
enjoyment and understanding of music.
Also many of those polyphonic songs
Kepler referred to were written to decidely non-religious words (to say the
least) and in this sense were certainly no images of God.
Still, by being
music, moving according to those dissonant tensions, cadences, and the other
rules of tonal motions, it imitates God.
There is also the profound remark
that the musician in truth enacts a play the subject of which is everlasting
time; but this I won't take up now. - So what are the inferences?
The com-
poser produces a piece of music according to the laws of the tonal construct.
By doing this, he produces an imitation, a mimema, of the heavens 7 of God.
did not know it, he did not intend it, he could not help it happen.
pens behind his back as it were.
He
It hap-
The listener hears tones-in-relation.
In
hearing this he becomes aware that this is an imitation of something which is
not tones, a mimema.
What it imitates he does not know and need not know;
yet he may have a sense of the direction in which to look for that counterpart.
In some mind this awareness may crystallize into an act of mimetic recognition
in which the counterpart of the mimema is apprehended.
stars, in God.
Kepler saw it in the
The result is a new recognition of the universe, of God.
I
would even say, more strictly, it is the recognition of a new universe, a new
God.
The universe, the God, whose imitation we recognize music to be are not
the same as they were before.
Not unly did the man who made the music imitate
something he did not know, which nobody knows, but also the imitation produced
the thing imitated.
This is like saying:
out he has done a translation; or:
a man writes a text and later finds
a man is charged with writing a transla-
tion, but he gets no text; when he asks for the text he is told that the text
does not exist, but that it will come into existence by way of his translation.
These are fantastic propositions. · I will try a metaphor to make them more
�- 14 -
manageable.
Imagine a man working on some material, some block of metal.
His _.intention is to produce a perfect surface - whatever he 'may consider
.a
pe~fept
sµrface.
This he accomplishes.
When he has done it he dis-
covers that his surface shows a reflection.
produced
~mirror.
He discovers that he has
It was not his intention to produce a mirror, he did
not even know that there are mirrors.
(I do not think here of mirror in
the conventional sense, as a surface reflecting visual images, but of
mirror in the most general sense, in · the sense in which a magnetic needle
might be .called a mirror:
its existence "reflects" and thus makes ap-
parent the existence of a magnetic field.
surface, the reflection may for instance
In the case of our man's metal
a~sume
The reflection may be vague, not well defined.
the form of
vibration~)
The chief thing about it
is that it is not the reflection of a thing that was there and seen before,
it is the reflection of something so far unseen:
·the mirror receives the
reflection from a direction where there was emptiness before.
The reflec-
tion leads to the discovery that there is something there to be reflected.
Considering the very special shape of the surface which . seems to be the
con~ition
for its functioning as a mirror, one might even suspect ·that the
thing reflected had an interest in becoming manifest in the reflection,
and secretly guided the hand of the worker so that the outcome would be as
desired.
This sounds a little mystical.
I refer to the ever recurrent
comment of .artists that while at work they feel themselves as instruments,
as tools of some power whose source is located outside themselves, - a
sort of Socratic diamonion for workmen.
However this may be, returning
to m
usic, the tones are the surface; if they are in the right r e l a tio n,
they will become a mirror; there will be a reflection from somewhere,
testifying that there is something out there to be reflected. · To Kepler's
eye the thing reflected, revealed in the reflection, was divine order.
The order of tones appeared as 'imitation', as the mimema of a divine
order.
What about the other arts?
mimesis to them?
of music.
What happens if we apply our interpretation of
The application there is not as obvious as in the case
The painter, the sculptor certainly do imitate in the conven-
tional sense of the word, do produce images; yet if the work of art is
essentially mimesis in the other sense, then the imitation in the conventional sense cannot be essential.
The painting, the sculpture, are
�- 15 -
essentially, like a piece of music, free constructs, that is, determined by
the laws of the construction, not by anything coming from outside.
That the
painting is a likeness of something is a secondary, an accidental factor, it
is not that which makes the pa.i;nting ·a work of art, a mimema.
In other words:
insofar as the painter makes an image he is not an artist, and insofar as he
is an artist he makes no imege.
has alsti
transc~ndent
On the other hand , as mimema, the painting
meaning, .a counterpart; but this counterpart cannot be
that which the painting
repr~s·ents,
of which it is an image.
A good painting
of a ch~ir is not essentially an image of a chair; it is es~entially a construct of shapes, lights, colors, which happen to look like a chair - the
refer~nce
to the real chair, is non-essential.
The likeness is merely an
element in the construction; it belongs to the immanent meaning.
cendent meaning has nothing to .do with 'chair', real or ideal.
_of our metaphor:
~s
The transIn the terms
the chair of the painting is mirror, not thing mirrored; it
not a reflection, but a
~eflector;
and what it reflects is certainly not
'chair'·.
I look at a Greek statue, say, of the god Apollo.
that this represents that particular god.
image of.
I know, I ·have been informed ,
I understand what the statue is an
Whether the model of this statue was a real person or an idea does
not matter.
I can deduce from this statue all kinds of thought regarding
Greek art, religion, culture.
the mimema.
With all this, I have only seen · the
i~age,
not
I try to see better, that is, to do nothing but see, forget all
information, speculation, rationalization, give the eye a chance to find its
a y undisturbed.
over my body.
After a while , the statue so to speak take s m over, t akes
e
My body assumes the attitude of the statue - not actually of
course, and not in · imagination - this has nothing to do with imagination - but
in what I would call body - thought; my body consciousness becomes the inner
counterpart of the external attitude of the statue, - I have the experience
of body which the statue would have if it .had consciousness.
In this case
the experience is of body at rest - not of body, the thing, in a state of rest,
but of body and rest as absolutely one.
expe~ience
where rest is
feit~
This is contrary to our normal
wheh there is no · consciousness of body, in com-
ple.t e .relaxation - body being ·the source of perpetual unrest.
Here however
there is full presence of body, full awareness, awak.eness of body - the statue
stands - and perfect rest. · In other words, it ·is rest not as absence of
�- 16 -
~ension
but as equilibrium of tensions.
unknown mode of body existence - and
This is a revelation of a previously
th~s,
not the God Apollo, or the
Greek idea of a god, or Grek culture, is what this statue is the mimema of.
Let us lastly consider tragedy.
Aristotle defines it as imitation, mimesis,
of human action - a certain kind of action - done in the medium of language - a certain kind of
l~nguage.
As long as the word
taken too literally nobody will quarrel with this.
imit~~ion
is not
Every tragedy has a
plot, action involving people, and in this sense imitates, represents human
action; and the making of a tragedy is concretely a writing - tragedies
are written - written language is the medium in which it comes to light .
a~
The only question is:
is this,
Aristotle seems to say, that which makes
a tragedy what it is?
Is written work a tragedy because it is this par-
ticular kind of imitation, representation?
I would
den~
it.
If
trag~dy
is mimesis in the sense in which
~e
now under-
stand it, it is primarily an autonomous construct, a language -construct,
not acrepresentation.
quality.
The representation in it is not its essential
On the other hand, as mimema it does have transcendent meaning,
is, significantly related to a counterpart.
But this counterpart is not
the story, the plot, the people, is not that which it represents - and
this includes ideas, the moral, anything that can be deduced from it.
This requires some clarification.
The term language construct seems to
imply that we consider a piece of poetry, such as a tragedy, primarily
fro m the
v i ~ wpoint
bf s yntactical construction, rhythm, m
eter, ve rsa,
rhyme, sound, - from a purely formal standpoint.
We .would then deal with
them as organized sounds in time - organized according to certain formal
patterns, not according to meanings.
We would then detach the constructive
element from the meanings, consider words apart from meanings. · This would
be a ·misunderstanding of the term language construct.
plus meanings, they are meaningful sounds.
are no longer words, no longer language.
Words are not sounds
Words divorced from meanings
If language is the
my construct, then meanings are a part of the material.
this material I cannot but always handle meanings too.
struct is a construct of sounds and meanings.
mater~al
of
In handling
A language con-
To call tragedy a language
consttuct does nbt therefore mean that it is considered, as we
say~
from
�- 18 -
does it profit us to live through it?
Aristotle's answer is:
only by
living through it can we learn from it; we learn through imitation.
.confess I am . not convinced.
I
What can I possibly learn from Oedipus rux -
and I take the word learn ·to mean what we usually understand as learning?
I do not want to .make any cheap remarks.
Seriously, the
i~ea
is that by
living through Oedipus' exper.ience and at the same time reflecting on it as we can because we are not really living through it - ·we might detect
the point on his way where he possibly erred and where the
cb~icecOf
another course might have saved him from his tragic fate.
But is this
really the ·moral of Oedipus?
Does the tragedy not do the very opposite to
us, . namely, drive home with the greatest possible force that no matter what
you do, how hard you try, fate cannot be avoided, that there is no escape
from fate, and if this fate is fall, that fall one must.
The whole im-
pact of this tragedy seems to me the experience of the inevitability of
fall.
And what could such an experience be · but of most depressing kind:
Still, this like any other tragedy leaves us
elated~
In its pattern· the experience of tragedy is similar to the experience of
a work of the · visual arts as I have tried to describe it.
It is not an
· illusion - believing something to be real which is not real - nor can I
ascribe it to imagination - lending the color of reality to something
which I know to. be not real
it is an experience of participation.
As I
experience a tragedy I remain what I am and where I am; at the same time
· my consciousness. spreads out and goes over into . the
p~ople
involved jn the
dramatic action - into all of them; in reference to the words, I am at the
same time hearer and speaker.
togethei, as we said, the
I become one with the
The words, the people, the action are all
c~nstruct
c6Mstruct~
- 1
of tragedy. - By participating in them
beco~e
mirror, and I
~eceive
the re-
flection of somethin~ · ~ Whatever it may be - that of which t~agedy is the
mimema" · I become aware · that the immanent order of the construct is order
.
·also in relation to something else,
th~t
there is something - not a thing,
rather a st~te, a mode, a dimen~ion of human ~xistence whose order is revealed in tragedy, in
we can say:
:'
·a1ation.
ref~rence
to which tragedy is 'in order.
we ex per ien·c·e ·tragedy as true.
In this sense
Th is is the· so·u rce of the
Take a·way tragedy ..: there is the suffer fog, ·dejection, despair,
the great visitatio~~' the inscrutabl~ catastrophies ~ the wh6ie 'chaos of
human misery.
This chaos tragedy transforms into order.
Tragedy does not
explain suffering, or justify it, or give it to us as a fact to which we
�- 17 -
the formal standpoint only, apart from the content.
The content - plot,
people, action - is itself an element of the construction - the most important
element - along with the language.
The writing .of a tragedy is not the making
of an image of people in action, or . the search for the most convincing (persuasive) way to present people in action; it is primarily a construction of
people in action, whose chief means of communication is language.
These
people ·and their actions and passions have no existence apart from the words;
in tragedy, as in music,
f~rm
and content are one.
The words are the tones,
the people are the melodies; it is as impossible to think of these people
apart from the language as it is to think of melodies apart from tones.
So
if tragedy is mimesis, the so-called content belongs entirely to the context
of immanent meaning of the mimema; the plot, the people cannot be that of
which the tragedy is the mimema.
Again in the terms of our likeness:
the
people and their action are not that which is mirrored, they are the mirror;
not the reflection but the reflector; or as Aristotle would say, they are not
that which is imitated but that which imitates.
With this in mind we can face the question how to understand, how to explain
to ourselves the peculiar quality of the experience of a tragedy, ·the difference between being a spectator in the theatre, having the thing represented
really happen to oneself, watching it happen to others, reading a report
about it.
These other possibilities - misfortune befalling oneself, observing
misfortune befall others, reading or listening to a story about such misfortune - are certainly most depressing experiences.
leaves us in a state of elation.
Take Oedipus rex.
well enough.
We desire it.
The experience of tragedy
How can we understand this?
Why should we expose ourselves to it?
The story we know
Of course, knowing the story,. and being made to actually live
through it - which is what happens in the theatre - are different things.
for what purpose should we be
be but a torture?
mad~.
to live through it?
But
What else could this
It is true that this is theatre, that it is not a real
story, real happenings which wa observe on the stage - and there are certain
styles of representation which emphasize this quality of non-reality.
matter how realistic or unrealistic the representation, . if
not come fully alive on the stage end makes it
co~e
tha~
But no
story does
alive in the spectators,
we might just as well stay home and not go ta the theatre at all.
So what
�- 19 -
have to resign ourselves; but it bridges the gap between suffering and reason.
Oedipus
Bex is not an explanation or a justification of fall, it is I would
say the logos of fall.
This is then one way to redeem fall,. and tragedy on
the whole, one way to redeem the suffering of man.
We understand that tragedy
originated in the cult of the god Dionysus, the redeeming god of the ancients.
We understand also Wh¥/in a truly Christian world there is no room for tragedy.
The Christian finds redemption in other ways.
I want to come to a conclusion.
In the last analysis the problem will boil
down to the question about the relation between a work of art and reality.
llie
have mentioned one theory which denied there was any relation between them.
If we admit a relation, there are the two possible interpretations of mimesis:
as image, where reality is the source from which the work of art is derived;
and mimesis as reflection, where the work of art is the source, the detector
of new realities.
I will close with two legends which 'imitate' better than
I would be able to, - the two different views.
One is the well known story of
the most famous painter of Greece, Appelbas;it is said that when he painted
grapes, birds would come and pick at them.
the great painters of old China.
The other is the story of one of
llihen he became old he began to work on a
painting which he showed to no one; he worked on it for years, and finally he
called in his friends and pupils, and there it was:
showing a landscape, with
mountains and a road leading from the foreground back towards the hills.
They
looked at the painting and at the old man, and suddenly they saw the man enter
the painting, begin to walk on the road, getting smaller and smaller until he
finally disappeared in'the mountains.
��2
G
Down all
chair
�- 22
love is out
And the
the tower
falls
Tilts
Traveler,
have
�- 23 -
Investitt.1re
Tonight for the first time I climb the stair.,
Turn on the light, that sends four rays
To the dark quarters of the bay and land.
How many have kept lights burninQ in ~heir towers?
solitary Platonist,
Image-seeking Celtic Yeats,
Collins in the mountain hut
Over twilight shires of mist.
Milto~'s
Think of Dante somewhere in banishment
Climbing another's stairs by candlelight;
Think of all whose height became a sign
Of the brooding eminence established by the mind.
Rats with electrodes in their heads
Jump on treadle for a charge.
·Action, passion, ·. peace · and · war
Shrink to pastime -- company bad. ~
Only rays that reach across dark shores
Find the resonance of what endures,
This lighted web of soul in the worid,
Communion of Platonists in timeless towers •
.•.
•,
..
�- 24 -
TO LEARN THE REASON FOR THEOLOGY
The Human Person and the
Ultimate
Pheme Perkins '66
Human beings are continually asking questions about the
finite beings we are .aware of our own limitations.
ultimate~
As
This awareness naturally
leads us to ask is the universe a continual sequence of finite beings or
is there some greater being beyond which there is no other?
perience of finiteness makes us
aw~re
The same ex-
of the fact that many of the other
beings that we encounter are beyond our understandin9 and control.
We,
then, might well ask the question of the intelligibility of the universe.
However, there is a still more basic question that we might ask:
anything exist at all.
why does
All such questions are concerned in one way or
another with finding an ultimate, an end.
The Greek philosophers were primarily concerned with the question of intelligibility.
They were convinced of the power ·of human reason to com-
prehend the universe.
The ultimate for them ·was the source of the funda-
mental rationality of the world.
imperfect.
universe.
The irrational and the infinite were
Modern men are not so ready to accept a rational, finite
Modern physics has reached the point at
whic~
not only does
measurement, i.e., the making of ratios, become very di ff icul t;i it becomes
actually and theoretically impossible.
The mathematics that has developed
along with this physics has long accustomed men to dealing with infinity.
Along with these developments psychology has led him to question the very
foundations of his thought and personality.
Rather than being concerned
with what makes the universe intelligible or why is there something and
not nothing, men today are concerned with the question of the nmeaning"
1
of human life. ) The question of meaning especially as it affects him
personally is the ultimate question of man in this century.
We sense meaninglessness as a very real and potent threat.
this threat that motivates our search for ultimate reality.
And it is
We feel that
our lives may be as randomly determined as the weather and that ratios
are only a big joke, for randomness is no reason at all no matter how much
1)
Jung, C. J., Modern Man in Search of a Soul, (New York:
19 33).
Harcourt Brace,
�- 25 -
probability theory one constructs.
In this irrationality we feel a threat to
our very person, the core of what we are.
meaning on
th~ h~man
penultimate.
The
An
~ltimate
person is nd ultimate at all.
ultim~te
that does not bestow
At best it is only a
must restore the very .center of man's being that
has been threatened by meaninglessness.
Thus, if. there was once danger of man's falling into Cartesian pride in the
power of his intellect, there is now great danger of his falling into the
despair of not knowing the way out of his own wretchedness.
Pascal, who
paints a very vivid picture of the wretchedness of man in an infinite universe
offers a ·way out, but .it is. not a philosophical one.
poses is ·that of religion, of Christianity.
finite meet in one person.
The path that he pro-
In Christ, the infinite and the
However, instead of being destroyed by the in-
finite the finite is fulfilled and elevated by it.
It was the great dis-
covery of the Judea-Christian tradition that God, ultimate reality, is personal, and consequently man's own personhood is not destroyed by God but confirmed by him·.
In Christian terms the basic threats to mankind are sin and death.
Meaning-
lessness has been regarded as a result of the separation from God brought
about by sin.
Thus when the Christian speaks . of the conquest of sin and
death he is also speaking of the conquest of meaninglessness.
doubtedly true that Christian kerygma
And it is un-
which forcefully presents the con-
nection between meaninglessness and sin has more success in speaking to men
today than that which does not.
Christianity has always claimed that it is
through man's special relationship to the ultimate,God, brought about by the
redeeming mission of Christ and fulfilled in the individual through grace
that sin and death are conquered.
Such a statement ·by no means denies that
the Christian still has to grapple with sin and its causes, the world, the
flesh and the devil.
It by no means invalidates his conviction that he will
be judged by God on the basis of his effort.
What it does mean is that the
final - though perhaps not in the individual case, as an individual can be
damned - outcome of the confrontation has been decided by
Christ.
th~
This decision is the foundation of Christian hope.
victory of
As Karl Barth
puts it in . the chapter .on hope in Evangelical Theology:
"Hidden deep beneath this inescapable No is God's Yes as
the meaning of his work and . word. This Yes is the reconciliation of the world with God, the fulfillment of His
�- 26 -
covenant with men, which he has accomplished and revealed
in Jesus Christ." 2)
Hope, then, is capable of overcoming despair and meaninglessness because
it is rooted in God, the ultimate,. who is not susceptible to the diseases
of finitude.
God has not only given the answer of redemption to men in
danger of losing
themsel~es
in worldly pleasures, this same answer has
been given to what one might call the psychological temptation of mankind,
that of despair.
God-given.
Note that I have said that the answer to despair is
Although as one looks back on the fact it does indeed seem
reasonable that a personal ultimate might provide an answer to the despair
that threatens man's personhood, man did not figure this answer out.
Maritain's interesting argument to the contrary,
of His personhood.
3
)
God had to tell men
The mere existence of such revelation has profound
consequences for our understanding of the human person.
Rene Latourelle
points out this fact when he writes:
"It is because God had made all things and in particular the
human creature as a reflection of His own perfection and because all things have their origin in God that a revelation is
possible between God and man. Revelation by the Word presupposes the language of creation of God, just as grace finds
a basis in the intellectual and spiritual nature of man. It
is not simply because they have been chosen by Christ that
our concepts and our human terms are suitable for proclaiming
the mystery. It is rather because they have relation to the
divine Being that Christ can use them." 4)
As we shall see in more detail, the foundation of the human person is the
divine person of which the human person is the image.
It is in this like-
ness that the salvation of the human person lies.
Having taken this brief glance at the problem, I wish to investigate the
relationship between the person and the ultimate as seen by two radically
different theologians, Paul Tillich and St. Thomas Aquinas.
St. Thomas,
of course, did not have to contend with this problem formulated as it is
today.
However, his understanding of the human person and his relationship
with the ultimate copes with the problem quite nicely.
Tillich, on the
other hand, sets out to deal with just this problem in The Courage to Be.
2) Barth, K., Evangelical Theology, (New York: Doubleday, 1964) p. 139
3) Maritain, J., Degrees of Knowledge, (New York: Scribners, 1959)
pp. 231-6.
4) latourelle, R., Revelation, History and Incarnation, in The Word (New
York, Kenedy, 1964) p. 48
�- 27 -
The courage to be depends upon an arrival at ultimate reality.
It is at this
fundamental level of being that man finds the power to conquer the fears
and anxieties that tend to destroy the humah person.
At this level radical
doubt, the foundation of meaninglessness, is rendered harmless, but not impossible •. Tillich continually insists that doubt is .a fundamental part of
the courage to be.
It seems that this courage only exists in the continual
conquest of doubt by the affirmation that courage makes possible.
This
doubt, then, is not only not harmful, it is necessary.
In traditional Christian thinking doubt is not dealt with so lovingly that it
is considered necessary.· Theological doubt is considered as sinful.
And
sin, although·it is not impossible for the Christian, is always harmful.
Thus, while sin may inevitably follow from the Wrong pursuit· of certain ends
that are good of themselves, it is never necessary in an absolute sense.
see the Christian, then, as caught between two worlds.
redemptive mission of Christ has been accomplished.
world seems to continue as before.
illustrate the situation very well.
We
On the one hand the
On the other hand the
The following quotations from Karl Barth
The first is from his book Credo:
"Actually everything that had to be done for the reconciliation
of man with G6d was, · a~ we showed in its place, already accomplished in the death of Christ. There lacked only its disclosure; for the divine act of reconciliation took place, not in
the revelation of his glory, but in the concealment of His
divine condescension. That then is what was accomplished in
His resurrection .from the dead • • • The present is the regnum gratiae, between the Ascension and the Second Coming. In
its form the unity between Christ and His own is at present
such as is not able to ·continue, or is able to continue only
as long as this time lasts but after that it must give place
to another- form. The form of this unity here and now is this:
that for the Church Jesus .Christ is hidden with God in the
same way that the Church itself is hidden in the world. He is
not immediately present to His own nor therefore are His own
immediately racognizable either to others or to themselves." 5)
In Dogmatics in Outline he elabtirates on this concept of the present time
which is the regnum gratiae:
"This time which now breaks in, the time of the Church, is at
the same time the end-time, the final time, the time in which
the existence of the meaning of the existence of the creaturely
world reaches its goal. Ula heard, ·when we spoke of Christ's
Cross and Resurrection, that the battle was won, the clock had
5) Barth, K., Credo (New York: Scribner's, : 1962). p. 164
�- 28 -
run down, but still God has patience, God is still waiting.
For this time of His patience He has put the Church into
the world, and the meaning of this last time is, that it is
filled up by the message of the Gospel and that the world
has this command to listen to this message. • •• It is
the time in which the Church is united with Christ only in
faith and by the Holy Spirit. It is the interim time between His earthly existence and His return in glory; it is
the time of the great opportunity, of the task of the
Church towards the world; it is the time of mission." 6)
Clearly such a situation of its very nature contains a lot of tension.
The
Christian must live in the tension between the imperative of the old time
and the indicative of the new without losing sight of either one.
His
mission to the world is to announce the new time, the time of grace that
is hidden in the old.
It is in this new order that the human person finds
fulfillment.
As we have already seen, tension is a necessary part of the courage to be.
But this tension is hardly that of a supernatural order hidden in the
natural.
Tillich is concerned only with the .tension that exists between
opposites in the natural order.
reality itself.
He extends this tension even to ultimate
He concludes Biblical Religion and the Search for Ultimate
Reality by saying:
"To live serenely and courageously in these tensions and to
discover finally their ultimate unity in the depths of our
own souls and in the depth of divine life is the task and
dignity of human thought." 7)
.
Salvation, then, is not obtained primarily as a gift of God.
Rathe r it
is obtained through the activity of the human mind that is somehow able
to attain to the unity between opposites, even those possessed by religion
itself.
Tillich has rejected Pascal's notion that it is necessary to go
beyond philosophy in order to avoid despair.
He insists that thought
itself is capable of overcoming meaninglessness.
Tillich reconciles re-
ligion and philosophy by asserting that they are really talking about
the same thing.
The courage to be is found in the God beyond God who is
attained by the exercise of reason.
As we have seen already the answer given by the Christian Church is somewhat
6) Barth, K., Dogmatics in Outline (New York: Harper, 1959) p. 127f.
7) Tillich, P., Biblical Religion and the Search for Ultimate Reality
(Chicago: U. of Chicago Press, 1955). p. 85 .
�- 29 -
different.
I have chosen St. Thomas Aquinas as the chief representative of
this tradition for the purpose of this paper, because he also was most careful to show that theology and philosophy are fundamentally harmonious disciplines.
As soon as we consider the way in which each of these men estab-
lishes the accord between theology and philosophy we encounter the fundamental difference between them.
for St. Thomas the basic structure of the
world is vertical; for Tillich it is horizontal.
for St. Thomas there is no
conflict between philosophy and theology because they deal with the same
object, God.
Philosophy has knowledge of God insofar as it · is possible for
human reason to know him.
Theology deals with the same object insofar as He
has revealed Himself to men.
As human reason itself is a creation of God and
is ordered towards truth which is God, any true knowledge that philosophy
has of God is not invalidated by God's revelation of Himself.
theology is not the same thing as philosophy.
Certainly
It possesses a knowledge of
God that is not accessible to the latter through the Word of God himself.
This revelation is held with absolute certainty not because it is based on
rational demonstration, but through faith in the truth of the revelation.
Thus we see that theology stands above philosophy by virtue of the superiority
of its knowledge but not in any opposition to it.
stand in a vertical relationship.
In other words, the two
In Tillich's horizontal scheme, however,
the two are shown as standing in seeming opposition and then unified when
religion is considered as the symbolic expression of ontology.
This funda-
mental difference in viewpoint has very important consequences in regard to
the ideas that each man has about the relationship of the human person to the
ultimate.
As we have seen in the passage quoted earlier from Latourelle the
very possibility of a theological understanding of the human person depends
upon the created world's ·being of such a nature as to admit analogy with the
divine and thus to admit revelation.
The importance of this link causes
St. Thomas to remark:
"It is therefore evident that the opinion is false of those
who asserted that it makes no difference to the truth of the
faith what anyone holds about creatures so long as one thinks
rightly about God." 8)
For St. Thomas man's relation to God in the
created beings.
natu~al
order is that of all
God is the source and preserver of the being, esse, of all
individual beings, antes.
8 ) S • C • G• II , Ch • 3 •
Furthermore
H~
is the end to which they all without
�- 39 -
exception tend.
ultimate.
The
Everything that exists has at least this relation to the
uni~erse c~nnot
be totally random, then, as it tends toward
an end, the Being who is the source of all beings and because He is the
.
.
source of all being and of all goodness and truth as well.
ments say very little about man's personhood, however.
These state-
This factor is
most seriously taken into account in the supernatural order.
Here man is
enabled to go beyond the contemplation· of the divine essence that is his
final end in the natural order.
life of love itself.
He is now able to enter into the divine
He has been transformed by God into a new creature
capable of sharing in divine love, in the life of the divine trinity.
Having taken this brief glance at the problem before us and the proposed
solutions, we must now proceed to a more detailed examination of Tillich's
horizontal structure, Thomas' vertical one, and the place of the human
person in each.
As we consider the world that confronts us, it is not difficult to conclude
that all of the things with which we come in contact have something that
distinguishes them from other things that we create in our minds.
that the former exist and that the latter do not.
existence we call being.
We say
The principle of this
Both Tillich and St. Thomas agree that the ques-
tion what is being is the fundamental question of philosophy.
We spoke
at the beginning of this paper of the search for ultimate reality as the
search for that being beyond which there is no
oth~r.
In· other words it
is the search for that being necessary before all other beings.
_find
ul~imate
Both men
reality in such a being, but they do · not agree as to the
nature of this being.
Tillich equates the ground of being that is the
source of all beings with what he calls the God beyond the God of theism.
This equation enables him to bring together the two opposites ontology
and religion.
As we saw, St. Thomas does not set up any such opposition.
In his vertical structure the fact that God and esse are the same is fundamental to the harmony of philosophy and theology.·
It is to a brief
consideration of Being-Itself that we must address ourselves •
.Tillich says that ultimate reality is that to which we essentially belong
and from which we are existentially separated.
What he seems ·to mean by
this statement is that man in his essence as an existing being has some
�- 31 -
part in Being-Itself or the ground of being, but insofar as he exists as a
finite being he is separated from the ground of being.
At first glanoe it
looks as though what Tillich has done is to translate into his own terms the
oid distinction about the infinite dist~nce betwe~h creator and creature.
note how he ha·s done so.
He has said that existence separates one from and
essence unites one to the ground of being.
Being, esse.
But
For St. Thomas God is pure Act-of-
Being is not conceived of as an attribute which, when united to
an essence, causes the existence of that essence.
not some extra large being that is the source of
esse, t6 be.
The foundation of being is
beingn~ss.
It is an act,
This act is the foundation of the world of beings.
All other
beings exist - that is, are beings - by virtue of their participation in this
act of being, esse, which is given them by God.
can give esse.
Only God, who is pure esse,
That is to say only God can create.
But in order for things
not to be God and yet still exist they must not only possess esse but be distinct from {t.
This distinction is determined by the ~ssence that ·is actua-
lized by the act 6f being proper to it.
identical.
esse.
Only in God are essence and esse
Any other name that we give to God is merely an aspect of His
Thus we see that· as long as anything exists God, who is esse
present to it in its own esse.
itself~
is
Since this esse is the innermost principle of
every being it follows that by its very existence every being is linked with
the divine esse whose effect it is.
In short, for St. Thomas ultimate reality
is that to which we existentially belong and from which we are essentially
separated.
Thus we may conclude that in Tillich's horizontal world existence
separates and essence unites while in St. Thomas' vertical world it is existence that unites and essence which separates.
Tillich insists that .being is to be understood as dynamic and living.
In
order to understand being in this way he asserts that one must consider nonbeing as being as ontologically basic as being.
Everything that is partici-
pates in the power of the ground of being to resist non-being.
of the ground of being is actual in many centers of power.
Thus the power
When Tillich makes
·such statements, it sounds as though what he considers to be of major import~nce
are the beings themselves that are the centers of this power and that
the ground of being is merely an abstraction to account for the existence of
these many sources of power.
tenc~
In other words·, the ground of being has no exis-
outside of the finite beings in which its power is exercised.
Such a
�- 32 -
statement leads to the conclusion that there is really no such thing as an
ultimate that is necessary of itself
unles~
one consitjers t he _mysterious
power that ·each being possesses in its-elf tha t keeps · it fr.om passing into
non-being ·as_ some kind of ultimate.
Even if Ti llich does not mean to be
this radical, there is another difficulty that arises when we ask for his
definition of power.
He says:
"Power is the possibility a being has to actualize itself ·against
the resistance· of other beings~ · If we speak of the power of. _
being-itself, we indicate that being affirms itself against .
non-:being_ 0 . 9) .
.
, .
· ··'
But what
doe~
a statement like that mean?
i s offering any
~f ~on-being
resistance to being then it must do so _ virtue of some power •. Power,
by
however, is defined as an attribute of being.
th~n
it is nothing but a sort of being.
being that
i~
Can non-being be? _ so,
If
In other words, it is not non-
so necessary but a destructive principle in being itself.
Or perhaps one might say that Tillich means that potency lisp . et the
very heart of being, and there is no such thing as pure ease.
But if
Tillich means ~hat, how is the. ~ffirmation of being over non-being possible?
If being of
necessity . con~ains non-b~ing
or. potency, then we have
no assurance whateoevsr that someday things might not be different .
The
destructive element might become mo.r e powerful _ .N on-being might start
.
affirming itself ove·r being. " on·e might. even E;ay_ that with finite beings
this
re~ersal
is exactly what eventually happens.
They eventually pass
out of existence either through death or destruction.
Their affirmation
is only possible for a · certain . amount of time and not for eternity.
other words it is limited just as the beings themselves are limited.
In
This
-limitation .would certainly · be the case if, as we conjectured above, Tillich
really means to imply that all beings are finite beings.
Qur only answer ta the
h~man
In such a case
person is that .he must affirm- himself as a
result of the power to be that he finds both in himself and in other beings,
limited though it be.
In a certain sense , then , to ·speak of ul t i mate
reality is meanin9less.
If "one is in
. then meaninglessness with all of its
answer of ontology to the
f~ct
d~st~uctive
hu~an ~~r~on.
~adical polarity of Tiilich's ' ~orld~
forced into such a statement,
consequences is the final
These problems are created by the
He h~s attempted to ·take- non-be i ng
·J
9) Tillich, P., The Courage to Be (New Haven:
Yale, 1952 ) p. 179
�- 33 -
as more than a logical opposite ta being.
But as the negation of Being-Itself
which is the antecedent and basis for all forms, there is nothing left with
which to characterize non-being.
It is 'not' in all senses of the word.
being has neither esse nor essence, neither power nor form.
Non-
It can be under-
stood only as a logical term used in describing the relations between beings,
the distinctions introduced by essence • . In trying to go beyond this statement we run into the kind of difficulties that we have just met with in our
discussion of Tillich.
We have already seen that for St. Thomas Being-Itself is not plagued with such
Non-bein~
difficulties.
results from God's creation because created beings
must of necessity be less than He.
Non-being is a privation, a lack of the
fullness of being that belongs to God as pure esse.
It is seen in its true
perspective as a logical concept.
With reference to any
It has no power.
being non-being is determined by the amount of potency in the being and hence
by the distance from God in the hierarchy of baings, each of which mirrors
God according to its essence, of the being spoken of.
more non-being:
can become.
The more potency, the
that is to say the more ways in which a being is not and hence
However as long as the power to become is present there must be
some being in which this power resides.
One of the important consequences of St. Thomas' doctrine of being is the proof
for the immortality of the soul that results.
Man's soul is the first of the
intellectual substances which thereafter comprise the rest of the hierarchy
of beings.
St. Thomas argues that since these substances are immaterial, they
have no potency with regard to corruption.
Their only possibility of non-
being would be for God to cease to preserve them in being.
However, God, the
author of nature, does not take from things what is proper to their nature.
It is proper to the nature of an intellectual substance to exist forever because its
co~plete
substance is the · recipient of its esse.
It then follows
that God will never cease to preserve intellectual substances in being.
We
have seen already that a universe ordered to an end cannot be meaningless.
would
se~m
It
that this argument would take care of the second threat to man's
affirmation which Tiliich discusses:
that of anxiety about death.
For people
used to divorcing the human soul from the body it might be sufficient.
But
for ·st. Thomas, who' insi~ts upon the real unity of soul and body in the formation of the human person such an argument would not be sufficient.
For him
�- 34 -
the human soul is not a subsisting individual .
·with the body-
It is made to .be united
Hence something is lacking in the immortal soul.
This
lack can only · be ·filled when one turns to the doctrine of the resurrection. · The third anxiety, that of condemnation, does not arise ·1t seems
to me ·' in a philosophical situation.
situations.
Condemnation only arises in personal
That is to :say 6ne is only condemned by another persbn.
Thus
one can only be condemned ultimately; i.e., · once and for all, by an infinite person.
What this means in effect is that the anxiety about con-
demnation was not possible until .mankind became aware of the personality
..
of the ultimate.
. the
l~w.
1110 )
In St. Paul's famous words:"Knowledge of sin comes through
In St. Thomas' vertical world
m~aningl~ssness is not possible
because the whole world is ordered to an end.
contemplation of the essence of God.
This erid for man is the
Although this vision of man's end
is a very compelling one, I suspect that St. Thomas was right in considering
it available only to a few.
We must continue our search for the relation
of the person to the ultimate elsewhere if we are to confront the problem
of meaninglessness in general that faces mankind.
religion to philosophy to find his answer.
Tillich turns from
for St. Thomas it is necessary,
as we have already suggested, to move from philosophy to theology.
However, we cannot go on to speak of the relation of the person to the
ultimate in more detail without saying a few words about Tillich's use
of the word God.
We have already seen that in St. Thomas the .words God
and esse are interchangeable because esse is the most proper name of God.
.
..
At the same time we ·saw that for Tillich Being-Itself can be
equat~d
only
with the God above the God of theism.
Tillich apparently dislikes the
idea of calling Being-Itself personal.
Still he cannot avoid the fact
that not only do men continually speak of God in this fashion, but it
is even claimed that h~ has . thus revealed himself to men.
Tiliich says
that it is untiue to speak unsymbcilically about Being-Itself.
I take it
that such unsymbolicai speech is part of the philosophical endeavor.
The
problem of how one speaki about God was solved in St. Thoma~ by the doctrine of analogy.
As we mentioned earlier all things are according to
t~eir proper mode images of God.
Thus any perfection that we atttibute
to creatures so long as it in no way implies limitation or imperfection
is
p~edicable
of God analogically.
10) Romans, 3: 20
Such
applicati~n
is possible because
�- 35 -
God is the source of the esse of every creature.
The way in which Tillich
deals with the attributes of God and the peculiar relationship that he sets up
bet.ween Him and the God above God make · it difficult to understand him as
attempting such a doctrine.
What Tillich seems to be doing is some kind of
de-mythologizing in which our experience of Being-Itself is seen as contained,
for those who .use them in religious · statements.
He explains in his book
Dynamics of Faith that God is the fundamental symbol of the object of our ultimate concern, i.e., Being.
He says that
w~
form a concrete image of God,
symbolic of our ultimate concern, from the objects of our experience.
He
speaks, as we saw., of the life of God as the conquest of non-being, and says
that the ground of being is the permanent creativity of God in everything that
is.
In other words we find our words about God understood in terms of our
previous philosophical analysis of being.
Under the force of his devotion to
non-being Tillich shifts the idea of divine preservation to one of creativity.
11
As Bonhoeffer points out in his book Creation and Fa11 ), there is a dif·ference between speaking of continuous creation, i.e., being continually
created and speaking of preserved creation which is the confirmation of the
being given in the act of creation.
Making God's life consist in creation
makes his life depend upon his having a ·relation to soma being other than himself.
It is to remove him from being a being necessary of himself and to make
other beings necessary to his being.
witho~t
The ground of being cannot be considered
finite beings in whom its power ~ of being is active, as we aaw above.
Tillich exhibits the relational nature of the divine when he says that divine
transcendence is the expression of the creature's freedom to act against its
Sssential unity with God.
For St. Thomas, on the other hand, evil is a n
accident, a privation that inheres in some good.
in terms of a relation.
Like non-being it is seen
It indeed seems mysterious that a creature oriented
toward God as a final end can
ac~
in view of some lesser end, but this fact
has nothing at all to do with divine transcendence.
Divine transcendence ex-
presses the fact that although ail beings are existentially united to God, as
we saw eariier, God is not ~hose creatures and in no way depends upon them.
.
.
.
Tillich co~es closer to this idea of .transcendence .when he speaks of the complete otherness of the holy.
dence of good and .evil that
However, he attributes, to the holy a transcenlead~
to similar .questions to those raised by his
reconciliation of being and non-being in the ground of being.
St. Thomas, does not place the life of God in His creativity.
For him God is
11) Bonhoeffer, D., Creation and Fall (New York: Macmillan, 1962), p. 23
�- 36 -
the most perfect intellectual substance.
His life is different from that
of any creature because he contains no potency whatsoever.
The life of
God consists in the operations of the intellect to know and to will, intellegere et velle.
These are the only two actions possible for a com-
pletely self-contained being because they remain within the agent.
How-
ever, unlike that of any creature, God's knowledge and his esse are the
same.
God is one.
No essential distinction .is possible.
God's knowledge
is not separate from His act of knowing.
Thus God's life is no way con-
flicts with His unity and transcendence.
Furthermore it is in terms of
these two actions of God that St. Thomas understands the doctrine of the
trinity which is the theological basis for a meaningful understanding of
the human person as the likeness of the divine persons, as we shall see.
ii
Tillich asserts that personality is established in the encounter of two
egos.
This encounter must include the reciprocity
and receiving answers.
~f
asking questions
Such a definition necessitates some sort of
equality between the two parties involved.
When Tillich speaks of a
person as individuality on a human level, I uneerstand him to mean that
individuality that is established in the encounter which he considers
necessary to personality as such.
One's individuality is established in
one's relationship to other individuals.
Since only human beings are in-
dividuals capable of asking questions and receiving answers, only they can
be persons.
The relationship in which human personality is established
must be free and reciprocal.
The human person entering into such a re-
lationship, then, must be free to act, and as· a result of this freedom
he must be responsible.
How can an ultimate which must create be free?
How can an ultimate whose power of being is actual in many centers of power
be established as individual?
How can an ultimate which corresponds to
Tillich's ground of being be personal?
The answer to these _questions i s ,
as we have indicated above, it cannot.
The question before us, then, is:
is a relation to the ultimate possible?
W~en Tillich begins speaking about the relation between the person and the
ultimate .he begins using language which is similar to that used by tradi tional theologians about grace.
According to Tillich man's
rel~tionship
�- 37 -
to the ultimate is.one of faith.
St. Thomas would agree that faith is neces-
sary for the relationship between the human person and the ultimate in the
theologiCal sphere.
But for. St. Thomas this mer i tor io.us ·faith is, as we saw
earlier,· complete ·certainty about t~ose truths whicih have been revealed and
are not known by reason.
By faith we assent to revealed truth and the saving
action of divine grace can now take place in us.
question put to the candidate for baptism is:
of God?
In the Roman rite the first
What do . you seek of the Church
When the candidate has answered, faith, he is asked: What does faith
obtain for you?
To this question he answers, everlasting life.
He is then
instructed that if he wishes life, he is to keep the commandments, and these
commandments are summarized in the two great commandments of love of God and
neighbor.
Thus in the liturgy of baptism the Church sets out this important
relationship between faith, the life of grace and finally ths reward of
.·. eternal life.
When Tillich speaks of faith he speaks of it as a state of being grasped by
ultimate reality.
Because the man of faith has been grasped by the power of
being, he is able to affirm himself by participation in the
the ground of being.
~ffirmation
in
Despite the s i milarity between the idea of being grasped
by something and the free gift of faith, Tillich means something very different by faith.
Faith is not the beginning of a new relationship between man
and God and man and his neighbor; rather it is centered upon the individual
man and his power of self-affirmation.
this affirmation.
Being is all that is necessary for
When we remember Tillich's insistence upon our essential
unity with being, it sounds as though what happens in this grasping that constitutes faith is man's realization of this essential unity with the ground of
being which is continually conquering non-being.
At this point all the dif-
ficulties that we saw earlieJ;' about this affirmation of being over non-being
enter the picture.
Consistent with his discussion of the relation of God and
being Tillich asserts that the relation between man and God gives symbolic
and personal content to ·man's relationship with Being.
relationship to Him is symbolic.
It is not a
pers~n.
The ground of being is the ground of
The personal enters in in our relation to
the fundamental symbol for ultimate reality, God.
~nly
Our
Here again we meet Tillich's reluctance to
attribute personality to the ultimate.
personality·.
God is symbolic .
It seems, ttien that the
possible relationship to the ultimate itself is that with which we begin
�- 38 -
according to Tillich, . the. essenti'al one. · This relationship is that which
..
is expressed symbolically in' our relationship to God.· This symbol, we
are told is deri~ed from our concrete exper~ance~ ' As per~on~ the most
·important ·item of this experience is our personhood.
It is · in terms of
this personhood that our relationship to ultimate reality is expressed.
It is this personhood that causes our search for ultimate reality · in the
first place. · T'hus ·we choose a personal symbol ?or ultimate reality, and
our ielationship to it is one of freedom and reciprocity.
Despite his rather thorough job .of "de-mythologizing" Tillictt .seems to
.
'
think that for a person to have a meaningful relationship to _
the ultimate
this relationship must be contained in symbolic for.m.
it seems, on the contemplation
o~
We cannot live,
He does not aay what it is in our nature that makes such
difficult or impossible.
'.
our essential unity with . being alone.
ex~stence
either
I suspect that with his understanding of being
and non-being one would be much too close to
affirmation from despair.
t~e
thin line which divides
We saw just how thin this line is earlier.
We see the importance of the symbolic when Tillich speaks of revelation •
.
,.
·'
He says that revelation is an experience in which an ultimate· concarn
grasps the human mind and creates a community in which the concern can
express itself in symbols · of action, imagination and thought.
I'
The effect
·of such an event of revelation is that it reconciles the estrangement
between faith and reason and transforms the existing situation in religion
and culture. -Of
r.
cours~,
it does so because it is received by a group of
men who constitute the community in which this concern is symbolically
embbdied.
This reception of revelation Tillich calls religion.
The re-
lation· of this concept to biblical religion and Christianity in particular
is that the New Testament picture of Christ has saving power for. tbose
who are grasped by it.
In other words biblical religion has saving power
· within it·s own community.
We can say of it that i t is a symbolic embodi-
ment of man's relation to being.
.r
The saving power of these symbols con-
sists in the ·afffrmation of the human pera_ n which occurs through the
o
relationship to Being-Itself which they symbolize • . Keeping this basic
symbolic character in rnind let us now
· about
th~ rel~tio~
ex~mine
what TillicW has to say
of the person.to the ultimata.
We have already.noticed ·the primary · fact about biblical religion , i.e .,
�- 39 -
the personality of the ultimate.
Very early in the paper we spoke of this
idea as the discovery of the Judea-Christian tradition.
How~ver,
Tillich
does not wish to go so far as to call Being-Itself personal and so introduces
personality as a factor in a symbolic relationship to Being.
It is such a
symbolic account that we find in the Bible, according to this view.
We have
seen that the basic requirements of personality are individuality and freedom,
both of which become actual in the encounter between two egos.
These require-
ments determine the symbolic and personal content that biblical religion gives
to man's relation to the ultimate •
.One of the first places that we meet this idea of individuality is in the doctrine of creation.
When we were speaking in philosophical terms we saw that
for Tillich creation implied the essential unity of man and the ground of
being.
Here this unity is repiaced by what Tillich calls personal distance.
God becomes totally other - which, by the way, is Tillich's definition of
holiness.
Because of this ''otherness 0 a reciprocal divine-human encounter
becomes possible.
The will of God is expressed in His command to the free
and responsible human person.
However, Tillich never lets one lose sight of
the ultimate which lies behind this personal God.
Thus we find him speaking
of the word of God as God's manifestion of Himself to Himself.
Word an element of Being-Itself which is manifest in many forms.
He calls the
When one
reads this statement one immediately recalls the power of being that was
actual in many centers.
~
It seems that what he means by the word of God is
the symbolic expression of the power of being.
personality, but it is not personal.
Being-Itself is the ground of
Thus Tillich also speaks of God as com-
prising both sides of the divine-human reciprocity and transcending it.
Those
particular beings know as persons are actualized through the power of Being.
It seems then that as soon as we start understanding God in terms of Being of
which He is the symbol the relationship between persons as applicable to him
vanishes.
Our relation to Being only becomes personal when God is taken as a symbol
having validity in its own right.
We have seen that our concern about being
threatens us in the very center of our personal existence.
The ultimacy of
our concern is expressed in the encounter with God by the unconditionality of
His power, demand and promise.
all others.
Being is symbolized by the person free above
Thus we see in personal terms the being for which no reason can
�- 40 -
be given, which is the object of our .ontological enquiry.
Of course, if
non-being is as basic as being, then no reason can be given for its existence ~ither. · Nor can we _
give· any reason for the conquest of non-being by
being.
.These acts are simply 9iven. of our exper.ience.
Being~Itself ~
oui being is affirmed through the affirmation of
c~nnot
h~man
say·why that should be
$0.
We may say that
but we
We may say that through the divine-
encounter we · ca~ discover what it ls to be a free and totally in-
dividual
· ~arson,
but beyond the symbols our only ground for personality
is the transpersonal affirmation .of being-itself • . In St. Tho·mas, as we
have already seen, God is his own necessity.
As far as anything else is
concerned His action gives being to both means and ends for the sole
I
.
reason of . communicating his beatitude and intelligibility.
Non-being
and the affirmation of beings find their 'reason' in God, who is ipsum
esse, To-Be-Itself.
Tillich elaborates on this problem of the relation of the .p erson to the
ultimate in his discussion of the incarnation.
the principle of divine self-manifestation.
can enter into a personal human life.
person
s~ould
He speaks of the · Word as
Because God · is personal He
When He
~foes
so we see what · a
be. · The a-personal element which tries to disrupt human
existence is overcome
becau~e
the personal . center united to the
center of the · divine life rules to whoie man.
p~rsonal
We have seen that the
personal center is that center from .which the free and responsible individual acts.
This center is disrupted by the anxieties of death, guilt,
and meaninglessness.
Thes~
anxieties .are overcome by the individual's
participation in the affirmation . of Being-It"self.
We may conclude ·, then,
· that the incarnation is the perfect manifestation of the coura9e· to be.
It is ·from this rionquest of the limits of
is analogous to · salvation.
~he
personal that we find what
Transformation in the ethical sphere takes
place because ethics consist in acting for or against the law of love for
which Christ stands.
God.
Love unites what · is
non-being.
in
• .·It unites man with
moral acts . must follo~ from this union because to ·act against ·it
means ·destroying one's self , b.Y
,,.
separ~ted
aiblical
confronti~g
eth~cs
cast~ng
one's self into the despair · of
confronts the human ·person with ·tHis decision
him ·wi th the commands of God.
.
At the very· beginning of
�- 41 -
this section we saw that personality is established .in the encounter between
two egos.
We have also spoken of the unconditionality of God's demand, power ,
and promise.
Thus it is in the confrontation with ·Gdd's unconditional demand
that the human person is most called upon to exercise his responsible freedom.
Tillich says:
••man is essentially finite freedom; fread6m not in the sense
of indeterminacy but in the sense of being able to determine
himself in the center of his being." 12). .
I understand him to mean that through the exercise of his freedom in his relationships with other egos man determines himself in his personal center
which is the center of his being.
The responsible exercise of his freedom is
most important in man's relationship with God, the symbol of Being-Itself.
If he acts against his essential union with God, or the ground of being, he
has no choice left him but despair.
This
the
em~hasis
i~portance
upon the importance of ethical action leads directly to that on
of the community.
We have seen that the community is necessary
for the symbols of man's relationship to being, to .be active.
By belonging
to such a community the religio'us man participates in the symbols of that community and thus expresses his relationship to Being-Itself.
In so doing he
may not even reach what Tillich calls absolute faith, the faith which takes
doubt and meaninglessness into itself.
This absolute faith is the state of
being grasped by ultimate concern about which ·we spoke earlier.
come expressed in the symbols of the community.
it must be so embodied if it is to remain alive.
It has be-
Tillich even suggests that
Thus the move from absolute
faith to the community, from being to God is necessary if the revelation is
to be passed on.
However once the community is established one has moved from
the realm of the ' ultimate to that of the symbols which render the ultimate
finite.
As we mentioned earlier, why it is that we must do so is not clear.
Perhaps ·the move is necessary in Tillich's system because of the demands of
the finite human person.
In conclusion we may say that Tillich has rejected the personal ultimate as
such.
He · has
tak~n
religidn as symbolic ontology and asserted that they both
are concerned with the same problem.
12) Courage to Be, p. 52
In both cases the affirmation of the
�- 42 -
human person is the result of his participation in the affirmation of being.
As we have seen there is some difficulty with the affirmation of being due
to the necessity
~~ich
Tillich accords to non-being and the being - non-
be ing polarity in.w,hich being somehow is always ascendant.
Thus the
guarantee which the human person has against meaninglessness . is basically
a philosophical one.
The philosopher has faith becaus,e he is grasped by
Being-Itself; the religious man, because he participates in the symbols
..
of his community which were created by this ultimate concern.
iii
We have now examined the philosophical relationship_ whicp .each man has set
up between the person and the ultimate.
We have seen that for Tillich
-·philosophy is as far as we can carry our investigation.
However, at the
end of the First two sections we were left hanging on the verge of a
theological investigation of the human person which it is finally time
to undertake.
This step, as we mentioned in the last section, . is made
possible through faith in the traditional sense of the word.
A theological
understanding of personality depends upon . the doctrine of the trinity in
which the radical personality of the ultimate is displayed.
Here it is
shown that salvation is not, as Tillich supposes, a symbolic manifestation
of a philosophical relation.
The human person is not asked to conquer
meaningle$sness because of some conquest of being by non-being.
Rather
his personhood is his greatest gift because it is the image of the divine
personality itself.
He is called to participate in the life of God, not
by an affirmation stemming from God's creative act, · but by parti6ipation
in the love which unites the three divine persons.
at the very heart of Christian theology.
which is
God.
ult~mately
Thus the trinity is
It speaks of the hasis of love
the only reason that can be given for the acts of
Thus it. is the reason for theology.
As Hugo Rahner remarked:
"The
Trinity is the informing principle and the sustaining foundation of the
Church, of sanctifying grace and of our final glorification. 1113 )
. Creation cannot be the foundation of human personality because it is the
completely free act of
13)
~he
triune. Godhead.
It is not the life or the
Rahner, H., The Trinity in Preaching in The Word, _p~ 202
�- 43 -
essence of God.
It is rather an operation of God.
As the source of that
operation we find the three persons united in one nature.
As St. Gregory of
Nyssa puts it:
"Rather does every operation which extends from God to
creation and is designated according to our differing
conceptions of it have its origin in the father, proceed
through the Son and reach its completion by the Holy
Spirit. 11 14)
We have already seen that the philosophical basis for our understanding of the
trinity lies in the life of God, who is so completely one that His very existence is His intellection and His love.
Through revelation we learn that in
this one God there are three persons and that we are brought into a participation in their life through grace.
As St. Thomas says:
"Hence since the charity by which we love God is in us
by the Holy Spirit, the Holy Spirit Himself must also be
in us as long as the charity is in us. And so the
Apostle says: 'Know you not that you are the temple of
God and that the spirit of God dwellath in you?' Therefore since we are made lovers of God by the Holy ·Spirit
necessarily the father and the Son dwell in us also." 15)
St. Thomas never tires of reminding us that we have now become friends of God
or as St. John says: "Beloved we are now Sons of God. 1116 ) which is as strong
a metaphor as one can get.
Although perfect possession of God only comes with
the beatific vision, our participation in the divine life begins here and now.
Undoubtedly the radical affirmation of human personality that this doctrine
involves is already clear.. Let us consider it in more detail.
We begin with the concept of person.
a person as follows:
following Boethius St. Thomas defines
"Persona est rationalis naturae individua substantia."
17
)
Person, then, fs the special· n~me given to individuals of a rational nature.
To begin with a person must be an individual substance.
substance must exist in itself, distinct from all others·.
of or common to something else.
That means that this
It cannot be part
Tillich also insisted upon individuality as
a criteria for personality, but he included only human persons in his category
of persons.
It also seemed that his idea of individuality was established in
14) Gregory of Nyssa, An Answer to Ablabius: That We Should Not Think of Saying
there are Three Gods, in Christology of the Later fathers, E. R. Hardy, ed.
(Phila.: Westminster, 1954) p. 262
15) S. C. G., IV, 21.
16) I John, 3: 2.
17) S. T. I Q. 29 a. 1.
�- 44 -
a relationship.
It depended upon a character of the spirit which he spoke
of as the personal center.
This statement does not mean to deny that
other things could not be individual substances in Tillich's view.
What
I mean by this remark is that the individuality upon which the human
person depends for Tillich is a spiritual
ind~viduality.
Thus if he
could prove the immortality of the soul, he would say that this proof
overcomes the anxiety about death.
But we have
al~eady
Thomas this anxiety is not that easily dismissed.
of all an individual substance.
seen that for St.
A person must be first
Therefore he asserts that no part of man,
body _or soul, can be a person because these parts are all made with a view
toward being unified in man.
Thus St. Thomas concludes that everything
which makes a man an individual including flesh and bones belongs to the
meaning of a human person.
Here we have an affirmation that does not
simply touch man intellectually and spiritually, it takes in everything
that a man is .• . It
the resounding Yes of the resurrection.
i~
In order
to be a person this individual substance must also be rational because a
person must have dominion over his ow.n actions.
Here we see Tillich's
criteria of freedom and responsibility strongly asserted but without the
accompanying talk of
relations~
Perhaps the reason for this difference
lies in Tillich's idea of the distinction brought about by existence and
the ·unity brought about by essence.
It is very interesting to note that
·in St. Thomas where the opposite is true in God where the three persons
have the same essence 'person' signifies a real relation subsisting in
the divine nature.
Created natures exhaust
the~selves
in one person,
but the eternal unity of the divine nature rests in three persons without
fraction or tension.
The relations which constitute the divine _persons stem from the -two int~llectual
processions which, as we
~aw,
constitute the life of God.
We
understan·d the Son as the perfect intellectual pro~ession by which the
Father perfectly understands His essence.
not generation
unders~ood
Here we find perfect generation;
as in any way _
passing from potency to act, but
understood accordin'g to the famous definition:
conjuncto in simili tud inem
18) S. T. I Q. 27 a.2.
nat~rae.
1118
)
"or igo v iventis a v ivente
The divine logos proceeds from a
�- 45 -
mode of intelligible action which, as we have seen, is an operation of God.
The Word is of the very substance and essence of the Father from whom He differs only by his relation of filiation as opposed to that of paternity.
we have reached a level that is simply impossible for Tillich.
that we too are called to be sons of God.
Here
We saw above
Our sonship is not the same thing
as our status as created beings made in the image of God.
It is given by
grace and is the consequence of the natural and most perfect sonship of the
second person of the blessed trinity.
The sonship of Christ is the ideal of
our relationship to the Father.
As we have seen, this relationship to the Father is completed through the
action of the third person of the trinity, the Holy Spirit.
The subsisting
relation which is the Holy Spirit is based on the second procession in God,
the act of the divine will.
The mutual contemplation of the Father and the Son
necessitates a mutual act of love which is the operation of the divine will.
Because it is so little understood we have no name for this relation.
it spiration.
We call
This act of love issues from the divine essence itself but is
distinct from the Father and the Son by reason of its origin from them.
Holy Spirit is the personification of divine love.
The
Rahner points out that:
"The passionate love of the Incarnate God for the Father is
the human manifestation of that spark of love eternally
exchanged in the bosom of the Father through the Spirit." 19)
The incarnate God is also the human manifestation of the love of God for men
which is so great that it makes men His friends by allowing them to share in
t he l ove that He has for Himself.
As St. John of the Cross reminds us:
"Love creates a likeness !between that which loves and that
which is loved." 20)
Through the third person of the trinity the three divine persons dwell in
men's souls making them here and now sons of God capable of union with Him.
As a conclusion to our consideration of the doctrine of the trinity I would
21)
like to quote Thomas Merton's poem, "Hymn for the Feast of Duns Scotus"
from which my title is taken:
19)
20)
ed.
21)
op. cit. p. 198
John of the Cross, St., The Ascent of Mount Carmel, Peers trans., (3rd
New York: Doubleday, 1958), p. 28
Merton, T., The Tears of the Blind Lions, (New York: New Directions, 1949)
p. 6
�- 46 -
On a day in fall, when high winds trouble the country
I visit the borders of my world, and ·see the colofed hills.
And while I walk upon theit coists
The woods and grasses tumble like a sea:
Their waters run after the dry shores
Of the path made for my feet. :
And I open the book of Duns Scotus,
To learn the reason for theology.
This is the book whose vision is not its own end,
Whose words are the ways of love, whose term is Trinity:
Three Who is One Who is Love.
One, because One is the reason for loving
And the One Love loved, But Three
Are the Three Lovers Who love and are loved
And are Love.
One is the Love we love, and love for:
But Three are those we love and
One our T~r~e Lovers, loving One another.
Their Ona Love for One another is their Love for us,
And One is our Love for all Three and all One
And for us, on earth, brothers, one another!
One God is the One Love propter duam amatur
And Three Persons of the One Love are quae amantur.
So to love One alone is little better
Than loving none.
But to love Three -is to love One.
Now today, while these Three
Love One another in me,
Loving me, and I love them,
Suddenly I can no longer .live in mortal flesh,
Because your book, O Scotus, burns me like a branding i~ on !
If I could only breathe I would cry out, if I could cry,
To tell someone what Voices robbed me of my being!
For the sound of my Beloved,
The voice of the sound of my Three Beloved
(One of my Three ~f my One Beloved)
Comes · down out of the heavenly depths
And hits my heart like th~nder:
And lo! I am alive and dead
With heart held fast in that Three-Personad Love .•
And lo! God, my God!
Look! Look! I travel in Thy strength
I swing in the grasp of Thy Love, Thy great Love'~ One Stre~gth,
I run Thy · swift ~a~s, Thy ~traigh~est rails
Until my life be<?omes !hY ~ife -_ an. sails o.r rides like an express!
d
�~-1
- 47 Word, the whole universe swells with Thy wide-open speed,
Father, the world bursts, breaks huge Spirit, with Thy might
Then land, sea and wind swing
And roll from my forgotten feet
While God sings victory, sings victory
In the blind day of that defeat.
Thus we have seen that Tillich conceives only of a horizontal, . polar world
out of which the human person must find a way .or be torn asunder by opposites.
St. Thomas' world
~n
the other hand is
~ut
by the vertical ascent of grades
of being to the divine Being, ipsum esse, which is not some thing but an act.
This act is so powerful that it is able without lqsing any part of itself to
enter Tillich's polar world
a~
a being subject to its laws and to transcend
them thus transforming human persons irito the likeness of divine persons
whose essence is the foundation of the world.
Man · does not merely affirm
himself with the possibility that his affirmation may fail.
by the grace of God, To Be itself.
cross.
In hoc signo vinces.
He is transformed
The world is marked · by the sign of the
�- 48 -
solennels
mains au menton
Je verrai
Les
les
I1 est
les clochers
chants
ces
font
�- 49 -
LANDSCAPE
Christian L. Harrison, '64
Prize French Translation,
1964
So that my eclogues might be chastely dona, I
Wish to lie, star-tellerlike, close to the sky,
And listen, hard by chiming towers, while my dreams blend
With solemn singing carried on the wind.
My chin hand-braced, from my high garret's listening post,
I'll see a prattling, singing workshop with its host,
The pipes and belfries - mastheads of modernity, And star-crazed skies that sire dreams of eternity.
Its sweet, on looking through the .haze, to see the sky
Give birth to stars, lamps light windows beneath the eye,
Grey streams of smoke flow towards the firmament,
And the moon pour down her pale enchantment~
Springs, summers, autumns - three fair seasons will I greet,
And when winter comes, to bore me with its sleet,
I'll close my windows, bind all shutters tight,
That I might build a fairy palace in the night.
Then shall I dream of blue horizons, and of green, cool
Gardens, fountains weeping into alabaster pools,
Of kisses, bird choirs singing morn and evening se~sions,
And of all of Idyll's most childlike possessions.
Winter, storming vainly at my casements now~
Can never startle from my desk my cradled brow,
For I shall be plunged in the ineffable thrill
Of evoking the Springtime with only my will,
Of drawing a sun from my heart, and making here,
With my burning thoughts, a tepid atmosphere.
�- 50 -
THE KETTLE LISTENERS
Veronica Soul '66
Allen unhappily faced Mrs. Leighton ·in the narrow hallway.
He had just
thanked her profu$ely for the lov~ly handmade curtain~ ~nd · ilias sorry to
have said anything at that mbment.
She was blushing and he avoided her
eyes while he· tried to . invent a plan of .escape. · The s . eam · kettle gave
t
the warning hiss - the slightest whistle unnerved Allen - .and he hastily
excused himself from her unchanging grin.
The door wouldn't shut properly.
Mrs. Leighton waited outside .the door as though expecting Allen to return
with a fresh load -0f compliments.
"Wlla t the devil if I do slam it ? 11 he said.
it.
But he .was too hesitant to do
Allen's voice was muffled by the whistling steam.
i'If I don't shut
it now, she might think . I~e left it unhitched for her and God help me if
that nestling rhino settles between me and the door.''
more intense.
stained teeth.
The whistle grew
Still .Allen thought he heard her -breathing through her teaAfraid that she might be moving
~loser,
he stuck half an
eye beyond the stubborn door.
"Oh, there you are again, Mr. Keeler", she chortled 1 "I ·thought you might
not be coming back, but there you are.'' ·"If you' 11 pardon me, I must
catch the kettle", he said quite loudly and slammed the door without
losing the doorknob.
It was a mark of great control not to open the door
just to watch her mascaraed eyes enlarge and the corners of her creased
lips drop to form another set of wrinkles where the cherry flavored lipstick had spread.
Allen ran for the gas jet and reached for silence.
The Brighton's Marmalade
jar, tightly capped and half full of stale holy water, rolled under the
stove, Allen had a habit of kicking holy water.
The jar and its contents
had been given to him by Mrs. Leighton the day after Ash Wednesday and he
amused himself by setting it in the center of the floor and keeping score
of how often he knocked into it by accident.
The high scores were usually
made at night on his way to the lavatory he shared with Rick, the "sometimes
sculptor~
who sold toys at the Jack-in-the-Box, the neighborhood kiddie
�- 51 -
hangout.
It was late March - the first day of spring - and snowing.
The radiator was
working overtime for a change and Allen was reluctant to turn it down, even
a half twist of the tarnished knob.
window.
He tied back the curtains of the front
They were outstandingly ugly and unevenly hemmed.
Allen had thought
of framing them and had even typed a label, "Gross Red Petunias in/on Yellow
Field.''
Mrs. Leighton had probably made them from left-over charity dresses
that were too small for her bread-fed shape.
Feeling empty, Allen shifted his typewriter in front of the window and
the snow for ten minutes.
mai.ct.sd
Then he put his hands to the sides of his face,
like blinders, to avoid seeing Mrs. Leighton's handiwork.
The snow fell for
another ten minutes before Allen dropped his hands and tacked the curtains far
beyond the window frame.
He wished that he smoked even though he didn't have
enough change to buy a pack.
wearing
He reasoned that it might stop his hands from
out the back pockets of his corduroys and he'd feel ' as though ha were
doing more than staring at a brick wall through sudden fistsfull of snow.
Hi s
Creigh Streat apartment faced the side of a film house which had bricked up
one of its two side exits.
On spring nights the depraved schoolboys would
pretend to play Spud while one of them tried to work open the door with a
broken penknife or a sister's nailfile.
"Even if I did smoke," he thought, "I don't have the price of a pack and that
would really upset me for a change.
I might be tempted to pawn my typewriter.
I might go so far as to ask the girl upstairs for a couple of smokes.
just 'til the banks open', mind you, or I could say there was a delay in the
mail
• my check from the magazine hadn't . arrived • • • temporarily out of
cash • • • so she wouldn't take the wrong impression of me."
Allen was easily sidetracked by minor difficulties.
Today it was the impres-
sions of a stranger; tomorrow he might find a miscolored growth on his foot.
Living alone makes a person notice matters worthy of careful musing - matters
that might be brushed aside by people with well planned days and lives.
As
Allen walked to the window, his outgrown bangs turned a murky brown in the
gray snowlight.
His hair was a fragil brown, the kind that has no permanence
and follows the modd of the day.
"Maybe she doesn't smoke.
But she looks like a girl who smokes.
They can
�- 52 -
surprise you, though.
Heavy tortoise rims, black hair bluntly chopped by
her own hand • • • probably a nervous social worker.
another Mrs. Leighton.
At least she's not
Allen forgot the curtains, although one of them
had swung back across the left side . of the window.
He wanted to dash to
her apartment just to stop the irritating curiosity.
He bent to the height
of the mirror and looked in.
"Ive been wondering • •
like that."
"
Wrong approach.
"I could never ask her outright
Allen's eyes were stunning and his expression equally as
catc;:hing, but his verbal approach was sometimes miserable.
"Pardon me,
I'm Allen Keeler from downstairs and I've noticed • • • No.
thd.n. there's anything in particular on my mind."
k
"Hello, Miss •. • • Miss • • • "
He frowned.
He smiled sweetly.
"Hell no, that sounds like
I.' m trying to get an introduction with out the middleman."
length of brown hair behind one ear.
it looks great this way."
Don't let her
~e
pushed a
"Needs a bit of a trim • • • even if
Perhaps he would meet her on his way to brush
his teeth and nonchantly ask whether she'd like a smoke.
t•eefore brushing?
No thanks."
He walked back to the window and slipped a hand into his pocket to practice
the casual .offering.
As the other curtain slipped· between his nose and
the window, Allen decided to stop a silly concern about the personalhhabits
.of a woman he's never met.
He found a sheet of scrap with one side blank and fed it into the typewriter.
He ran a line of type
He stopped.
a~ross
the top.
It read:
"Sheila's a nice name for her.
Sheila, Sheila, Sheila •
Mandy isn't.
'sometimes be a Christine ~ •• I'll see if Rick's in.
A Sheila could
He'll introduce me
to her, we'll say hello and then I'll come back ready to work.
But she
·might refuse without saying 'No thanks, I don't smoke'."
Allen jumped up, knocked the door open, started for Rick's and nearly ran
He had tried to break f~om ~is pat~ and lost his balance.
into -Sheila.
looked down at Allen in concern and said, "I' ·m terr lbly sorry!
. hurt?"
"Not at all, thanks," he replied without moving.
she asked.
Are you
"Are you sure?"
Allen lept to his feet and apologized several times as he
walked backwards to his apartment.
didn't latch.
He pulled the door shut, but again it
Leaning against the door
fram~, .
Allen nudged the door open
She
�- 53 -
and watched her climb to the next landing.
She looked back to see Allen
gnawing a pencil while mumbling "Sheila, Sheila • • • ?• 1
and shouted at -her, "Yes, thank you.
the pencil from his mouth, he
repeat~d
away and Allen slammed the door.
He caught himself
Everything's fi,ne really. 0
the same assurances.
Then taking
"Sheila" turned
0Q:CO:t:-k11ob still intact • .
He tied back the curtains and poured out a cup of strong green tea.
written anything worth keeping in weeks," he said.
"I haven't
"I'm nearl_y out - f typing
o
paper, physically. :unfit, don't smoke, take my morning constitutional around
Bradstreet Square three times, have a mother and father who
like them.
Children and dogs don't bother me.
a high holy water record, and make bad tea
l~ke
me.
I even
I'm an unsteady writer, have
• and worry about the private
1 i fa of • • • and .God bless Mrs. Leighton while I'm th inkir:ig at all!:" he
. . be llowe.d.
Hours later Allen was peering out the crack in the door.
since God blessed Mrs. Leighton.
It's the week-end.
He had been there
"I wonder whether she goes out at night.
Probably spends too much time staring out the window.
mother would tell her to get out of the house - take an airing.
Her
So much win-
dow watching can stiffen a girl's back."
Sheila still hadn't come down and the building was entering the nightly after nine silence.
Allen straightened with some pain.
Taking a light raincoat
from the chair, he fitted the waterproofing over three layers of woolens.
He
re-tied his sneakers, his only protection against the melting slush.
Once down the front steps, he started along Creigh Street.
Two lefts and a
right, and he entered Carradine's, a corner bar, off-beat, with a dark cafe
set-up in tae back.
In the corner where a good Dixieland group used to lodge,
. the punchboard of a shimmering juke box glowed in reds and yellows, a familiar
combination.
The
ne~s
columnists congregated and conversed under the irrepres-
sible beat of the big pop imports.
Carradine was having trouble with a reddened and burly regular.
to a
~ovie,"
touri~t
Carradine muttered as he stalked past Allen.
"Ji'm,·going
A middle-aged
couple was appalled at the drunken brute's behaviour, but sat silently,
afraid to tackle such a huge reeler - especially after ~he management had
walked out.
Maxine trotted forward, her plum hair flowing to her apron strings
Her face was heavily touched by the paints of a modern Nefertiti's cosmetic
�- 54 -
box.
A native of the North
Atlantic~
southerner for the joy of it.
she spoke like a self-educated
"Now Everett, look heah," she drawled,
"you jest git yo'slf out o' ma howse."
ffiaxiMe, he
s~aggered
With a well directed shove from
through the side door like a reprimanded child.
tourists were impressed by such a
st~iking
southern belle,
The
maxima was the
salvation of Carradine's.
Allen observed these nightly .exhibitions from a nearly hidden tabla jammed
between a beaten wood phone booth .and the wall.
He
finished the glass of
seltzer spiked with · 1emon juice. - "on the house" while iYlaxine ran . the show.
_.Maxine's a girl who. smokes.
All'e n mused.
Allen's head.
Now if Sheila handled herself that way • • • ",
The stomping beat of the next record shattered its way into
"Damn!"
municative tonight.
he shouted, a little unsettled.
Again the tourists were aghast.
"What's the matter, Mr. Keeler?
Allen was com-
Maxine coddled Allen.
Don't you like the longhair mods?"
Allen
lifted himself from the pinched chair and thanked Maxine as he slipped past
the visitors' table and - headed for the night air • .
If was snowing again, · coating the half-jelled slush.
clock illuminated 11 :48.
Creigh :·street was deserted.
A girl bent over a
asleep but Sheila's light was on.
. of . the uncurtained window.
her lips.
Th• Savings Bank
Mrs. Leighton was
t~pewrit~~
in front
A cigarette shook in .the uncertain bl inch of
Allen walked slowly past the .boarding house twic• to assure him-
·self that it was Sheila with a real cigarette.
"Yes, it's lit," he said,
as though she might nibble or suck unlit cigarettes.
Allen was cold and calm, ready to work.
wetprint trail on the thin carpeting.
switch.
Nothing happened.
He flicked on the ove.r head light
The desk iamp was almost as disappointing -
•
.only fort¥ watts.
He mounted the stairs and left a
.~ 1
'
"The housemother is
to disturb the bugs," he grumbled. ·
probab~y
~'Christine
in .bed, and I wouldn't want
- Sheila - might have a
spare."
Hearing footsteps, he tho.u ght it was Rick. . "Footsteps on the stairs at
this ungodly hour?" he observed· ·1oudly in mock anger while the kettle hissed
,, before the .inevitable explosion.
There was a hesitant knock.
Soma of his
forty watts flooded! ithe haii as the door opened. ·
'·'H ello, I'm Mandy Plummer.
I live above you and l' ve just · run out of • • • 0
�- 55 -
"Yes, I know you smoke and no,' I don't have any," he said, cut short by the
whistling kettle.
"What?" she called, unable to hear him.
"I'm Allen Keeler, also a writer, and I .need another light bulb," he shouted<
in one breath, "Would you have one handy?"
at top blast.
The kettle was asserting itself
"And yes·, I know you smoke, and no, I don't have any," he
added.
"And no, what?", she mouthed above the chaos.
"And no, I don't have any •
would you happen to have • • • ?" he attempted.
nNo I wouldn't and thanks," she yelled and slammed the door.
Breaking in again, she walked up to Allen and hissed in his ear, "And I wish
you'd stop calling me
Sheila~
·The sound keeps me awake nights."
Mrs. Leighton in he.r nightdre.s s reached the second landing in .time to see
Mandy hand the detached doorknob to Allen and slip up the stairs.
her kind give you any bother," she advised..
"Don't let
"Her father's nasty too.
He
wouldn't send you a calendar come Christmastime, if you bought his coal and
sent him a greeting card."
like a bulldog's.
She gave a grimace that revealed a set of teeth
Allen wrinkled his nose.
he called, pointing to the stove.
"The kettle, you know • • . ,"
She didn't seem to· hear, so he walked to
the stove, turned down the jet, and repeated softly in the tremendous silence,
"The kettle, you know •
"
He reinserted the knob and closed the door.
Mrs.
Leightqn smiled faintly in her blushing pink nightgown, until she heard the
door latch.
Allen was safe again.
*
*
*
*
*
*
*
*
*
*
Allen lay in bad trying to sea the brick wall .through the late morning mist.
There was a slight pawing at the door.
He grunted, skirted the holy water,
and proceeded carefully and shoeless to the door.
11
0h, I hope I didn't wake you, Mr. Keeler.
I thought\1you might like a pot of
tea with me, as you didn't seem too well last night • • • I mean you were so
�- 56 -
abrupt and • •
II
"Mrs. Leighton, that's awfully nice of you, but I've been up for hours and
if you don't mind, I'd just as soon make my own tea. 11
f98ut you really don't look as bright as a young man should and with the
weather being so dreary you should certainly let me fix you a pot and I've
brought some headache pills - they're the white ones - the pinks are for
nausea • • • "
She had edged her way to the stove and left Allen at the door with a handful of pills.
mrs. Leighton started to wash the brown stained cups as her
mouth rambled.
"Sometimes the city has wretched weather, don't you think,?
But living near the bay with the harbour three blocks down, we have to expect a mist occasionally."
Allen might have agreed with her, but since she was becoming settled too
quickly, there was a greater need to dishumor her.
said cheerfully.
"I rather like it," he
"There's nothing like a good hearty breath of fog mixed
with car exhaust so early in the · day.
I'm sure it'll last 'til evening."
Mrs. Leighton was peeved by Allen's apparent delight as he ripped open the
window.
The steam heat had failed at daybreak and the room was chilled
enough without the added air.
Leighton wouldn't notice.
Allen shivered in his pajamas and hoped Mrs.
She buttoned her sweater and tried to shield the
flame from the damp breeze.
"Isn't it a bit chilly with the window like that?" she whined.
"I'm sure
the owner wouldn't be pleased to know you're letting the heat go."
"Don't fret, 11 he said with a curious grin.
see.
"We have an understanding, you
Too much hot air isn't good for the lungs.
only half the winter.
Hot air is best after dark.
reaches a high point around midnight.
That's why the heat works
That's why the
Haven't you ever noticed?"
h~at
He looked
at her intently with his mouth set in half a grin.
"Oh, really?"
Her teeth chattered. · "Well perhaps you ought to slip on a
jacket," she said, watching him hop from foot to foot.
Allen was desperate to reach the closet but he wanted to outdo the good Mrs.
�- 57 -
Leighton by politely holding his stand.
He curled his toes into the woolen
tufts of the carpet, the only luxury item in his room.
Industries via Mrs. Leighton.
Courtesy of Goodwill
As she started towards the tea canister, Allen
aimed a sheet of newsprint at the telltale jar.
just after the page settled above the holy water.
Mrs. Leighton glanced down
Allen was rigid, hoping
she didn't see . the jar.
"Maybe I .am a bit lightheaded, after all," he sighed, grasping the back of
his neck.
"I think I should rest in bed today,
window?" he said.
Would you mind closing the
While Mrs. Leighton gladly shut out the cold, Allen jumped
for the screw-capped jar and tucked it under his shirt.
"Thanks very much.
In fact, I feel better already," he said holding his
stomach.
"Do you have a pain?" she asked.
'No' f' m fine·.
1
His stomack looked ill-shaped.
Just lat me lie down a few minutes. II
arms across his chest, Where the cold jar now rested.
Allen had folded his
Falling into bed, he
dumped the jar under the covers and faintly smiled at his
un i~v ited
nurse .
"I think the water's going to boil," he said,pointing to the stove.
She didn't react and stood oddly watching Allen and the bed covers.
The
kettle gave the warning hiss and Allen leaped up and across the room,almost
knocking into Mrs •.
Leighton~
blessed Brighton's jar.
She was standing tuhere he usually kept the
"I'd lose a month's score for a mistake like that,"
he thought, expecting a mild sweat although the room was swamped by the
lingering cloud of cold mist.
Allen looked pale and fragile as he stopped the
whistle and reached for the teapot.
The tea egg was disgustingly full of
swollen cold tea leaves from his last binge.
Mrs. Leighton was not unshaked by Allen's alternating jumps and frigid poses.
"He doesn't look like the kind to drink so early," she thought.
"But he's
been . trembling e· er since .I came. · It ':s always so sad when · they start young."
v
Her hands twitched and she fumbled with her sweater while staring at the bed
with the lumpy jar nestling under the blankets.
Allen tapped her shoulder lightly.
sit down and have some
tea~
"Mrs.Leighton, you look strange.
Should I phc)ne you a doctor?"
Come,
He took her arm
�- 58 -
and walked filer towards the door. · "Even better," he insisted, "I' 11 see
you downstairs and have you rest for the· ·day." ·
"That' a· very kind of you," she protested, . "but. I'm fins ;. '"
"But I don't think you are,•• he said cautiously.
on your feet just to make me tea.
hop right in bed with my tea.
"You shouldn't stay
Besides, all the work's done and I'll
Promise."
Allen's sincere and concerned
attitude persuaded his fairy godmother ti:> depart
~omewh.at
puzzled.
Rick watched the farewell scene with -great pleasure • . "Lovely day, Mrs.
Leighton," he called down the stairs.
"If you think so, Mr. .• Sheridan," she murmured.
"If the bloody churchbells didn't come dinging through my _pillow every
Lord's Day at 10:15," he added beyond the hearing of . Mrs. Leighton.
Allen started back to his room.
basket on my doorste_
p.
"Well, if it isn't Richard Brinsley in a
How's the . 'School", Mr. Sheridan?"
"Just scandalous," Rick answered.
"I've called it off for a day.
Sunday,
you know."
"Calling hours beg'in ir{ 30 seconds. "
o Join me for tea then," Allen said.
uror ladies they'rs earlier, I notice," Rick teased.
~·spying
again? 0
. uNo ·• • • stumbling to the jake in one of my morning -stupors."
"Worked late at the shop?.0
"Yes.
u~til
.
I had a very per'siste·n t young lady who wouldn.' t .let me closw sho~
she . decided . on a
gr~~~
frog that hopped with a growling . croak in
favor of a brown frog that hopped ' with a croaking growl.
girl for eight
years~"
.' ·,
"You like them young then?"
.-
'
....
"Oh she's n'o t much.
Y9.U _shou+~ see her s!S·tsr."
Very strong
�- 59 -
"Older?"
"Three years at least.
"No thanks.
U/ant to meet her?u
I know her hefty mother.
She's
marr~d
- her _mother, I mean.
And mechanical frogs aren't my· sport. 11
"Too bad she doesn':t have a similar fetish for kicking jars.
fun.
Team sports are
What's the score?"
"Almost minus sixty.
covery."
Mrs~
Leighton was within two feet and a glance of dis -
Allen reached under the covers
and replaced the jar on the floor.
"What kind of tea would you like - green or green?"
"Anything's O.K."
"Good, because I've already made a pot of green."
Rick took a seat on the carpet and watched Allen dig in the · dresser · for some
jeans.
uvou have good feet," Rick said.
"Of course, they' re perfectly good feet.
They work the same as yours, 11 Alle n
said.
"No, I mean they'd be good for sculpting, " Rick said earnestly.
He hadn't
worked on a piece since he stopped teaching part time in the county schools.
'"Why did you stop?" Allen asked sharply.
'.'Why hav.en' t you written for a month?n Ric'k cut back.
seen a new scrap for
day~.
'.'That basket hasn't
I know because I sometimes hunt for stuff that I
think you should have saved."
"Should I wire my father to come to ff:3tch me? - because I miss my mother's
clean floors? · betause I don't like living alone? because anything?'' , Allen
said~
glaring at Rick.
"I like selling toy$, Allen."
"The way you like church bells, sure."
" I love church bells .
I simply don't like being wakened s o ear l y on m
yv
�- 60 -
day off."
"I asked you something."
"I'm waiting
•• ,"Rick . said coolly.
"Your .cup's on the table."
"I didn't mean that.
then I do
sq~ething
I mean I'm waiting
If I can't sculpt full time,
that's good until the time comes."
"You enjoy taking quarters from kids for .. lit.t le croaking tin frogs?"
"More than you enjoy not writing."
"Hell, you might as well be a happy janitor, with that kind of reasoning.
I think you've qui.t ."
Rick .didn;t a~sw~r.
Street.
Allen's voice was harsh,.
He was _
thinking. about the day he moved to Creigh
The apartment was roach · infested· but cheap and salvageable if he
could . dig
~~ep e~ough.
His suitcase contained more tools than clothes.
His bankbook recorded the length of hii teaching career and would keep him
supplied with materials for months of undisturbed sculpting.
on the stai-!'s with a ·can. of
~a-Roa.ch
Allen met him
tied in a black ribbon.
The apart-
ment ·was par-tially car.pated _in bright blue and had no closet spacs.
Allen
spent the day uprooting bug colonies and sounding the walls.
If his
apartment had a closet, Rick's had.to have ·one too.
A large sur-
face . of wallpaper
ha~ be~n
It did.
sacrificed to unboard the door, but there was
a bonus • . On the closet floor rested a filthy bust of John Paul Jones.
Allen was a little disapp,o inted be. ause there was no bottle of Old Crow
c
to accompany the matchless fellow on the floor.
with Allen to ·oelsbrate the discovery.
ba6ks,
socks~ .
Rick split a cen of beer
The bug spray had doused paper-
blankets, and the hands of the two
youn~ celebr~nts.
Allen
had christened him "Briesley" after the playwright, while airriing the last .
of the spray at Rick.
Allen then invited him to shower
~nd
bed in the
room down the hall while the fumigated place had .a night's airing.
They had talked about Allen's almost published story and the color of Rick's
hair - the :shade of white sand that deepened to gray when wet.
�- 61 -
''That's completely the fault of my mother.
at the water's edge for months on end.
She used to walk along the beach
You can't escape a thing like that
without some damage," Rick explained.
"That's funny," Allen said.
"I thought it happened from smoking.
lucky she didn't watch the sea.
You're
You might have come out with blue-green.
Do
you like seaweed soup, by any chanc·e?"
Rick decided to leave his mother on the beach and play on someone else.
now it didn't seem so easy.
He tried to make a recovery.
a wealthy matron's son,u he joked.
But
"You're obviously
"She sends you weekly checks and canned
spaghetti from her villa on the Mediterranean."
Allen scowled and Rick was afraid it came out more seriously than he intended.
Allen snapped back, "Of course.
How d,id you know, Mr. Sheridan?
I've spent
years trying to conceal it."
"Simple.
You don't smoke, you drink_ tea, own a raincoat, a typewriter, some
dirty clothes
and you bought a new pair of sneakers last week.
Leighton is passionately in love •
And
Mrs.
"
"With the bartender at Carradine's," Allen cut in.
"Yes, and your thrifty bargain basement tea service."
"And my long hair."
"And your pierced ears."
Allen looked in the mirror, and cried, "My God, you're right • • • they are
pierced!"
"You:l-re lovely today.
So early in the ·mor·n ing, too."
Allen grabbed at the compliment.
"If I wear a fresh shirt, might I join you
on .Your tour of the USS Constellation this afternoon?"
"She's back at the pier?'', Rick asked, rolling on his side, . and handing the
cup to Allen for a ref ill.
0
Sure - with the money for repairs . coming in - teadily for years, they had
s
�- 62 -
enough to rebuild the old crate and hold a reception . every week for a year."
"Probably had enough to buy the workmen a case from -the brewery, if you
want to be serious about it," Rick added.
"Rick • • • how are you waiting?
What difference does it make whether
you're a toy clerk or a hamburger pusher?
kind of work you should do.
postponing •
Either way, you don't do the
It's not waiting at all •
more like
except that one day you won't want to sculpt.
Or sell
toys. 0
;'What about my eight year old charmer?"
"Drop her.
0
She has an tJgly brother and her mother's a witch."
5otJnds wonderful," Rick mumbled and left the room.
"As slander," Allen added, but Rick had already
but
s~opped
papers.
at the door and turned back.
gone~
He almost followed,
Mrs. Leighton had forgotten her
Allen leafed through the features section while jamming his feet
into the clammy soled shoes.
He looked at the typewriter and pulled a
stack of papers from the closet - things he had started a year ago, a
sketch for a short story he wrote last summer.
the machine a long gentle stroke with · one hand.
Anything he could remember or imagine about Rick
He hesitated, then gave
Allen typed for an hour.
mostly nonsense.
He threw those sheets into the basket and the crumpled ball bounced onto
the floor.
He started again.
A his~ory of the shoeshine boy who waited outside Car-
radine' s and who told him to get a haircut.
"The sign of a growed man
is that his father don't have to tell him when to git a haircut and he goes
by hisself ."
A mother is a thing "what takes care of you ...
Mrs. Leighton, following with a paragraph
threa nights of
gr~en
and called Tom Jones
clothesline.
tea.
~ntil
a~out
He wrote about
the taste of beer after
He wrote fondly about a rouguish cat he owned
some fat wench poisoned it for breaking a
He wrote about a friend of his · father's who was shot in an
IRA skirmish ·and about the loneliness that stayed with him even after Rick
had come there.
It was late and only the 40 watts saved him from having
to stop in complete darkness.. Around seven he quit because his fingers
ached.
�- 63 -
He ate two liverwurst sandwiches and the remains of a jar of big pickles.
Then
~e
took a load of trash to the rear alley.
Furiously the janitor
motioned him back to the door.
"You can't empty trash around here.
This is a nice clean building.
It's
not collection day and don't go messin' my courtyard with your crappy
trash.
Hell, take it back to your room already."
Allen stalked back domn the hall, and out the front door.
bloody mess to the street then!" he shouted.
11
1111 carry the
The street was empty.
Six
weeks of typing refuse mingled with tea drainings were dumped in the nearest
city litter can.
A tottering lady approached him and shook her wrinkled finger at his nose.
"That's illegal in this neighborhood.
You could get a stiff fine if I re-
pnrted you."
"What's a grim piece of fish like this doing on the city streets after dark,"
he asked himself.
for this month."
"Yes ma'am," he said calmly.
"I've already paid my fine
He added with a smile, "While we're here together like
this, is there anything I can deposit for you? a five spot? or your hat
perhaps.1. 11
He bowed and dashed off in the opposite direction, circled the block, and
re-entered the boarding house.
his afternoon's work.
He found a pen and began blocking out some of
At eleven he was typing again.
Rick knocked and entered.
"I've been walking," he said.
hit the keys.
0
I'm sorry · about this afternoon."
still silent.
Allen continued to
"I think you're right, Allen."
Allen stopped typing but ignored Rick.
to notice Rick.
Rick paused.
Allen was
He was marking a page and didn't seem
"I have some things in my room • • • we could start right
away • • • I mean tonight, if you like.
Allen rose from his chair.
I'd like to see your feet again.u
His voice was loud and barely under control.
"Damn you, Rick! You know I don't want to be disturbed when I'm busy •
and I'm busy, so get out and don't start with your act of repentance.
Your
dreary downcast eyes are so tearjerking that I could vomit in technicolor.
�- 64 -
Do you think I should kiss path cheeks twice because the prodigal son has
found out that fife was sweeter back home?
this?
You'll be laughing in your toy shop by tomorrow with all wounds
healed and out of sight.
dages.
Haven't we been through all
I'm not your nurse any more.
Go back to your frogs.
They must be sick with worry - afraid you
straightened out and quit the frogpond.
and I don't!"
We're out of ban-
Go to them, boy.
They need you
Allen was choking with rage.
Rick leaned back against the wall holding his breath.
He turned and
hurried out, slamming the door.
Allen stopped working at four and slept until ten.
He decided to return
Mrs. Leighton's papers and planned to borrow a dollar to buy more scrap.
Rick was huddled
Allen stopped.
o~
the floor in the hall, asleep.
He wanted Rick to say something.
minute as though expecting another tirade.
Rick looked up as
Rick eyed him for a
Allen started to speak without
clearing his throat.
· "Aren't you working today?" Allen sounded strange and tired.
"Yes, I'm working." ·
"l.t's nearly 10:30.
You're late."
"I ·know."
11
Why are you sitting here then? 0
"I ' m waiting." .
"Well is there something you want?"
"Yes, I want to
see· your
feet. II
'
"Are you kidding?"
"I said you had good feet • . Remember?
Or did you think that I wanted to
sell clicking ladybugs and pastel jumping ropes all my life?"
"Oh, for another twenty. years at least · • • • but .I guess not, -if . you' re
really waiting."
�- 65 -
"Whan are you taking your next break - a day, a week from now?
My appoint-
ment book's open."
"Didn't know you owned one •. But I' 11 believe you this time."
Allen unlaced his shoes, walked into his room and shut the door.
the papers on the bed and kicked his shoes past the jar.
water in
t~e
He tossed
After changing the
kettle and combing his hair, Allen re-opened the door and looked
at Rick in mock surprise.
"Richard Brinsley Sheridan," he cried, "Do come in.
on~
The kettle's
I've
got a bit of rum for special Mondays."
"Thanks, but I don't think my
namesak~:l
took too kindly to drinking this early.
Before work, I mean."
"Don't make excuses," Allen .said.
line at all.
"Hr;J was . a damned playwright.
Not your
I didn't know he had working hours anyway."
"I think he ·had tea breaks • • • in the afternoon," Rick said.
"And morning, Mr. Sheridan.
Don't trip over the marmalade • • • the cap's
loose."
Allen tied back the curtains.
"Awful, aren't they?" Alle.n said, tugging the
left one a second time.
Rick picked up the · comme;nt at once.
"Beautiful r
I' 11 take a dozen. "
"Cash?"
"Charge it."
"But sir," Allen protested, "ladies 1 scullery wear is on the fourt h floor,
next to .brooms."
The kettle was lowly rumbling as Mrs. Leighton appeared in the doorway. "Excuse me Mr. Keeler, but I forgot my papers here yesterday.
I hope you've
finished with them."
"Sure, thanks!" Allen was shouting in unison with the tea whistle.
"Don't
�- 66 -
move," he said, jumping for the papers.
"They' re right here on the bed.
Just stay put, Mrs. Leighton." He grabbed the pile and handed _t to her.
i
She smiled and stood in the doorway aa though waiting for Allen to ask
her in for tea.
spotted Rick.
She looked anxiously into the room towards the stove and
"Oh, company!"
She wava·d her ·ringers in a sHly g·r eeting.
"Hello Mrs. Leighton," he called to her.
"So glad you're feeling better."
"That was a mistake," Allen thought as he saw her eyes spark at Rick's
comment.
door.
"Well, if you'll excuse me," he .said quickly and closed .the
Rick had silenced the -kettle. · "Noisey beast, . wouldn't you say?", Rick
asked.
· "Oh, I'm rather fond of him. · Two years together • . We're hopelessly
attached," Allen explained.
"Chummy. ·Hope I'm not interfering," Rick said ser ~ously.
"Not at al.L
Three's company; four's a crowd · "
Allen pushed the door open and just missed slipping Mrs. Leighton's nose.
She remained
steadfa~t,
"Sorry," he mumbled.
"No~
blinking at him.
"Is there a section missing?"
everything' s here."
:She was · till° hugging· the papers.
s
"Are they too heavy for you to manage?
Might I help you?
Sheridan~
come
help her with the papers, won't you?" he called.
"Can't you do it?" Rick called back.
'!'D on't bother, please," she said.
"I don't want you two boys to quarrel."
"We're not quarreling,·" Rick said, looking ver·y surprised.
"Well then if we' re not quarreling," Allen whispe.r ed to . the woman, "you
�- 67 -
must excuse us.
She didn't
hea~
The kettle, you know ••• "
him and. raised her stumpy eyebraws while Allen innocently
repeated, "The kettle, the kettle," and slowly closed the door.
�- 68 -
FROM EUCLID TO DEDEKIND
Samuel Kutler
Dedeki-rntl "creates" the system of real numbers by postulating that every cut
(A , A ) of rational numbers such that any number in A is less than any
1
1
2
number in A is effected by some number, be it one of the given rationals
2
or a new irrational.
In this property of the real number system Dedekind
finds the "essence of continuity. 111 )
Dedekind assumes that "every one
1
will at once grant the truth of this statement," a) when the expression
is interpreted geometrically.
His object is to place the differential
cal ulus on a perfectly rigorous foundation by giving a purely arithmetic
development of the real number system.
It is often said that the Dedekind cut is prefigured by Eudoxus' definition
of the same ratio given in Euclid's Elements as the fifth definition of
Book V.
Dedekind himself calls "this manner of determining the irrational
number as the ratio of measurable quantities
• the source of my theory. 112 )
What follows is an attempt to present the manner in which this definition
is the source of Dedekind's theory.
Let Ol be any straight line whatsoever.
The point P on the line 01 or on
01 extended is defined to be a rational
point (with respect to 01) whenever 0
OP and 0 1 are commensurable or an
l
L
x
R
irrational point whenever they are
incommensurable.
Let A and 8 be incommensurable magnitudes.
Let X be the irrational
point on the line 01 such that
A:B :: OX : 01
Then, geometrically, Dedekind determines the irrational point X by the
A
8
"i
1) Essays on the Theory of ~umbers, R. Dedekind (trans . by W W Beman)
. .
Open Court 1948, page 11.
1a) Ibid, page 11
2) 1.Q.!Q., pages 39-40
�- 69 -
separation of the line into two classes such that every point of the first
class lies to the left, (of X and hence) of every point of the second class.
We now seek the arithmetic determination by means of Euclidean definitions:
By Euclid V, Def. 4, there must
nA >ma
and
be
numbers n, m, s, and r for which
sA <.rB.
Then from Euclid V, Def. 5, it follows that
n·eX > m•Ol
and
s•OX < r·Dl •
From which it follows by Euclid V, Def. 7 that
m:n
r:s
>
A':B.
r:s
< A:B
>
OX:Ol •
and
m:n
<
OX:Ol
On the line 01 let L and R be points such that
m:n: :OL:Ol
and
r:s::OR:Ol •
Then L < X < R.
Clearly just as the ratios m:n and r:s correspond to the rational points L
and R, so given any rational point P on 01, there will correspond some ratio
say XL p:q where
pA greater than qB whenever P is to the left of X and
pA less
than qB whenever P is to the right of X.
Thus, just as in the geometric definition of the irrational number X as the
separation of all the rational points into two classes such that every
~
0
rational in the f irat class - such as L - lies to the left of every rational
in the second class - such as R - we have effected a separation of all ratios
into two classes such that given any ratio in the first class - such as m:n and any ratio in the second class - such as r:s m:n
< r:s •
We are now free to abstract from (forget) the geometric representation and to'-:.
simply define the positive irrational number X as this separation or cut.
Finally, if we descend to the correspondence between a ratio p:q and a
"rational number"
*,
the rational numbers.
we have created the irrational number X as a cut in
Moreover, at the root of this analysis is the "cele-
brated definition which Euclid gives of the equality of two ratios. 113 )
3) Ibid, pages 39-40
�-62SECTION IX~ On the Construction of the Several Conic
Sections in which the Origin of the Unknowns is Neither at
the Center of the Figure nor at the End of its Major Axis •
.on the Equation of the ·.Locus_ pf
Problem I
.~
Circle
Let a line AB be given in length and position. It is
required to find the p~int M not on the line AB such that if
AM and. BM be drawn AM g BM 2 ~ ~ m : l'l.
Analysis
'4\
Let the problem have been solved and let PM be dropped
perpendicular to line AB cutting it at the point__R~ and let
the determined line
AB = a
Jv\
and the undetermined lines
~_;::;:;AP : x
.
i\ __________ ~,,,/"
I
and
PM - y.
_ "
~
,
The ref ore PB = a - x
__..------~
and
,MA~
x2 + y2 A "':.·~-iyp ''t . - ----- 1- -_1.
and
MB2 = a2 - 2ax + x2 + y2
C
l> t:
Now according to the conditions of
Fig. 41
the problem "
..
·
(x2 + y2) /(a2 - 2ax + x2 + y2) = m/n.
Therefore mx2 + ny2 = ma2 - 2max + mx2 + my2
Now let
mj n
Therefore mx2 - nx2 + 2max + ma2 + my2 - y2 = O,
or
x2 - 2max/(m-n) + ma2/(m-n} + y2 = o.
(1)
=
i
"'..
,
\
Now since there are no other conditions given ~ the problem will
be indeterminate .I and since the equation contains both unknowns in the second power ; have1ng the same sign ) neither of
which has a coefficient ) the locus will be a circle. But
since there are second terms : the center of the circle will
not be the origin. Therefore let
z = x - ma/(m-n)
Therefore z2 - m2a2/(m-n)2 + ma2/Im-n) + y2 = O.
(2)
Therefore y2 = m...na2/(m-n)2 _ z2 ,
which means that the locus of all points 1s a circle whose
center is the origin of the unknowns "'lf. and. z.
-~
Construction
Sinee A is the origin of the unkno~m X and
x = z + ma/(m-n)
let
AC = ma/(m-n)
Therefore C is the origin of the unknowns y and z. Therefore
the locus will be a circle inscribed about C as center and.
having a radius equal to
1
�~-
-63V mna ;! L (
Now let
Therefore
m:n} . . . . ·-
mn = g2
·
= V a2g2
mn.a.2
V
= ag
Therefore ag/(m-n) = rad1us9
which gives the final ·solution to the problem.
Proof
Let MP be dropped from M perpendicular to AD extended.
Now by the property of the circle
CE 2 - cp2 = PM2
ag/(m~n)
But
CE =
and
CP
Therefore
CE - CP =
CE + CP
and.
=V mna 2 /(m-n)
=z
v
= V mna! I
mna!
/(m-n) - z
(m-n) + z.
= CE2
Since
(CE
CP)(CE + CP)
Therefore
cE2
cp2
But :.· ·
PM = y
Therefore
PM2 = y2
But
z2 = x2 - 2max/(m-n) + mna2/(m2 - 2mn + n2)
Therefore
mx2 - nx 2 · - 2max + ma2 + ny2 - ny2
or
(m-n)x 2 + (m-n)y 2 - 2m.ax + ma2
= mna2/(m-n)2
- 6P2
- z2
=O
and. (2) above)
(from (~)
= o~
which gives the locus required.
c~.E.
F.
Problem II
To find the locus of the equation
x2 + 2axy/b + a2y2/b2 - by - b2 =
Let
z = x + ay/b
Therefore
z2 -
or
z2
o.
by _ b2
= by
= Q.
+ b2
Therefore the equation gives the locus of
a
parabola.
�The unknowns z and y d.o not have their origin at t he
vertex of the diameter for there are still three terms. But
if one lets
u = y + b
Then
z~ = bu
which gives the equation of a parabola whose vertex is at
the origin of the unknowns.
Let A be the origin of the unknWtt-ms and. let y go in the
direction of H and x in the direction o'f' G.
Npw since y + b = u
let AH be extended. through A to I making
IA= b
Therefore t is the origin of the unknomn u;
and since z = x - ay/b
let IO be drawn parallel to Ag and let
IO =a, .
Through the point O let the line OAK be drawn. And through
any point B ~ on the line AH~ let the line PNB be drawn parallel to OI meeting AK at P. Now since the triangle IOA is
similar to triangle ABP then
IA ~ IO ~g~AB ~ PB
and since b/a = y/(ay/b)
then
PB = ay/b
Therefore PM = x + ay/b = z
We now have PM = z and IB = u. But since the coordinates
· are OP and PM 9 we will have to find some way of expr essingOP
in terms of u.
Therefore let
AO = c
and the unknown line
OP = w
Now ; since the triangle AIO is similar to the triangle
fll_\ .
APB
AI g AB ~ g AO
AP
:~r--I+
Therefore AI g IB gg AO g OP
or
b/u = c/w
/ 'I_\?
/
l/
Theraf ore uc = bw
,·
0 1···
/
and
u = bw/c
j(
~'
/ It -p
But
z2 =
I' ,,
Therefore z2 = b2w/c
\>~....... .
mow let
f = b2/c
- 1/
-l
r-•J . 't- ¥(\_
Therefore z2 = fw
Hence M lies ona parabola of which b2/c ~s the parameter.
F
/. / i
- -· k/
I
'.;"'
bu
.
•
Construction
Given the lines AG a..11.d AK 9 let there be a · line PM parallel
to AG and passing through ai1y point p· on the line AK.
Let
OP = w
and
PM = z.
With f' as the parameter . let a parabola be drawn with AP as
,
diameter and with the vertex at O. Now since
z2 = fw
Therefore z2= bu
�Therefore by subst1tuting the values given above
·
·
x 2 + 2axy/b + a2y2/b2 =by • .~2
.
· hich was the line to be constructed. · The read.er may wish to
w
develop the case of the hyperbola for himself.
End of Part I.
PART TWO~ On the Fixed Coord1~te System
Section I: On. the Giving of Names
""
In Part I we began with figures and found some convenient
point from which .to commence measurement. Here we shall be
engaged in a very different activity.
Let us begin with a point , Oj somewhere in space and let
there be a line through it. Now let us nakk ·off on the line
any arbitrary magnitude we . hoose from the point O~ and let
c
us call the new point 1. - Now by means of the constructions
which we have inheri.ted. from Descartes 9 we may mark off the
point whose name is two or ~hree or the square root of 22.
If we now consider that part of the line which lies on the
·other side of the point o ~ we will find. the points whose names
are negative numbers. Unfortunately 9 as will be proven in the
Senior year ~ our present method will not allow us to name
every point on the line. This problem , however., need not concern µs for the present abecause? on the one hand , given a
number we can always find the point denoted by that number 9
and. 9 on the other hand ~ given any particular point we can
always find a name for it.
Thus far we see that the points on the line hav~ been
given such names as zero ? +l , +5 Q +2/J., -3/79 and -7V 11 •
Now through the point O, let another line be erected
perpendiuular to the given straight line and let the points
on it be given names after the same fashion. For convenience
sake ~ let us call the first line the x-axis
and the second
one the Y-axis. Now that names have 'b een assigned to the
points on both of the given lines . it will be an easy matter
;
to give a name to any point which lies anywhere at all in
the plane determined by the two intersecting lies. For instance
if I wish to name some point P ~ I can drop a perpendicular to
the •-axis meeting 1 t at xi - and drop another perpendicular
.
to the Y-coord.inate at y 1 • This would allow us to give: .;.the
point P the unique double l'lame x1~Y1 , which it shares with
no other point in the plane. Thus any point in the plane
may be given a name which is proper to itself and which it
shares with no other point.
Sffbolically~ we shall wrlte the name of the point as
P(x1 ., Yl) or more simply (x1 ~ Y1}.
For instance ,~ if x1 is 5 and yl is 7· the point will be known
1
as
P ( 5 7. .) or ( .5 : 7)
,
·
But if the point P_ lies to the left of the point 0 x1 itself
l
will , or· course 9 be .a negative number. Thus (x1 ~ Y1) might be
1
<;
(-5 . ?).
�·-66.. ·"
•;
E.xercises
1. Construct a coordinate system and. locate the following
points
a. (3 ; 4~
b. ( 7" -2)
c. (-3 ·
a. That point for which x1 = -2 and y1 ~ -4.
(x11 7) ? where x1 = 3.
~-
*)
It will be noted that the plane has been divided. by the
coordinate axis into four sections which have the following
characteristics. In the first section both the x and the y
coordinages of any point P are positive. In the second section
counting counter-clockwise ~ the x value of any point P is
minus bu t the y values are still positive. In the third
section , they are both minus~ and in the foursth ~ the x is
positive while the y is negative. It is mus tomary t o name
these sections of the plane the first quadrant ~ the second
quadrant ~ the third quadrant ; and the fourth quadrant ~ respectively.
Proposition I
Problem
Given a coordinate system .and the two points (xl ~ y 1 ) or
P1 and the point (x2 . Y2) or P 2 • Let it be requ1"ed to find
the length of the line P1 P 2 •
If P1P 2 is parallel to the x-axis ~ the length of the
line will equal x 2 - x1. This equation holds no matter
which quad.rant the points are in. Similarly ~ if the line is
parallel to the y axis ~ the length is y 2 - y1 .
But if P1 P2 is not parallel to eitner axis~ then through
the point Pi ~ let a line be drawn parallel to the x axis and
through the point P 2 let a line be drawn parallel to the y
axis and let them meet at the point M.
By part 1 of the pr oof :
P1l~ = X2 - x 1
P2Iv1
y 2. - y 1 .
=
and
Therefore
Q.E.F.
Exercise
1 . By use of the last formula , find the distance between
the following sets of points~
a.
b..
c.
( 5 ') 2 ) and ( 1 . - 8)
(5 9-2) and (7: -11)
(5 . -3) and (-7 . 2).
�L
2
�s
e
x
=
�Definition
By the wor~ slope I mean the tangent of the angle which
a given line makes with the x axis in a counter-clockwise
direction consid.ermng the angle never to be more than two
right angles. Thus > if when extended. ~ the lines goes from
the first quadrant to the third quad.rant ~ its slope will be
positive ·; but if it goes from the second quadrant to the
fourth quadrant its slope is negative. This division includes
all lines which are not parallel to either axis. Thus 9 in
Fig. ' ~ the slope 6f AB is positive ~ but the slope of CD is
negative. If a line goBs from the first quad.rant to the
sedond quadrant or from the third to the fourth and remains
in them no matter how far extended. it will be parallel to
the ~axis and vrill have the slope of zero. Those lines ?
on the other hand ~ which go from the first to the fourth or
from the second to the third will be at right angles to the
x axis and the tangent will be meaningless.
It is current practise to use the symbol nma 0 to refer
to the slope of a line. Thus we may write
m = tan e
or
m = AB/AC {Fig . .5)
Slope
From the first part of the manual) we know that the locus
of every equation of the first degree is a straight line. It
follows that
Ax + By + C == 0
is the general name of the str&a.ght line. Furthermore 7 we
know that if
c =
0
the line goes through the origin. Now from the equation
Ax + By = 0
it follows that
y/x = -A/B
Therefore the general formula for the slope of any straight
line is
m = -A/~
Let us agalh.n consider the full equation
Ax + By + C = Oo
It follows that
y = -Ax/B - C/B
But if we let
~C/B = b
then
y = mx + b
Thus it follows that given the general equation
Ax + By + e = o
y = mx + b
where
m = -A/B
and
b = - C/B.
�s
s
�- l
I
I
-71Since
QP/SP 2
an'
lPi/SP
by substitution
=r
=r
(x - x1 )/(x 2 - x) = r
(Y1 - Y~/(y - Yz) = r
x = (x1 + rs 2 )/ll + r)
y = (yl + ry 2 )/(l + r)
and
or
and
Corollary I
If the given line is to be bisected then
x = tx 1 + x 2 )/2
y = (y1 + Y2)/2o
Corollary II
If two straight lines intersect ~ the point of intersectior
is given by the simultaneous solution of the equations of the
two straight lines.
For if the lines are represented by the equations
Ax + By + C = 0
and
A ~ x + B" y + C " = O ~
there will be only one pair of values for y and x which will
satisfy both equations. This set of -values will give- ·the
coordinates of the point which is on both lines that is to
say ; the intersection of the two lines.
1.
slope
-t.
2.
a.
b.
J.
find a.
b.
Exercises
Name the line which goes through (L -5) and has the
Name the line which goes through (1 -2) and which
is parallel to 2x - Jy + 4 = 0
Is perpendicular to 5x - y - 15 = 0/
Given the points A (-6 ~ -4) and B ( 10 ~ 8) ~ C (2 9 7) ?
the equation of the line through A and B.
the equation of the line through C perpendicular to
1
AB .
c.
The perpendicular distance from C to the line through
A and B.
d. the length ' of AB.
e. the area of the triangle ABC. (Hint: use the results
of c and. d.)
4. Find the distance between the point of intersection
of the lines Jx - 4y + 2 + O and x + 2y + 4 = O and that of
the lines 5x + y - 4 = O and Jx + y + 2 = OJ
5. Locate the mid.point of the line AB determined by the
points (2 1-7) and (2 ~ -6).
tf·.- 1. . . ......
r'J '. ' '' , , ,c;..
6. In what ratio ~f is the line-,, joining the points
( - 5 ·; 7 ) and ( - 3 " 7 ) •
,'
. ) ~.~ .Given the two equations in Corollary II 9 find the
point ot~ · 1ntersection.
i'
�I
( '/-.._ L ,
( '/-.' I
f-.
_J
7
�s
�we
+
a.
e
f
=
=
+
=
�I . ·
'
...
-75Thus the parabola may take.one of the four following
dep2nding on the direction on which it opens:
a. y = 4ax (opens to the right)
b. y2 = -4ax (opens to the left)
2
c. xi") = 4ay (opens upwards)
d. x'"' = -4ay (opens d.o"l'.Ai~wards)
As in th~ case of the circle it follows th~t if the vertex is
no longer at the origin ~ but rather at the point P (h ~ k) , the
new figure has the equation
(y - k) 2 = 4aix - hi
or
(~ - h) 2 = 4~ iy - m~
hence
y - 2yk + k = ~4ax - 4ah~
or
x2 - 2hx + h 2 = i4ay - 4aki
which has the general form
Cy 2 + Dx + Ey + F = 0
er
Ax2 + Dx + Ey + F = O
or more generally
Ax2 + Cy 2 + Dx + Ey + F = 0
where if A = O? the diameter is parallel to the x axis
and
if C = 0 9 the diameter is parallel to the y axis.
Let us determine these two possibilities.
Let it now be required to find the vertex) latus raetum 9
focus ~ directrix ~ and eccentricity.
forms~
Case I
Let
Cy 2 + Dx + Ey + F = 0
Hence
c22 + Ey = -DX - F
or
y + Ey/C =-Dx/C - F/C
or
y2 +(E/C)y + E2/4c 2 = -(D/C)x - E/C + E 2 /4c2
or
(y + E/2e) 2 = -DIC (x + F/D - E2/4CE)
which has the form
( x - I~) 2 = ± 4a ( y - h)
where
k = E/2C
h = (4CF - E2)/4Ct
and
a = -D/4C
Hence the . latus rectum is -D/C and the vertex at V (-E/2C ,
. - (ti,:.:; -f-.C F. ~) /4CD) .
Now since the distance between the vertex and the focus
equals i the la tus rectum , the focus is at F(h+a., k)/ 9 where 7
h + a = -E/2C - D/4C
f
•
or
~ + a = - ( 2E ~ D) /4C
.:·i ([- ~- f ~J - 1 c 0 ) - E/ c)
F
Yft
and
k = -(4CF - E )/4CD
Therefore the focus is at F (-(2E + D)/4C ~ -(4CF - E 2 )/4CD).
1
L
_::)
�-76-.
On the other hand - since the directrix is parallel to the YaxH3 and passes through the point on the diameter which is at
a distance f:f'om the vertex equal to t the latus rectum 9 its
formula is
or
Case II
If
Ax 2 + Dx + Ey + F = O;
it is clear by the same reason that the latus rectum equals
-E/)-A ·
vertex is at V(-D/2A, _(4)""-_ '}Ae- )/4~.l)0}9
focus is at F(-{~/L A (J/-'i+A r~-- t- -)/ -'J~l\D) .the directrix is y ~
( r)'-- :f;:,F _t- t--::;_-../4 f\E
in either case the eccentricity is 1.
the
the
and
And
If in a parabola a tangent be drawn from the point
( x1 ·: Yi) . the equation will be
.
Case I ~ A = 0
yy 1 = 2a(x + x 1 ) (Part I ) Section V) Prop. IV)
or
yy1 = -D/2C (x + x 1 )
Case II C = O xx 1 = -E/2A (y + Y1 )
The Central Conics
And for the same reasons as given before ~- we know that
the name of the central conic whose center is at the origin
of the coordinate syste~ and whose axis is the x co~rdinate
is
x 2 /a2 ± y 2 /b = 1
where
a = the length of the semi-major axis
b = the length of the semi-minor axis
and if
c = th~ di~ta2ce from either focus and. the center 9
then
a 2 - c = - b (Part 1 9 Section VI ~ Prop. I)
If , then , we take ~ n2w+center a~ C~h ; k) we have
~~(i2h~ ~x
; ~l,-±k!2{~2: ~ky + k2) = a2b2
2x2 ± a 2 y~ _ 2b 2hx ; 2a 2ky +(b 2h 2 ± a2k~
Thus
b
a2b2) - .
whichhas the ~enera~ form
Ax + Cy- + Dx + Ey + F = 0 (I)
Where? if A and C have opposite signs the figure names is an
ellipse 7 but if the same sign ,l an hyperbola. Note that the
signs of all the other terms are in P.art determi~ed by ~e
signs of h and k.
j ;
·.
,
.
;
//
or
~l
-.
-?..
'
~~~~-· _. -~(~,~) : ·1
r/ i
·'
/·~-t-·,·
_./_,., \ ·._ '.
\ ,'.
. ,// J fE-·----- -,_,
!
\. r
.
.... ' ·"- --
f
~---
-----
:
c....
·. ·
.
(
i-~
Fig. 12
-...
\1
-+
,
-~cl
I
- J """
!>
_____________
/
,/'
Fig. 13
-·
!
IJ
·nx;y)
·
r'
~:
,==
,;,:
c:~ .\
. '.
'=-
.- ,' ,/
---· -
l
. ~ 1 5J
/
l
b .......
//
· ·~ -l.r7
.
I
(~ --L);_ (~ ~-7
_>)
c..: z.._
-
}---:~/
··~1tr=:---=O- ----;>·~
i
__
/:
- ~ ......-)
·---- -· -p:-c1 ,1· -·
---
i :x
-'I ,
--~
. . _.-
-
; .,
~'---· ··-c~u, -, tJ .. - . \, hl'ilr··.
vi.
!'·
---~
.
;
!~
-'-(- .~~·
"I~- - .t:
J.
.1_ _ __
_..1_.J_ (_
,:.._-1,-,)'-:..
1..-
�-77Now "' by complet~ng the square ~f (I) we 2et
2
A.(x +D/2A.) · + C(y + E/2C) = (DC +EA.. - 4A.CF)/4AC
Now l~~c + E 2A - 4ACF =
Suppose that .
M
M ¢ 0
Therefore (x + D/2A)2/(M/4A2c) + (y + E/2C) 2 /(M/4C 2A) = 1
And if we always · let~ be the semi-ma.jar axis ~ we know from
Part I ~ Section VI~ Propo IIs Cor. VIII that th~ may have
one of the following two forms depending on whether the
major axis is para~le~ ~o the x ~oo~dinate or the y coordinate:
_I.
(x - h) 2/a - (y - k) /b = 1
~ or II.
(x - h) /b2 ± (y - k)2;a2 = 1
Therefore h = -D/2A.
and.
k = -E/2C
And since · b2 agreem~nt ; a is 2greater than b ~
.
if AZ.C
a = M/4A c and b = M/4c2A
and. the major a~is is parallel t~ the x ~oordinate
But if A> C
a = M/4c2A and. b = M/L~A C
and the major axis is parallel to the y coordinate.
Now since the vertices lie respectively at a distance
of a and b from the center _ the vertmces can be found. in the
:
following manner.
In any central conic whose axes are parallel to the
coordinates ) let the top-most vertex be l{nown as V19 and let
the others be numbered in a clockwise direction.
If A~ C ~ the position of V 1 (x 1 ~y 1 ) is given by the following
1
equation~
Xl = h = -D/2A
and
y 1 = Ii :l: b = -E/2C + V MA /2CA
or .
Yl = (-EA + V MA ) /2CA
Hence v1 and V1 have the form V(-D/2A .1 (-EA ± V VJ.A )/2CA) ~
and v 2 and V4 nave the form V(-E/2C ~ (-DC ± v- MC) /2CA).
But if A > C ~ the formulae are reversed.
Since c 21s t2e distance from the center to the foci and
a - c = ±b2
or
c 2 = a2 • b2
Therefore (Case I) ·
cL = M/4A 2c !f M/4Ac2
or
c 2 = (M(C • A)) /4c2A2
Likewise (Ca~e II)
.
c = (M(A + C)) /4C2A 2
And if e be the eccentricity
e = c/~ (Part I - Section VI ~ Prop. III)
Therefore e 2 = c /a2
·
or
e 2 = (M(C + A)/4c2A2)/(M/4A 2 c)
or
e~ = (C !f A)/C
e = (1 !f A/C)
And since c is the distance between the focus and the cen-ter 9
then where the focus is at F(x , y)
1
�-78- .
If A ( C
and
x
or
and. the
But if
=h
= -D/2A
..
= l{ ± c = -E/2C ± V M(C -T- A) /2AC
y = (-EA ~ VM (C ;: A j ) /2AC
foci are at
F(-E/2C (-DC ± V M(C .'.f j)) /2_t\C)
y
A>
C) they are at
. F(-E/2C ' (-DC -: v MTA !f C)) /2A.C).
And if as in Part I . Section VI Propo III ')
we let d e.qual the distance bet·ween the center and the d.irectrix , then d = a/e
but
c = ae
therefore d = c/e 2
Case I A < C
or
d = (V-M(C =FA)/2AC~/((C !FA)/C)
or
d = V M(C =FA)/ 2A(C !r A)
Now sinee A ( C ~ the major axis is ~~rallel to the x coordinate.
Hence the directrix ix
x =h - d
or
x = -D/2A - V M(C .+ i0°/2A(C ~A)
Therefore the equation for the directrix is
x =-(V M(C !f A}+ D(C !fA))/2A(C
y
y
= 1{
:P. A)
Case II
- d
or
= - (V_M_(A-A.-!f-C..... + E (A ~ C)) /2C (A. ;: C)
)
Now let it be required to find the parameter of · the major
axis
If P eqnals the parameter _., then
P/2a = b2/a2 (Part I , Section VI , Prop. I~ Car. V)
Therefore P = 2b2/a
or
P = (M/2~ 2A)/(V M/2C-'£ A)
or
P = M/2C A x 2CV A/V M
or
P = V M.A./AC
Case II
P = V MC/AC
Since in the case of the hyperbola : the equation of the
asymptotes is +
.
x/a =-y/b =._0 iPt. I~Sect_._VII Prop. II~ Car. III)
·
or
x/(V M/2AV C) - y/(V M/2CV A) = 0
AxVC = =F CyVA
Now let it be proposed to find the equation of the tangent
to a conic section at some given point P(x1 9 y ).
If the section have its center at the ori~in ; then (by
Part I ) Section ¥I+ Prop. IV ) ~ tbe formula for the tangent
is
xix/a - y y/b 2 · = 1
o
I
1
or
x(x1 + D/2A) ± y(y 1 + E/2C) _ l
1'-1741\ 2c .
.
IVl/4C2A
-
Thus ? if a point P(x1 y1 ) be given on a con:Ec section , whose
formula is given . the formula for the tangent is also given.
Let us· now return to t~e formula
·
A(x + D/2.A.) + C (y +E/2C) 2 = rvI/4AC
in order to discover which conic section is represented by
any given equation.
�-79Let it now be required. to find. the conditions within
. the general e~uatio~
Ax- + Cy + Dx + Ey + F = 0
which determines whether the figure be an ellipse ; an hyperbola .
or some degenerate section.
It has already be2n shown that 2
A(x + D/Q'A) + C(y + E/2C)
= (D 2c + E2A. - 4ACF/hPAC
BLut since
n2c + E2 - ~ACF = M
A (x + D/2A)
+ C(y + E/2C) 2 :::: M/4.AC
Case I~ Where M > 0
.
Therefore (x+D/2A.) 2 /(l-1/4A~C) + (y + E/2C) 2/(M/4C 2A) = 1 (I)
Now if C is greater than Q , the two fractions agree in sign
and. hence the equation represents an ellipse , but if C is
less than O the fractions disagree in sign and. the equation
represnnts an hyperbola.
Case II~ Where M ( 0
We may still retain equation (I) as given in Case I. Now if
c is greater than o ~ then both the fractions are negative 7
and hence their sum cannot equal positive 1. Hence there is
no locas.
Case
Now since
III~
Where M = Oe
A(x + D/2A) ~ + C(y + E/2C) 2 = H/4AC
then
A(x + D/2A) + C(y + E/2C) 2 = 0 tl)
If C is negative ·. the equat~on max__be rewri tten as
(VA (x + D/2A ))
- (V C (y + E/2C)) 2 = 0
and. since this may be factored , it represents the equation of
two intersecting straight lines .
And since both ofv the factors equal 0 when
x = -D/21
1
and
y =
2C
the two lines will intersect at the point P(-D/2A. ) .=,E/<~C)
(Pt. I-. Sect. III , Prop. II : Cor. I)
If C is positive equation (1) may only be satisfied when
x = -D/2A
and
y = -E/2C
Hence the equation represents the single point P(-D/2A :. -E/2C).
Let us s~art w~th the equation
A.x + Cy + Dx + Ey + F= 0
and. let
M = l~E2 + CD2 - 4ACF
Thus in the case of the parabola - M equals either AE 2 or cn 2 •
The results of the foregoing may be arranged. in the following
chart.
3
.A.C ) ~
AC ~O
AC = 0
parabola
ellipse
hyperbola
i'il > 0
parabola
M <.O
no locus
hyperbmla
pair of parallel
single point
pair of interM = 0
secting lines
lines.
This can be more accurately stated in the following chart.
-Ef
�- 80 ...
Case
Central
\'T here A Z C
Parabola
I~
no center
Center
(-D/2A
Major axis
V MC/2A.C
no bounds
Minor axis
V MA/2AC
meaningless
Vertices of
Major axis
(-E/2C ~. -DC
Vertices of
Minor axis
(-D/2A ; -EA :!: V MA/2CA )
Directrix
X=-D /2A- ( v™I'1 ( C.'fA) /2A ( c+A) )
Parameter
V MA/AC
-E/2C)
± V~l"IC
·~c
)
meaningless
-D/C
Tangent at
the point
(x . . y 1 ) on
1
the curve.
-D
yy 1 ;2c(x+x )
1
Foci
(-D/2A..
Eccentricity
v
Asymptotes
(For hyperbola
only)
l~ .x
-EA:t° V-M~_--(
C-f-.A......
)2.A C
A CC
+ AC 2 /c
( ( f ',;:.
4 '... F t 0 ~--?l-1
CV/
-- t:1 ~ c)
1
VC = .:r Cy V A
·Thus if C is positive the fi gure is a parabola when A = O.
arr however ., C is less than A. one may use the same formulae
by changing A with C and D with E.
Exercises
1.
Find the equation for the d:trectrix. axis
at the vert~x of the following parabomae ~
a.
y + 4x - 4v -20 = 0
be
9y 2 + 72X -u24y - 12B = 0
Co
l~x 2 -BX + 6~ + 1 = 0
a. 5x2 - 40x + 4y + B4 = 0
and. tangent
2o
Give the names of the parabolae having the following
propertiesg
al
focus at (J . 0) ) vertex at (2 . 0)
bo
focus at (l . J) s. ~ertex at (1 ~ 5)
Co
focus at (2 , 3) ~ directrix x = 6
d.
Vertex at (1 . 4) ~ axis parallel to Y-coord.inate
opening downwards ~ parameter = Bo
�-81-
3.
Locate:; the foci. vertices and eccentricity of the
following el~ipses ~d give the lengths of "'che semiOaxes.
a.
9X + 25y = 225
b.
25~2 + 162 2 = 400
.
c.
9x 2 + l~y - 64y ~ O
d.
2x + y + 12x - 4y + 22 = O
~.
4x 2 + 9Y 2 + 24x + 36y + 36 = 0
4.
Give the names of the ellipses having the following
propertiesg
·
a. center (-3 : 2) '.! a = 2 b = 1 ~ .major axis vertical
b.
vertices (4 , 2) and. (12 .,. 2):;. b = 3.
foci ( - 3 :· O) and ( - 3 2 ) ~ major axis = 10
c•
d. · focus at (-3 , 11) s one encl of minor axis at (0, 3) ~
major axis vertical
e.
Foci (1-, 3) and ( 7 ~ J) ~ the sum of the distance from
any point on the ellipse to the two foci equaJs 10.
5.
In eahc of the following equations " determine whether
the given eqaation represents · a hyperbola or a pair of
intersecting lines. If an hyperbola. locate the center 9 foci ~
vertices . and eccentricity :· and find. the lengths of the
semi-axesand. the equations fo the asymptotes. If a pair of
lines , find ~heir s~parate equations.
a.
9x - 16y + 72x = 0
b.
lmx 2 - 29Y 2 + 72y - 288 = o
c.
y2 - x + 4x - 5 = O
2
dj
y 2 - 9x - J6x + 12y - 9 =0
2
e.
y2 - 4x ~ 2x + y = O
f.
4y~ - 16x 2 + 16x + 4y + l= 0
g.
~y - 25x · - lOOx = O
6.
Find. the hyperbola having the following propertiesg
a.
6enter at (2 3) ; a= 2 . b=3~ transverse axis
horizontal.
b.
Vertices (-3 -5) and (-3 - 7)~ b=5e
c.
foci at (-2;-2) a..nd (8 . -2) 9 slope of an~, asymptote
4/3
d.
equations of asymptotes 4x + y - 12 = O and
4x + y - -12 = O~ hyperbola contain~g point (1 , 11)
f.
equations of asymptotes 2x - 3Y - 2 = O and
3Y + 10 = -~ hyperbola contamn~ng the origin.
g.
the line x ·+ 9/5 = O is one .of the directrices and
(-5 · 0 is the associated focus and the center is
:
at the origin.
h.
x = 0 is one of the directrices~ · (16/5 , 0) is the
associated focus g eccentricity = 5/3.
i
j
Section
IV~
On Rotation and Transformation
Thus far we have only dealt systematicall~ with those
figures whose axes are parallel to one of the two coordil13.tes
that is to say -. with equations of the second degree in two
unkno~ms in which the coefficients of the xy-terms = O.
Let
us consider the more general case.
�-82Let there be any section placed with in a gi v en coordi nat e
system such that its axes are :not parallel to the coiordinates .
In order to reduce this problem to one of the cases
with which we have already .dealt we must choose a new pair
of coordinates so that its axes become parallel to the
co~rdinates.
Our task then will be to find the new equation .
Proposition I
Theorem
Let there be a conic section given in a coordinate sys=
tern so oriented that its axes are not parallel to the coordinates of the system.
Let there be established a new co~rd.inate system having
the same origin as the original system but whose coordinates
are parallel to the axes of the given figure. I say that if
a point P be taken on the ellipse 9 whose name with respect
to the first axes is (x ~ y) ? then with respect to the new
axes its name will be (X " ,. Y" ) ~ where
x = X RCOS 0 + y·sin e
and
y = y · cos e - x · sin e
From the point P let PM be dropped perpendicular to the xaxm s and PM " perpendicular to the x ,. - axis -; and from the point
Mtr let M ~ N be erected perpendicular to the X-axis and M"Q
f3erpendicular to PI-L Thus M" N is parallel to the y axis and
M"Q is parallel to the x axis.
Now since x = OM = ON + MN
But
ON = OM ncos 0 = X " COS e
and
MN = PM sin 0 = y ~ sin 6
Therefore x = x cos 0 + Y"Sin 0
and in like manner
y = PM = PQ - MQ
But
PQ =OM· cos e = Y"COS 9
and
MQ = oM~sin e = x · sin 9
Therefore y = Y " COS e - X"Sin e
0
(~.
E .. D.
A we did i n the cas e of t rans lation ,. s o h e r e t oo we mu st
.s
show that it makes no difference whether one rotates the
coordinate system or rotates the figure about the origlb.n of
the systemo Thus it must be sho1rm that it makes no difference
whether one chooses a new framework in which to view the
old figure ] or ~ a new figure considered in reference to the
old framework ..
Proposition II
Let the figure be as before and :et the conic be rotated
0 degr~es about the point O ~ in the opposite direction 5
making she axis of the section parallel to the coordinate
axes of the system. Therefore the point P will have travelled
e degrees on a circle about O as centerc If its new coordinate
by x ~ and y · ~ I say it is still true t hatg
x - x pcos e + y-sin e
and
y = y · cos e - x nsin e
�-83. ~ · -~
-. ' ~
I
I
,!
j
Fig. 14
.)
Fig.
15
�For since x = OP cos a
y = OP sin a
But
x~ = OP cos (e + a)
= OP(cos a cos e - sin a sin e)
= OP cos a cos e - OP sin a sin 8
Therefoee X" = xcos e - y sin e (I)
Again
y · = .. OP sin (a + e)
=OP(sin a cos 0 + sin 8 cos a)
= OP sin a cos e + OP cos a sin e
Therefore Y" = ycos O + xsin e (II)
Hence : by multiplying !I) through by sin 09
x · sin 8 = xcos e sine - ysin2 e (III)
and (II) by cos e
y · cos e = ycos2 Q + xcos @ sin e (IV)
subo (III) from (IV)
Y " COS e - x·sin e = y(cos2 Q + sin2 e)
or
y = y · cos e - x · sin e
and in like manner
x = x · cos e + y · sin e.
Q. Eo D.
In the foUJ.th Proposition of :Book I of 'fhe Elements ._.
Euclid proves that two figures are congruent . that is to say~
they look alike ~ if one may be superimposed on the other.
Let us see if there is some relation between two equations
which name two congruent figures.
Let the~e be a general equation in two unknowns of the
second degree
Ax 2 + Bxy + cy2 + dx + Ey + F = 0
and let
x = x , c 0 s 0 - y . sin e
and
y = X " Sin e + Y'COS 8
and. expanding and rearranging terms , we obtain a transformed.
equation of the same form as the above general equation 9
namely ;
A" x" 2 + B" x y" + C- y 2 + D · x · + E ~ y" + F ~ = 0
in which the coefficients are given by
A " = Acos 0 + Bsin 6 cos 8 + Csin~ 0
B- = -2 (A-6) sin ~ cos 8 + B(cos ~ - sin2 e)
C· = Asin2 e - Bsin 6 cos 8 + Ccos2 e
D = Dcos @+ E sin 6
E" = -Dsin 9 + Ecos 9
p
F~
=
f
o
First let us determine through what angle the figure
must be rotated in order that B·· = 0/
Let B" = 0
Therefore -2(A-6)sin 9 cos 0 + B(cos2 8 - sin2 8) = 0
or
(A-C)sin 2& = B cos 29
Now if
A. = C
Beas 2G = O
But since B ~ O ·
cos 2e = o
therefore e = 45 degrees
�s
D
D"
s
D"2 +
2 +
or
I
or
=
En =
2
=
e
s
s
�s
R - " -
+
was
we assert
on
measure
s
F
=
ons
we
�-87and arrive
the eQ_uation
+ C•1~ + D· x + Epy + F · = 0
where A is positiveo
Case I~- Where W I: 0
B2 - 41\C = O~
If
t.hen
.A"C - = 0
'::<~re ei t{J.er
A• = O
and
D ., I: 0
b
~r ..L
~- ~
ecause ~ F o
C· = 0
or
and
F 0
In either case . the figure is a _par~o}~·
But if
B2 - 4AC < 0
then
C" > 0
and. the figyre is an ellipseo M
oreover, in the case of the ellipse,
But if
B2 _ #J\ C ) ·o
the elliipse will be imaginary if
then
C I... O
H' is less· than O; but, H is invariant;
and the figure is an ~rbola.
hence, if IJ is less than o, there
Since
~N = F(h-AC - B~) + BDE - E2A - D2C
is no locus.
the results determined. in the last proof may be placed in
the form of a chart which is merely a more general form
of the chart given in Section III.
a~
A'X~
J.,;j
•!
B2 -
4AC.) 0
ellipse
no locus
single point
Ji> 0
.N .C. 0
N= 0
Section Y:
B2 - 4AC = O
parabola
hyperbola
parabola
hyperbola
pair of inter- pair of parallel
se'lling lines lines
On the Consequences of the Relation
of the Conic. Section to the General
Equation of the Second Degree.
Proposition I
IF
S =Ax 2 + Bxy + Cy2 + Dx + Ey + F = 0
and
s 'I = 1\ "x2 + B"xy .rp. c "y2 + D. x + E ~ y + F " = 0
and if S and s - name two conic sections that have four
po i n ts in common 1
I say that for any J!- - the equat:lon
_
S :i
=S
- gS " = 0
is also the equation of a conic section -which passes through
those same four points.
First of all ) it is clear that S r• = O is also a second
degree equation -, and hence names a conic.
But :- since the four sets of values which satisfy both
the equation S = O and s· = O also satisfy the equati on
sn
S-gS · =0
is the name of a conic section passing through the fmur
given points.
Q.E.D.
If
and
and if
Lemma I
s = Ax + By + c = 0
S " = A " X + B·y + c· =
s
SS .
=
;~
0
�E
�Propmsition II might · also have been solved in the
following manner. Since both sides of an equation can be
divided by . any one of the coefficients we are essentially
inter~sted in only five coefficients.
Thus . if we substitute
the· five sets of values for x and y , we will have five
equations in five u.nl{no~ms and can solve for the five coefficients. Substituting these coefficients back into the
general formula : we l·lfill have the equation f cr the conic
going through the five given pointso
As we have shovm - five points determine a conic ., but
1.
Having n+l coefficients - is like having n points; since
there will be fewer unknovms to be · sought .
2o
Having the center is like having tv·Jo points for .; from
each given point another point may be derivedo
J.
Having a diameter is like he.ving three points since the
center is also given.
4.
Having the diameter and the angle at which the abscissa
meets the ordinates is like having four points ~ for " if a
line be drawn through a given point at the given angle and
extended to a second point such that it be bisected. by the
diameter and if another li:ne be dravm joining the given point
with the center of the diameter and if it likewise be extended
such that it is bisected by the diameter - then these three
.
points together with the ends of the diameter will make up
four points.
5.
From //:4 if follows that if the axis be gi ven 9 it is the
same as if four points have been given.
6.
An asymptote is equivalent to . two points .
7.
A lii1e parallel to the asY!Ilptote is lilrn one point.
6. Since it is possible to solve . the general equation for
the focus F(x1 : Y1 ) (for instance in the limited case dealt
with in Part II . Section V) . we proved th~t
x1 = -E/2C
.i
Y1
=
(-Ee±
V
M~C-=f!-M )/2AC
we can always substitute the given values of one of the col!fficients : which acoording to #1 is lUce havin·g a point.
Therefore . having a focus is lil{e having two points.
9.
For the same reason- having the eccentricity is like
having one point an:l
·
10. having a vertex is lil{e he,ving two points.
11. The directrix is equivalent to two points 9 for ~ we have
both its slope and its position.
12. A tangent is equivalent to one point . but
lJo if the point of tangency also be given it is equivalent
to two points.
14. For reasons similar to those given in //8 ,. the parameter
is also worth one polhnt.
�-90Section VI;
Slrntching a Curve.
No matter how far we may wander from Apollonius ~, we
must remember that up until this point all of the formulae
we have derived are ultimately based on geometrical principles.
In this Chapter we~all face the problem from the opposite
point of view ~ and try to see if we can get a rough idea
of what a curve looks like b~ starting from the formula.
First of all , we may make a long list of values for x
and. , by substituting . derive corresponding values for y. By
continuing in this rather boorish style till we tire ~ we
may draw a line connecting all the points so derived and
claim to have a fairly decent notion of what the curve looks
like.
For instance ., let the given equation be
y
= x3
We may then draw up the following
table~
x
0
1
-1
2
-2
.5
-.5
1 .. 5
-l .. $
1
-1
8
-8
.125
-.125
3.375
-].375
Now if on a graph l we locate the points corresponding to
each pair of values ., we can begin to get some notion of what
the curve looks like.
The crudity and roughness
of this method may never be
completely eliminated since
it is not possible for us
to plot all of the points.
Nonetheless . there are
certain guides of a very
general nature which
should prove helpful to us
in our (endeavor.
A moment . s glance at the
table dra1>m up for the last
example reveals the fact that
in this case , if P(x 1 ~ y 1 ) is
on the curve c then Pl-X1 -Y1)
is also on the curve. In terms
of the curve _ this means that
,
if I pick any point on the curve )
and draw a line connecting it with the origin ~ and continue
the line so that it is bisected by the origin ; the line will
agalhn fall on the curve.
�-91If any point P be tal-rnn on the curve and. the line PO
be dra't'm through the origin and extended to meet the curve
at p~ 1 it is clea~ . th~t
OP = OP P,
Since this is true for any point P i it is reasonable to say
that the curve is sympi~~ical about the origin. Is it possibl E
to look at an equation and to tell whether its graph will
have this property or not befor~ sketching the curve? Since
the distinctive characteristic of such curves is that if they
contain th~ point P(x 1 ·~ y 1 ) they also contairi the point
P (-x1 -Yi) ; we may easily devise a test to tell us wil~erEfJ.
given equation represents a curve 1,1Jhich is sym.metrical· ·w1 th
respect to the origin or not~
I,f -1.he sig_ns .91.. both x and y 11!.~ be__ chan_ged without
cha!}_gi_gg th~~ati.Q.!l itse~f . then the curve is
£~etrica~__1!i th re§Eect to the ~riEin.•
In otir case , since
= x . I apply the following test.
Let
-Y = C-x)
.
Therefore y = x3
·. ·
which is the· very sameequation with · which I began ~ and. hence
if I supstitute· symmetrical points for each other ., I will
arrive at the same curve with whcih I began. Therefore . the
curve is symmetrical with respect to the origin.
Let us consider the more general case. Given an equation ~
let it be proposed that we discover whether or not the given
equation represents a figure which is symmetrical with respect to some point and if so , to find what that point is.
If for the moment we assume that the figure is symmetrical
with respect to a point (h .k)
3
·-. . .- ·---- ·-i·--- - ;- ·- 7
/
_.'
~---------------·-··
I
. .P. ( . _ _ ·) c.,-~--~--·- i
/-±::::~ ( :
l
!;
·11 .
i- ·\ 2 L
- Pig. 18
I
- , i 1 ~·- '
l:z.)
Loosely speal{ing , if the curve is symmetrical with respect to a point : then if a line be drawn joining the center
of symmetrj and any point on the curve . and if the line be
extended. an equal distance on the opposite s:lde of the center
of symmetry ._. it will aga~n meet the curve. S peaJ~ing mollTe
properly . if any point P~x . 'y) be tal{en on the curve~ and if
the point (h , k) · be the center of symme·t ry .~ the point
P1(x1 · Y1)· will also be· on the curve where
:
�-92x 1 = 211 - k
and
y1 = 2lt - yo
Hence we conclude that if an equation in x and y be given and
if it is possible to find .some h and some k such that if
2h-X be substitutd.ed for x and 2k-Y substituted. for y and the
same equation result as was given in the beginning :. then the
figure will be symmatrical about the point (h !k)c For
example ; giyen tbe equ~tion
xj + yJ - Jx - 9y2 + Jx + 12y - 9 = O
let it be required- to discover whether there is a point of
symmetry.
Let it be assumed that there is such a center and let
it be at (h , k). Theref~re
(2h-k)3 + (2k-y)j - J(2h-X)~ - 6(2k-y) 2 + J(2h-x0 +
12(2k-y) - 9 ~ 0
~
Theref 03e
~
.
Sh -12h2~+6hx2-x3~sk3-12k y+6ky2_3y3-12h2+12hx;3x2_
24k +24ky-6y +6h-3x+24k-12Y-9 = O.
Now e must discover whether nhere are any values for h and.
k which make the coefficients of the equation just derived
equal to the coefficients of the original equation.
I
x3 = x3
II
y3 = y3
III
-(6h-3)x2 = -Jx2
6h - 3 = 3
=D~y~ +6y 2 = _y2
IV
k = 2.
12h2x
v
12hx + Jx = Jx
h = 1
VI
1'2k'2Y - 24lcy + 12 y = 12 y
k = 2
VII
:-gh)-- 8lt3 + 12h2 + 241\:2 - 6h - 2li·k + 9 = -9.
Now if the values for h and le ; arrived. at above , will also
satisfy this equation ) we will have done that which was rerequired. Therefore . by substitution . we get ;
-8-64+12+96-6-48 + 9 = -9
or
O= 0
Therefore the locus of the given equation is symmetrical with
respect to the point (1 . 2).
Now let us consider the parabolao One might also say
that it has a kind of symmetry , but is evident that it is no
longer symmetrical in the same sense in whQ~h we Jtavc"'.:·be.en
considering up to this point. Ro"tlghly spealcing , we mean that
kt is possible to draw a line through the .parabola in such
a way that the part of the curve 01,1. ouc sic o•- ~.·. 1 ill ue · · _ similar
to the section of the curve on the other side of the line.
If one wishes to consffi.fil.er this similarity in terms of Euclid
Io4 ; a certain amount of caution. mast be employed for in this
case it will be impossible to malrn the sections coincide
without talcing one of the halves out !616 the plane and. turning
it upside d.o1flm. Another way of stating the same thing is to
say that one part of the curve is a mirror image of the othero
�-93How may we restate this character of symmetry in such a
way that we can deal with it within the confines of geometrica:}.
analysis? In other words ~ how can the notion of similarity
of lool{s be translated into an algebraic expression? A third.
way of stating the present notion of symmetry is to say that
if a line be dra1rm from any point on the curve perpendicular
to the line of symmetry . and if it be extended an equal di:s:tanc~ on the other side of the line of symmatry ) it will agamn
fall on the curve. Vhat are
the conditions under which
an equation represents a
symmetrical figure?
To begin with:, it is
clear that if the line of
/
symmetry is the Y-axis , and.
if the curve contains the
·- --.--- -----,.point (x-y) . it also contains
i
\
the point (-x ~ y). Since
,/
r'
this is true for every x and
\
-~,(-·-,._~) 1-j )//,., ,_---+-__\ I-') (
')'
every y , if an equation re- J f
( '() J,_ "I 'j._ '- -'· \
-·
presents a curve symmetrical
I
',
with the Y-axis , then we may
substitute -X for x in that
equation and get a new equation
which will also represent the
Fig. ::_c)
given figure <; and hence will be identical with t i13 given
equation. Fo:i;- exam~Jle tet the given equation be
5xb + 10x~y3 + 9x2 y = 27.
Since x appears in even powers only ) it is clearly indifferent
whether we use x or -X : for in either case y will be the same.
Hence the figure will be symmetrical with respect to the Yaxis.
This is not the -only condition : under which such symmetry
may take place. For example let us take the equation
5x) + 10 x3y3-llxy = O/
mm this case . the substitution leads to the equation
-5x5 - 10x3y3 +llxy = O
which is the same as the given equation.
In general, therefore we may say that if an unknowns
appears in even powers only ~ or if it appears in odd powers in
every term in the equation . with the exception of 0 7 then the
figure is symmetrical. Since we may divide the la.st equation
bhrough by -X -, it is ultimately sufficinet to say that e.n
equation represents a figure symmetrical about one of the axes
when the other unknown appears only in even pm·J01·s.
More generally ., "(i• may say that if when a CUTY8 c r~1'.":1. tains the
Te
point P~x ; y) ; it also contains the point P 1 ( 2 ~ ·-·f . .-,. \ ~ :~_ 1. 1.s
symmetrical with repsect to the line x = h _ as 0 ~.;;,.~1 L . ::: ,.<'-: n
,
from Figure A.
For ex.2 mple :. let us consider the equation
x y - 4xy + 4y = 1.
·-
A
)
7
)\\
�k
h
=
=
0
2
=
=
=
4
=4
�-95there are two Y " S which are each equidistant from some contaant
quan:t;ity. F~r example ; .given the equation
y - 4y - x = O (which may be solved by completing
· the square)
or
y2 - 4y + 4 = x + 4
(y-2)2 = x + 4 (Fig. a)
or
+ ·---ir;--or
y - 2 = - V x + ~
Therefore y = 2 ± V-X-+-1}
Hence the curve is symmetrical with respect to the straight
line y = 2 , since y = 2 plus or minus the same quantity.
However . suppose we are given the equation
y = ?.x·± V x + 4
(Fig. b)
We are led to conclude that some l~ind. of symmetry exists about
the line y = 2x. But here we must widen out definition of
symmetry since the lines bisected . while they are still parallel
to the coord.ina te system .; are no longer perpendicular to the
line of symmetry. Let us define the line of symmetry as that
line which bisects all lines which join two points on a curve
and are dra\:m "parallel to some straight line. 0
I
i ,'
,'
..·'
--·
--- - _
,.~
.. _.. ...,.
-· ....
I ,·) , .
/
/
/
~!
/
I/ '
/
__ ,
1_+--·- - - - /
. _J .-- )_ ·-_
/
.
/· I
/
:;
·"
,
Fig. a
if-
,I
,'
/
I
/
,.
I
/
,/
./
Fig. b
We h~e not yet discoverd a method of finding an axis
of symmetry which is perpendicular to the lines ·w
hich it
bisects ; but which is not necessarily parallel to eitherof hhe
coord.~rate axes.
In order to do this - le-i; us employ the socalled method of reduction used in Section VII of Part I ,
thought 'li'rn might also have used. the method of rotation discussed
in Section IV of the present part.
Let th~ given equation be
x + xy + 2x = O
Let
z = x +y/2
or
x = z_ y/2
T~erefore z2 - zy + y2/4 + zy - y2/2 - 2z - 4y = o
or
4z2 - y2 - Bz - 4z = o ·
Therefore y = (-4 ± V-Y-6 - 4(4Z2~+-8z_),____ )/2
or
y = (-4 ± 4v--=r: 2z ·~~--) /2
~rt1ich ~ according to the foregoing principle : is symmetrical
with respect to the line z = -4
but
x = z - y/2
Therefore the line of symmetry is
x = -4 - y/2
or
2x + y + 8 = O
��-97Let us ~alee on~ more exampleo
2x y + 3Y x £ y3 £ xy - y - 2 = O
Therefore y = 2/(2x+)xy+y2+x-l)
or
y = 2/((2x+y-l)(x+Y+l))
l
'·
Therefore the asymptotes are
"'
x ;'.
2x + y - l = O
II\
and
x + y + 1 =O •
~I
As we can see from the last
two equations . in general if
___ __ _ ___ _ .J_ _-t--o___ - --- - A
-one solves for one of the
·-,
unlmowns in any way whatsoever ,
that is to say : even if that
\ l
same unkno~m appears on the
other side of the equation ~
I ·
I '
then if the result is a
(Fig. 21 .
fraction whose denominator can
be factored into linear equations ,
then the asymptotes may be arrived at by setting each of the
factors equal to zero.
Unfortunately :. this method does not always work. For
instance : if we were given the equation
y = (x - 2)/(x2 - 4)
in th~ case when x = 2 the numerator becomes O as well and
hence one may not claim x = 2 as an asymptote. Since an analogous difficulty will artse in the next section ; we shall
defer our discussion 16f this point until that time. GBBera.lly 5
the problem isg how can one lcnow that the numerator does
not become O when one or more of the facclrs of the demomiator
is set equal to O. In the present case _ there is of course ,
no practical difficulty because one can always substitute the
given value for x~ For in~tance ., if one has the equation
y = (y - x)/(x - 4)
can one be suieh of ·what happens to the numerator when
x2 - 4 = O?
,~, i
'
i
' - ...
r
I
Extent
One other characteristic of geometrical figures seems to
be oll some relevance in consOl.d.ering their general shape. This
characteristic : unlike the others ~ cam1ot strictly be said to
belong to the figure itself but arises when the figure is
placed within a coordinate system. The characteristic is
merely thisg certain flil.gures remain within definite boundaries .
For instance . a circle at the origin ~ with radius l q is
bounded. by the lines x = l ~ 2 = -1 ; y = l and y = - 1.
Let us consider the geometrical phenomena a bit . more
closely in order to discover whether ther are any algebraic
conceptions analogous to them. From the figure it is clear
that x may actually equal 1 : but may never be greater than 1 ,
or if so the curve would lie beyond its boundaries , thus contradicting the hypothesiso
�-98-
22
or
if
or if
is
g
2
ever if
x
=
=
s an
-2
�-79-
~e
hezerd
_gueas
g
~ re
now in
·csiti~~
R
t~
soffiewh~t ~ore ressons ~le
re~i '.j_rdinz
the
~:-:-:. ri c
of L"1e
curve of ~ fiven e ~ u"tion. ~lolti~[
will atill be necees~ry g~d tencc
errors '.Ifill still b€ ·Wl-woiu··-. ..:le.
J. ··---
. 1-
L>ove !!"!et!!~d fl, hot·:c::vcr, should
tne re:·uer to J :r.ore ~easiolc
and en1ightenea g:u0r;:-:.
i '
~e~ u~ 7· cs~ t:;e riroblerc cf
l
\
discov . . rinz the extent~ 1ihlcr: r,1re
.
Fig;. 24J
not pnn·llel to tr~c ocordi~ · ·te '.:! Xes.
To :.-;. c.sc t.i'lis ~0 roble ··o r:.:di.c "3 lly is to :;G. fo!' tt.;; equ·:-i ti·:m oft~;e t g.·:ig:ent to a
curve ~ t '.i::lY -~· oint. Li {e t!~E qi4'eoticn po::;ed ::i.t 'l..r.e c~a of tl"Je aeotion en
asyn.t;totc..s, tfiio r-·rvul(:ill, 1.,·hior, ocosrr,~ cru.·: i;:i,l for ~ ·-f; 11'ton, :-ti~.y not be solved
within t~e cnfinec of J~rt~sian ~n3lynis, 2nd b~ca~c one ot the roots for
t:-:c discovc::ry of the Cr lcul.•.Aa.
The
G
le~d
0
CONCLUSION
�
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The Collegian
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The Collegian, June 1965
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1965-06
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Annapolis, MD
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PDF Text
Text
�Egypt
While pageantries of East or West
Fade from the ancient land,
These mortal mathematicals
As in the dawning stand,
Constructing their geometry
Of shadows on the sand.
Holiday
On a crowded beach radios croon
By many a languid knee;
The boy has found in a caverned shell
Ocean's melody
And carries home this distant voice
That sings of Odyssey.
�Album
Ah, Valentines of yesterday,
The sullen fire of time
Consumes your lace and satin hearts,
The ribbon and the rhyme!
You too have been in Arcady,
Earth's ambrosial clime.
Vienna Wood
Beside a path there is a bench
Which histories encumber;
Hearts and years and names are carved
Deep in the aged lumber;
Sometimes a bird picks at a heart
Or nibbles at a number.
Missing the Mark
Rip van Winkle slept for years,
Rage removed his mate;
Apoplexy, ataraxy ! They are reprobate
Who leave the world too soon perhaps
Or certainly too late.
Guardian
The clock has stood a century
In the shadow of the stair,
Ordering the day's events
With mild,. ancestral care,
Save for those last departures
That take it unaware.
�.:... ,
\~
~
1.-
M
••
.....
f'
New Troy
Up from the ruins of his pyre
They say the phoenix flashes
To be the one undying bird A hope experience dashes,
As Virgil knew, who is the world's
Connoisseur of ashes.
In Memoriam
Men are estranged by nature's walls
Of mountain, plain, and sea;
And legend everywhere recalls
A last catastrophe.
The world's great age begins anew
When the wild ape scorns his tree.
Webster
The spider spins ex nihilo
An apprehensive thread
Stretched over space and solitude,
Yet by a dream he is fed
Of banquet cloth and winding sheet
About the winged dead.
Escape
The shadows seen on sunny days
Are children of the night;
They hide behind the shapes of things
From the lordly eye of light
Until their vast, kind mother comes
And covers them from sight.
�"'t
,
'
/"
-
.. '~·=.~·.:. ',"')j..
,.
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••
,,,
•1
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•'I,:
,
..... ,'_, ,···· .. · ...:
•••
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���
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Title
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The Collegian
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The Collegian began as a student newspaper; became a college community literary publication in 1952 and continued until 1969; became a student newspaper again in 1969; discontinued publication from 1980 until 1989 when it again became a student literary publication.<br /><br />Click on <a title="The Collegian" href="http://digitalarchives.sjc.edu/items/browse?collection=26">Items in The Collegian Collection</a> to view and sort all items in the collection.
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Annapolis, MD
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Scofield, Iola
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Poems and Drawings
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1965-06
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Special Issue of The Collegian, entitled "Poems and Drawings". Published in June 1965.
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Annapolis, MD
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St. John's College
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English
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St. John's College owns the rights to this publication.
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pdf
The Collegian
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https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/32c7f7c06bc33e901e5622c2e6a8d288.pdf
aa19271309831733b8ccfb5b5e50fa1c
PDF Text
Text
\
1
0.,
\..
\
\
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I
"\ ~
".
\
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�T HE
C0 LLE GI AN
of St. John's College,
Annapolis, Maryland
and
Santa Fe, New Mexico
TABLE OF CONTENTS
.Jacob Klein , Tutor •
The Prize Solution to the Junior-Senior
math Problem (1965).
Alec meiklejohn's Maytime
(Reprinted from The Progressive)
.
13
John ·Hetland, '65
The Prize Solution to the Junior-Senior
Math Problem (1965).
1
James McClintock, '65
Liberal Education •
.
15
. mil ton mayer ' .
Lawrence Fischler, '68 .
Poems 1962-1965
Eva Brann, Tutor
From Euclid to Dedekind - Sequel •
*
*
*
*
*
*
*
*
*
*
Editor. .
Susan Roberts
Sally Rutzky.
Associate Editors in Annapolis
Deborah Schwartz
Vida Kazemi •
Associate Editor in Santa fe
Paul Ollswang, r.m.o.c. •
• Art Editor
Faculty Adviser
Eva Brann.
Cover drawn by Paul Ollswang, Class of 1966
.
17
23
29
�ON LIBERAL EDUCATIO
Jacob Kle
the very be
is
of a
this case - Liberal Education meant the education of free men.
very be
one detects an
in the mean
of
From the
free men"
In ancient times free men are contrasted with slaves and, moreover
men who,
not slaves
are
with
in menial labor and have to do
to cope with the necessities of life.
To br
up children to the
them up for the en
level of free men means to br
and duties
of a life which, secure in its subsistence, is attuned to the
sensual and intellectual exercises and to the
of bod
Such life tends, however, ta move
act iv
be it in games, in
traditional lines
the
ic affairs
However !'free
free himsel
idols of the market
the free man may be
~~._·~~
Baconian
he has thus still to
from the shackles of conventional views which pass for the
truth of th
He has to cultivate pursuits in which the truth of
made an attainable
is
arts of freedom, the
the acquisition
there are
These pursuits constitute the
liberal arts''.
Liberal Education, then, consists
the liberal arts
from the very
ifficulties in the understand
these arts.
tice
ite conversation or in
Its freedom is
, the
nance of
of
These difficulties relate
2) to their
1
and the prac-
to their conte
of men
and
st
Let me
of the difficulties which relate to their content
liberal arts Music,
- is characterized
that their content can be
=-~__,;;;,,-'-~
The Greek word that
, the learnable,.
ithmetic
Geome
the
and therefore
ies these three
is
Thus the traditional liberal arts are
or
0
knowable.
Cassiodorus calls therefore such a liberal mathematical
mathematicalH, that is, understandable
* Lecture delivered march 25,
's
, California
965, at the
learnable
a:id
held at St
�-2-
art quite
sui~ably
an ars doctrinalis.
We should not forget that anti-
quity had, inofficially, as it were, a fifth liberal preoccupation '
the inquiry into nature ( 1J nep \
history _ as it was called ·later.
,
here, too.
01
vUO'EWf.
4.
I
t.O''tOp .. a
.
) , natural
There was something to be "learned"
And we know that Grammar, · Rhetoric and Logic were added to
the list, the emphasis shifting gradually from the quaternity of the
mathematical arts to these trivial supplements.
answer is:
Why this shift?
The
the ultimate foundations of the original four - or, if you
please, five · - liberal arts remained doubtful, becoming the concern of
a deeper investigation, the subject matter of philosophical reflexion.
The pursuit of truth in these arts, through which thG freedom tif fuan
was meant to find its integrity, seemed to become truncated and encroached upon by defihitions and
hypothes~s
which lacked certainty and
persuasiveness and put limits to our ·understanding.
be said of . the trivial
~rts.
It can be said,
This could not
h~wever,
that integral
knowledge was not achievable in· any of the seven arts.
. ,.
(scientiae, ·.·' ·
That is why
it is proper that they preserved the name of "arts" ( 'texva 1.
contradistinction to · "knowledges"
...
..
E~:n:O';t·:tllf:La t.
sophical wisdom was meant to supply what they ware
lac~ing.
)
)•
in
Philo-
And, what-
evet else may be said about Liberal Education, we are justified in
setting down as a -first rule that Liberal Education requires - for the
learner as
well · ~s
for · the teacher - the practice of philosophical re-
flexion and the awareness of its guiding role.
Let me turn to the difficulties inherent in the preservation of · the
liberal arts through generations of men.
Words used in common speech .do not always preserve their commonly accepted meaning.
This . commonly accepted meaning itself ranges, more
often than not, over a series of connected shadings and connotations.
In the perspective of a detached inquiry the meaning of a word usually
loses its "natural.0 ambiguity, becomes more fixe.d, _gains. a definite
significance determined by the .scope of the attempted and sustained
investigation, which investigation may lead to the establishment of a
science, an art, a
~lxv~
.
The inquirer then turns, of necessity,
into an "expert" who is able to pass his knowledge on to others, who is
�-3-
able, in other words, to become a teacher.
deed become
~technical"
It is thus that words do in-
and transcend the habitual and familiar.
Special
terms, moreover, may be coined to satisfy more fully the understanding
gained in the investigation.
And yet, the ''technical" ·use · of words
tends, in turn, to become accepted and to win a familiarity of its own.
The passing on of sciences, arts, and skills, especially of intellectual
ones, cannot quite avoid the danger of blurring the original understanding
on which those disciplines are based.
understand~ng,
The terms which embody that
the indispensable terms of the art, of the
,
"t€X'Vrl
in
question, the "technical" terms, acquire gradually a life of their own,
severed from the original insights.
In the process of perpetuating the
art those insights tend to approach the status of sediments, that is, of
something understood derivately and in a
matter-of~course
fashion.
The
technical terms begin to form a technical jargon spreading a thick veil
over the primordial sources.
Again, whatever else may be said about
Liberal Education, we are justified in setting down as a second rule
that Liberal Education has to counteract this process of sedimentation
and to find the proper ways of doing this.
The background of what I have been saying so far is classical liberal
education.
But in the last four hundred years the background of the ·
educational scene has changed tremendously.
rules I mentioned has increased accordingly.
The pertinence of the two
Let us take a glimpse at
this change.
m
usic has al mo s t ceased t o be a liberal art. - Arithmetic, Geometry,
Astronomy, and Natural _
History have merged and expanded into a towering,
multi-storied edifice called Mathematical Physics to which are attached
a number of ancillary disciplines, the mightiest among them named
Biology. - Analytic mathematics
h~s
formed an entirely new New
Atlanti~
The arts of Grammar and Rhetoric have transformed themselves into the
preoccupation with diverse languages, and especially with the classical
ones, which preoccupation is called Philology and embraces quite disparate subjects as, for example, classical philosophical texts, poetic
works, literature in general, and the modern novel in particular. - The
art of Logic has become, on the one hand,
ah · a~junct
of mathematics and
•.- -
�-4-
has usurped, on the other hand, the place of the uppermost level of all
knowledge.
Philosophy is ' taught as . a special discipline by Professors
of Philosophy and is, more often than not, identified with" mathematical ·
logic. - I omit mentioning a plethora .of ·other sciences cultivated in · ·
our univsrsities. - All these disciplines are
suppos~d
to be classifia6le
into two vast domains, that of Science proper and that of the Humanities.
'The subject matter of Liberal Education is thought to belbng almost exclusively to the latter domain, the domain of HLlmanities, which includes we . ought to .note -
~!story
The multiversity of our
and all kinds of historical disciiplines. ·
u~iversities
rather than to decrease.
is likely ta increase in the future
Will a genuine Liberal
Educat~on
be .able )o
remain a desirable goal 7 Will the idea of. a "fr.e a man" persist?
will depend, I submit, on whether the two rules I have
be observed in the process of learning.
referr~d
This
to
~ill
It is safe to say that in any
good course of study - whatever the subject matter - these two rules
find, . to a greater or lesser degree, their
applicat~on:
the learner is
made to reflect on the assumptions underlying the way the subject
matte~
is presented to him and the technical notions governing the presentation
are shown to arise from fundamental insights· freed from their
sedimentation.
~tatus
of
I would not venture · to state how often or hbw rarely
this actually occurs. · A little later I shall have to come ba'c k · to this
question again.
What is to be aimed at, at any
r~te,
is the ·setting up
of a program of study in which those two rules can be consciously and
persistently applied at all timee.
'.I
Let me talk, then, about such a program. · It has first of all, to select
the material which would
com~el
the learner to reflect and to get · rid
of the sediments in his thinkihg so as to enable him to reach ·the level
of intellectual clarity.
This
m~terial i~
available in the great docu-
ments of human seeing, hearing, imagining, and understanding, that is to
say~
in the Old
Testam~nt,
in the works of Homer, Aeschylus, · Sophocles,
Eur ip'ides, Plato, Aristotle, in the New Testament.. in A-ugustin, Thoma·s
Aquinas, Dante, Francis Bacon, Shakespeare·,
Galil~~, · D~scarte~,
Newton,
Locke, Hume·, Housseau, Kant, Hegel, Darwin ·, the great novelists of the
19th
century, Nietzsche, Freud, UJ-hi tehead and many · others. · The task is
�-5-
to read these works, which contain our intellectual heritage:- which, in
turn, is permeated by vagueness and sedimentation -, in such a way as to
re-awaken the insights in which they are rooted and to reflect on these
insights and their ultimate assumptions.
This task is tremendous; at
best, only a beginning can be made.
Those works present human speech, bereft of its spontaneity, but composed artfully and purposefully.
To understand the content, the art,
and the purpose of this speaking, help is required.
The -signifying func-
tion of words and the ramifications of this function are at stake.
It
is necessary, therefore, secondly, to arrange for a concentrated study
of the interconnection of words, of their inflexions and concatenations,
of the grammatical rules in which they are bound and of the flexibility
they still may preserve.
This study should by-pass the familiarity of
the mother tongue and its sedimented use.
Two foreign languages, pre-
ferably an ancient one and a modern one, should be chosen, the scrutiny
of which may provide the learner with an understanding of what Grammar
entails.
And it is in translating that the learner should be able to
recognize the similar, yet different structure of his mother tongue.
Translation, moreover, should acquaint him with the various rhetorical
devices Language uses to articulate thought by means of combinations
and stratifications of sentences, by means of figures of speech, metaphors and idiomatic expressions.
To understand the embodiment of
thought in speech - this is the aim of such a study of Language.
W
hat characterizes words is the union of their sound with their f unction ing as signs.
autonomous.
This union can be broken:
both sound and sign may become
The nacked sigris - turned later on ihto symbols - consti-
tute the skeletal language of mathematics, as the nacked sounds become
the tonal language of Music.
Liberal Education cannot
di~pense
with the
task to focus its attention on both.
It is necessary, therefore, thirdly, to study Mathematics, always bearing
in mind that this studying has to be reflective and cannot be satisfied
with a sedimented understanding of mathematical relationships.
begin here is an open question.
How to
But it is not questionable that -
�-6-
whatever the beginning - the mathematical considerations have to be tied
to the inquiry into nature, be it to the observation of celestial phenomena
or tp the investigation of events and conditions on this our earth.
Everything around us, as we know, all motion and change, hangs on number,
weight, and measure.
After a while, the shores of the new New Atlantis
of pure mathematics may be within our reach.
And, fourthly, music too, the region of sounds, either tied to words or
received in their purity, should be opened to our understanding vying
with our pleasure.
I cannot omit mentioning in this connection the
mysterious .link between musical sounds and sequences of numerical ratios.
The musical formalism, in pitch, rhythm, and meter, seems to be an ultimate formal reflexion of the rhetoric inherent in human speech.
I have been speaking of
mod~r~
using a Baconian phrase.
pure mathematics as a new New Atlantis,
Now, Bacon's New Atlantis, as we know, pictures
this island not as a mathematical one, c.omparable to Swift's Laputa,
but as treasuring a vast laboratory in which man "interprets" Nature in
extracting her secrets from her and subduing her to his will.
Thus
Bacon - though neglecting the tie between mathematics and the inquiry
int~
nature - anticip~ted the work of the centuries that followed him.
We have indeed transformed our habitat from a place of nurture into a
place of experimentation.
Our relation · to Nature is quite Baconian.
Liberal Education ignore this tremendous change?
Has not the Baconian
enterprise added a new dimension of freedom to man's life?
to control the ways of Nature and to put them to our use?
The freedom
Yes , it has
done that, but it .has also brought us face to . face with forces which
we seem
un~ble
to
~antral.
liberal Education has, therefore, fifthly,
to apply itself to experimentation, not to increase the sto.rehouse of
our powers, . not to reach any new and . unexpected results, but to gain
insight in the condition of possibility of such undertakings so -as to
understand how they come about and what caution they demand.
The ways
of the inquiry into nature proper to Physics and to Biology have to be
sctutinized and marvelled at.
This program of liberal learning I have been · trying to sketch is the
program of St. John's College.
Can
Needless to say, we do not live up to
�-7our own goals.
But I am not here to speak of our faults and defects.
What I have to speak about - briefly and in a most elementary way - is
what both Learning and Teaching mean and do not mean.
teaching are mysterious processes.
Learning and
To understand them fully would mean
to discover the secret of our lives.
For we are - perhaps above any-
thing else - learning and teaching animals. - I hope we all agree that
teaching does not consist in telling and insisting nor learning in listening and repeating.
The image of the learner's soul
is not an empty
pitcher into which the teacher pours the fluid of knowledge.
This pic-
ture of teaching and learning, by the way, however wrong, is ineradicable.
There are perhaps two ways of describing teaching and learning
in an appropriate manner.
The word of the
t~acher
The one is that of begetting and conceiving.
acts as the form which in-forms the material of
the learner's soul, in-forms the capability this soul has, and transforms it into a knowing soul.
view.
This is, on the whole, the Aristotelian
The process of learning and teaching is a generative one, and a
great deal depends not only on the activity and effectiveness of the
teacher's word, but also on the receptivity and potentiality of the
learner's soul. - The other way of describing teaching and learning is
that of soliciting and gaining insight from within.
Through questioning
and arguing the teacher compels the learner to pull out of himself, as
it were,: something slumbering in him at all times.
whole, the Socratic and Platonic view.
This is, on the
Here again a great deal depends
on the quality of the teacher's questions and on the quality of the
learner's soul.
But just as questioning has its place in the Aristote-
lian scheme, begetting is an important element in Socrates' practice.
Learning from books, by images, through associations, and whatever other
ways of learning may be mentioned, falls easily into the patterns of
those two fundamental views.
I doubt whether modern psychologies of
learning have added anything to them.
It is perhaps not unimportant to note that the role of the teacher who
engages in questioning cannot simply be identified with the role of the
"midwife" that the teacher has occasionally to assume.
image, mentioned only
in~
This "midwife''
of the Platonic dialogues, in the Theaetetus,
�-8-
and nowhere else, is a tricky one.
The midwife, the
delivers
women of children that have been fathered, and the teacher is a "midwife"
only when he delivers
th~
learnet's soul of opinions - mostly wrong
ones - "fathered" by others.
Truth, according to Plato, has no father.
At any rate, a program of Liberal Education
~mplies .
teaching both as
begetting. and as soliciting, in fact, more the latter than the former.
The great vehicle of learning is discussion in
w~ich
begetting, questioning,
refuting, and again questioning take .Place . . This is not to say that all
drudgery, all routine work is
that too.
el~minated.
The learning process requires
But it is not the pivot on which. failure or success depend.
.
How to gauge whether learning has actually occured is extremely difficult.
for what has been formed in the learner's soul or .what insights , have
been re-awakened in him depends on factors often totally unknown to the.
teacher.
Both learner and teacher are members of a learning community.
Inasmuch as this learning community is an institutionalized one, it is
bound to fall short of its goal.
the conditions for learning.
All the institution can do is to set
This in itself is an immense task.
learn~ng
under these conditions does not consist in "mastering"a body of .knowledge e .
!
The conditions. merely provide the horizon in
take place.
fruitful learning can
w~ich
The conditions determine the existence of a ... school".
The root of the word "school" in Latin as well as in all our vernacular
Leisure meant
languages is the Greek word for leisure,
schooling, that is, the opportunity to learn.
totle's Politics (VIII, 3):
Let me quote from Aris-
"Nature herself, as has often been said ,
requires that we should be able not only to work well, but to use
leisure well; for, as I must repeat once and again, the first principle
6f ail ·action [he m~ans, t~e end for the sake of which an action is
.
'
undertaken] is leisure •
and therefore the question must be asked
in good earnest, what ought we to do when at leisure?
Clearly we ought
not to be amusing ourselves, for then amusement would be ·the end . of
life."
And Aristotle goes on:
''It is clear, then, that there are
branches of learning and education which we must study with a view to
the enjoyment of leisure, and thees are to be valued for their own sake."
To study for the enjoyment of leisure and in leisure means. to be engaged
in Liberal Education.
This kind of education does not look for some
�-9-
goal or good beyond itself.
It is in itself ·its own end.
Long before
Aristotle and long after him, even under totally different social conditions, this statement defined liberal learning and Liberal Education.
What this understanding of Liberal Education assumes is that man's
proper and specific character is his desire to know.
this goal is man really man and really free.
On!'y in pursuing
To acquire the various
means that enable man to persist in this pursuit is to cultivate the
arts of freedom.
Liberal Education is a precarious and even perilous kind of business.
Let me show you the great obstacles that stand in
of repeating myself.
way, at the risk
i~s
These obstacles are not external impediments,
nor do they stem from non-rational sources in man.
On the contrary,
these obstacles are rooted in what is specifically human in man, and it
is not possible not to meet them.
1.
The first obstacle is the learning situation itseif.
the ideal learning situation?
What is
It is the more or less continuous
contact between a student and his teacher, who is another student,
more advanced in many ways, but still learning himself.
This
situation usually does not prevail; in fact, it is extremely rare.
Since time immemorial, institutions of learning, especially of
higher learning, have been established, called "schools" - and
the ambiguity of the term
be~omes
immediately apparent.
Institu-
tionalization means ordering of activities into certain patterns;
in the case of learning activities, into classes, schedules, courses,
curriculums, examinations, degrees, and all the venerable and
sometimes ridiculous paraphernalia of academic life.
that such institutionalization cannot be avoided:
The point is
both the
gregarious and the rational character of man compel him to impose
upon himself laws and regulations.
Moreover, the discipline of
learning itself seems to require an orderly and planned procedure.
And yet we all know how this scheduled routine can interfere with
the spontaneity of questioning and of learning and the occurrence
of genuine wonderment.
A student may even never become aware that
there is the possibility . of spontaneous learning which depends
merely on himself and nobody and nothing else.
Once the institutional
�-10-
c.haracter
~f :
.learning ·tends to prevail, the goal of Liberal Educa-
. . tion may ba ·comp1etely lost .sig.h t of, whatever other goals may be
successfully
reached~
to learning.
. And I repeat, this obstacle is not extraneous
It is prefigured in the methodical and systematic
character nf exploratory questioning.
It
h~s
to be faced over and
over again.
2.
The second obstacle to Liberal Education is our condition as
heirs of intellectual traditions.
Here again it is man's own
rational nature that brings this obstacle about.
Animals do not
pass on their skills to their progeny in. such a way that those
j
skills can accumulate and grow.
that.
M.an, and only r1.1an, does precisely
Each generation adds something to what had been previously
built and preserved • . _ are proud of this fact and call .it progress.
We
And, indeed, such progress does exist in definite -areas.
.But .· th is
very fact confronts us with the ever-present danger of sedimentation
and pefrifica~ion of our kriowledge that I talked about earlier.
are fond of pointing to the European universities
of
We
the · fifteenth
and sixteenth centuries which exhibit those petrifying tendencies
rather c1early arid are prone to exalt the fresh wind of the ·
Renaissance and Humanism that blew all the accumulated dust away.
But it behooves us to look at our own institutions of higher learning .
and to
di~cern
This danger
these same tendencies · among us. ·. We·
~re
not immune.
is inherent in all learning and all 'scholarship, and
Liberal Education can never ignore it.
·3.
But the most sE,lrious obstacle . i.s .the relation of Liberal Educa-
tion to the political community, the state.
The Greeks, you
remember, saw in leisure, in schooling, the source of a twofold
activity:
the pursuit of learning
~nd
of political ends.
Greek
thought, in fact, circles continuously about these two highest
poles of human life.
The relation of man to his citizenship, to
the obligations that flow from his being a citizen, a . member of a
political community - this relation is one of the great and standing
themes of all classical philosophy.
Man conceiVE.ld as a politica l
animal and man conceived as being . desirous to kno.w are not necessarily
�-11-
identical.
What complicates matters is tho immediate .a nd compelling
interest . that any state takes in the education of its children and
youth.
Plato's Republic is devoted to · this theme.
(Poli tics, V, 9):
Aristotle says
''Of all things .· I have mentioned that which most
contributes to the permanence of ccinstitutions is ·the adaptation of
education to the form of government" · and in VIII, 1.: . HNo one will
doubt that the . legislator should direct his attention above all to
the education of youth, or ·that the neglect of education does harm
to state.s.
The ·citizen should be moulded to suit the form of govern-
ment under which he lives."
And let us listen to the champions of
political doctrines rliffering sharply from the conservative and
aristocratic via.ws of Aristotle.
considered education to be
form of government.
We all know how decisive Jefferson
for ~ the
preservation of the republican
In a letter to John Adams (October 28, 1813),
for example, he speaks of a bill he had prepared but which was not
adopted by the Virginia legislature:
general diffusiOn of learning.
"It was a bill for the more
This proposed to .divide every county
into wards of five or six miles square, like your townships; to
establish in each ward a free school for reading, writing, and
common arithmetic; to provide for the annual selection of the best
subj~cts
from these schools, who might receive, at .the public ex-
pense, a higher degree of education at a district school; and from
these district schools to select a certain number of the most
promising subjects, to be completed at an university, where all
the useful s ciences should be taught.
Worth and genius would thus
have been sought out .from every condition of ·life and completely
prepared by education for defeating the competition of wealth and
birth for public trusts. 0
This educational scheme is conceived as
a means to an end, a political end.
And . Horace Mann. in the
of the nineteenth century, has this to say: .
~'The
midd1~
establishment of
a r.epublican government without well-appointed and efficient means
for the universal education of the people is the most rash and foolhardy ex per ime·nt ever tried by · man." · How often is the phrase
"education for citizenship" used in our schools today! · I need not
mention the present-day pressure for a .change in the educational
system of the country· to be undertaken for the sake of political
�-12ends.
The demands of the political community to which we
are indeed inexorable.
b~iong
It is important to understand, however,
that the idea of Liberal Education cannot be easily reconciled
with those demands.
It is important to see that there is a definite
tension between the exigencies of political life and the selfsustained goal of Liberal Education.
This tension is very great.
Consider that ultimately the existence of a state (any state)
involves the question of life and death for any of its members.
But consider also that no less is at stake in the commitment to
leisure according to the true understanding of this word.
I can
hardly think of a better illustration of that tension than the
story of Archimedes' death, which is well known to all of you, but
which I still shall recount by way of conclusion.
There are many versions of that story •. It seems, at any rate,
that Archimedes took an active and even decisive part in the
defense of Syracuse, his home town, when it was besieged by
the enemy, and that he contrived, by means of ingenious
machiner~,
duty.
~is
to repel the attacker.
He was fulfilling his civic
end came when a Roman soldier stepped close to the
place where he was drawing his figures on the sand.
how Plutarch relates one of the versions:
This
~s
"A Roman soldier,
running upon him with a drawn sword, offered to kill him
Archimedes, looking back, earnestly besought him to .hold his
hand a little while, that he might not leave what he was
then at work upon· inconclusive and imperfect; but the soldier,
nothing moved by his entreaty, instantly killed him.''
The
figures on the sand and the problem they represented were for
Archimedes a question of life and death; or should we perhaps
say, a question of more than life and death.
Whether this
story be true or not, it makes us see the precarious position
that is the lot of any genuine searching and questioning; it
makes us see the ultimate incommeneurability between this kind
df
and
~e~rching
th~
and qLlestioning, the basis of all liberal learning,
implacable conditions of our existence.
But what would
the world be like if that searching and questioning were not
possible at all?
�-13-
PRIZE
SOLUTIO~
OF THE
1965 JUNIOR-SENIOR MATH . PROBLEM
James McClintock· 1 65
Given the co-ordinate system 0 and some point in the first
quadran~
P, to
find the shortest line through P bounded by the axes.
Through · P aAd with OX and OY as
asymptotes
dra~
the hyperbole APB.
(Apol.II,4) From the point P draw
MPN tang~n~ to the hyperbole (Apol.
II,49)~
which . will intersect the
axes in the points
II,3) t
sa~,
of the
mand
N.
lih~s
(Apol.
y
I
A
1•
j
I
m \
M'
through P
8
which are bounded · by the axes, MPN
is the shortest.
For suppose another line M'PN' be
drawn.
Figure I
Now M'PN' is a secant, for
otherwise it would be a tangent and M'P would equal PN'.
But this is
impossible since it can be seen that M'P is less than MP and PN less than
P'N since angles MM'P and PNN' are obtuse and angles M'MP and NN'P are
acute.
Also PN is equal to PM (Apel. II,3) hence M'P is less than PN'
and M'PN' is not a tangent.
Now the rectangle M'P,PN' will equal one
fourth of the rectangle contained by the transverse and upright side of
the hyperbole.
(Apol.Il,10)
Also the square on MP, which is equal to
PN, is equal to the same rectangle (Apol.II,3).
to the square on MP or PN.
Hence M'P,PN' is .equal
Now superimposing the rectangle on the
square as in Figure II, it can be shown that the perimeter of the rectangle is greater than that of the
m
square and hence M'PN' is greater
than MPN.
Draw ffi'N and CE.
rectangles
mo
The·
D
~·
and ON' are equal be-
cause they are the remainders of
the original square and rectangle
after subtracting M'N.
Hence
ED:DN::M'D:DC (Euclid VI,14).
N
p
Figure II
N'
�-14-
Therefore, due to the vertical angles at
8~
triangle EDC is similar to
triangle M'DN and angle ECO is equal to angle DM'N.
But angle DM'N is
equal to angle M'NP because M'D and PN are parallel.
Now, the angle
M'NP cannot exceed half a right angle for if it did the side M'P would
be equal to or exceed the side of the square which is contrary to the
construction.
Therefore angle ECO is less than half a right angle.
Further the angle DEC is greater than half a right angle fat the sum of
angles DCE and DEC must be a right angle because the triangle COE is
right.
Therefore angle DCE is less than angle DEC and consequently DE
is less than DC.
Now DE:MM' and DC:NN! hence MM.'< NN'.
inequalities we have:
MM'+DE<DC+NN'.
Adding the
Now adding the equalities:
ME=M'D, CN'=DN, M'P=M'P, and PN:PN; we have:
MM'+M'P+PN+ND+DE+EM<fYl'P+PN+NN'+N'C+CD+DM' or the perimeter of the square
is less than the perimeter of the rectangle.
Therefore MPN< M'PN'.
Q.E.F
�-15-
PRIZE SOLUTION TO
JUNIOR-SENIOR MATH PROBLEM (1965)
John Hetland '65
A point P (a,c) is given in the first quadrant.
8
The problem is to determine that line passing
through P and intersecting the positive x-axis
in A and the positive y-axis in B which makes
the line AB least.
Draw any straight line APB through P meeting
A
the positive x- and y-axes in A and 8 re spectively, and call the acute angle at A angle
=a
AB = a
Since BP
sec ¢, and AP
sec ¢
=c
¢.
csc ¢,
c csc ,5.
+
Since, as ¢ increases through all acute angles, sec ¢ increases continuously through all values greater than 1 and csc
¢
decreases through
all values greater than 1, and since a and care positive and finite,
there will be one value of ¢ for which a sec ,S
.
d
~
and this will be the only value for which
+
c csc ¢ is minimum,
(a sec
AB = a sec ,5 + c csc ¢;
d
d¢ (AB) = a sec ¢ tan ¢ - c csc
d
When d,S (AB)
a sec ,5 tan ¢
sec ~ tan ~
csc ¢ cot ¢
sin
cos
tan
3
3
3
AB will be minimum when tan
= o,
= c csc ¢ cot
c
=a
~ =
¢
¢
+
c csc ¢)
= O.
¢ cot ¢.
¢;
c
a
c
¢ =a
_
¢ - 3vr-C
a
.
If the equation of the minimum line is desire9, it is easily found in
�-16-
the slope-intercept form, y
m = slope
~
= mx
+ b:
-IT·
=
y-intercept
=
=c
+
a tan ~
=c
b
= -tan
+
a~J ~
Then the equation is y
=
or y
=
a '
-~
x
+
c
+
a~ ~
3/ :£ (a - x) + c.
'\
0.
�-17ALEC .MEIKLEJOHN'S MAVTIME
(Reprinted from.The Progressive)
Milton Mayer
The Lord got a lot of mileage out of Alec Meiklejohn, and the Devil a
ninety-three-year headache.
~cod
Yo~
don't see it happen often - a very
man, or even a very bad one, perking along for a
perking right along to the .end . . · ~ don't suppose
tha~
~~ntury
and
you often see
a very good man, of any age, and when one suph dies very old, and . in
his last days is still amending his
coun~ry's
Constitution in a little
house on a little hill, there is a man to sing of.
I am old myself, and Alec was old enough to have been, not just my
father, but my grandfather.
that I could never
br~ng
He was old when I first knew ' him, so old
myself to call him Alec face to face; and what
could I do, since no men could call Alec Mejklejohn Mister, or Doctor,
still less Professor, and, . least of all, Alexander?
As I grew old I
found that I could address him as Alec when I wrote him.
And so I
addressed him a few weeks before he up and died.
it was last November,
Alec
wa~
to visit Amherst as the trumpeted guest
of the college whi~h had f~r~d him as president forty years before.
To
my invitation to him and Helen to stay with us there he wrote briskly,
in a hand
th~t
hadn't changed since l had known him, that he'd be com-
ing alone; Helen couldn't come; the college had him booked pretty
solid; but he hoped that we'd have time for a walk and
·Always a walk and a talk, and never, in his
~ - talk.
ninety~third
:
or any other
year, about his troubles, but always about Man's troubles with human
freedom.
I threw his . note away; one doesn't keep young people's social notes;
and in a few weeks he was .dead. ·
He had grown hugely old withoµt ever aging,
sudden, he
~as
whisked
~way
~nd
now, of a characteristic
with a cheery bye-bye to keep another en-
gagement, to walk and talk about freedom, not with Man, . but with those
�-18-
creatures of whom Augustine says that their perfect servitude is perfect
freedom.
He would argue the point with them, speaking with the tongue
of angels and the caritas that was always his, as it is always any true
teacher's:
the caritas that wills the good of the other and not one's
own.
He would not be still, for angels any more than he had been for men.
Not in the matter of freedom; his will for the good of the other, the
good that ·required freedom, would not permit it.
If he found himself
differing with the angels, as sooner or later, he always did with men
when the discussion reached out to the furthest horizon, he would say
so and why.
He would not call for consensus or lament disagreement -
or be disagreeable.
He would not break with men or with angels.
If
they broke with him
The day he was fired by Amherst, in 1923, he closed his commencement
address by saying to his colleagues, and still louder to the trustees,
"I differ with most of you in most of the issues of life, and I'm
going to keep it up."
At that scandalous commencement twelve "Meik-
lejohn" seniors refused their diplomas and eight faculty members resign~d,
and Amherst's indignity ended only in 1957 when Alec was asked
back to address the
stu~ents,
alumni, faculty, and trustees jammed into
Johnson Chapel and all on their feet with ovation at the beginning
and end of his talk.
There had been no bitterness in him thirty-four
years before; but neither had he resigned.
Alec Meiklejohn dead was livelier than most of us, old or young, who
gathered at memorial
knew it.
meetin~s
across the country last winter.
And we
And our words showed that we knew it; not one of them was
really memorial.
The speakers celebrated Alec as if he were there.
They praised him as if he were there.
They argued with him as if he·
were there.
Joe Tussman of Berkeley went back to his own student days
under Alec:
"Who fought more gallantly for freedom and human dignity?
But why, then, did he reject our 'individualism'?
defender of academic fieedom?
servant of the state?
Was there a stronger
But why did he call the teacher the
Religious freedom? - certainly.
he say No to our 'wall of separation'?
Then why did
And freedom of speech?
Wasn't
�-19-
Mr. Justice Holmes· and 'clear and present
natural rights?
No natural law?
danger~
good enough?
No
must we . even think about the 'Social
Contract?"
Alec would be argued with; he would wrestle any man in the house, not
for a quarter, but for free and for freedom.
was argumentative; still less, contentious.
whom, and by whom, gentlemen are made,
Nor was it because he
He was that gentle man · of
Freedom to Alec Meiklejohn was
not a right - oh, that, too, but only by the bye.
Freedom was first
of all a duty.
I thought (end think) that Alec's readin_ of freedom as absolute was ing
valid because men are not ffieiklejohns.
may some day be.
But if one man, was, then men
When men, including me, are able to say
trut~fully,
as Alec said truthfully, .. I have never been able to persuade myself that
other men's motives are worse than my own," the Meiklejohn reading of
freedom as absolute will be valid.
I intended to contend with him, because I am contentious.
did, because I am also obsequious.
disserve him.
But I never
But not to contend with Alec was to
I always intended to serve him - when I should be old
enough.
I intended to contend that until men should be as he was - angels - he
was compelling them to choose anarchy with their freedom.
I intended
to say that I myself would choose anarchy if that were the price, but
that I could not defend my choice philosophically, but only temperamentally as a natural-born aginner.
I intended to contend that as J.
Milton had thrown the Papists to the wolvas and J.
s.
Mill the atheists -
on the ground that society had to draw the line somewhere - so every
society would have to draw the line .somewhere.
Until men should be
angels.
And now Alec has slipped away from me and I must serve them by contending
with his disciples, such poor sticks, as they themselves
w~uld
say,
Hugo Black, and glumly take the side of Felix frankfurter, who once
Alec that he ought to go to law school.
(Alec brightly accepted the
advice on the condition that Felix go to philosophy school.)
The
~s
~old
�-20-
Moiklejohn doli:trine,which protected all speech, verbal and written,
sacred and profane, assembled and associative, simply rejected the
police power over the mind of man, with no nonsense {as Roger Baldwin
said) about clear and present danger.
The only clear and present danger that Alec could imagine was the
least circ~mscription of freedom.
to the
ine~pedience
This merry idealist, whose answer
of freedom "under the
circumst~nces," . was,
~Free
d6m is always expedient" - I do believe that he would not rejoice to
see the police empowered to take that first little mincing step of suppressing the cry of !'Fire!" in a crowded theater.
"No matter what a
. person believes in" - and i f he believes that the . crowded theater is
on fire? - "we must hear him.
That is the essence of freedom.
only way to fight Communism is to let it speak itself out.
The .
That
i~
. true not simply of Communism; it is the only way to fight · anything."
If men were angels
All right, then, said Alec, but men will never be angels until
first free.
~hey
are
We will have to try freedom - with its mortal risk - . or
we will nev~r k~ow for sure that it won't work.
that nothing less does.
And we know for sure
So what have we to lose?
Alec's adherence
to the First Amendment was licentious, his faith in the prevalence of
truth ecstatic •
. His ecstacy conspi~ed with his intellect, the teacher with the advocate,
to constitute his power. · And his power was always his own, and never
his pulpit's.
Here was
~ Solon~
yea, a Poplicola, in common mufti.
A
non-lawyer an·d a ·non·- judge, · this philosopher of freedom -moveq American
law and
Ameri6~n
jutisprudente more forcafully than any man except
Holmes and Hand, both of
th~m
lawyers and
judges~
shaped the Court, whose minority always (and
moved to the measure of his doctrine.
More than they he
~ajority
increasingly often)
As the majority, at its greatest,
was Learned Hand's, so the minority, at its greatest, was Meiklejohn's
The echoes of his words were, and will be, always louder than the
gentle words.
Alec could never
separ~te
freedom from learning and
teachin~,
as dean at
Brown, as president at Amherst, as founder of the Experimental College
�-21-
at Wisconsin and of the San Francisco School of Social Studies after he
"retired."
To be free, men must learn; but to learn, they must be free.
In the struggles of the civil liberties market-place he was his own
Socrates, and in the harder struggles of the academic shades he was
(as Scolt Buchanan put it)' his own Plato.
first of all, and last (for man would take care of the rest), free the
mind of man.
Use the best and most modern, which was also the most
ancient, equipment:
of the ages past.
the mind itself in living contact with the mind
He was godfather, as he was, in ninety-three years,
to so many things, to the "great books" movement, and he loved the Latin
pun which was the motto of St. John's College, where his spirit ever
presided:
I make free men out of boys by means of books and balances.
So seamless were education and freedom that Alec leaped from bed one
night in the last year of his life to write an amendment to the Constitution
dir~cting
Congress to provide
fa~
universal education "in
view of the intellectual and cultural responsibilities laid upon the
citizens of a free society by the political institutions of selfgovernment."
He seemed tall because he was so slight and long-headed.
He was spare,
really wispy, but he played tennis and swam into his eighties.
(His
life-long love was the cricket of England, where his father had been
an impoverished textile worker.)
He was eagerly, but never aimlessly,
on the go, never too tired for the banter that anneals the yo ung to the
old or the concern that binds the old to the older with hoops of steel;
and he was older than us all.
Incessantly spry, and not just active;
the only man I ever knew (to paraphrase T. R.) who could dance around
sitting down.
No one who knew him, says Harry Kalven, ever thought of making conces sions to him because of his age.
You never said of him, "How remarkable
for a man of his years," but, rather, "How remarkable for a man."
an abstract discussion he once tried to persuade Roger Baldwin that
gaiety of spirit was the most desirable of all personal attributes.
He may have been prejudiced, because he himself personified that
In
�-22-
attribute.
His;.g~i~ty
was unshakable - even, I think, when it should
have been shaken • .
After .all, he was playing a
decli~ing
market ·in the . last fifty or seventy-
five years of his life in the land of McCarthy,
~here
a third of the
adults have been intimidated into taking oaths of nondisloyalty and
further intimidated by having taken them.
He was playing a declining
market against the homogenization of TV Man.
And he was certainly
playing a declining market in a world which abdicates history to "stop"
Communism (or Kaiser Bill, or Jeff Davis, or Abe Lincoln, . or Socrates,
or Christ, or the Devil).
Alec himself joined that abdication · to
"stop" Hitler, pleading the while that "no fighting, however successful,
will help to establish freedom unless the winners know what freedom is."
His plea was in .vain, as he who knew Athens should have known it would
be.
The market declined precipitately, and Alec· lived to_ say that "the
most tragic mistake of the contemporary American mind is its failure to
;
recognize the inherent strength and stability of free institutions when
they are true to themselves;" but he abode, . dy.ing . as he lived, in the
hope-against-hope that the tragic mistake was only :contemporary.
So abiding he lived, and in his fullness died. . I. F.• Stone, one of the
many who caught fire from him, and from whom, in turn, so many catch
fire, called him one of the few men who have lived who combined "such
deep conviction with such courtesy toward opposing points of view , such
foreboding about man's .fate with so sweet a serenity and so ever-fresh .
a joy."
Peter : Weiss, who
h~d
been a student at st. · John's spoke at
one of the memorial meetings and said, "Here passed . Alexander Meiklejohn,
with a twinkle in his eye, the truth by his side, freedom in his bones,
conviction in his heart, and scorn for no man."
�-23POEMS
1962-1965
Lawrence Fischler '68
TO LINDA
Am I any more than these
Most tangible of things?
The dry gruff of the morning's
First yawn,
Tight to the bndy .like the sticky
Ointment of some lab~l-l~ss ja~.
The smiles of the workihg crowd
Teeth a-glitter in the sunlit
Afternoon;
The iron tram shuttling on
The daily way of town and batk.
Yet you would assign difference
Coupl.ed with a special fa.me,
Majesty though I am strange! to crown,
Elegance though I have neither
Vest nor stance
And all for love's most pliable
Of hands.
But no, I will not seek to change
your tiny dream,
Nor mould your orisons to my reply,
For still, beneath your guileless faith
The truth presents,
And even in full splendor
I meet not half your vision.
�l
-24-
"O for the engine to keep back all clocks. 0
-- Ben Johnson
I would eternalize this instant
Make now an everpresent thing
Till all that's volatile can sing
Of stableness
And the transitory moment is the
Evermore.
Spinning, the world and I twist
forth till having rounded a full
Axis we face • • •
Mutually unrecognized.
And I who spoke of the strangeness
And the time,
Who spoke while tracing
The axis line to · indiscernability,
I know the world and he
(the former self, the former me)
illill never touch Our palms with lines diverse.
Yet let i t be;
Time in the throttle of a forward
Speed,
for though the cry is fear of the
Mutable
The ver whir of engines
Laughs at my denial.
�-25RITTENHOUSE
SQU~RE
January 22, 1964
Like icicle reminders of the Northern Sea
Or snow clusters singing of the Steppe
The moon's light hung between .the ribs
Of trees seems claimant for an air of wilderness!
Dark estuaries - asphalt in the day
Around
thi~
concrete
swim sullenly
fi~ted . island
Till meeting plunge unseen into the bay
Of. other ,treats,
crossing : wid~ ar~hipelagos
In a lace work of dark streams.
All winter's sorcery has come aliye.
Thin twigs like fingers starkly clutch
t~e
air.
Apartment buildings cliff on every side
Each window now component:
Orion's light!
While neon orange shimmers on the ice.
Island?
Forest?
Girdled by the city's heights
The snow has made your wild outline all deceit
Till benches loom like
py~amids •
.
�-26-
Carnivals have laughter and your eyes
No different sing of joy!
Orange
tasselJ~d
dolly cotton stuffed and hung,
This avenue of stalls and popcorn jokes,
Nickel games and the ferris wheel's
Rapport with night
has given place and time
To you
0 slender waif!
A palace of electric brightness to receive
You,
Saluting caravans who for quarter pay you court.
While you, pin held against the shooting
Gallery wall,
with smile diapason find reply,
as pops of copper lightning
whizz
full measures of applause.
*
*
*
*
*
*
*
*
TO A SOUTHERN CHILD
It is your southern accent that brings joy,
The long drawl of quick Northern sounds
That somewhere in your mouth grow lazy,
Fall forward fearful of your teeth Spewed finally like some humming sound!
And after that, your freckled Carolina face,
Aryan smiling, touched by loose blond strands.
The upturn of your nose cannot be Eastern
Where Jews and Latins made olive of the Sun.
No, my goose white kiddie, there is no
Darkness here nor nervous tinklings in your
laughter.
�-27"Mens salis placidi vul turn f luctusque quietos
ignorare iubes?
Mene huic conf idere rnonstro?
Aenean credam (quid enirn?) fallacibus auris,
et caeli totiens dsceptus frauds sereni?"
--Vergil
Because of accident, the randomness of motion,
What use the guiding instrument of things?
What honor to it-panacea to broken conquests,
Crutches for imagined thought, geometric only
As imagined?
The bastard liar would deceive us,
Pretend to actions the quality o.f words.
Yes, it is a paradigm for striving.
No, only the disorder smashes us to understanding.
llihat is the greatest crime?
Not accident but our deception in an
Entirely thoughtful passion • • •
*
*
*
*
*
*
*
*
Because asked for, the faith not given
All memory burns as insolence.
The joys?
The penny quick smiles?
No paradise beyond derision.
Laughter the succor of all pain
Escapes a lie of sound.
An irony.
No.
A steel against remembrance.
The awful Hitler of pursuit
Finds weaponry:
remorse.
Evasions confine themselves
To thought - then die
In real remembrance.
�-28-
mother, the ghosts that haunt you down
Are they so different from my own?
Those hounds that on your gentleness
Broke murder, eating delicious of your flesh ,
Are they the heritage in your caress?
That every kiss is sucking madness
Pulling the horror from my blood?
.'
That every smile is deceivin9 gladness
.
'
Entirely removed from love?
The soul of children cannot tell
True gifts from all things given.
And warmth of hand?
And lullaby?
Thy breasts white peace?
Were they all lie?
No, I am no matricide
Though madness stalk as heritage.
Even this is cord renewed to you.
Our
~hared
and delicate white bridge.:
�-29-
. FROM EUCLID TO DEDEKIND - SEQUEL
Eva Brann
In the last COLLEGIAN (June, 1965) Mr. Kutler gave a precise Euclidean
construction which might warrant the assertion, made by Dedekind him1
self and often repeated, ) that Definition 5 of Book V of the Elements,
the definition of "same ration," is the "source" of the theory of irrational numbers in terms of cuts.
In working over Mr. Kutler's pre-
sentation in the Senior mathematics tutorial, the question naturally
arose whether or not Euclid himself might have agreed that the definitions of Book V could be used in this way.
Dark suspicions voiced in
class led me to try to pin-point tho junctures where the difficulties
arise.
I came to the conclusion that only an abrupt re-interpretation
and a concentration on purely incidental results could lead to Dedekind's
assertion.
The following notions, introduced in the Definitions of Book V, are
relevant:
a.
Euclid tacitly expands the realm of magnitudes formerly thought
comparable, that is, of magnitudes thought capable of having a relation or ratio to each other, from those which are commensurable
and have to each other the ratio of a number to a number to include
all magnitudes which are merely Eudoxan, namely those which can be
made to exceed each other by multipli~ation (Def. 4).
b.
The ba s i s of the com abili t y of the ratios t hemselves is th e n
par
laid by defining "same ratio"
Eudoxan,
c.
i~e.,
general,
and thus proportionality, for these
m~gnitudes
(Def. 5).
The definition of ratios other than same, i.e., of greater or
le~s
ratios, then completes the assignment of meaning to an order -
ing
of ratios.
It is this last iteni which actually suggests a 'parallelism with Dedekind cuts.
By Definition 4 we can find
n~mbers
n and m such that,
given the incommensurable general magnitudes A and 8, either nA>mB or
1) Dedekind, Theory of Numbers, p. 40; see, for example, Heath, Elements
II, p. 124; llieyl, Philosophy of Mathematics and Natural Science, p. 39.
�-30-
nA < mB; Definition 7 then allows us to say that in the first case
2
m:n < A:B.and in the second case m:n > AaB ).
Now since A:B is a ratio of incomrnensurables, the case m:n = A:B can
never arise.
Hence the ratio A:B seems to separate all the number ratios
m:n into those less and those greater than · itself - it seems to be a
cut-producing irrational ratio.
However, there is a difficulty about
interpreting A:B so immediately as producing a Dedekind cut • . This is
the fact that the number ratios separated by · A:8 cannot ·really be made
to correspond to the rational numbers. · For · the numbers used in Definition 7 are chosen one by one, as test multiples:
Even if .i t were .
possible to interpret number ratios as fractions within a Euclidean
context (which it is well known not to be), we would still not have the
"number body'' of rationals but only isolated members.
3
)
This ·collec-
tion of numbers would not be dense and would fail to have the charac¥
teristic required of cuts, namely that at least the lower segment should ·
have no greatest or the upper segment no least member.
Furthermore the ratio of incommensurables A:B cannot in any way . be understood as ordered among the number ratios i.e., as an irrational ratio
among rational
ratios~
for while an axiom according to which ''a magni-
tude which can be made both greater and less than
a~
assigned magnitude
can also be made equal, provided the magnitudes are homogeneous," was
curr~nt
in Euclid's time, th,re is no evidence at all that the converse
was acceptable and that two magnitudes having such a relation may be
4
concluded to be of like kind. ) There is, therefore, no warrant for
~eking an irrational number correspond to the r~tio of incommensurables.
In fact Book V is carefully
~ramed
in terms of .general
mag~itudes 5 )
and
the comparison of number ratios with ratios of general magnitudes is
avoided until Book X,· where incommensurables
are~
of course,
excl~ded
2) For, taking the first case as an example, if m and n be the multiplying
numbers, for ~A > mB, nm= mn, which fulfills th~ definition of A:B > m:n
or m:n < A:8.
3) Mr. Kutler reminds me that this understanding of the mult.i ples, while
not disturbing for Def • . ? where only one pair of multiples meeting the
given conditions is required, raises a great problem about the meaning
of Def. 5. Everyone will remember the discussion in the Freshman year
concerning th~ practi6al u~e of that definition~ i~~., how any assertion can ever ' be made about "any equimultiples whatever."
�-31from such
p~oportions
(Props. 5-7).
Hence the number multiples used in
Book V must be regarded as purely auxilliary testing numbers and should
not be used in proportions at all.
It might be argued, however, that there is a way of reflecting the fact
that all number ratios are either greater or less than A:B in a homogeneous medium which is obviously continuous - the straight line.
Mr.
Kutler showed how, having chosen a unit segment, one may, with the aid
of Definition 5, find unique points on a line to represent A:B and every
m:n, such that all the points standing for m:n less than A:B fall to the
left and all those standing for m:n greater than A:B fall to the right
of the point representing A:B.
This is a perfectly orthodox Euclidean
procedure, since Euclid himself names the segments which yield these
points rational and irrational respectively (Bk. X, Def. 3).
Further-
more one might argue that Euclid himself shows that as many rational
points as you please lie between any chosen rational point and the given
irrational point (Bk. X, Prop. 2).
Is this, then, the legitimate way
to make the transition?
Here it becomes necessary to have a look at the sequence of Dedekind's
argument.
Ostensibly he begins by analyzing the naturally given con-
tinuity of the straight line so that after finding its essence he may
create a number system which shall possess the same property (p. 9).
In fact,. :however, he begins not with the classical one-dimensional continuum but with a line already re-interpreted to be the analogue of a
number system, namely with a line which is a collection of point individuals,
Now for the classical understanding the notion of a collection
of individuals and the
notio~
of a continuum are mutually exclusive
(Aristotle, Physics V, i i i ; VI, i).
The continuity of the line is
something underlying its points, a pre-mathematical quality the discus6
sion of which has no place in the Elements ). The way points lie on
4) See 0. Becker, "Eudoxos-Studien I I I", ·Quellen und Studien zur Geschichte
der Mathematik, etc.,III, 1934, p. 244.
5) Dedekind, on the other hand, is quite ambiguous about the kind of magnitude which is the result of his construction, so that one may understand the reals to be the- cuts themselves or the number producing
them; the proof of the continuity of the real domain (p.20) bears
either interpretation.
6) From the classical point to view the emphasis is far more on the fact
that a line is everywhere divisible than on the fact that a point is
hit whenever this is done (Heath, Elements I, p. 156).
�-32-
the line could, therefore, never constitute the "essence" of continuity
for Euclid, and .the above construction would fail to have a meaning.
But
then, the whole enterprise of creating a continuous number system would
have seemed self-contradictory to the
~ncients,
for whom number is the
discrete magnltude par excellence (Bk. VII, Def. 2; Aristotle, Metaphysics
XII, x, 12).
�
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Roberts, Susan (Editor)
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PDF Text
Text
-
..
l
'
�55
first, DE:Df comp. CA:AG, .µpright:transverse,
second, pllg AP
, -~-:
The
.
•
fi~st .
•
=. gnornon
AHJ.
r'
follows from the proportion DE:Df :: AU:AN,
since AU:AN comp. AU:AB, AB:AN, and since AB:AN :: AC:AG, therefore
DE :OF comp. CA :AG, upright : A :trans\(erse .A.B.
_
U
The second is
1.
sho~h ·
in 4 steps:
Since pllg NP= pllg GH (by congruent triangles)
= pllg GQ.
pllg " = p.llg
GQ
pllg -AL = pllg
the~efore
pllg MP
AL (since GN:AG),
2.
But
3.
and
4.
therefore pllg JM =- ·pllg MP, and. gnornon AHJ
JM (pllgs abou_ dia.),
t
= pllg
AP.,
Q.E.D.
Since all these steps are convertible, the generalization · ~~ I.12 is
proved from I.41 by writing _
this _proof backwards.
�1
56
ANALOGY AND UNDERSTANDING
Robin Smith '68
Freshman Prize Essay
(Santa Fe)
[The quotations from the Republic in this paper
are mostly from Paul Shorey's translation. However, I have occasionally made slight alterations
to suit myself. J
Part I
Probably the most commonly used - and, indeed, the most effective means of explaining is the analogy.
Analogy, generally speaking, ex-
plains the unfamiliar and unknown by means of similar things which are
familiar and known and which have the same relationships among themselves as the unfamiliar things.
Unfortunately, this definition tells
us that analogy explains the unfamiliar and unknown in terms of familiar
and known things which are analogously related , for "in the same relationship" may be considered synonymous with "analogously."
does analogy create any understanding of some matter?
How, then,
The answer to
this question seems to be contained in the Republic, in the three important comparisons of the sixth and seventh books:
the simile of the sun
and the good, the analogy of the divided line, and the allegory of the
cave.
The simile of the sun is introduced at 506E as an account of "what seems
to be the offspring of the good and most like it."
Socrates describes
the good in this indirect manner because he fears the insufficiency of
his powers for a direct description:
II
• • I fear that my powers may
fail and that in my eagerness I may cut a sorry figure and become a
laughing stock."
However, Socrates has just finished describing the
corruption of philosophic natures and how the philosopher is useless in fact, ridiculous - in existing society.
Glaucon will later exclaim
at ti,e extreme to which Socrates' comparison !oes, .. Heaven help us,
such a hyperbole!" ( *'ArroA.A.ov ,t
oadi15~~~~Ajl'£ ). What is to be made
of the laughability of Socrates and of the philosopher?
The answer to this question is not immediately forthcoming.
let us examine this simile which Socrates is offering.
However,
In setting it
�COLLEG'IAN
of St. John's College
Annapolis, ffiaryland
and
Santa Fe, New Mexico
T H E
January-February
1966
TABLE OF CONTENTS
Error and Sense Deception in Descartes'
Meditations .
• Robert Licht, '65
1
A Generalization of Apollonius I. 11-13
• John Steadman, Tutor
53
• Rob in Smith, '68 (Santa Fe)
56
Poem •
.Veronica Soul, '66
67
Poems.
.
James mensch, '67
68
Lil jenwall, '68 (Santa fe)
70
The Son of God as UJord
John UJetlau fer, '67
72
De Bellis Caelestibus
.Pheme Perkins, '66
83
Wolf and the Shepherd
.Jonathan Aurthur, '68
84
A Midsummer Night's Dream •
.Margaret Rottner, '66
90
. David Long, '66
95
Analogy and Understanding •
. Jama a
· Poem (Greek and translation) •
Apollinair e 's Le Pont Mirabeau
*
*
* '
*
*
*
*
*
*
*
Susan Roberts •
Editor
Sally Rutzky
Associate Editors in Annapolis
Deborah Schwartz •
Vida Kazemi.
.Associate Editor in Santa Fe
Paul Ollswang, r.m.o.c •
. Art Editor
Eva Brann
Faculty Adviser
Cover drawn by Paul Ollswang
1
66
�SENSE -DECEPTION
IN DESCARTES' MEDITATIONS
ERROR AND
Robert Licht '65
Honorable Mention
Senior Thesis 1965
Preface
It is not our intention in this thesis to reveal the possible paradoxes
in .Descartes' Meditations.
Rather, our effort has been directed to an
attempt to 6ring to light 6ne
was written.
sig~ificant
end for which the Meditations
To accomplish this we found it necessary to undertake a
somewhat laborious analysis of certain arguments, mainly in the fourth
and sixth
m~ditations.
: ror this reason, our argument for
part is a kind of discontinuous comme'n tary.
the·~ost
This' is unfortunate sirice
the continuity* depends mainly on the cont"inuity of the text of the' :
Meditations.
Therefore, as an aid for the reader we have placed page ·
and
references in the left-hand margin of those sections which
pa~agraph
deal with the fourth and sixth meditations.
~o~er ~dition 1 )·
Since the
.
has been used thrqughout, except where references are made to the French
2
and Latin editi;n >, the r~ade~ is respectfully req~ested to consecutively number the paragraphs of the fourth and sixth meditations of his
copy.
*
*
*
*
*
*
*
*
*
*
*
*
*
"
so soon as I had acquired some general . notions
concerning Physics • • • I observed to what point they
might lead us, and how much they differ from the principl~s of which we ha~e made ~se ~~ to the present
time, I believed that I could . not . keep them concealed
without greatly sinning against the ·i'aw which obliges
us to procure • • • the genera1 ·g·o od; of· :an mankind.
For they caused me to .see that it is possible _ atto
tain knowledge which is very useful in life, and that,
in~tead of a speculati~e ~hilosophy • • • we may find
a . practical philosophy by means of which, knowing the
force and the action of fire, water, air, the stars ,
heavens and all other bodies that environ us ~
• we
* of our argument
1) Philosophical Works of Descartes, Vol. I, Trans. by E~ · S. Haldane
7 G.R.T. Ross, 1931 ed., Dover Publications, N. Y.
2) Meditatione·s· De Prima Philosophia-Meditations Metaphyslgues, Latin
text with French translation of the Due de Luynes; 5th ed., ·:·Librarie
Philosophique J. Vrin, Paris, 1960
�2
can • • • employ ·them in all those uses to which they
are adapted, and thus render ourselves the masters and
possessors of nature. This is not merely to be desired
with a view to the invention of an infinity of arts and
crafts which enable us to enjoy without any trouble the
fruits of the earth and all the good things which are
to be found there, but also . principally because it
brings about the preservation of health, which is without doubt the chief blessing and the foundation of all
the other blessings in this life. u
-Discourse on the method of Rightly
Conduriting the Reason, p. 119,
Dover edition
Introduction
It is hardly possible to discuss, or even mention, Descartes' Meditations
without referring to the "problem" of doubt.
We are not so original
that we have found a new path, without doubt, into the Meditations.
In-
deed, we begin, openly, with doubt.
The plan of this work is simple.
In this introduction we make some general
observations about the first two Meditations with a view to laying the
groundwork for the arguments that follow.
Our main considerations are
doubt and its origin and limitations, then certainty, and finally , the
cogito.
UJe then proceed to a discussion, in some detail, of the fourth
Meditation and its arguments on the subject of error, and then a similar,
but more extensive discussion of the sixth Meditation.
UJe close with
various conclusions about certain arguments, and some discussion of the
implications of others.
While we have not here examined closely the dif-
f i cu l t and i m
portant arguments of the third and fifth Medita t i ons, we
have not neglected them either.
arguments that they contain.
Where
relev~nt
Further, we
~ave
of the fourth and sixth Meditations with some
.. place" in the work, which has entailed
fifth.
we refer to particular
.prefaced our discussions
6o~sider~tions
som~ ~ttention
of their
to the third and
If the objection were raised that the Meditations cannot be fully
understood without reflection on the third and especially the fifth, we
would not disagree.
Doubt and Its Origins and Limitations
"But i t may be tha·t although the senses .so.metimes deceive ~s concerning things: wh{ch a~e hardly perceptible,:
..
'•
: .
�3
'or very far away, there al'e yet ma.ny others to be met with
as to .which we ! cannot: reasonably have any doubt, . although
we recognize them by their means. • • And how co.u ld I
deny that these hands .and this · bbdy are min~, were it not
perhaps that I compare mys~lf . to . cert~in persons, devoid
of sense, whose cerebella are so troubled and clouded by
the violent vapours of black bile• • · ."
(p. 145)
This passage contains both the immediate origins and the limitations of
doubt. · It does not contain the purpose of doubt, which is bound up·with
its opposite, certainty.
It is a question of appearances,
origins of . doubt however, do lie primarily in.
pose of the Meditations
!~ ~ clearly
~ts
'the deepest ·
opposite, for the pur-
stated in :the opehing paragraph:
I must once· for all seriously undertake to rid ·
•
•
•
myself of all the opinions which I had formerly accepted.
• • • if I wanted to establish any firm and permanent
structur.e in the .sc.i ences .. " ,
(p. 144) .
0
Again, it is a question of appearances.
Having discovered that many of
his former opinions are false, which he once held as true, and that he
.
.
; .
.
had accepted as most true th6se he had ''learned either from the senses, ·
or through . th~ a·enae~ ·.. ( p. 145) he i~ i~Clined ' to doubt the senses.
For
his senses h~ve, in the pa~t, occasionally deceived him about ~ppear~~ces,
"and it is wiser not to t'rust entirely to anything by which we have once
been deceived> (ibid·).
Thus the immediate· origins of doubt are in the
knowledge that he has, in .the past, been deceived by his senses.
Cer-
tainly, ~!though t~e partic~lar deceptio~~ of se~~e are n6t ~pacified,
other ·than things, "which . are hardly .perceptible, or very far away",
.
.
they cannot, on the face of it, ·be very serious, that is, so serious as
to
disr~pt ~fgnificantly
is
r~asonable
the course of his life.
to assert that "it is wiser
things that have once deceived us.
no~
O~
the other
h~nd,
it
t6 trust entirely" to
But if we consider the end in view,
that is, the desire for certainty, then we may justify elevating doubt
to a more serious p.o sition.
rule:
This "elevation" is to raise doubt to a
. . • reason already persuades me
no
that I ought
' -~..
;·
less car efully
.
to withhold my assent from matters which are not . entirely certain and
indubitable than from those which appear to':tm~ -'- ~nife~tly to be false."
(ibid).
But, in elev~ting doubt, we must n~f target its limitation -
he is not mad, he does not "de,ny that · these hand~ ~nd this body are mine. 1.1
�4
Thus. we have the immediate origin of doubt in the fact that his senses
occasionally deceive him.
And this doubt is limited for, in the world
as it appears to me "normally," that is of things which are neither
"hardly perceptible" nor "very far away" there are many other sensations
"as to which we cannot reasonably have any doubt."
But the deeper origin
of doubt becomes a powerful lever.
In the search for certainty, the fact that the senses deceive us takes
on a new significance:
"• •• owing to the fact that the destruction of the foundations of necessity brings with it tha downfall of the rest
of the edifice, I shall only in the first place attack those
principles upon which all my former opinions rested." (p. 1~5)
methodological Doubt and the Search for Certainty
We have stressed the humble origins of doubt for reasons which will become important as we proceed. . However, the fact that the senses dece·ive
u~,
if only occasionally, is . at first a tool for the discovery of cer-
tainty, and in the end, deeply revelatory of nature.
As a tool, doubt
supplies us with two rules to carry forward the program set out initially.
The first is to "withhold assent" from all opinion, and the second, to
consider as false all opinion, that is in the least doubtful.
With this
beginning Descartes proceeds to apply doubt as a method for the sake of
certainty.
Two conclusions at which he arrives are {a) that there "are
no certain indications by which we may clearly diGtinguish wakefulness
frcim sleep •• • u (p.
debeiver.
14~),
and (b) that it is possible that God is a
From (a) he draws a further twofold conclusion; namely, that
in sleep his ideas "are but 'false delusions" (ibid) (when we dream) but
that even so the ideas "are like painted representations which can only
have been formed as the counterparts of something raa1 · an'd· true." (ibid)
And, although a painter can paint_ fantastic imaginary figures, he must
derive the parts from something "real and true" although the form may
nowhere exist.
But we are dreaming and thus the appearance of things
in our dream do not come directly from our senses and, on that level at
least, we cannot be certain that the appearances represent anything real
in form.
�5
ff
• • although these general things,
to wit, a body, eyes,
a head, hands ••• may be imaginary, we are bound • • • to
confess that there are at least some other objects yet more
simple and universal which are real and true • • • " (p. 146)
And th.i.9.r is true of "all those images of things which dwell in our thoughts."
(.ibict..): , Of ·. ~hese uobjects • ~ • more simple and universal" than the
..: appear~nces
0
pertains corpora.al nature in general, and its extension,
figure, of extended things, their quality or magnitude and number • • •
also the place • • • the time which measures their duration," etc. (ibid)
The twofold conclusion of (a) is, therefore, that there seem to be two
classes of ideas; the composite, of which appearance is formed, and the
" 'more simple and more universal" i.e., (to anticipate) the ideas of
nature tha·t correspond to matt)ematics.
He then alludes to the dubious
state of the natural · sciences •1which have as their end the consideration
of composite things, 0 (p. 147) comparing them with the mathematical
sciences "which 6nly treat of · things that are very simple and very
"'
',.
general without taking great trouble .to ascertain whether they are
actually existent or not, contain some measure or certainty and an
element of the indubitable" and the truths of which are certain "whether
I am awake or ~sleep." (ibid) .
Implicit in this
which is admittedly lacking in demonstration,
concl~sion,
is the greater part of the arguments ·in the rest of the meditations.
Here on one side we have the appearance of composite . nature brought to
'
..
'
•"·.:.''
the mind through the senses, which appearances a~e at least doubtful
a nd hence without ·certainty. On the . other we have the certain, necessary
idea~
of
to which
math~matics,
. ments conform.
th~
composite appearances in their ele-
This latter, is the first account of the certain and
necessary.
· : ~owever
the second conclusion (b), that God might
more powerful , for His
decept~on
b~
a deceiver is far
might be so persuasive as to deny the
very · certainty of mathematics~ .,As the more powerful ·argl:iment, it promises
the ·most . devastating. attack on the foundations of his opinions.
, ·. l .
fore, to that end he
as~umes,_
~
1
.::
There-
.that God is
~~
"some evil ·genftis: :not less powerful than deceitful (who)
:
has employed his whole anergiea in dec~iving me~ I shall
�6
consider that the heavens, the earth, colors, figures, sound
• • • are nought but illusions and dreams of which this
genius has availed himself in order to lay traps for my
fl
credulity; I shall cohsider myself as having no eyes,
(p. 148)
What remains to him, however, is a rule:
He may suspend his judgment.
We must stress that this radical doubt of all existence is a method
which he assumes ("I shall • • • suppose,n etc.)
Although he may require
of himself, for the sake of knowledge, an absolute suspension of belief, common experience, in which the senses occasionally deceive us,
does not make that demand:
•
• · nor will I ever lose the habit of deferring to
them
(common opinions n. b.) • • • so long as I consider them
as they really are, i.e., opinions in some measure doubtful • • • and at the same time highly probable, so that
there is much more reason to believe in than to deny
them." (ibid)
11
· •
The balance . of this passage asserts what we have stated above, that
universal doubt is assumed (" .
for certain time pretend {emphasis
added) that all these opinions are entirely false.")
Certainty and the Cogito
The quest for certainty soon ends in the cogito.
Even if there is an
evil deceiver, "he can never cause me to be nothing so long as I think
that I am something. 0 (p. 150)
now that all body is denied?
But, he asks, what is this
exi~tence
He considered that he, in the past, con-
ceived of himself as being nourished, moving ("walking"), sensing,
which were "attributes of soul."
But, nourishment and movement are
attributes of body, and sensation also cannot occur without body.
Thinking alone cannot be separated from self.
"just when I think."
thing
II
Therefore he exists, but
Therefore, he is a thinking thing.
As a thinking
it is very certain that the knowledge of my existence
taken in its precise significance does not depend on things whose existence is not yet known to me." ( p. 152)
Further, a thinking thing is
" • • • a thing which doubts, understands, conceives (intelligens),
affirms, denies, wills, refuses, which also imagines and feels (sentiens.")
(p. 153)
Now, previously sensation, or
''feeling~ · could
not occur
�7
·"without body," (p·. 151) and yet, in the above description of the
faculties · or attributes of a "thinking thing," sensation is present
(and significantly last in the list, in
translation.)
~he
original as well as the
Therefore, since the "knowledge of his existence" does
not depend on things whose
~xistence
is not yet known to him, and . that
means the ·knowledge of body, the case for sensation is ambiguous.
Descartes then
~onsid~~s
the case for sensation:
"
. I am the same who feel.s (sentis) • • • who perc. ives
e
certain things, as by the ' organs of ·sense (e~~hasis added,
n.b.) sines . in truth I ·s ee · light, I hear nq·ise, I feel
heat. But . it will be St!id _hat the~e phE;Jnomena .are false
t
and that · i · ~m drea~i~g •• ~still it i~ ai .least ~~ite
cer.tain ~ ·that i-t seems to me that I can sea light, etc • • •
That cannot be false; properly speaking it is what is in
ma called feeling (sentire); and used in this precise
sense that is no other thing than thinkin9." (p. 153)
There follows the famous example of the wax (p. ' ts4) which we shall not
6onciern our~elves with~ ·~ther than ·t6 note ~he conclusiont
"But what is this piece of wax which cannot be unders~ood
excepting by (the understanding} of mind? It is certainly
.the same that . I seef touch, imagine, and finally it is ·
the same which I .have always believ_ d it to be from the
e
beginning. But what must be particularly observed is that
·its perception is neither an act of vision, nor of touch,·
nor of imagination, and has never been such although it may
have appeared formerly to be so, but only an intuition of
the mind, which may be imperfect and confused as it is at
· present, .a·c cording as my attention is more or less direc·t ed
to the elements which are found in it, and of which it . is
COmpOS8d e II (p. 155)
.
.
The
. ex~mple
of the wax is for the sake of an examination of the senses.
The end of that examination is to discover what can be known with certainty.
--
Descartes does not 'conclude that the wax is not known at all,
.
but that the "perception" falls into two ca ~agar ies :_ "the clear and
distinct" and the "imperfect and confused."
appearance.
It is a matter of the
What arises from the sensation is an idea, and in that
sense it is quite clear that it is mind which perceives.
But implicit
here in the two categories of per.c aption are two categories of ideas.
If we recall (p. 146) what we have characterized as the first account
of certainty (see above, p. 4), the direction of the mind
11
to the
elements" of the wax, by which means its perception is "clear and
�8
distinct" is to regard the wax as an object of mathematics.
This is,
of course, at the center of Descartes' arguments in the meditations,
and we will have much occasion to return to it.
However, the discussion of the wax does not clear up the ambiguous
status of the faculty of sensation, which, on the one hand, is a mode
of thought and thus a part of "thinking essence" (to anticipate a
later definition) and, on the other, is intimately connected with body.
_
The difficulty is deepened by the idea that knowledge of his existence
"taken in its precise significance" cannot depend on the existence of
anything "whose existence is not yet known to one." (p. 152)
In its
precise significance, then, his existence, as he can know it, is dependent wholly on mind.
The "lev_ r" of doubt has established that he
e
can separate in thought, the idea of body, and in separating it, in
no way jeopardize the certain knowledge of his existence.
Thus, it
might be argued, as Descartes eventually does, that mind is independent,
and hence distinct from body.
But the "realm" of mind, of cogito, since
it includes all thought, necessarily includes all the faculties of
thought that have ideas arising from corporeal objects.
Sensation, as
a mode of thought, is obviously most directly related to body:
"one
cannot feel without body." (p. 151) · Hence the ambiguous situation of
this faculty. :
Examining the problem a little more closely, we find that the problem
of sensation is intimately related to the above mentioned division of
the categories of perception, or of ideas:
" • • • bodies are not
properly speaking known by the senses or by the faculty · of imagination,
but by the understanding
on~y • • •
" (p. 157)
The categories of per-
ception reveal a distinction among the faculties, and this distinction
is not merely that mind may be understood as made up of faculties, but
that there is a real "cleavage" between the understanding, Which becomes a faculty of innate ideas, and which is the source of all ce r tain
knowledge, and the other faculties.
Since our theme is the deceptions
of sensation, we will return to this discussion.
�g
The "Place" of the IVth meditation
Certain developments which Descartes' thinking has undergone before the
rvtti
meditation must be noted.
As we saw in our introduct.i on, the cogito
includes all faculties of thought,
Separated from the cogito, by · the
method of doubt, ·1s : a11 corporeal nature.
further, we noted there the
implicit begi~nihg~ of a distinction among the ideas of mind • . In . the
IIIrd Meditat!o·n, among other considerations, Descartes begins an exarninatioh of 'his idea•, now explicitly dividing them into categories.
sida~ed
an
Con-
frbm the Viewpoint of the first two Meditations this represents
exarnin~titiM
bf the· cogito as regards its various faculties and the
ideas associated with them;. . from. the point of .view ·o f the lVth :Meditation ,
the distinctions among the ideas, and implicitly, among the faculties,
become fundamental ~nderlyin~ assumptions~
B~~ore con~idering the ·
.. place" ~f the rvth !fte.di_.i;ation more ·t:16~el/, let us examine· certai·n
passages from the Illrd.
Now as to what concerns ideas, if we consider them only
in themselves and do not relate . t.hem . to anything else
beyond themselves, they cannot 'properly speaking be false.
· We mu~t not fe~r likewise that falsity can enter into will
and into affections, for although I may desi~e evil things ,
or even things that never existed, it is not less true that
I desire them. Thus there remains no more than the judgments which we make, in which I must take the g~eat~sf ca~e
not tri d~ceive myself. But the principal error and the
commonest which we may meet with in them, consists in my
judging that the ideas which . are in me are similar or
conformable to the things which .are outside me • • • " (p.159-160)
0
But of a ll his ideas all are not all of equal status .
nsome appear
to be innate, some adventitious, and others to be formed • • • by
myself."
And consi'der'ing nt'hose·ideas which appear to me to proceed from certain
objects that · are outside me" he inquires into .!•the reasons which cause
me to think them similar to these objects," and f·inds that he is .
"taught this lesson by nature" and, further, that the ideas do not depend on his will (both these considerations will become important in the
VI~
meditation).
arise from sense:
The .. objects" here referred to are the ideas that
"I feel heat, and thus I persuade myself that this
�10
feeling, or at least this idea of heat, is produced by something which is
different from me."
Although nature seems to teach him that the ideas of objects outside of
him conform or correspond to the objects, he notes that
the "teachings of nature" are different from the "light of nature. 11
By
the ·former "I merely mean a certain spontaneous inclination which impels
me to believe (emphasis added) in this connection."
But the light of
nature is what enables him to recognize that the idea is -true.
11
But
these two things are very different; for I cannot doubt that which the
natural light causes me to believe to be true as, for axample, it has
shown me that I am from the fact that I doubt."
(p. 160)
This distinction, between the teachings of nature, and the light · of
nature, represents a distinction among the ideas in mind, which continues the discussion begun at the close of the preceding Introduction.
The distinction is based upon the idea of necessity:
"And finally, though they (the ideas of objects, n.b.) did
proceed from objects different from myself, it is not a
necessary consequence that they should resemble these."
(emphasis added) (p. 161)
Therefore, we find that the cogito contains two basically different
kinds of ideas.
(It contains more, apparently, but the basic distinc-
tion among the ideas is our present concern.)
On the one hand there
are ideas which the light of nature causes us to recognize as true.
On
the ·other, there are the ideas of objects which nature teaches us to
believe conform to the objects.
The former ideas are characterized by
necessity, or certainty, and the latter by a belief that they indeed
represent things as they really are.
no necessity in the judgment.
But, in this latter case, there is
This distinction among the ideas of
mind leads to a consideration of the distinction among the faculties.
As noted in the Introduction, the cogito, or soul, or thinking thing
"is a thing which doubts, understands, affirms, denies, wills • • •
which also imagines and feels." (p. 153)
The cogito is, initially, all
the (thinkable) faculties of thought, ·and they are, through doubt,
distinguished primarily from body, from the world.
�11
As we see, there is a progression in the meditations from this first
separation (Meditations I , a~d . II) to a consideration of the differences
among ·the ideas and faculties, in the IIIrd Meditation.
distinction
betwa~n
The crucial
ideas .of rational necessity and ideas of "corporeal
nature" underlies the discussion -of error in the succeeding discussions.
further, the realm of
. ~d~as
of rational necessity is the understanding
or faculty of tt_pure intellection, '' and this realm contains the innate
necessary ideas . of . mathematics and certain "common
and ultimately of God.
notion~"
initially,
Already, ldoking ~ac~ on the doubt of the first
two Meditations, we see a developing twofold treatment of corporeal nature
in Descartes.
That is, the methodological doubt originally postulated
.
..
will become, because of the distincti6ns ~mong ideas developed beginning
in the IIIrd Meditation, in the · fifth and sixth Meditations, and idea
put forward as a real doubt.
That is, the suspension of belie.f ,in the
first Meditation, occasioned by a need for a
meth~d
to attain certainty, ·
will be misrepresented in .the last as a· serious consideration based upon
the lack of
certain~y
in our
judgments~
B~t
it is our contention as
noted previously that, in that sense, Descartes does not doubt the
existence of the material world, rather, as we shall show it is the idea
or appearance of the world that is held in doubt as to whether it represents nature as it really is.
This latter idea is the distinction we
will show in its .development, commencing in the
IV~
Meditation.
To return to our discussion of the "place" of the IVtih Meditation, and
how it follows the IIIrd, the above mentioned distinction among id.e as
may also be characterized as the distinction between
false.
for,
~s
Descartes states:
~The
tru~
principal error . . •
in my judging that the ideas which are in me are
the things - which are outside , me."
the
(p. 160)
and the
con~ists
conformable to
The error in judgment is
intrinsically related to the distinction as regards necessity · in "' ideas,
as we shall discuss shortly.
However,' Descartes mentions a further
falsity, material falsity, ·which is, in part, the subject of the sixth
Meditation, but which, in the end, has a common ground with error i n ·
judgment.
"For although . • • it is .only in judgments that falsity,
properly speaking, or formal falsity can be met with; a
certain material falsity may • • • b~ found in ideas, i.e.,.
when those ideas represent what is nofhing a~ though it
wer.e something." (p. 164)
�12
This falsity has its ground in a still further distinction among the
ideas i.e., as between those ideas of corporeal objects which it is
possible to perceive clearly, i.. e., as the objects of pure mathematics
(e .. g., extension, length, etc.) and those which "are thought by me with
so much obscurity and confusion that I do not even know if they are
true or false" that is, whether they are "the ideas of real objects
or not."
The former category is, of course, problematic since it
represents a meeting ground of innate mathematical ideas and perception.
But the latter category, for our purposes in the discussion of the IVth
meditation, is understood as the realm of the ideas among which judgment erroneously chooses, i.e., of formal error.
This is only to
repeat What has already been established at the outset of the Meditations,
but in a slightly different guise, namely the deceptions of sense.
Jn
the present instance the ideas are so confused that it is not possible
to tell what, if anything, the idea represents.
But the case of
mistaking the square tower for round is rooted in the same kind of
falsity, as we shall show.
Before proceeding with the analysis, one further argument from the IIIrd
Meditation should be added:
"By the name God I understand .a substance that is infinite
(eternal, immutable) independent, all knowing, all powerful,
and by which I myself and everything else, if anything else
does exist, have been created." (p. 165)
God, the creator is the revealed God of traditional religion.
This is
very important from the view-point of the deceptions of sense.
If God
created us, and He wills the best, why do we err, that is, why are we
deceived?
This discussion of the third Meditation does not, in any way, attempt
to elucidate it.
IV~
Meditation.
It simpl y- is an attempt to .define the "place'' of the
However, a close analysis of the devious II!rd Medita-
tion might well reveal that the "place" of the fourth is by no means
clear.
for example, the argument for God's existence in the IIIrd
Meditation is followed by a second argument for God's existence in
the
V~
Meditation.
comparatively
11
Why are two arguments required, and why does the
trivial 0 discussion of the true and the false intervene?
�13
We will let these questions stand since our purposes here are more
modest.
The Problem: · ''Of tlie True and the False"
What is "true" has so far been the subject of the first three meditations.
indeed
What is true is what
canno~,
in· thought,
i~ ratid~ally
be . 6t~e~wise.
necessary and certain, what
The "realm" of this
.
the understanding of the "purely intelligible" ideas.
And, according to · the distinction made in the
·~formal
this account is of
are
~responsible
of the
meditation,
thir~
falsity," or the errors of . judgment.
ou:r; . senses are "deceived," how
is ·
The problem of
~. ccount
the fourth Meditation is not "truth", but to give an
false.
trut~
'. .
in error, that is, in what sense
are~
·for the mistake?
If
This is . not ·an idle question, . and
Descartes' conclusions, that err·o r is, in itself nothing, and t_hat our
faculties are not responsible for error, ihdlc~tes t~e direction in
which we must look for the answer.
Error is "formal," and li. s in the
e
act of mind only insofar a·s we disregard · its material basis.
Fi~st,
however, anticipates our discussion.
the
a~d t~state
of the fourth Meditation.
~rguments
* ' * .*
In this
let us analyze
This,
~action
*
*
we will avoid any initial
view of God since we think that
by such a discussion.
mar~
*
*
*
*
discu~sion
•.
about
Descartes~
problems are raised · than solved
The l!Ird Meditation concludes that God, the
creator of all things including man, cannot be a
l
*
deceiver~·
However,
.
it is something to be considered ''with more care 11 (p. 1·71).
serves as the prelude fqr the discussion in the
para. 1, p. 171 -
Meditation.
The very first distinction set up in the Medi.tat ion'""
following Descartes' usual
sequent discussion.
IV~
This
syn~hetic appr~ach,
is central to the ·sub-
This distinction, significantly, is between the ·
categories of ideas already implicit in
th~
very fir•t
Medi~ation.
"Very feui thing" are known "with certainty respecting corporeal objects"
"
and "many more are known to us respecting . t .he human . mind, and· yet more ;._··
still regarding God himself."
.
'
For the sake of the subsequent d.'.t scus$ion
he will not consider "sensible or imaginable objects," rather, he will
�14
concern himself with those that are "purely intelligible" and which are
''incomparably more distinct than the idea of any corporeal thing."
Since
his concern is with "formal falsity 0 in this Meditation, as we have
noted, this distinction is justified.
Reconsidering the fact that he is subject to doubt, which is, in effect,
as euphemism for the fact that his senses occasionally deceive him, he
finds that he is an "independent and complete being," and that the
p. 172
idea of God, of a being complete and independent "presents itself
to my mind" as so clear and distinct that he is certain that his own
existence is, in every moment of his life, dependent "entirely on Him."
God is, in this place, the "epitome" of certain knowledge, and, for that
reason, the guarantor of all other certainty.
This, of course, continues
the discussion of the end of the II!rd Meditation, where the idea of
God allows him to consider "other truths which may be derived from it"
(p. 171).
The idea of God is the road "to the knowledge of the other
objects of the universs."(p.172)
The fourth meditation in this light
is the most obvious detour from that road, since if God is perfect he
cannot deceive (para. 2)
men (para. 3)
(deception being an imperfection), and further,
having been created by God, they have received their
capacity for judgment from Him, and it follows from the fact that God
is not a deceiver that the capacity for judgment will not "lead me to
err if I use it aright."
But if all this is true and correct, it
.(para. 4) would seem to follow that men are never deceived.
In one
respect it does follow, namely, "when I think only of God," for then he
sees "no cause of error, or falsity."
experience shows him.
Hot;Jever, he is deceived, as his
He is "subject to an infinitude of errors."
Now,
reconsidering the initial distinction between ideas - on the one hand
of certain ideas, e.g., of self as thinking thing, unextended, incorporeal and not "in anything pertaining to body'' (para. 1), and on the
othe r, t he ideas of "corporeal things , 11 we see that the pr esent di scussion is an adumbration of that distinction.
The certain idea of God
does ncit admit ·of error or falsity, but the ideas of experience, i.e.,
experience throught the senses, does find him
should note well the word used: "subject 0
).
"subjec~"
to errors
(We
�15
To
retu~n
to the argument, we find the two categories of
terized in a rather strange way.
id~as
charac-
Qn . the one :hand, there is the idea of
"Supreme Being" and on the other
11
a certain negative id.e a . of nothing. u
The latter idea . is, ··tif course, very difficult to
unde~stand
in itself
but is meant to suggest the opposite · of the idea of God (an idea which
we shall place in the cate·gory of rational necessity for the sake of
.f~ture argument).
Descartes is
II
in a sense something intermediate
between God . and nought, i.e.,
being."
between the Supreme Being and non-
further, "insofar as I am not myself the Supreme Being" and
"particip~te
• . •• in nought or non-being" he is "subject (p. 173) to
an inf initudf;i of imperfections" and thus "ought not t'o be astonished"
that he falls into error.
This . idea is extremely
sugge~tive.
For one
thing, an implica~ion of a kind of hierarchy of ideas is in it, With
the highest rational necessity on one · side ~ • a co.m plet.e absence· of such
· necessity on the other, and "imperfection" between. · This last middle
realm of imperfectipr is where error occurs.
Further, upon exa~ination
two difficulties are formed in this idea ·which themselves are fertile.
For one., since the idea of God is "implanted" in him, he cannot be said
to b. .strictly between .11 Supl'i3me Being" arid "non-being."
e
Rather, there
:· is an element of the former in him as rational necessity.
the .idea of
for another,
"~
negative idea of nothing" is troublesome. It is;. first
.
of all as we noted, hard to think of in itself. · Sebond it s~ggests what
is furthest from rational necessity, or mind in its ' 0 purely intelligible"
·. i
· aspect, namely, what does . not pertain to it at all; body.
This last
non-be. ~ng
ui i th body.
· idea is perhaps too extreme, . that is to connect
Nevertheless, the suggestion is here of a polarity between r a t i onalnecessity. on the one hand,. and., .accepting the "extreme" idea in part,
natural necessity as body, on th-e .9ther.
re-ex~min~
We shall have occasion to
'this idea.
From h.is "intermediate., status · (cir
inf~riority
error .is not a real thing "but simply
a 'defect"
to God) he concludes that
and that he falls into
error "from the fact that the power given me by God • • • of distinguishing
truth from error is not infinite."
para. 5 - However, the above charac-
terization has a flaw in that it might suggest
th~t
error, as a defect,
is a "pure negation" which flaw Descartes wants . to correct.
As a
�16
defect, error is tta lack of some knowledge _
which it seems I ought to
possess."
Descartes then proposes the difficulty that if God is the
author of his faculties, then any faculty of his should be «perfect of
its kind."
Further, had God so willed, man would not be subject to
error, and if God wills what is best 1 th.e n "is it better that I should
be subject to err • • • ? 41
It is our opinion that the reconciliation of
this difficulty is more important than its setting out.
fore discussing the conclusion,
l~t
However, be-
us examine the origin and intent
of the statement of the problem.
On the one hand our certain knowledge of God reveals His perfection,
from which it necessarily follows that he cannot be a deceiver.
He is the author of our being.
Further
But experience teaches us that we are
deceived, and since God must will the best, it would seem better that
we err.
If we examine this problem in the light of the initial dis-
tinction between the ideas, i.e., let "God" mean the "purely intelligible ..
ideas, and deception the ideas of corporeal things, or appearances, then
the conflict becomes an internal one among the faculties, namely the
faculty of understanding, and
what~ver
for our ideas of corporeal things.
problem of God.)
faculty or faculties responsible
(We admit that we are neglecting the
Understood in this way, the reconciliation of the
paradox (of how God wills the best and we are nevertheless deceived) is
extremely interesting.
para • . 6
The reconciliation, simply stated, is that a man's intelligence
is "not capable of comprehending why God acts as He does."
The terms
of the paradox, as we have reformulated them, are rational necessity on
the one side and the .appearances on the other.
Now, because of the
inability of man to understand the ends of God's actions, and because
God is the creator of nature as we know it, "this reason suffices to
convince me that the species of cause termed final finds no useful
employment in physical (or natural) things" (emphasis added). This conclusion is of course extraordinary and
far-re~chihg.
First, the tra-
ditional view (of the scholastics from the ancients), that the form,
that is, the appearance, of natural bodies is understood as an end in
nature and represents what the thing is (in Aristotle, for example,
as thought eternally by active
intellec~),
is utterly
~enied.
It is,
�17
of .course, not so important that
Descarte~
here denies the traditional
view, as it is that the status of the appearanc.e s, the "ideas" we have
of nature through the senses, is now such as to have no necessity in
themselves.
sin6~
This, of course, is not a new revelation in the Meditations,
it seems the entire argument
m~ght
be founded upon the denial
of any necessity in the appearances, and the location of all certainty
i~
the understanding; this idea is clear enough in the example of the
wax in the IInd Meditation.
state~ent
th~m
Rather, the
i~plications
as regards error, are most important.
out as we crintinue the
of
thi~
particular
We will try to draw
~rgument.
The argument then moves on to a direct consideration of the source of
error, and finds that it re$ts "on a
~he ·
co~bination
of two causes • • • on
faculty of knowledge that rests in mei and on the
or free will -
th~t
pow~r
of choice
is to say, of the understanding and at " the same
time of the will" (emphasis added).
Before considering
t~e
argument in
detail we will state the "mechanics" of error.
First, error is not in the faculties themselves.
Second, the will is
"subject to no limits" while the understanding uis of very smail extent
and extremely limited."
Third, this "disjunction° of infinite will and
finite understanding accounts for error in that the will is not kept
within the bounds of the understanding.
We will now return to a
view of the argument and consider the following:
clo~er
The Will and Judgment;
The Understanding; Judgment and Freedom.
The Will and . Judgment
In the first through third Meditations, error and judgment are quite
cl·o se. ·: ;:In the first, judgment is suspended through the method of doubt.
In t .he ·second ( p. 156) error is found ·in judg.rnent . . . T_ us it is somewhat
h
, puzzling when Descartes· asserts that error rests on the will and the
· understanding.
The ·question is, what has judgment to do with the wi ll?
First, as concerns the will, error is_ not found in it (since error is
the lack of some knowledge we ought to have, and is thus nothing in
itself but represents a defect).
.
Second, it is free and is, (p. 175)
. , I
apparently, synonomous with free choice.
Third, it is, as we noted,
�18
"so extended . as to be subJect to no limits·."
compared· with
othe~
For this faculty, when
faculties
"is • • • so great in me that I can conceive no other idea
to be more great; it is indeed the case that •• , for the
most part • • • will • • • causes me to know that in some
manner I bear the image and · similitude of God."
The will is a faculty of action; "the faculty of will consists alone in
our having the power of choosing to do a thing or choosing not to do
it (that is, to affirm or deny, to pursue or shun it)."
This definition,
which is immediately revised, makes it possible to understand judgment
as, in part at least a characteristic act of will.
However, there are
certain difficulties concerned with the freedom of will and judgment
which we will discuss in the proper place.
The above definition of will
is immediately revised to include the notion of freedom:
it consists alone in the fact that jn order to affirm or deny, pursue
or shun those things
gl~ced
before us by .the understanding (emphasis
added), we act so that we are unconscious that any outside farce conThis freedom admits of degrees, the lowest degree
strains us
being indifference.
in its place.
We will discuss the problem of freedom more fully
We must keep in mind a question about the «infinite"
character of the will:
What are the infinitude of objects it may
affirm, deny, pursue or shun?
How do its objects differ from those of
the understanding?
The Understanding
In light of our previous distinction between the ideas , the references
to the understanding, and its relation to the will become most important.
p. 174 -
"For by the understanding alone I (neither assert nor deny
anything, but) apprehend (percipio) the ideas of things as to which
I can form a judgment."
speaking found in it."
Further, as in the will; "no error is properly
The remaining characteristic of the understanding ,
its finiteness, is not explicitly delineated.
That is, although we have
asked what the infinitude of objects might be ' that the will acts upon,
it is nevertheless plausible that the idea of
justifies the infinite extent of the will.
'
.
is lacking for the understanding.
0
free choice" completely
But this same justifioation
If we ask why the understanding
�19
cannot be infinite. as .. well we ars fa.reed tb seek out Descartes' intent.
.
.
It is riot ~09 ob~cure.
Th~ exa~p1~:~f ~h~ · wax indicates ~~at the under-
standtng ·is, as ·We have characterize~; it, the realm of rational necessity,
the ideas ·-ot ·:which ·as nciear and dislinct" and· have the quality of "discreetness.-" · ·Tha.t.· is, .. it is possible . ,to isolate the ideas and thus
enumerate them.
This, of course, does not guarantee that there is a
tci ·t '.h'e·· possible
· f.lnite limit
number · of its ideas, as Descartes observes:
"though th.ere is possible a~, infinitude of things in the
world (fr which I ha.va no ict"a·a· ·in my understanding, . ·we .
· annot fo·r all that say that ,it is deprived of th~s~
c
ideas • • • but simply it does not possess these. ·, (p. 174)
.
.
•
.
•
· 1:.
· It is; further, as. t.he ·
vth _ Medita.~ion,
the realm of "innatE;J" . ideas of.
which we are able to discover "an infinitude of particulars-" (p. 179).
Thus the
f~nite.~~a~acter o~
•
'
.
l
'
.
.
the understanding has to do with the
.
' ..
' .. ,' ~
..'
t • '
quality of its idea:s;; . their necessity., 6",larity and .d.istinctness; and
·
· .~··::': '-.:
certainty: .
p • 175 ~ para. 9:
for S'ince .' I understa'nd nothing but the
power which God has given me for understanding,
the- e is no dol;Jbt that all I .unqerstand '· l
r
understand as I ought and it is not possible
that I err in this·.-" ·. (emphasis · ·a dded)
II
It is crucial to .understand two things about the understanding:
It
";.
"
doe~ _ not err, and i~s ideas have necessity, what we have ~alied rational
·· 1
• ·
Judgment and Freedom
Judgment, then is to be understood as the act of free will.
...
:. ;
But the
.
will must· also he : understood·: as being free not to act' . i. e ~ , not to·
judge.
is
As we n~cited ~ ther- ',are degrees of · freedom.
e
The ·lowest degree
indifference · ~ ~~
p. 175, para.8: · ~ · : ~ . · . ' this indifference which I feel, whgh . I am
not swayed .to. one side rather than the oth,e+ by
lack of reason, is the lowest grade of liberty,
a~.d : rather evinces a . lack or negation in kpowledge
than a perfection -0f '... the will."
.
..
. ..
.~ ~
;
'
. :·. :,, :'i I: .;.
. ..
On t~~ .~bther··. h~Nd ,,. ·t l¥'/e greate$t freadom is to be found wheh the understanding
pla~es tki~·gs before the judgment:
�•
20
" • • the more l lean to one" ( o·f two contraries n. b.)
" - whether I recognize clearly that the reasons of the
good and true are to be found in it, or whether God so
disposes my inward thought. - the more freely do I choose
and embrace it. And undoubtedly both divine grace and
natural knowledge, far from diminishing my liberty,
rather increase and strengthen it." (emphasis added)
If the reader wonders what has happened to the conflict between freedom
and determination here, it is not without good cause that he does so.
It is clear that the greatest freedom of the will is in the direction of
rational necessity.
Indeed, the very possibility of judgment, as the
act of affirming and denying, is questionable in the realm of the
understanding.
For
ex~mple,
the following passage in the
V~
Meditation
should be -noted:
p. 180:
•••
I have already demonstrated that all I know
clearly is true. And even though I had not demonstrated this, the . nature of my mind is such that I
could not prevent myself from holding them to be true
so long as I co nee ived them clearly." ( e.mphasis adde.d)
11
If the greatest freedom is ·found in (rational) necessity, where is the
least found?
The question is much clearer, however, if we ask what
the distinction is between the objects of the understanding and those
of the will?
It is the distinction between ideas, of course, the
ideas which contain rational necessity, on the one hand, and those
that are of corporeal objects as they appear to us through the senses.
para. 9 - Error, then, is found neither in the understanding, the ideas
of which are true, certain · and necessary, nor in the will, the ideas
of which have no necessity.
of negation.
Error is nothing, it is a
defect~
a kind
It comes about by precipitous judgment, i.e., by our
failure to "restrain'' the will within the bounds of the understanding.
p. 176:
"Errors - ~ •• come from the sole fact that since the will is
much wider in its range and compass than the understanding,
I do not restrain it within the same bounds, but extend it
also to things which I do not understand: and as the will
is of itself indifferent to these, it easily falls into
error • • • "
�21
prope~l~
Formai falsity, since it is nothing,
most _
.$trange phenomenon.
speaki8g, in · itself, is a
~ay
We must ·ask in what
senses might be r·elevant to formal falsity?
'the
decept~ons . ~r t~e
Immediately the possibility
is raised that sense deception is "material falsity."
lmp.etus ·is given
to this. ~rgument by asking aga,in how it is possible that error, as formal
fal~i ty, ' is ·not · found in t·he will itself'?
What dcl'es ·. ~ ~ mean t _ at we
h
affirm· or - d~riy something we do ~cit undei•tand?
The answsr sugges~~
itself that we make a 'judgment about somet.h ing which has no ground of
certainty in ·it, i.e.,. no rational necessity, in short, an idea of corp6real nature as it appears to
section of the
paper~
However~
u~.
We
~ill retu~n
Descartes
giv~s.
to ·this in the next
an example of the
"operation-" : of error that is of g~eat im.portance as rega:~d·s · t'he above
speculations.
exampl~
para. 10 - The
is central to the erideavor of the Meditations
and occurs throughriut in various ways.
.
-
.
.
.
~
He has two ideas of himself.
.
One is that by which · he is what he is:.
·u.
•
•
when I la taiy examined
· Whf!lthe~ anything existed in the war ld, and fou·nd • • • it folfowe.d
that I myself .existed • • • " . This is .his idea
thing or essence.
The
"great Clearness II that
id~a
of
self as· thinking
presented itself to his mlnd
.there fOllOWed
11
and I believed this with so much the
a
~ith-~uch
great incll.natiOrl or" my Will;
greats~
freedom
as I
possessed the less indifference to it." ·
The other idea is of self as
a
"representation· of corporeal nature."
tt
•
and it comes to pass that I ·doubt · ~hether this
thinking n~ture which . is in ~e, or rather by which I
am · what I am, differs from this corporeal · nature, . or
wheth~r both ar~ not simply the same thin9"
Wa
mu~t conside~
the implication of this :question and its immediate
consequences~
In our Introduction we noted Descartes' view that what underlies the
. appearance of things 1s something umore simple and un.iversal, fl and
the implications thereof con~idering natu~al objects as mathematical.
The same distinctio·n lies· hidden in t~. e above . ~xample. · ·rhe ·· answer to
.
.
his question· rnust involve ·the · pos- ibility of bringing the a·p·p·e arances
S
�22
into the realm of rational necessity.
We will discuss the problem as
it ·evolves later in the VIlli Meditation.
for the present, the immediate consequences of the example also can be
found in the first Meditation:
p. 145 and 148 bottom -
tt
reason already persuades me that I
ought no less carefully to withhold my
assent from matters which are not entirely
certain and indubitable than from those
which appear to me manifestly to be false.
.,
We might cbmpare this with the following in the IVili Meditation:
p.
176, para. 11 :
11
•
•
for, however . probable are the conjectures
which render me disposed to form a judgment respecting anything, the simple knowledge that I
have that those are conjectures alone and not
certain and indubitable reasons, suffices me
• • • to judge the contrary."
p. 177, para. 12 - From this he concludes that "the light of nature
teaches us that the knowledge of the understanding should always
precede the determination of the will."
The contrary is the "inverse
of free will," and in that precipitous act is found the "privation"
in which formal falsity, or error, consists.
We might ask, by way of
objection, why Descartes did not make further distinctions between the
will and judgment, especially in the light of paragraph fourteen:
•••
the will consists only of one signal element,
and is, so to speak indivisible • • • its nature is
such that nothing can be abstracted from it (without
destroying it) . 0
11
The will is a faculty of action and error is not found in it, but in
its act of judgment, which, if by paragraph fourteen we cannot abstract
anything from will, seems a contradictory proposition.
this objection is subtle:
The answer to
The act of judgment clearly, by the light of
certainty, is deprived of the necessary vision of the understanding,
except when it acts upon what the understanding presents to it, in which
case it must affirm it.
This "deprivation of visionc• (our metaphor),
like freedom, contains degrees.
The judgment may also be blind
the example of the desire for food which is poisoned (p. 194).
as in
This
blindness represents judgment when it is ·most subject to nature, just
�23
as its perfect vision (the "perfection of~ will", · p. 175), its greate~t
freedom occurs when it is least subject · to nature, when it is within ·
the bounds of the understanding, which has no dependence on body, i.e.,
on nature.
in
Thus, the suspension of judgment
the face of uncertainty,
is the suspension of act; which, as we shall see is the suspension of
its "par.ticipation" in nature (understood as the "composite" feiculties
of sensation)~ .This becomes at the clbse of the fourth M~ditation, t~~ ·
"principal perfection of man," that is, the "regulat.'ive 11 principle or
"resolution never to form a judgment on anything wi tholit :· having a clear
and distinct understanding of itu
(p~ · . 78),
1
a principle which, in the
first Meditation is the nmechanismu of methodological doubt.
Descartes' argument and statement of the above principle occurs within
a discussion that
ret~r~s
to : the
~~oblem
of God. ~nd error.
"• •• I
must not c9mplain ttiat God concurs with me' in forming the acts of the
will, that is the judgment in which I go astray, because the acts ate
entirely good and true, inasmuch as they depend on God."
In what sense
the acts are "good and true" becomes clear in the v1th meditation.
We
will note here, however, that the basis on which . they are good and true
has to do with the distinction between
and the objects of the will.
tation.
th~
.objects of the understanding
This distinction evolves in the v1th medi-
note here, however, that the basis.on Which they
W~ ~ill
b~tween
good and true ·has to do with the distinction
understanding and the objects of the will.
~re
the objects of the
This distinction evolves
in th~ VI~ m~~itat~o~ as the distinction between s~lf as mind, and self
as compbslte ~ind and body, and ultimat~ly, the distinction of rational
and natural necessity.
The objects of will are "good and true"
becaus~
of their source in the latter, but, as we shall see, cause a "material
falsity" as well.
The Imperfections of Man
p. 177,
para~
·1i - It is an imperfection of man not to use what .is in
his power, namely, t(f a.u s.pend judgment.
God that we fall into error. (as
have caused it,
as : ~t
It is not an imper.faction of
fo~mal falsity), .s·i~ce he could not
is, in itself, nothing.
created · .man so that he did riot err~ . for
one
But God could have
thing' to have given. to
�25
the existence of material ·things in a different light.
The distinction
there, between the realm of certainty and the realm of possible error,
raised more troubling questions about the distinction between mind and
body than the initial doubt of the first Meditation.
Initially, the
common experience that the senses deceive us occasionally was justif ication for doubt.
Then, for the sake of certainty doubt was raised to
radical doubt, the result of this was that there can be no certain
knowledge intrinsic in the perceptions of sense, was implicit in the
enunciation of the question of the fourth Meditation.
But, remembering
our remarks in the Introduction, the original methodological doubt did
not deny a reasonable basis of belief, in short, did not deny the existence of material thin§s.
Thus the stated intent of the
VI~
"to inquire whether material things exist," is misleading.
no real question of his bodily existence.
feet, flesh, etc.
IV~
There is
He is "made upn of hands,
He is sitting before the fire.
Rather, the question of the
meditation,
He is "real 0
•
Meditation must become more complicated.
for on the one hand we have rational necessity, which in itself must be
the criterion
fo~
all intelligibility and which, is independent of what
.the senses bring us.
But on the other hand, we have numerous other
ideas, ideas which in the main come from, or are traceable to, sensation.
There is no question of the existence of these ideas as ideas, but there
is no rational necessity in them either.
That is, although I judge the
ideas to be of something "outside" of myself (and although I mayynot
have ·any persuasive doubt that they are
not)~
I cannot see any necessity
in the judgment and hence no certainty in the idea itself, and ultimately,
if the idea is my contact with nature, no necessary knowledge of nature.
Nature is, as far as my ideas of it are concerned, unintelligible (since
the intelligible is the necessary).
become:
How can the (undoubted) existence of nature be brought into the
realm of rational necessity?
serve?
Therefore our question must now
More importantly, what end would this
The latter question we shall return to, since Descartes' view of
nature and of man may find ground in it.
The former question can, for
the sake of a general discussion of the meditations, be re-stated again
as:
What is the necessary mode of our sensible perception of the exis-
tence of nature?
tion.
And this returns us to the "place" of the v1th Medita-
In the V~ Meditation (the proof of the Existence of God (p. 182)
Descartes says:
�26
•
•
I cannot conceive anything but Grid himself to whose
essence existence (necessarily} p. rtains;"
e
11
and (p. 110)
" • • • I recollect that even when I was still strongly
to the · objects of sense, I counted as almost
certain those truths which I conceived clearly as _regards
• • • arithmefic and geometry, and, - in general, •
pure and ab'stract mathematics;."
~ttached
-;-· ... ;
and finally (p. 185)
"And now that I know Him I hav. the means of acquiring
e
a perfect knowledge of an infinitude of things • • • of
those wti ich ·pertain· to corporeal nature insofar as · it is the
object of pure mathematics, (which have no concern .with
w~ether it exists or not)."
.
The question of rational necessity and nature would . seem to have been
answered by the fifth Meditation.
If God is the paradigm and guarantor
of all existence, then, insofaras 1· can consider natur~ as the object
of pure mathematics, · the certainty of which has always ·been known to
me and which is guaranteed by God, I can have knowledge - ·rational,
necessary knowledge
of corporeal nature.
The
6~tch,
however, is the
last clause;
"which have no 1Jon,ce11trr with whether it exists or not."
Knowledge of corporeal nature that is in the realm of necessity by the
nature of rational necessity, (which has, in itself no dependence on
body) has no concern with whether nature exists or not.
For the fact is, that even if corporeal nature can, through mathematics,
be brought into the ·. ~ealm of rational necessity (leaving as id~ the . ... :
.
.
[
.
~
great prob.lam of the basis of this correspondence) thi~ apparently . d~es
not account for all the ideas of consciousness, but only for
distinct ideas.
clea~ _ and
Consequently, the other ideas of consciousness, those
without rational necessity, are not satisfactorily accounted for .in
V~
Meditation.
Moreover, the
IV~
Meditation raises the
que~tion
th~ r·
of the
disparate ideas of consciousness by showing that there is no necessary
correspondence between them and concluding that, in the absence of
certainty, judgment on such matters
mus~
be suspended.
Now, this
question is raised as an example (p. 176) for the sake of the major
·: · ': 1
�27
co~clu~~on
~qual
er·e of
IV~
of th,
Meditation.
But both
imp<?rtance, indeed, t,hsy
.t~e
comp~ement
example and the conclusion
one another, since the
example . is, the parad igm~.tic example ,of all such conclusions.
.
.
.· .
\.
.
·. ·.
'
, .
;,
'
;_,
'
The idea
of .Corporeal 'lat)re .exists in ~h.e . meeting. ground of body and mind.
~
'
'
·•
•
•
'
'
I
'
'
•
' •
.ins.afar. as consciousn,ess. is of ideas, body, insofar as the ideas
to be of. bod.ies (he . has a
p. 176).
called
~
representation of corporeal nature"
But the content of the ideas has no necessity that can be
ration~!,
understanding.
the
"ce.rta~n
mind,
•
i.e~,
meets the criterion of certainty in the
tha~
But they
and the mode of their existence is, to say
~.
lea~t, ~Ysterio~s •
re-examine · b~iefly
. ·,; Let us
a statement in the beginning
of ~ the IV~
Meditation:
"I am • • • something between God and nought, i.e., placed
in such a manner between the supreme being and non-being,
that there is in truth nothing in me that can lead to error
insofar .as ,a ..sqverign Being has formed me; but that, as I
in some . degrea parti6ipate iikewise in noght~ or in nonbeing •• ~ ! ~ ought riot to be astonished if I should fall
into ,error."(p. 172) ;:
The idea of a supreme Being, like the ideas · of mathematics·, is innate:
~s neither derived from the sen~es nor in.vented •. We are · hus ·"endowed"
t
. . . wi:'_t~h a faculty of certain knowledge.
_ f this c.e rtainty ·(as in the
o
within it.
vth
And insofar as God is the guarantor
Medita.t ion) there can be no error
But he is ''between supreme Being and non-being."
extent that re
in .non-being he is imperfect and falls
"participat~s"
.. into er.ror.
Now, as we :.have noted, a.lJ~~ough he is
, nought" as a
con~cious be~ng
he .is no.t
., .participates i~ . being as w~ll.
"bet~een"
.
po~sible~
'
.
.is the
Consciousn~ss
r~alm
.
,•
.
Therefore we must ask
'·
but shares or
'
The realm that is
s~nse
deception is
·· what non-being _is, . and in what
The an~wer now wo~ld .seem to be that we
.way we "participatett in it.
"participate" through
between God and
is divided into two
in whjch errpr and
....
:
;·
11
~trictly betr-~'
~
.realme as we pointed out in previous discussion.
properly
.
And to the
ideas~
ag~1~
...
'
ideas in the realm of the sensible, ideas
that are not clear and distinct, that is, ideas of nature as it is
known through the senses.
As we $hall see, in the
VI~
Meditation this
is the realm ·Of mari"·considered as ucomposite" of mind and body.
�28
The purpose of this rather long introduction is to discuss the "place"
of the vrth Meditation.
We have tried .to show that the intent:
"to
inquire whether material things exist," must be understood as an inquiry
· into the faculties of sensation, i.e., those faculties, or that realm
of consciousness which is not the "pure intellect," rather the realm
where man is subject to falsity, both formal and material.
The Form of the Sixth Meditation
We have divided the sixth Meditation into three parts.
The first,
through paragraph five, (p. 187), the second, through paragraph 11,
(p. 191), the third, which is itself divided into three parts, includeg
the remainder of the Meditation.
Part I
p. 185, para. 1 - The distinction developed in our Introduction to
this Meditation is noted initially, i.e., "that God possesses the power
to produce everything that I am capable of perceiving with distinctness."
God is guarantor of certainty, and existence insofar as nature
is the object of pure mathematics.
The imagination is then considered
in relation to existence as initially defined.
Since imagination is
"a certain application of the faculty of knowledge to the body which is
immediately present to it" that "body" must therefore exist.
p. 135, para. 2 - The distinction between imagination and "pure intellection1' is then discussed.
Two ideas emerge from the discussion.
Although the imagination can "image" the objects of geometry, its
capacity to do so is limited.
What the understanding "sees," without
effort, the imagination, if the idea is not too complicated (in which
case it becomes confused) can "image" part by part (e.g., a pentagon).
This leads him to conclude that the imagination requires
~a
particular
effort of mind in order to effect the act of imagination, such as I do
not require in order to understand."
Imagination and will are alike in
respect of action.
p. 185, para.3 - Further, the faculty of imagination is not a
11
necessary
�29
element in .~~ . ~l'latu~e, " · because it is different from the undera.tanding,
whfoh is ·nec~s.sary and it' ''depends on something . which differs fr·om me."
Ndw, what follows , this is mos't important.
Descartes' remarks become
subjuncti~e· ·i n mood ...when a · further . 'distincti.o n .b etween ·"pure intellection"
.
.
.
.
.
and imagination is. . considered. '. lf trie · imagination depends on something
,. · ·
,·
:.
'
differeri't . from me "it may be that by this means . it can imagine corporeal
objects."
Imagination and · ·intellection th. n differ .in that the former
e
"turns towards the body" ·w hile the ''mind in . ts intellectual activity. ·. •
i
turns on tit.s elf ·and considers some. of the id~as which it' possesses in
. itself."
~ow, the ima~ination ~hen it turns towards body "thera beholds
·in it som~th~ng confo~mable to the . ids~ which it · ha~ either conceived
of itself o~ perceived by the s~~~es."·
But ~t is (p. 187)
clear
that · imagination is . . this way orily if body exists. . ·He ·c an only say
"with
p·robabili~y"
U:i. t body exists.
a
,para. 4 - But in turn3=,ng toward b.ody, . the · imagination also has .. less
distinct ideas" i.e. , of various sensations ( e .• g.
scents, pain").
The.s.e .ideas "hetve to come to the imagination "through
the · senses, an~ · by memor.y."
Therefore it is necessary to
tigation
· feeling~
w~ich
a.
is
a~
11
.
11 investigate
·j_5 a (para. 5).. "mode of thought,
; the nature · of sense perception" which
which I call
"colors, ·soun.d s,
To this end he will follow a · program of inves-
.follows:
Of "thosl;:) . matters" which I hitherto held to be · true having
·. perceived them through the senses (i.e., his former
opinions) and the foundations on which my belief has rested. 11
b.
Of his' reas·Of'S for doubting (a.)
c.
And "which of . them I must now believe."
Part II
para. ·6 - The above . program is . clos~ly
'.
paragraphs .
be true.':
'
first he crinsiders
~th~
in the succeeding three
matters which I hitherto he l d t o
.These :were the following:
parts (head, hands, feet, .etc.), that
affected him iri various ways
follo~ed
and · th~t~
That he is ~ .body and made
he- i~
up
of.
among other bodies which
thereforep he felt
p~in
and
plea~ure as well .as appe~ites .(hunger, thirst, ·ate.) and passions (joy,
sadness,
~nger,
etc.).
Outside of himself he ·experienced figure, extension,
�30
and motion of bodies as well as other "qualitiesu (hardness, heat,
light,color, scents, sounds, etc.).
These "outside" experiences in
effect constituted a principle of (p. 188) "otherness," by which he
was able to distinguish among bodies.
On this basis he believed himself
"to perceive objects quite different from my thought. u
objects were experienced without his consent.
Further, the
Because these ideas were
"more lively • • • clear • • • more distinct than any of those which I
could frame in meditation" they did not Qriginate in his mind but from
"some other things."
He was persuaded that all his ideas proceeded from
sensation, and that his body was uniquely his, from which he could not
be
s~parated.
But he could not account for the consequences of the
actions of body on him (why sadness follows pain, "dryness of throat a
desire to drink," etc.).
He reasoned that "nature had taught ma so."
Further he considered that "all the other judgments • • • regarding the
objects of my senses" (p. 189) had also been "learned from nature."
This
distinction between "teachings of nature" and "light of nature" should
be recalled:
(see IIIrd meditation, p. 160).
p. 189, para. 7 - But these beliefs came to be . doubted by other experiences,
notably that his senses deceived him and that his judgments based on
external sense were in error.
Also those based on internal sense, as
in the pain an amputee might feel in his missing limb.
In addition to
this the distinction between waking and sleeping casts doubt on whether
his ideas of sensations proceeded from external objects.
Further, it
was entirely plausible, since he was in ignorance of God, that he was
dece i ved in everything.
from this he concl uded that he «did no t be lieve
that I should trust much to the teachings of nature."
And even if the
sensations were involuntary · that was yet no reason "to conclude that
they proceeded from things different from myself."
para. 8 - However, having discovered 'more clear 1 y the author of my
1
being " it seems that he should suspend his judgment and neither " rashly
admit"' what the senses teach us, nor "doubt them all universally."
p. 190, para. 9 - Now the argument that follows in the succeeding two
paragraphs is crucial but rather elaborate.
Hence we shall attempt to
make it clear by dividing it into its elements.
This is especially
�31
important in . pa.r agra.ph · 10, where the argument . .r~sts ,· ·in part on arguments
·.. · . . .
· : .fro·m th'e I II rd M~d,i t~~ion, which ·a·rguments, in turn, are couched in
· scholastic terms.
Now Descartes' use of such terms has been treated as
a subject in itself (e.g., Gilson.!
Etudes Sur ·le Rois De La Pensee
11
.
.
Medievals Dans · La· For'ma'tions Du SysUme Cartesian" Librarie Philosophique
J. Vrin, Paris 195·1)-'and ther~~ore .we must try · to separate the intent of
these terms ·within ·t he '·cfontext of the present argument from the formal
usage as Dascarte$ ~n~~~~too~ it.
establish~d
argument is
·in
first, however, the ground of the
par~graph
9.
Par~Qt~ph 9 begins the consideration of part (c) of the above mentioned
.· progtam.
First, he may be certain that the fact that he perceives things
as different suffices to assure him that they
~
different, since "they
. may be made to exist in · separation at least by the omnipotence of God"
and further, that _ ~od
_
But the fact
th~t
_ is
the guarantor of his clear and distinct ideas.
the separation may now be said to "compelfl his judg-
ment does not revea_ "by what · power this separa.tion is made."
l
That is,
certainty only pertains to :his 'judgment in _this · matter, and therefore,
t•I rightly
conclud~
am thinking thing."
~herein
that my essence
~onsists
solely in the fact that I
Further, teconsidering the beginning of the argument
he has both a necessary · idea of himself as a thinking thing and
"a distinct idea of body, inasmuch as it is only an extended and unthinking
_
thing," he is forced to the conclusion that his thinking essence, or
soul "is entirely and absolutely distinct from my body, and he can exist
without it."
That is, self as thinking thing is a necessary idea; but
-to ·think body_ is not to :think it necessarily, . since self as thinking thing
.may
.<.
always. be thought apart from the idea of body.
Both ideas ·exist, but
dnly one has essence to which existence necessarily pertains. : It is to
be remembered that this definition, which we have drawn ou.t, is · Descartes'
definition of God (p. 182), that is of supreme Being.
··para. 10 - Before considering the arguments in the next paragraph, there
· fs a small but important matter of translation to be cleared up • . .(p. 190· ..
.;' .:·191) In the Dover edition the first s.e ntence reads " • • . faculties of
imagination and feeling" whereas the .Latin edit.ion reads "facultates
imaginandi and sentiendi. 11
Similarly, in the Dover edition, top of page
.. . 191~"-'ilih~re . it reads "passive faculty of perception" the Latin reads
�32
"passive , •• facultas sentiendi."
The Frs rmh translation (by the Due
de luynes) correctly uses sentir in both places.
for clarity and consistency.
We will use sensation
Where useful, the Latin and French text
will be referred to.
We may organize the argument in the
which Descartes enumerates.
a.
10th
paragraph around the "faculties"
They are as follows:
Of imagination and sensation.
From the preceding paragraph
we may understand these faculties, that is the ideas they
produce, as unnecessary on the one hand ("without which I
can • • • conceive myself • • • as a complete . being") but
which, on the other, "cannot be • • • conceived apart from
me. n
b.
Of "change of position"('ichanger de lieu," "locum mutandi")
and "assumption of different figures" ("se mettre en plusiers
postures,"
11
varias figuras induendi 11 ) .
What is meant here
is the faculty of locomotion, of bodily motion.
c.
Of "a certain passive faculty" of sensation, which receives
and recognizes uthe ideas of sensible things," but which
"would be useless to me" if there were not.
d.
An ttactiue faculty capable of forming and producing these
ideas."
This faculty "cannot exist in me (inasmuch as I
am a thing that thinks) seeing that it does not presuppose
thought ...
Before considering the relation of these faculties, let us consider
Descartes' schoiastic terms (which clarify the relation of the faculties.)
Substance:
(a') '. Intelligent substance" (substantia intelligente) .
'
In reference to (a.) the faculties of imagination and sensation, since
they "cannot be conceived apart from me" they must "reside" in an intelligent substance .
essence •
That is, since he is a
11
substance whose whole
is to think," all fa cul ties of ideas must be in him con-
sidered as in intelligent substance.
This is to disregard the problem
of qihether Descartes has a precise notion of substance.
"Thing" (res)
and "substance" are equivalent terms, regardless of what a "thing" is.
(b') "Corporeal or extended substance" (substantiae corporeae)
�33
This raters · to (b.) the facu~~y of locqmotion, of the movement of self
as body. · As a "thing" body ..:is . cha;r .act~r ized by "extension" chiefly.
The "faculty" which is·, ·in.volvad cannot be that o.f thought, · To think
(clearly and distinctly). body is to think "some sort of extension
but no· intelleetion ·a .t all."
Substnace is here too equival.ent to "thing,"
but now understood as exte.nded thing.
Intelligent substance· means
thinking · (or unextended) thing (which, of course, is clearly presented
· earlier in the Meditations, e.g., ~· 165) and corpbteal substance means
exteAd~d
thing (also found
earl~er).
Corporeal or
is also relevant to (d.) the "active faculty".
extend~d
substance
·T his "faculty,. which, if
it is to produce the "~deas c;>f sensible things" perceived by the "Passive
facu1ty of sensation,-" must be external ("different from m ") and, since
·
a
it "does not preSUPP0.S8 thought' II must be Corporeal SUbStanCS' Or extended thing, or body.
(Or "God himself" for that matter.)
Formal and Objective Reality:
·w•
will not ~oncern oursel6es with a discussion of . these terms other than
to nrite that they arise in the III~d Meditation (p~ 16~) · in the context
of an argument . similar to the present (i~deed, Descartes quotes himself
here), and, further, that "formal" and ;'actual," ·and "objective" and
"r:epresentation 11 seem to be equivalent.
"Formal" refers. to a thing as
it is (in its · "form·;u · it seems) artd .'·' object.ive 11 to the thing as idea.
Considering the t.a·r ·ms in their context, as relevant to (d.) the active
faculty, we may understand the author's intent as to establish that the
cause of the ideas (which have
·o bjective reali:ty") is in the bodies
11
.(corporeal substance in which the :faculty resides), which are "real" im,
themselves and which ~•reality" is represented in. the ideas.
this is a periphrastic statement of an
assum~d
That is,
correspondeQce between
,,. material nature, or ·extended things, ~nd rni~d ~s i~eas (thinking thing.)
We say "assumed" because of the equ,ivo.cal use of the term "reality."
On the side of rational necessity, the . "r. al"
e
i~
the certain, necessary
clear and distln'ct idea' and . is necessarily "absolutely distinct from
body" ( p~eced.ing paragraph). · That is, if" the idea of body is not
rationally necessary (al thtlugh it oa.rt :be . clea~ and disti.nct, too,) but
exists (and exists necessarily . in·:,,~he . sens~ - [~h.~t he cannot prevent the
idea:
they occur without his will) then it does not seem "real" in the
�35
cause or result in id_ as (al.though i t. is not primarily responsible for
e
thefrn). - Both faculties (a)' and (c) are
.
.
the _category of "intelligent
j,n
.
··substance", and for ·that reason cannot be though- apart from self.
t
On the other hand, faculties (b) and (d) are in the category of
tended ·substance. . In ·addition, both are
in nature.
11
ex~
active 11 . and represent action ·
They are faculties of body, faculty (b) regarding self as
body, and (d) regardin~ bodies other . than · self.
We will now consider the conclusion Descartes draws from this paragraph.
·. • We ·must allow that corporeal th~ngs exist . 0
•
Simply stated:
ever, it
How-
qualification of this .conclusion that deserves our
~s - th~
close attention:
"However, they are perhaps not
e~actly · what
we · per-
ceive b'y the · serises •· ·• • as . external objects."
The origins of the· ·c onclusion·, "that corporeal things exist" can. be . de- rived from t8e conclusioh of paragraph 9 (that body is distinct
soul) .?ind _
the beginning of paragraph 1 O:
fr~m
"I • • • find in myself .
facu.l- ties e.mploy ing modes of thinking peculiar to themselves." . To . h__ .
t is
must ~e acid~_d· the idea {stated in IIIrd Meditati?n, p. 159) that the_ideas of corporeal
objects~
althdugh they do not necessarily in them- ,
selves _permit us to . judge that the things of which they are ideas
neverthe~ess
have an unquestioned existence as ideas.
Thus the
~xi~t,
faculti~s
which pro~uce ·.them as · faculties of ideas, cannot be thought apart from
self as thinking .1:;.hing. · If we consider the (10th) paragraph dialecticaU.y,
the author next C-onsiders self as body alone by considering what he
already . knows_ from .ex per ienc'e, that is, he has power ("faculty") of
bodily
m~vement
• . From self as acting b6dy he moves to a
conside~~~ion
of self as body ,acted upon, · implicitly connecting the notion
notion, that he knows he is "acted upon" by m ans of
_
e
wi~h
~ensation.
the
fi~ally,
in conside_ ing . the "active faculty" he "discovers" that to be "act_ p _
r
e
upon" something must
_ a~t.
But it is also clear that these senses deceive us, and ' ~i~ce God is not
a de6~iver, He "does not communicate these ideas : to me im~ediately 0 but
by corporeal c:>bjects, whioh we perceive in an
way.
11
obscure ·and ·confused,"
.
�36
., which1 .a.tetMcoaceived
But these th
11
" i. e
are
in the ob
as external ob
an idea of self as
th
of pure
the
That is
in the
since the faculties
cannot be
of
in itself
the idea
There is no rational
of
against its
the existence
Whether or not the 10ili
, we can
ob
re
, to
is not a persuasive
---
their existence
do not in fact exist
that
upon
, universal doubt is a demand intellect
the sake of
proof" such as the 10 1111
is not meant to "restore
To
do not exist.
a
of
perceive them..
confused,
to us the
of common
that we are without senses, without
to say that
for
the fact of all
The method did not seek to
experience as such, and a
ence.
in
of pure mathematics.
the conclusion of the
;
which one has
if we consider
we consider it as the ob
We must we
medita-
from self as th
But, on the other hand, the answer is
the
must
It is affirmative if we consider
The answer must be equivocal.
the faculties involved.
is.-;.·:_:
11
Are we here any closer to answer
tion?
and
in the seo:;>es :
, etc., it not
It is not that material th
existence, rather it is a
If on the one hand, our perce
that
ion of
we
is nobscure and
but, on the other hand the possib
of
we are forced to reconsider our faculties of sense and to see
whether it is
for them to br
us certain
The conclusion, that soul is distinct from
have no
br
necess
us certain, indisputable
of nature
, and that the ideas of
, denies that the senses as such can
This, in turn, forces a
reconsideration of the way nature itself must
is not necessar
exist, if it
in the way our senses tell us it exists.
It is
necessary, then, to seek for a common ground for rational necess
of the
of the senses to the end that a secure knowledge of
nature may be
of certa
, and
(since the senses, to reiterate,
within us, cannot
sentence of the
us certain
the criterion
).
The last
asserts but does not demonstrate that whatever
�37
in· the .senses may _be "comprehended" . as a pure mathematical foJim, car:i be
brought Jn.to ._ · real~ of rational · n_eces~ i ty, tha~ . is,·· a necessary. "exthe
.. .
~er~al obj~ct" i~
·~
.
.
-
the way .that such objects necessarily (insofar as it
is possible for us to know) must-· ,e xis.t .
To recapituiate ~~iefly:
thinkin~
definition at a
the statement, i~ the llnd Meditation, of th~
thing,
listed . ~s
·faculties those of imagination
and . . "feelinQ," but, we· noted in our Introduction, left their situation'··
as regar~s body so~~what . amb~guous.
In th~ fou~th . Meditation, ~ - dis- ;
tinction between our · ids.a s as perceptions from sense, and . thos~ of
the
,.
under~ta~ding,
was seen ras underly~ng the problem of error.
This · dis-
tinction was . given its most emphatic enunciation in the question of
whether th~ :idea . of self as .thinking thing, ~nd the idea of s~lf as
"corporeal representatia.n" could n~cessar.ily be understood as one thing,
"or . -~-~ether · both are . ·not .s imply . the same thing...
Further, this dis-
tinction we ·may · now ··understand as a develoi:frnent of the original am-..;. ·
statu~ ~f
bigu?us
ra~se~ there as
.
.
.:
·:
the faculties of ·sensatioM though the implicit question
td the differences b~t~ean the under~tandi~g and the
" _ r:
;
.
.. .·will,_ the lat tar unde·r stood as a faculty ·of action, _which action· must,
in effect, be suspended to . avoid error. . In ·the beginning. of the
vrth
Meditation, the distinction as regards the faculties ~·comes expiicit
in the discussion of the differences
intellection,u and imagination.
betwe~n unders~anding,
or "pure
The latter is seen as "turning toward
bod'y" af1d thus .d_ pending "on something which differs from me, ' while the
e
1
former
~ ~urns
on itself, and considers some of the ideas which it
·. possesses. in itself" (emphasis added).
This discussion, in turn, leads
to an ex.amina.tion " f "sens~ perception'" which recapitulates the arguo
ments about (a) his former opinioos
whi~h
rested on nature
~s
it appeared
to him, (b) the origin of doubt in errors of judgment concerning the
external senses, and finally, (c) what he can know with certainty.
·~
.
:
l~~t a~gument
~~.
-.
.
is
mos~
important to us.
restatement· of the cogi to:
' a~:
body."
~ppearance
it is merely a
"I am a th inking tti ing (or a substance whose
whofa""essence qr:. nature is to ·think)."
self
In
This
He concludes that his . idea of
thinking thing, is "entl.rely and ·abso. utaly distinct "
l
from my
As a c·onclusion it is merely an echo of the !Ind Meditation.
But, unlike the !Ind
.
.
Medita~idn~ · a defin~tion
,.
.
.
.
of whaf a thinking thing
�38
is, is not
Rather, he finds in himself
modes of th
iar to themselves • • •
The amb
be
11
tion and
status of these modes of th
the one hand
faculties
is now
are not necessary to his idea of self as a
but on the other
be conceived apart from me ..
11
leads to the discussion we have outlined
which consists in
This
11
to this
faculties of
The conclusion, and its
and mind ..
that cor
'
exist, but that
are
in effect sets
the ideas of sensation from those of the understand
11
not
what we perceive
the senses,
The conclusion, we have tried to show, is no conclusion at all, since
the
in the existence of
th
was not,
the or
terms of doubt in the first Meditation,
Rather, we maintain
the
of the conclusion
of the wax, that nature is to be understood as
the
the
restates what is im-
of
is the
to ac-
of an at
count for the ideas of sensation, i.e., the appearances, in terms of
the rational
of the understand
distinction between mind and
, becomes in
within mind itself, and the
self as a composite be
As a consequence, the
, a distinction
of the
of mind and
of
The
of this
will be discussed later.
sections ..
1
the teach
of nature ..
with the
of section III, concerns
Part B, from
of nature...
between the first two sections
end, and
with the
18, deals
16
15 we consider a transition
c
is from
19
to the
basis of error ..
11
Descartes
are,
to an examination of sensation as
is,
truth in the teach
as obscure and confused.
s such as
There must be some
of nature, since God is not a deceiver on the
one hand, and man has the
in himself (from the
Med
�39.
of cO'rrecd.ng hia···a frors.
He now defines ·nature as either "God H.imself
or the · order and disposition which God has established in create.d things."
His· ·own nature is "the ·camplexus ·of all things which God has given : me , u
.
para. 12 - ·The most . important teachiMg of nature is
~
.
'
that ~ he ~~'a ~~dy .
. . :·:. . . .
hunger, thirst, etc. ·' "nor can I
.
pain~
whi.ch undoubted:J,y experiences
..
..
. ··.,
. :·
' }
doubt there being s9me truth . in thi$. "·
para. 13 - from these teachings of nature he concludes . that ' he (as
'
'
thinking thing) is "intermingled 11 with body:
''I seem to compose witti
The sensation of pain, etc. have a two.fo:ld nature; the·y
..
are both signs and "real" experiences, they are "none . other . than certain
it one whole."
:
confused modes of thought which are pr'oduced by ~~e ~nion and appateni
inter~ingling
of . mind and body."
For a wound is not perceived by the
under~tanding. only' but the p'a i'n is "felt" as well.
. r.F
(The 'idea ·of self as composed ·of mind and · body is extremely .difficult . .
to 'reconcile in the Cartesian scheme, since· it requires the intermingling
of two ap·parently different "things" - extended,. corporeal, things, and
unextended · "intelligent substance, 0 i.e., thinking thing.
However, the
idea of composite self may be thought of as · - physical model, i.e., a
a
model of body as a · metwork of nerves or faculties of sensation.
This
do~s nof recciMcile the tiltimat~ · ~iffic8lty of the necessary distinction
between ideas and bodies that act, but merely prov ides a ·scheme fo.r . the
succeeding ~iscussion.)
para. · 14 .:. Nature teaches him as well that "many other bodies exist
around mine" and that he pursues ·or shuns them.
The particular
sensa~
tions of these bodies themselves have "certain variations · which answer"
ta · his sensati6n~~
(But, to labour · ~ point, there is not ·rational ·
necessity to establish this.)
Ne·v e·rtheless,
:, .. ·u.
.
:
r
. ; , -. : .
tt it is quife certain that my body (or ~athi~ - ~Ys~lf ••
inasmuch as I am formed · of body· and sou'l} may rec'fHve
different impr~ssions agreeable and disag~~eabJe from
other bodies which sur.r ound it." ·
· · .-· ·.· .'
' .. · '
-: •..~ r,
p • . 193, pa.r a. 15 - But,:; re.flecUng on . what
finds that
s·.om~
11
na, ture _ h~.~
.
. .:
ta!Jght . him, . ' _: . ..· . .
he
.
..
'
teachings" .have not re!aJ,lY cpme from nature.
~.
, '·
1
.~ath'3f_,
�40
"have been
inconsiderate
about
of "inconsiderate
noth
are as follows:
11
That where
affects the senses there is a void; "That in a
warm there is
in me,u etc.
nature..
which is
similar to the idea of heat which is
This leads him to re-define (or refine the definition of)
is nature "the sum of all
No
me
God,"
because it is necessary to exclude mind, (that is, we assert
tellection") since i t has
, i.e , known
) ..
An
of
him ideas which are known
"the light of nature
the
in-
a rational
the he
of
of natureu is the idea "that what has
once been done cannot ever be undone.
"mat.tars which
Further, the mind can know
to
here
but which are "no
contained under the name of nature,u e .. g., we
those other
of
mathematics
Nature
then
is now
of mind and
ars true in
of nature so re-
of self considered as mind and
i .. e .. , those flconfused modes of
, etc.
God to me as
those
, " and the
to th
and shun the
of pure
which can be known as the ob
,"e.g., to seek the
However, conclusions about
outside
us" cannot, in this view of nature, be
reached "without
hav
The
0
examined those beforehand "
beforehand."
mind if it is to know any-
Sensation must be informed
with
word here is
outside us."
II
This distinction here between internal and external can now be understood
as
between self as composite
and nature as
there seems to be a h
is
·~~·~w·~=,
0
to
until it acts upon us, and then within us,
"confused and obscure ideas. 11
Le., the
itself
teach
This constitutes our
of nature."
Above this is mind itself
in itself without
mind itself that
~-'--~~~of
is made intell
nature,
Le., the
to
as the ob
of pure mathe-
matics, and this can
the medium of sensation.
not the medium of sensation as
, which must be confused and
obscure, but the medium of sensation considered
, i.e., the distinct idea of
as
as the ob
But
of
, extension,
�41
etc.
How this happens ·is quite mysterious and seems to have to do with
the imagination in its ·:dual capacity: of · " imaging•.• the mathematical forms,
however imperfectly, and turning toward body.
concern.
Also, it shtiuld
b~
This is not our immf.3diate
noted that although \this ·scheme seems to
represent a hierarchy, it cannot Tepresent an ascent:
is imperfect and must be informed by mind.
between mere experience·and
the : re~lm
experience itself
There .can be no continuity
of innate ·ideas. - imagination and
sensation are not necessary to the conception of self as thinking substance.
B.
The
Decieptioh~
of Nature - p. 194, para. ·15 - The author now con-
sideri the . teaching of nature more·· closely.
Although our senses de-
cei\Je about external objects, and therefore "falsity enters into: .t .he
judgments I make, 11 it' seems that his- internal senses, i.e., the··
teachings of
nat~re
which he regarded as true, also
ample, we desire food that is in fact poisoned.
d~ceive~
For . ~x
But there is a better
(para. 17)- example in "those who when they are sick desire to drink
or eat things harmful to them-."
0
The body is like a machine, tha·t obeys
the laws of nature" even when "badly made."
This analogy brings him
to conclude that the inner deceptions are "natural" to it.
That is,
thirst is a natural, and in the analogy, naturally necessary sensation,
even when, because of other factors, (e.g., i l l health' i it is hershful
to drink.
But if health is good and an end to ~hich the body ~~i · been
made, then this "natural" desire does riot "follow the order of nature."
But, the author
"natur.e."
claims~
~bout
the distinction -equivocates
the word
The former example, the analogy of man and machine, is
"purely verbal characterization" and hence "extrinsic. 0
The latter,
however, is ttsomething which is truly found in ·thirigs.u · Therefore
what is "naturally necessary" without regard for the good of the whole,
. is not ., therefore, natural .in "the order .of nature. 11
As a "composite
whole " the (p. 195, para. 18) order of nature would seem to mean the
continued existence of the thing, and therefore "it is a real error of
nature~
tor ·it ··to desire something harmful to it.
f :
Now running throughout this section there. has bean an argument we have
.largely ignored, _that . is, of the goodness of
.
.
Go~~
.
'.. ' , ,
If God. 'is good, then
.
'
�42
we must ask how it is possible to be deceived.
The apparent answer is
that God has left it within our power to correct ourselves.
But the
question returns more intensely, when we consider that our natural
faculties, in themselves, when functioning as they should (we have
thirst, etc.) do not act for our good.
This, says Descartes, is a
"real error of nature, 11 and, compared to the error in judgment that we
fall into, seems beyond our ability to correct.
The former category
(of error) can be corrected insofar as self is considered as mind.
But
the latter category, of self as composite of mind and body, of "confused modes of thought" seems to be enslaved to a blind but necessary
nature.
For, although Descartes claims that the comparison of body
and machine is a "verbal characterization," nevertheless it is clear
(and becomes clearer in the succeeding section) that this, too, is
nature.
We will return to these arguments (the Goodness of God and
natural necessity) in the concluding section of the papLt • .
At the end of the
19th
paragraph, Descartes says ". • • it still re ma ins
to inquire how the goodness of God does not prevent the nature of man
so regarded (as a composite whole n. b.) from being fallacious.
C.
The Natural Imperfection of man - This last section, with its
strange emphasis on the mechanics of sensation, seems quite puzzling.
For one thing, it is simply an anticlimax.
The reader, burrowing
through these often devious meditations, with good will and serious intent, finds that, in effect, these metaphysical roots have grown up into
the trunk of physics, and now finding himself suddenly above grou nd, he
is not blinded by the light, but rather sees clearly a scene he can
never have before exper ienc'e d, and in fact, which he perhaps cannot
·"experience. u
We shall ask why the concluding pages are this way, but shall hold the
question until we have examined them.
p. 196, para. 19 - Man as composite of mind and body, the goodness of
God notwithstanding, is
0
fallacious. 11
Descartes begins his inquiry into
the sources of these failings by considering, again, the distinctions
between mind and body.
Mind is "entirely indivisible" and body "is by
�43
·nature always
As: a ·thinking . ~~ing
divisible~"
b~
is one. · As a tomposite
.of mind and body 1 however, if he were to lose· a· part of body his mind
would not be diminished thereby.
"
As corporeaL· cibject
for there · is not one of .these
·divide into parts .• "
"· Ih
h~
is divisible,
.which my mind cannot easily
addition ·"the mind does nbt (para. 20) receive
the impressions from all ·parts of the body immediatsly, but only from
· the brain, or perhaps even . from one of its, smallest parts · .. · • • "
this part, "whenever it is
~isposed
s~~e
in the
added) conveys the same thing to the
mind~"
particulat
~ay
ahd
(~mphasis
To this "·innumerable ex-
. perimsats" testify.
This paragraph is important in that it begins to
basis for the. ~passive faculty" .of sensation.
To
the succeeding paragraph uses a mechanical model.
and body are
"intermin~led"
basis of this model.
est~bli.sh . a
mechanical
demo~strate
the idea,
The fact that mind
mak.e s it . necessary tq consider car_ f.u lly the
e
First it should be remamb. ~red that .mind ·is dis-
tinct from body, i.e., body is not thought
necessarily _ wh~~eas
Second, the ... intermingling" of mind and body, . or the
mind is.
composi.t_e~ ; ·
refers,
we argue, to the faculties of sensation which both act and are acted
~ upon.
Therefore . the limits of the
· to be determined.
mechanic~!
model, seem
nece~sa~ily
That is, when qonsidering the brain in its '" smallest
. parts"· (later to be called "inmost") we · are necessarily dealing with
body which "conveys the same thing to mind."
The realm of idea appears
to remain distinct from the motions which produce it.
(That this is so
follows from the major di'stinctions previously made.)
para. 21 - Turning to body, then, the author discusses movement.
The
· analogy of the cord, which serves · as a model for the nerves, is also an
· a.nalogy and _
·model for efficient causality.
argued that .. "
~
• it is
~anifest
In the IIIrd Meditation he
by the natural . light that there must
. at least be as · much reality in the efficient and total cause as in··1ts
· effect.
for • • ,; whence can the effect · derive its reality, i f not:·
.from cause?"
( p. 162)
Returning to the above mechanical mode.l, in ·
light bf this understanding of
caus~lity,
we can begin to · speak in a
particular way ._:about · natural necessity ·• . In terms of the model before
us, of the motion· of the action of body·: on nerve, and also in tho sue. ceeding paragraph, of the models of
th~
action at its
tetminu~~ · ilih~t
�44
happens, happens necessarily.
As in the previous analogy of man and
machine (p. 195), the badly made machine "no less exactly observes the
laws of nature.u
(And it should be noted, the laws of nature implicit
as that idea is in the work, is nevertheless mentioned explicitly only
here, at the end of the treatise, in a discussion of body and motion.)
The realm of body is the realm of natural necessity.
Returning, however,
to the model of the nerve, the important conclusion is as follows:
"If
we pull the last part that the first part • • • will not be moved in any
way very differently from what would be the case if one of the intervening parts • • • (p. 197) were pulled, and the last part
remain unmoved."
• were to
And since the nerves must reach from the extremity
to the "inmost portions of the brain which is • • • their place of origin, 0
any action upon the nerve in the intervening region will cause the same
motion in the brain as if the action had been at the extreme end of the
nerve.
That motion in the brain is one "which nature has established
in order to cause the mind to be affected by a sensation of pain" which
is "represented as existing" in the extremity to which the nerve reaches.
And this model, "holds good of all the other perceptions of our senses."
We sea here the bodily, hence mechanical source of sense deception, and
that the deception is not intentional on the part of nature which acts
blindly and necessarily to some immediate Pfd.
The discussion (para. 22)
of this "end," that is the end of the motion is discussed next.
Considering the brain, he finds that the motion set up in it produced
(he claims)
0
one particular sensation only."
further, since there are
numerous sensations which arise in the brain, the motion in question
"causes mind to be affected , by that one which is best fitted and most
generally useful for the conservation of the human body when it is in
health." (emphasis added)
From this, that is from the idea of natural
necessity considered in regard to the whole of man, he concludes that
God is good.
For pleasure and pain, that is the pursuit or avoidance
of things, contribute to the conservation of the body, but only "when
he is in health."
Here, again, the conclusion and the qualifications
must carefully be weighed.
We suggest here that the goodness of
if applicable only when we are in health, is suspect.
G~rl,
By this s :.: :;1: :·a8nt,
.
to reconcile the goodness of . God with illness and death becomes extremely
�45.
d~fficult
since it
Fequire going beyond natural necessity as evi-
wo~ld
d_E;!n:c;:e .of God' -s gooc;I-; ·:creations in order to !;>peculate about his ends, which'
ar•, we have been told, inscrutable.
~hat
they:
n~cessarqy.
God has so
constit~ted
our bodies
seek to conserve themselves, but this same necessity
· . is subject to .imperfection, .and thus becomes destructive of the . body.
,_,.,P·
198, para. 23 - "from this it is quite clear that, notwithstanding the
~upreme
goodness of God, the nature of man inasmuch as it is composed of
mind and
When
..
~ody,
we~are
~·~
cannot be otherwise than sometimes a source of deception.''
in ill health the deception of sense must be a real error of
nature, that .is of our (composite) nature;
Thus the deception of sense,
when considered as false opinions in mind are harmless next to their r eal
consequences in the body.
para. 24 -
Descarte~
conclusion.
then draws the Meditation and the treatise to its
It is significant that the
conclusiori~
in this ·1ast para-
gr·a.ph do not, in the main, refer to the immediately preceding discussion,
but return tci 'the prior considerations, namely the doubt of the exists.nee
of material things, which was originally established as a methodological
c6n~ideration
in the first Meditation (p. 148) and .which, as we
~ave
tried to show, is not the primary concern of the last Meditation, although
it was written under that guise.
Before considering the significance
of this paragraph, let us revlew its
conclu~ions.
first he discusses the preceding discussion.
It has been "of great ser-
vice" to him in recognizing "all the errors to which my nature is subject~
.. · But, more importantly, it allows him to "avoid them or correct
· ·'them more easily." ·Now
into two categories.
0
all the errors" to which he is subject fall
One, which
i,s the errors of judgment.
is
the subject of the fourth Meditation,
We have already seen that the correction of
_these errors rests, initially, on the rule by which he suspends all
jLJdgment.
(Having applied this rule, he can correct the "weakness of
not . being able to concentrate on one particular thing.
Apparently,
the more he is able to do this, the greater the possibility of applying
·:-:·it'.
\..:
the understanding to the idea in question and hence b. ing it within the
r
sphere of ratio~al neceesit~~ · that is, science.)
The other category of
. nature is, of course, the· '.' real. errors" of nature. . It. is clear that
�46
them would seem
'~avoid
ible, and to
that, at this
require a
in the treatise remains specuwhich the 11 real errorsH have
However, the very means
lative.
sub ,,...,.,.,..,..,.....
correct• them would
of
, that is, the
causal
(such as the idea of
the direction and
the
ma tics .. "
), seems to im-
will take ..
such
of
of the
become,
stated,
of pure mathe-
, the "ob
Such a certain, secure
' on the
of mind, has within it the
errors.
the real
to br
Thus we find that the
and the
common focus the error of
This focus is twofold.
us to br
It is, first, the
the certain
)
11
11
real errors" of nature ..
rule 11 which second, allows
of the
to bear on the
means of rational neces-
of natural necess
in mind that this in turn rests on a
we must
which must exist between the way nature
exists and certain
to br
- it is not our intent here to
of the basis of that
is a secure
this
to a
).
ical
to l
the
The consequence of
science, a science of real effect
in the world.
In the first Meditation, in compar
the state of the natural sciences
ith that of the mathematical sciences, Descartes states that
fer in
of certa
in that the former had
consideration of composite th
certain,
and hence
whereas the latter
and very
ich
Were very dubious and un-
treat of
that are very
and an
(p. 147)
, in the second Meditation
concludes "that its
may be
as their end the
• contains some measure of
element of the indubitable
touch, nor of
41
0
dif-
of wax
after the
Descartes
is neither an act of vision, nor of
• but
and confused ..
an intuition of the mind, which
or clear and distinct • • • ac-
as my attention is more or less directed to the elements which
are found in it, and of which it is
At the end of the fourth meditation
II
he
(p. 155)
11
! notice a certain weakness
�47
my
in my nature in that I cannot
on one
thought.." (p. 17R)
The "model" of sensation at the end of the sixth meditation is an involuted effort in the direction suggested above
That is, he directs his
attention to the source of his imperfection and confusion to see it in
its elements.
The ''model" attempts to isolate the
understand it in its necessary obedience
act is the bod
of nature, to
the "laws of nature. 11
The
aspect of sense perception, and the result is to isolate
the material basis of the deception of the senses, to point out the real
in our nature.
Let us review the possible relation of
error, and sense dace
The ord
affect our
of sense
dece
but for that
reason have a consequence of some moment for Descartes, which is to keep
us from certain, necessary
of nature.
be seen, in the light of our real
of nature, as
The
This, in turn, can now
,
us in bondage,
i~e.,
of the real errors
us subject to that nature,
freedom of the will is within the confines of necessary know-
ledge, the least when subject to error which, we now argue, is understood
a material basis.
as hav
freedom is freedom from nature.
The
The conclusion of the first part of this paragraph, that he "ought no
to fear that fals
to me
my senses,
may be found in matters every
we claim is mislead
presented
Our argument for this will
than to note that he appears to
sent radical doubt for reasons that are not
we
However,
the conclusion in light of the
preced
what falsity he ought to fear?
day" matters, since it was
reasonabl~
discernible.
basia of belief:
them than to
in the
Certa
not
that there is a
"there is much more reason to believe in
them .. " ( p. 148)
';'Everyday" matters might be inter-
preted as the "usual" course of his life, when he is in health..
But
there is much to fear from the deceptions of sense when he is in illheal th his "natural"
to conserve his body might then be to the
detriment of his
He then discusses his most "ridiculous" doubt, that of whether he could
�· : :. :. be certain whether he. is: awake or
a.~leel'•
.. He
~nswe~s
this by com;::luding
that "when I perceive things as to which I know distinctly,. both the p.lace
• • • and the time at which they
1
ap~eared
to me, and when, without any
~n:terruptioni• he ·c an:' b~ '~ ertain that :·h e _is awake. · · Why iS this · part-icular
doubt
0
1
hyperbolical and r·idic~lous?" • It must be noted that "place,"
"ti.me": ~nd ·continuity are for · ·D escartes three mathematicizable aspec'ts of nature. . Nature.
'
..
is . not
fntermi"tte;nt, for orie thing, and ·for another,
when he thinks he knows he exists, and this t 'h ink.lng (on 'its' lowest
1
level) is ·"a continual ·perc· .ption of 8. contin·uO:usly ·a cting nature.
e
When
he is dre·a ming th.~re · is no continuity· of perception, a·nd hence this· ·ton
is not a problem as regards the distinction.
...
. · II .
.
I ought in no wise
to doubt the truth of such matters • • • after ' having called ·up all mY
senses., my . mernory
a~d , : my und~rstanding
to examine them • • • " and there
.. is :nothing in one _of. them . -~'.repugnant to what is set forth by the others"
do~br
he ." ought not
" , .
the truth of su.c _ matters."
h
"But. because of the exigenc.ies of· .~c~ion( f la neces.site des
affa,.ires ~)often oblige us to examine matt&rs carefully", . we
must confe~s th~t the . life · ~f man is ve~y freq~ehtly subject: to erro~ in resp~ct to .individual objects, an~ we.
must in the end. acknow~ed~e ~he infirmity of our' nature. ff
The co'iitinuity of nature, - wh±ch we may understand as "la . necessit·e' des
_ affal~~s",
it~
continuous necessary acting - although it may serve to
convince . ~s of the . distinguishability of waking and sleeping (b~t of
.w hich com.man
experien~~ seems to be equall.y convin.c ingf is the source of
whi~~ .
.our real .imp_ rfections
e
"we must in the end acknowledge."
Notes Toward Some Conclus"ions
·rirst let us clarify some distinctions that . have arisen in this paper.
T~e
·a·ppearances;· ·and '. their concomitant faculties, · the imagination (13nd
memory) and · the · faculties of · sensation, were noted in the crucial .tenth
~~ragraph
of the sixth Meditation (p. 190) ~s .those "without which I can
easily conceive
myself ~
clearly and distinctly as a complete being; While,
on the other hand, they cannot be so conceived apart from me."
gan the development of the distinction between self
self as composed of mind and body "intermingled."
~s
This be-
thinking thing and
As we have noted, this
�49
represents ari "inroa.d" on the _ cogito" as originally _.sat forth in the
"
second l'r1editation . ( P• 153) . but; as :life also · noted, this :-" inroad" is the
development . of· an ambiguity .already prf3s~nt (p. 151, bot~om).
com'p osite
self
Alth()ugh
is an "inte.rmingl.ing" of:. mind and body, . i t should be .
· noted again tha·t the distinction . between ext.ended and unextended supstance (corporeal and intelligent) is not th1;3reby obliterated.
The .
'm echanical model of . sensation UJhich repr·e sents motion to the "inmost"
parts of · the brain does not account for the idea itself, but is merely . its
" (bodily) origin. · We cannot ·say. the the "last motion" of
-.th _~ ,
"inmost"
part of · the brain is an idea, since i t must remain the . motion of extended
substance. ·· The autonomy of mind m.ust be preserved.
A further ddstinction within self as composite should also be made clear.
That is what the imagination is.
of
second~ty ~ faculty , of .
neces~ary under~tanding
of
. " tion admit
· like:·
~t::re·
First, as we
~ave
the ideas as appearances.
noted, it is a kind
This brings .us to the
that the appearances _ brought
degrees of clarity..
~~ . us
through sensa-
They may .be "confused and obs_ wre"
c
sensations, or they rnay be to somB ..exteqt _ istinct.
d
The im-
portance of th1s· lies in the claim that one . may;. have a distinct idea of
. co'r 'p ore·al na:ture (although there is. the crucial qualif ica.t ion that one
can.not . "derive . any argument . from Whic,h there w.ill necesaar ily. be deduced
·. the existence rif bodytt (p. 187) there is no necessity of
in"·the. most "distinct'! appearances).
exist,np~
even
ThiS' claim seems to· be the founda-
. ~' tion on whiCh the possibility of understanding na_ture as the obJec,t of
pu.r e ma;t-hema.tics rests'.
. •-: ··ate·.,
A distinct ·idea of r:iature. :~s of figure., .. ,e;xtension,
i.e., mathematical. . One might .well question . the .,n ecessity
'basis 'o'f . this correspondence~ is it merely . fortuitous?
this
.9.f the
UJe will not pursue
question~
Error, Sense Perception and Doubt Reconsidered
_ . We have argued that radical doubt is not a denial, in itself, . 6f
,
~xistence,
. . . :·_ and for this reason hav~ had , to interpret _the sixth Me~italib~ ~~ - having
an intent nther than what is stated.
-·
Thus we have ~riderstood th~ · sixth
·. Meditation as the end . pf ~n ~rgument that has divided c6ns~io~~ri~~s into
.; .
.
.. .
.
.
'
'
:
~
t .wo realms .• . The o.n~ . , t wh~ch: . llle... have t .e_
rmed the . ideas of. -~ationai ·necessity
· ... .
, ;
'*
..
. .. :.
�50
of sel
that is
Which
th
as th
the use of radical doubt
is determined
as a "lever,
11
that is as a
to
consideration for the sake of
the "firm foundation in the sciences .. "
ances, of the ideas of nature
The other realm is of the appear-
the senses, in which ideas
to us
there is no
or necess
necessar
This is the realm of formal and material fals
of error and sense
be
that is, to
ich existence
s not
and from which the idea of doubt in the
is derived
means of reflection on common experience
doubt, in itself, does not require of us an absolute su
This
of be-
the
lief, rather, there is more reason to believe than to
II
of nature.
However, our
about error and sense
reconsider radical doubt
in the
requires us to
error is noth
nts we make about ideas.
in itself, it lies
We have tried to show that the
errs are in the category of the appearances,
ideas about which
for it to err in the other realm.
since it is not
seems to h
ment of this
The
on the example in the form of a
ion in the fourth meditation, where it is seen that there is no
to determine whether the idea of self as cor
certain
tation is the same as self as th
th
re pre sen-
The diff
' of course
lies in the fact that existence necessarily pertains to the latter, but
not to the former.
It is at this
that radical doubt may be mis-
ion about the appearances is, if existence
' since the
to them as ideas, does
does not necessar
what the ideas a
re
, exist?
nature,
is the stated intent of the sixth Meditation to answer.
answer in the form of a
ob
"
• that
We ar
0
..
re-
, that he has ua very great inclinatio
(the ideas) are
to me
that the existence of corporeal nature was never
the basis of doubt.
cations;
Descartes
proof" we argue, is irrelevant, and mere
states the initial position,
believe •
that it
This is the
Rather, the real
are
senses" (p. 191).
from this the
and
and
lay in the
not exactly what we perceive
self as
ifithe
of mind
mechanical model of sensation
The
�51
result, · ili~ · argued; w~s an Understanding of the appearances as ~a~ing
necessity through an examination o.f. their · bodily origin, under.lying
which
e~amination_was
an implicit "physics" based on principles derived
·.
from the understanding.
·.
. .
I
..·
.·
.
The origin of the appearances· then was seen . as
arising from natural n~ces~ity~ :f~e :a~~um~nt that followed . from this
\ , -.
#•
'
was the understanding of the mateilai · 6a~i~ · 6r : ~an~~ ' ~ec~~tion, ·that is,
of the "real errors" of nature and the imperfections of man.
Now' i t is this material basis of th~ 'deC~p:tions of the senses that· 1'8quires us to consitjer the origins of ~adi~al doubt~ · Although· i t rs ·
a
0
tool" in the beginning of th~ t~~a~ise, in the end it·~eems j0stiffable
t? say that its basis is a.radical distrust
o~ ' natui~.
Th0s
radic~l :
doubt seems to be a demand of thought . for . De~cartes; 'notwithstanding its
apparently merely methodological use at the beginning of the Meditations.
It is inextricably bound up with both the beginnings and the end of his
idea of science.
The desire for a "firm foundation in the sciences"
has as a decisive part of its end a "practical philosophy" and is a desire for freedom from nature by making ourselves the "masters and possessors of nature."
In this respect it is not the least puzzling that
Descartes found the greatest freedom where he found the greatest necessity,
in an autonomous intellect.
What is this "nature" for Descartes that it demands such a science?
Nature and the Imperfection of Man
Nature for Descartes seems to be twofold.
On the one hand in its funda-
mental actions, the action of ' bodies, it is necessary.
This necessity
is primarily on the level of the elements of which it is composed (viz.
the wax - p. 155, end of paragraph) which elements correspond (somehow)
with the mathematical nature of our understanding.
On the other hand, the
necessity of nature seems to us to be bl"irld·, without ends that we can
comprehend other than the immediate effects of its continuing efficient
causality.
The imperfections of man mirror nature.
The example of the dropsical man
who desires .to drink is an example of both necessity, insofar as the
�52
desire
the necessary
drink is the result
of nature
and
act is
blindness, since the end of
In this view what accounts for man as a whole?
should the action of the
be
blindness of nature, from our extrinsic
Further, in this view,
ive of the whole?
of view, can
The
appear
to us as accident
for Descartes, the science of nature, which reveals its necess
the 1
t of our understand
appearance to us.
contains the
bless
its
Rather it frees us from our former illusions, and
of
of this life,
to which we are sub
, does not for that reason
a last
free
foundation for en
us from the accidents and
the
ions
�53
John Steadman, Tutor
of the characteristic
A
of
in 1. 2, can be stated:
Givan any
ordinate, as its other side is to the
and
exceeds
a
to the similar
with diameter AB, center C, and upr
there be a
with side DF.
On any ordinate DE make a
so that DF:DE :: AN:AU.
to P, where EP is
I say that
for let BU be
similar, and
the transverse
Ef
=
ide
Draw AN at the same
Then AN is the notr
t.
Join BN and ex-
AEPO and
to AN.
AP.
and extended to UJ, where
Elli is
to AU.
�:::
re ct
sq
=
=
are
same sides
icate ratio
since
Therefore
=
is
2
extend
show
�55
first, DE: DF comp. CA: AG, · tJ.Pr ight: transverse,
second, pllg AP
=.gnomon
AHJ.
The fi~s~ : foll6~s from the proportion DE:DF :: AU:AN,
since AU:AN comp. AU:AB, AB:AN, and since AB:AN :: AC:AG, therefore
DE: DF' comp. CA ·: AG, upright AU: transverse
.~.B.
The second is shaw·fi : in '4 'steps:
1.
Since pllg NP= pllg GH (by congruent triangles)
2.
pllg MP = pllg GQ.
But pllg .GQ = p.llg AL (since
3.
and pllg·AL
4.
therefore pllg JM =· ·pllg MP, and. gnomon AHJ
the~efore
G~bAG),
·..
= pllg JM (pllgs about dia.),
pllg AP.
Q.E.D.
Since all these steps are convertible, ·the generalization ' 'of I .12 is
proved from I.41 by writing this proof backwards.
�56
ANALOGY AND UNDERSTANDING
Robin Smith '68
Freshman Prize Essay
(Santa Fe)
[The quotations from the Republic in this paper
are mostly from Paul Shorey's translation. However, I have occasionally made slight alterations
to suit myself.]
Part I
Probably the most commonly used - and, indeed, the most effective means of explaining is the analogy.
Analogy, generally speaking, ex-
plains the unfamiliar and unknown by means of similar things which are
familiar and known and which have the same relationships among themselves as the unfamiliar things.
Unfortunately, this definition tells
us that analogy explains the unfamiliar and unknown in terms of familiar
and known things which are analogously related, for "in th·e same relationship11 may be considered synonymous with "analogously."
does analogy create any understanding of some matter?
How, then,
The answer to
this question seems to be contained in the Republic, in the three important comparisons of the sixth and seventh books:
the simile of the sun
and the good, the analogy of the divided line, and the allegory of the
cave.
The simile of the sun is introduced at 506E as an account of "what seems
to be the offspring of the good and most like it."
Socrates describes
the good in this indirect manner because he fears the insufficiency of
his powers for a direct description:
"
• • I fear that my powers may
fail and that in my eagerness I may cut a sorry figure and become a
laughing stock."
However, Socrates has just finished describing the
corruption of philosophic natures and how the philosopher is useless in fact, ridiculous - in existing society.
at ti,e extreme to which Socrates' comparison
such a hyperbole!" ( *'An.oAAOVi
Glaucon will later exclaim
~oes,
oaL~t5~~~~Afr£
).
0
Heaven help us,
What is to be made
of the laughability of Socrates and of the philosopher?
The answer to this question is not immediately forthcoming.
let us examine this simile which Socrates is offering.
However,
In setting it
�57
out, he first separ.ates .those things which are into two ·classes: ( 5078)
"W.e predicat.e· 'to be' of ma.ny·. beautiful ·.things and of many good things.
we speak of a good in itself and a beautiful in
and later, "
. ." .
itself •
There is here the replacemer.t of many (good) things by
'idea (of the g"b°od) • . nh:iteova·r' the idea we . caii ti.that which
'
· ·~ l'aal.ly is". · · \hd·: .the- one ,· t:1ass of .things," . Socrates 'continues,
1
'aria
11
.r: · ·=
saert
each
"can be
·but not thou·ght, while the ideas can be thought ·b'l.Jt' not seen . ..
thtfs/' 'we ' have thef division of what
· · and "thei. class
or'
i"k into
the class'
of
v'isible objects
i.d'eas, and we have·· the tacit ·assum.ptia·n that the ideas
~a.~e : 'the ~t:i're reei'l.
,· Tha setting
.~ar l.d,
ou~.now
becomes more
. ~pacific.·
to the ,world of sense perceptions.
It is to·rafer to the visible
Sacra tea· observes that sight
is uni_ ue among the · senses: ,in tha· it requires, in addi tfon t'o the organ
q
t
. of v·is:i1!ln and the · ob:ject ·seen, a · third element - light
op~rate.
Now, Sotrates ·lays dciwn the immediate
~
before it can
~p~cifications
for his
simi.(Le. · first, the ·sun is the source of ·light and therefore the cause
of ...vl$.:j.on.
Second~
neither vision itself nor the eye is the sun.
thi:;i> e.ye is the most 'sunlike of the organ·s ·of. sen's e.
Third,
And fourth, the
sun., . while it is not itsslf vision, · is, a·s · the. cat 1se of vision, beheld
by--
v..i,~Jon
by , ~ht;J
itself.
Here ·Socrates tells us that this was what· he meant
offspring of the good, which, as he says at
, ge.ne~~.ted ,. n .a proportion with itself:
i
soac,
"the good
as the· good is to reason and the
,objeqts. of reespn;· in the intelligible world, · so is the sun to vision
·. a~d .. .tti~ ·
objects. of. vision . in the visible world."
po.rctioQelity further:
He explains the pro-
when the eyes are "turned" on the objects of
the njght, rather than those of the day, they appear as if vision were
not;.. in.·:them.
day~
However, when the .eyes are "turned" on the objects · of the
vision appears_ to be . in the .same
eyes~
..
Thus~
the same eyes .will
appear to possess or not to possess vision as the . light of . the sun is
present or absent.
Likewise, when the soul is directed at that place
"where truth and'being shi'rie", it knows ' tlle objects 'there and appears
.
.
to ~bs~~ss reasori~ b~t·ili~eri it is t~r~~d fr~~ th~re to the place of
:<
"b~~omiri~ ~nd passin~ · a~~y«~ it appea~~ to 6a w{~hout reason. Now,
~ sodra~e~ draw~ th~~c~h6iu~iori he h~s b~en ~i~i~~ fori
hThen this,
which gives their truth to the objects of knowledge and the power of
"
�58
knowing to the knower, you must call the idea of good, and you must
think of it as being the cause of knowledge and of truth insofar as it
is known."
Here it seems to me that the analogy has come to its natural conclusion:
the sun is like the good in that the one makes objects in the visible
world visible, while the other makes objects in the intelligible world
knowable.
But Socrates has got his proportion, whether it is a true
one or not, and he is, at least for the moment, going to treat it like
one.
Accordingly, he goes on to say that, while it is not just to con-
ceive of either the truth or knowledge as being the good, but only like
the good, nevertheless they are the most like the good of any ideas just as the eye and light, though they are neither of them the sun, are
nevertheless most like the sun of things in the visible world.
reaction to this seems very significant to me:
Glaucon's
ttAn inconceivable beauty
you speak of, if it creates knowledge and truth but is itself more
beautiful than they.
for you surely cannot mean that it is pleasure .. "
Laucon indicates here that the conversation is leaving him somewhat in
the dark now; Socrates has left .the simply understandable bounds of
the "proportion".
In fact, rather than try to elucidate Glaucon's con-
fusion, Socrates continues to extend the comparison:
"The sun not only
gives the power of being seen to visible objects, but it also provides
for their generation.
Likewise, you are to say that the objects of
knowledge not only receive their being known from the good, but also
that their being and essence are provided to them by it, though the good
is not itself essence."
Glaucon is now utterly at a loss to see how
the discussion has arrived at such a statement as this, though it
started as a simple likening of the sun to the good.
Therefore, Glaucon
laughs; part of his laughter is surprise, but the explanation of the
rest will have to be reserved for later.
In the simile of the sun, it should be noted that, first, Socrates is
not really justified in carrying the proportion as far as he does;
second, that the entire analogy is constructed with reference to sensory phenomena.
context.
The significance of this will become clear in a later
�59
Part II
The discussion now turns back to the question of the n~ture . of t~e gobd
and its relation to the intelligible world.
The simile of the
suo~
whatever it may .have of immediacy and vividness, i$ limited in its extension:
it cannot be carried beyond a certain point without strain.
Therefore, Socrates tesorts to a mathematical object for his comparison,
and this time he constructs a genuine proportion.
The primary tonsidetation is identical to that of the previous consideration, the Worlds of the visible and the intelligible, ruled over by
the sun and the good •. However, this time Socrates chooses to represent
them by a line divided into unequal parts according to "the ratio of
their comparative clarity and obscurity." (5090} · He then divides each
section again in the s~me ratio as the sections themselv~s.
conside~s
Now, he
what the divisi6ns of the sections are to represent. . for
the two parts of the visibl~ sectio~, he suggest~ th~ interpretation
of shadows and reflections generally (images)
things of which they are · the images, as the
fa~
.one section, and .those
othe~~
Socrates asks
Glaucon if he agrees that "the division in respect of truth and falseness is that, as the
opihabl~
that of which it is the
is to the knowable, so is the likeness to
likenes~?"
Glaucon
ag~ees,
and thereby agrees
that the visible world is an image of the intelligible.
this .is a hypo~hesis to which Glaucon is .assenting,
has
pr~pared
In effect,
However, Socrates
for this hypothesis with his assertion that the sun is the
offspring of the good.
There is a s·imilarity of . relationship between
parent and offspring, model and copy, a thing and its likeness; and
Socrates asserts that the same relation holds between ideas and visible
objects, between being and bscoming.
It is the
p~rception
of this
sameness which . is the understanding of the truth in the analogy.
Next, it is necessary to turn to the section of .the line representing
the intelligible world.
On one part of this_ line. ,. we are to consider·
as images the things imitated in the for.mer part.
method is characteristic of this section:
The hypothetical
the sou+ pr?ceeds "from
hypotheses, not up to a· first principle, but down to a · conci~~sion. 0 ·
However, in the other part of this . s~ction, . the soul . 0 g~e~ · from the
· .
�60
hypotheses up to an unhypothetical beginning," and moves through the
realm of pure ideas, making no use of images.
This last statement - that the soul makes no use of images in tha last
part of the intelligible section - is ·particularly significant in terms
of the discussion leading up to this point, for the entire discussion
is a use of images.
In them, an imperfect understanding of the ideas
is helped by the perception of relationships like those among the ideas
also occurring among things in the visible world.
of analogy is evident here:
of the unfamiliar.
The essential nature
that it explains the familiar in terms
However, whether the perception of a same relation-
ship can be reduced to any simpler terms is as yet unanswered.
On the last section of the line, images are no longer employed, or, in
other words, the soul perceives that which is not an image of anything;
the unhypothetical idea of good.
Glaucon is understandably mystified
by this, and therefore Socrates turns again to the first part of the
intelligible section, to clarify the nature of it with an example.
Considering the study of geometry, Socrates points· out that geometers
postulate those things which they intend to use in their investigation
and then proceed from them consistently to conclusions, all the while
taking . the existence of those things postulated as being beyond question.
Further, he notes that geometers employ visible objects as illustrations
of the ideas they are talking about.
In other words, geometry exactly
fits the conditions of the objects on the first part of the intelligible
section :
it treats the visible objects as images of its own and procee ds
by the hypothetical method.
In this section, for some reason, the soul
is unable to rise above its hypotheses and move in the realm of pure
ideas, unaccompanied by images, up to the unhypothesized first principle.
The upper part, by contrast, is those things which "the reason itself
lays hold of by means of the power of dialectic, treating its assumptions
not as absolute beginnings but literally as hypotheses ( 1:'cD ov1:'
t
e,
uno s 0'1:' L ~
t
),
L
underpinnings, footings, and springboards so to speak, to
enable it to rise to that which requires no assumption and is the
starting point of all, and after attaining to that again taking hold of
the first dependencies from it, so to proceed downward to the conclusion,
making no use whatever of any object of sense but only of pure ideas
�61
moving ·on through id·s as to ideas and : epdi119 ·with. ids.as."
·,: ·.
...
Glaucon's re~ction to t~fS is much different from his reaction to ths
.. .
,·..
conclusion.of tb~ simi~e of the sun.
grasp
Rather than iaugh, he tri~s=to
. w.hat~ i .s .bej.n9 said, ~nd .i ndeed he returns a g~od ac.co'~~t of it
to Soc;-ates ., _ Thus, t~e anal.ogy of the divided : i'1n~ and" the ~eiati've ·
positions of . .the.. ar;::.tivities. of
r~ason, thinking, .bell.~f · , .. ~·nd imagining
on it_. compq~e . an analogy that is .much ciearer than the
••
;
•
.
•
:
.
'.
.
l
•
•
s"imi1e
of the
sun f.or: .two . .
. ,r.e.asons: . f ~rst. , because. the. ~bject now used to ·axplaih
:'.
,;,
'
the
good is an.. ideal obj~~:t' instead of .a physical one'; 'and s- c:cind:, : becai.is·e'
e
the propo.rt.l.or;t is u,sed only in its true sense.
•
.,
••
,
,
•'
Still, it' must be. bot·n:a
I
in mind that th~ . simile of the sun is responsible foi getting us whe~e
..:.
we a+e •. }hough
Plato . has .here .a
~eason
clea~
perience and thought.
is superior to
vi~ion,
vision is
prior· ~ ·
Vet
statement of the relation between sense exSense experiences .can only cau~e knowledge of·
...
;,·,
: ,. t " .
ideas in the way that a things' shadow can ~ause ~isi6n of th~ thin~
i
tsel.f ~ : · Sense experience _s i;hus ·the imitation . of knowl.e dge, and.., its
i
objects ' are· the imitations of knowable obj_epts; . but only knowledge and
i ta·- o'bJad·s ar~ real~
Part I II
be~
The simile of the sun gave us, at least in ·a way, the relationship
tween the ·-good arid the objects in the war ld of · being; ·the arialcig.y of the
··
· - -.
· ... l
'
div iqe.d line . explained the relatio.nsh"ip between the world of "baing . and
the world
·.·•
oi
becoming. · Now, Socr~tes ptepa~es 'tci ~ake the ascent ·from ,.
, .. ·.-· , _
1
.
the visibl~ world to the ..ideal world ~~nascent whi6h he will describ~ · :~
as
educat ·.i~n·~<~ ~ He begins
iii' 514A to 'construct ·'his allegory . .'. '-Compare
:
'
our nature in respect of education and the lack of it t6
as
~his.~' x
H•: presents .us
~ith
experience
men chained as prisoners in a cave where
-
sunligb~ . ~ey~r - ~nter~·~ ·
sue~ ~n
.
.
.
' :'"
......
.
:
..
.
(! · :
They are unable to move or turn their heads, and
.,
all .~8at ; .···t·.he.y-. .. . . ..$ .8 .9 is the shadows thrown on the wall of the cave by
can. _. ..·.
objects , held · befpr~~
there 8:11 ·their
fire.
men .fn such a situation, if they had beeri ·
liV~!3-' ~ould .i.m~gine
the ca_ to be the real world, and
ve
the sh~9:ow~.:. ~.nq . tha fire tq be .t rue objects and true light.
..
Wisdom, for ·
these, woulc;l ..:.b e the .ability to disce.~n. the shadowy shapes and to remember
their ,i;:ustomary
seq~ence .s.
�62
Socrates now begins to describe the ascent.
reaction "when one was freed from his
fetter~
What would be the prisoner's
and compelled to stand
up suddenly and turn his head around and walk and lift up his eyes to
. the light, and in doing all this felt pain and because of the dazzle
· and glitter of the light was unable to discern the objects whose shadows
he formerly saw, what would be his answer if someone told him that what
he had seen before was all a cheat and an illusion, but that now, being
nearer to reality and turned toward more real things, he saw more truly?"
The first step of the ascension is the turning of the prisoner's vision
away ;· from the shadows to those things of which they are the shadows,
and this step will be painful to him.
The description of this as a
«turning aroundN is important; the same language has been used many
times already by Socrates, for instance, to describe the turning of the
soul from contemplation of the world of becoming to the world of being.
Apparently, this turning
arc~nd
comes only through constraint.
The man in the cave would be pained by looking at the unfamiliar objects,
and he would be still more pained by looking at the light of the fire
directly.
Rather than stay and look at these things, he will turn again
and flee to the shadows he is familiar with, regarding them as more real
than these other things he has seen with such pain.
In short, he will
flee the unfamiliar objects and turn again to the familiar ones.
There
is a resemblance between this behavior and the "doglike" behavior which
is to be ingrained in the guardians in the ideal state:
the guardians
are to love and protect what is familiar, and to hate and destroy what
is unfamiliar.
Perhaps there is here a suggestion that this doglike
temperament will have to be utterly destroyed before the guardians can
become philosophers.
Whatever the case may be in this matter, Socrates next has his prisoner
dragged up into the light of the sun - an experience that would be most
painful of all for this prisoner, and which he would resist as much as
he could.
llihen he reached the outside, where the sunlight, the cause
of true vision, is abundant, his vision would be
~verwhelmed
and he
would be blinded by the light, unable to see any of what we call the
real things,
Then, gradually, his vision would become accustomed to the
light; at first, he would be able to look at shadows and
~eflections,
�63
then the actual physical objects, and finally the sun itself.
Ultimately,
he would understand that the sun is the cause of generation and growth
and nurture in the visible world.
But now, Socrates would have this man descend again into the cave.
Ob-
viously, he would not want to; he would have no desire at all for the
honors and merits he might gain among them disputing about shadows.
theleas,
, shou~d
Never-
he make the descent, he would find himself blinded by
the darkness and unable to discern the shadows he once considered real.
If he should be required to speak about the shadows while still in this
condition, he would appear ridicul6us to the men in the cave, and they
w6~ld
think that his vision had been
corrupt~d
(the verb used is
6 L acp8 € Cpw, which is also used in the charge against Sacra tes in the
Euthyphro and the Apology "corrupting the youth").
Furthermore, they
would kill anyone who attempted to lead them out of the cave, if they
were able.
Now, Socrates proposes to apply this allegory to "all that has been said. ••
He constructs the comparison as we might expect:
as the cave is to the
visible world, so is the visible world to the intelligible world.
How-
ever, this time Socrates is careful to put his allegory in its proper
perspective:
"But God knows whether i t is true."
He proceeds within
this more or less hypothetibal framework and attempts to reach up to the
good once more, this time with a firmer understanding of his method.
At once, he tells us that, "in the region of the known, the last thing
to be seen, and seen with difficulty, is the idea of good '. and that " this
'
(the idea of good) is indeed the cause of all things, of all that is
right and beautiful."
Exact'ly what is meant by this is clarified by
the last statement Socrates makes about the good:
"
anyone who
is to act wisely in public or in private rriust have caught sight of this."
Here is the real significance of the entire discussion about the idea
of the good:
without a vision of the ultimate human good - for clearly
that is what Socrates means by the good - there is no wisdom or even
significance of any intelligible sort in the world, as far as men are
concerned.
Just as the man in the cave would not want to descend again, once having
�64
lived in the light, so · the
who .has
philo~Opher
c~ntemplated
the good
and understood it as the · t~~e ' 6au~e of· everything of value will not want
0
to argue about the shadows of justice and virtue
ordinary
me~ •
are seen by
·~ : -.c
. The phil9sopher will appear ridiculous because of his
inability to opine a$
por~ant
:~hich
o~dinary
men do · about these shadows..
It is im-
to remember that visio~ ·is 6bscured in two ways: by coming from
light into darkness and by coming from darkness into light • . Therefore
.
.
.
'
thinking that the same thing happens to the soul, a sensible man will
not laught at a confused soul until he
ness is affecting it.
det~rmines
which sort of blind-
"And so he would deem the one happY t in its ex-
perience and . way of life, and pity the other; and if it pleased him to
laugh at it, his laughter would be
le~s l~ughable
than that at +the ex-
pense of the soul that had come do·w from the light above."
·n
Perhaps, then we now hav~ an sxplanation of Glaucon's laughter.
Soc-
rates has taken Glaucon and, after examing with him those things of the
visible
~orld .
in which he has confidence, rudely turned his soul ·.from
that world to the world of ideas, directly confronting him with the
idea of the good.
Glaucon is blinded by ·this - however dim his
perce~
tion .of ·it may be - and his perplexity only grows as Socrates persists
in expanding the . "proportion".
Socrat~s . is
Therefore ; ·he laughs both at the ideas
presenting him and at his · own inability to comprehend them.
He is shocked into laughter by the ~n~~miliarity of Socrates' statements
(for unfamiliarity is closely akin
time
h~
this
~ay~
io
ridiculousness), but at the same
strives to see more clearly the thing that is blinding him.
. ··.'
In
he . is also inclined to laugh . at himself •
'
.
;
·~
The allegory of the cave has thus combined the simile of the sun and the
an.alogy of the divided line, creating an im. ge of th.ese two images in
a
·, .
. .I'
ord.er .to explain to mdvament of the soul. be.tween the war lds of becoming
and being.
It
~eems
that the . allegory takes the two previous comparisons
as hypothese~ of ·a sett, and then develops .them, drawing conclusions
about the world· of becoming from ideal hypotheses.
The cave is, in a
sense' an image of the line' but. it is a dyna: ic image' par fray fog motion
m
along the line.
The allegory is not yet finished; it has yet to yield
its most important comparison.
�65
I
ies the
51RC, Socrates
education:
11
0ur
of the cave to the process of
argument indicates that the true
this indwell
of
t~e
for
soul and the instrument whereby each of
is that of an eye that could not be converted from the
us
t
darkness to the
organ
the whole
Even so this
must be turned around from the world of
gether with the entire soul
also the
But if this is
of the
toit is
education~
state in the
for the
of
that work is taken up with a discussion of the education of the guardians,
If this is the case, then there is a
the education of the
deal of difference between
ians and the true education, for the true edu-
cation seems to be a violent and
1 process
required to look at ob
the truth of his former beliefs
which
and whose truth and
one in which a
are painful to his unaccustomed soul
Let us consider for a moment what education is.
truest sense the
of virtue
Certainly, it is in its
The education outlined in the
allegory of the cave, however, is intended to direct the wisdom in a
soul ar
n, the true nature of virtue be that it is wisdom,
and conse
cannot be
t but
rates describes the other virtues as
directed aright?
11
akin to those of the body
is true that where they do not pre-exist,
by habit and
, a th
are afterwards created
ncy but, ac-
that never loses its
to the direction of its conversion, becomes useful and bene-
ficient, or, again, useless and harmful
be
The
virtue that tru
to the soul of a man is thus wisdom - a virtue which, str
aannot be
However, the process of education is the
this wisdom
with the entire soul, from the
of the world of
of
and shadows
to the ideas themselves in the world of be
Now, it is possible to answer the initial question of this paper:
an analogy can create understand
are
For it
Wisdom, on the other hand, is different:
of a more divine
cord
Indeed, Soc-
first, it
ap~ears
that a
in a certain sense, in that they trust the th
familiar with more than unfamiliar things.
From this, we immed
how
men
are
�66
can
iar -
process
se
around
sudden
dif
·au
The
im those
around in the
worlds
show us the sameness
are
�67
THE WHITENESS -Of TRUST
Veronica Soul '66
Now all is at a winter's end.
You call me briar rose
b~baLl~b'.
I'll come.
I bl6om -
Behind the unwashed glass of greenhouse panes·
And fear to tread the icy surfaced lake
-~hen : ~i~t~r~~ ~a~~ · h~s made its soiid stand.·
Don't think I never dance or run or walk
My way to this chill~d·: 6~unt~'~ edge of wave,
Nor stop at every ' dan~eli6n · gone
To seed.
Don't think I never l6bk on youths
Without the will to ~howe·r th.em with white
That isn It cold like sn~w
'or . lovers . gone • .
I stripped the spring of flowering weeds to stop
The fall of s· ads of trust' Upon my hair,
e
Until I watched a stone among the stones,
Milk gray and worn, half hidden by its peers.
Because that heavy gray can't come to me,
I'll seek it out along my walking ways.
Each barren day I'll rush to see it still
Until it's bruised away by rain and wind.
When you outdraw that stone
in ~ strength,
don't think
I'll never dance until our ways are one -Unless you will to dance a separate piece,
Deny each dandel iOf!'' gone to seed.
Then white on white confuses memory
When snow and seed mix seasons and love's blown.
�INVOCATION
James mensch
The viol
breaks foreward with its sweet song
into the quiet night air
with the breath of lts
it
it,
it moved on the stillness of the waters
as that first
lliho will answer it?
Will the powers so impregnated
birth
to a new creation in
recall
that first command;
is it that song of the maiden
for the false marriage of her sister;
so sweet her song,
the
takes it for a love's
Who will answer it?
67
�69
THE l 'I GHT THEN
James mensch '67
If I could reent~~ the womb of things,
if . I could breathe the air expanded
(the breath of angels) ·
and like a spirit disembodied
soar over the earth covered with snow
If I the secret~lacas of things could enter
the lighted windows, m~~ic lanterns, of.the houses below;
If I could op~n my mouth
so as to sw~liow the . moon
and sing (not breaking the curio~s stillness of the night but
becoming it)
and if my song cou)d enter . all the pl~ces .
of the snow like the moonlight arid linger o'er the drifts
and if I could become my song ••••
Or in late summer, be the wind after the rain
making of the leaves voices to sing
the whisperings of secrets
and be the cricket's comment
and be the fallen leaves painted
and the wind
blowing over the house tops and the chimneys
and the brick gardens with .the closed
yet exhalent sweetness of night flowers;
and laying the egg as in ' the ·· parting of the
breasts of chaos, .
nose about the damp, dark, and empty places,
and be the exhausted sleep of lover.s ,,
the empty fountains pricking· the pregnant qu'iet of night
which cascades onto the plains ': of joy all unbroken
while she weaves her embroidered cloth
of wheeling stars upon the wo~~ of darkness •.• •
�OlL t\U1QCDX 3Q
'lo
t..3n 53rin,1rin 5nd3x
'lo
'lot)
\tJc
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' , q 3 t.. ; j
1D.1,3'{'{D ,q
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5
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:
I
~dn3f\ nc23Xndg 1ni3gp'{g
f..
1on 1i 13 'f..osoi 3qoi
"
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I
3rtM.ond1 3 lL . ' 1 .o
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'
..
'
u
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u
3
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lL~ ',q 9
dMqn t..od.J...n t..ori1"831LD
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t\Udi3dncb 1DX 3.1, Sn.J...nd3.1,l[,
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f..OJ0.1, D.1,f..Od3cb Md0.03
t\3TI Socb3dri 1DX 'nsm3t\D
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f\Of\U\/3.0DX 3Q 1nnoX3dri
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n.ouriocb un
n13 Socb3dri
tl;
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·Snod131\0 S13~1X.o n3~ ininx
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•SnuXo •
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ilt.
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D.1,t\3TIDQ ~lLOX 1D.J.,D3X
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D.1,t\DlL D\/Ocb 3Q t\M1Lnd3n
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'noiMOCT t\U.1, nd13X D.1,DX
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uq~ soixdv
, {\.~ ,e3cbldi.o
1
t
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I
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(
),
IN
j
~noH
OIW 3Hl
�71
AT THE MID HOUR OF NIGHT
( Anacreontea)
.~
James liljenwall '68
Greek translation prize
(Santa Fe)
..
Once, in the middle of night,
when the Bear
was turned" 'round
near the : hand of Arcturus
and the races '. of. men
lay broken by toil,
Eros halted: at ·my door
rattling the bat. ·
,
.··.
HUJho is hammering·. on · my door;
who tears me from my dreams?"
·"Open up! . Don't be :afraid.·
I am a ch~ld, wandering
alone th~ough the moonless nigh~,
and · I am soaked."
Quickly I light~d a lamp,
taking· pity
at his .words.
Then ! ' opened wide the door,
and a .child:· it was!
wit~
and
wings, a quiver,
" bow.
a·
I sat him down near the fire,
warming hfs
artful hands, ·
drying his long-flowing hair,
until at last,
when the . chill h~d let go,
Eros spoke: .
'>
"Here, let's - give the bo~ a tiy
to see if it prevents my shot
with a string that is wet."
. ~-
But .he easily strung the bow
and shci't ·ma ·
in the · breas't ·: ·
I wa~ cert~in .he was mad!
But l~~ghi~~ he leaped up, saying:
.·;
.
"0 fr,iend . brighten up!
,
Tris " ~~rro.ws are ·harmless for us,
though you will suffer in your heart ~."
. ~ . /\ . ,·.. \... ~:.i ~:·. ~~-·-~: .~.-- ··:· .:.. .
:
..
.
.. ~ ..· ::.
'·
'...
)
.. ,. . .
- p ••• ...
·· '
.. .
.
'
�72
THE
so~
OF GOD AS WORD
John Wetlaufer '67
Honorable Mention
Sophomore Essay '65
Indeed, men cannot speak properly of such
matters. For who can unfold in cogent enough
fashion this statement, that, "the Word became flesh and dwelt among us,'' so that we
should then believe in "the only Son of' God
the Father Almighty, born of the Holy Spirit
and Mary the Virgin.
-- St. Augustine
Before trying to draw out the implications that lie within the opening
verses of The Gospel According to St. John, the endeavor of explication
of these passages must be defined.
So many integral problems are in-
volved with such discussion that the meanings implied in the passages
to be considered overlap with the premises upon which discussion is
based.
For instance, on some immediately apprehendable level the mystery
of the trinity, or rather the notion of unity and plurality of persons in
the Godhead, is present in those passages.
This in turn casts dubious
light on such things as the law of the excluded middle, for we find ourselves saying, "God is one and God is three," and, "God is the father
of the Son, and the Son of the Father, the Son and the Father being one .
ff
To what can the reason fasten when that law, which has been a veritable
rock in pr evious contexts, is shown to be a here t ical idol wi th fe e t of
crumbling clay?
The entangling vine of nonsense spreads its creepers
and grasps the human mind, befuddling and reducing it to perplexity.
However reason should not be forsaken but, instead, submitted.
be indulged in, for pride and curiosity,
th~
It cannot
1
motions of a dead soul, )
originate from indulgence.
But it must be passive, awaiting the perfection
of God ' s gratuitous light.
For the words in the first chapter of John
contain that from which articles of faith are derived, and articles of
faith, or principles, are not proved but are used to prove something
2
else. ) Moreover one does not seek to understand those passages to the
1) St. Augustine, The Confessions of St. Augustine, Bk. XIII, Ch. 21
2) St . Thomas Aquinas, Summa Theologica, Q. 1. a.8
�73
3
end of belief, .but believes them in order to understand. )
Therefore. we
must remember that Holy Writ .
is called higher because it leads to .higher things by
what are above reason, _
and moreover because
. it came.· down . from the · fath~r of - Lig~ts by inspi~ation. 4)
m~nife~ting
and that when ~ we tije ~6rd~ in de~cribing God
The supreme Being i,s .s o above and beyo.nd ·e·very · other ·
nature that whene.v er any statement is ma.de concering . ·
it in words which are also ·applicable to other natures,
the sense of these wo~ds in thi$ case is by no mea~s ·
that in whi~h th~y ire applied to other .natures.S)
How then. are we, to infe.r the truths· in the Word of God· and in the words
••
of Holy Script?
use cannot be taken. ~s they ate ..applied· to other n~t~~es.
stood by
.. ·
I'~
First we . must exp1ain why · the sense of the .words we
6
~t. Th~mas )
the words
literally and spiritually.
of ~·sacred
doctrine
ar~
As ~nd~r
each
to · b~ t~ken
In.the ' spiritual sense the signlficati~n
made is not o_ ly . that thing that the word names, 'but also that which the
n
thing named signif;ies. . (Spir:itual signification ·g ives rise to ·three
interpretiv~
senses; the allegorical, in which we are instructed in
belief, th~, moral in ·w hich we are instructed in chcfr ity, and the analogica~ _
whereby we. are taught what to hope for.) . Thus · it · is · seen that the ~ords
used are
mains a
sign~
and that which they point to· is not single.
questio~. a~
.:
But there re-
to -tha nature -of the · sign.
Again as St. Th~~as write.a , there is "nothing nece~. s.ary .. to faith con.:.
1
tained under the spiritual sense which is not elsewb.era · put forward ·:".
7
clearly by tha· ·" . i.:pture .i n its literal sense." )
scr
: ;
;·
f'Or it is written :'•_;
. ,.;_
'~
th~t believeth · on ·t he Son hath evei··lastirig lfre .and. ·
h~ tha~ b~lieveth not on the Son shall not: sea . life but
the w~ath rif God abideth in him.8)
He .
.
!
a, new
commandment I give unto you, , That ye love one
another;·as I have loved you, that ye _also 19ve one
an.othe~. 9)
:
·"
St. AnseJ.m,. Proslogium, Ch. · 1~ ... ~. :"i . :'
....:;
St. Bonaventure, On the Reduction of tha Arts . to Theology, pg. 5
St. Anselm·, Monologium, Ch. Lxv ··.. ·
St. Thomas · Aquinas,. Q. : ·h a.10
ibid
8) John 3:36
9) John 13:34
3)
4)
5)
6)
7)
. _c.
,
. ~ ·'
'
:
�74
(The first is taken as showing in what we are to believe and for what
we are to hope, while the second is the commandment unto charity.)
So
the signs that are spiritual seem not so much to tell us in what to
believe and hope, and how to behave.
Rather they are to clear the dark-
ness of the human intellect so that man might be a seer of the Light,
even though it be "through a glass darkly."
Therefore the signs, or,
symbols, are meant to point to, or manifest, what He is.
Now the reason
for being unable to apply the senses these words have in other natures
beside the Supreme nature is becoming more clear.
For the words whereby
man signifies things are images, in that they separate the form from the
thing signified.
Though the form is separable, the thing signified does
not exist apart from its form, but with its form in whatever it is
informed.
However the existing thing itself is a likeness, and this
likeness is made through or after the Divine exemplar, made materially
from nothing and existing entirely in the Creator.
In effect the being
of the thing signified is entirely in an Image, this Image being the
only properly called image.
It is derived, but same in essence, and
through it are all things derived.
Thus our representations, made with
analogies to created things, are at least three steps away from what is.
Or, stated another way, our metaphors are like an alternated proportion
that originally was between magnitudes not of the same kind.
However,
as Aquinas quoting Dionysius says, "it is more fitting that divine
truths should be expounded under the figure
of less noble than nobler
bodies 1°)This, in part; is the case because man is less apt to error,
11
being freed from notions of actual representations of Divine truths.
(Here Aquinas is speaking of the method, that is, the method of the
metaphor, and it is of this ,he is speaking when he says "less noble".
for instance, manifesting truths by metaphor, a poetic device, is less
noble than by a philosophic method.
In no way do we say that God should
be expressed by what is base or even in a method that is base.
Rather
we must proceed in humility, resisting the temptations of pride.
There remains another way of predicating something of God which has not · ·
been dealt with, namely a statement made substantially.
take the example of St. Thomas, "God is good."
10) St. Thomas Aquinas Q. 1. a. 9
11) St. Thomas Aquinas, Q. 13. a. 2
11
)
That is, i f we
By this. we do not
�75
mean that he is the cause of all goodness, nor do we mean it in a nega•
.
tive se'n se, that is·, "God is nbt non-good."
.
.
.
Instead it is an imperfebt
attempt of the created thing to. represent the perfection of _
that f°rom . ..
.
.
. ,
.
which a. 1, perfection · 'is derived.
1
.
..
\
.
So, though it is not properly in · ·
the form of a metaphor-, i t retains that same limited characteristic tha"t
all words applied. to . the Supreme nature possess.
be given the form of an analogy:
so is God . t .o the Good.
As the
cr~ated
In fact it could everi'' ·
world is to
goodnes~,
Alf.our symbols and f igut•es of speech are repre-
sentations of .incomprehensible relationships.
By this I mean they are
relationships that man is comprehended in but comprehends not .
Thes.
e
. ·=
.::
limitations made clear ·we have shown to what any endeavor of explication
of Holy Writ is re.str.~cted. '. .We are in a position:of discussing; discursively passin~ from principles to conclusibn;~ : ~b~ut ~ha~ which is
not discursive but manifest.
To what end, then, can such an endeavor
. ... ·.·.
: .r
be?
for what need has Holy Writ of feeble comment that is necessarily less
..
representative of
th~
Truth than it is?
It can have none.
it not the case that this endeavor is simply
th~t
should not be, a work of curibsity and pride?
Anselm, who wr.ites,
11
which we have said .it.
Should we not be like s~: ·
! do ·not endeavor, O Lord, to penetrate thy sub-
limity, for in no wise do I compare my understanding with
if we
scure.
heart
al~o
add what
Further, is
follow~ t~is
statement the purpose
th~t 11 ? 12 )-
be~omes ~ess
But
ob-
"But I long to understand in some degree thy truth, which my
believes arni ' 16ves."
This in turn is similar to St. Augustine
·when he writes, ·"Let me know Thee, O Lord, wh·o knowest me;
·. .
.
Thee as I am known."
13)
(When first
~orisidered
let me know
this may seem full pf
pr ids, .f or Augus't ine..: is known as he . is, and thus · he would appear to be ·
~sking
to know God a• He is.
But this, as will .be shown later, is
possible only t6 th~ · per~ons of the Godhead i and · can we ~ay that St. ·
Augustine hopes for the understanding .that. the Godhead possesses?
Though {i is
~r~tt~~ that we a~e all Gods 14 ) it is only in · so · much as
we are limbs in Christ.
Thus Augustine is asking to know God as He
is known to the mind of man made into Christ.
This is to say, "not fn
12) St. Anselm, Proslogium, Ch. 1
13) The Confessions of St. Augustine, Bk. X, Ch. 1
14) John 10:34 and Psalms 32:6
�"
76
a mirror," that is the mind of man, "darkly, 0 but in the mind of Christ,
his exemplar, and clearly.
St. Augustine asks not to comprehend God,
but to see His light in itself and thus become light.)
Thus the en-
deavor is not one of curiosity but one which is based on what is to be
hoped for.
further it is appropriate that Augustine's words should be in the CONfESSIONS, following his conversion but preceding his exposition of
Genesis I.
For when he speaks after conversion it is a confession of that
which he believes in ·and hopes foi, and it is done in order to
rouse up twoards You my own affections, and those of
other men who read this, so that all of us might say,
"the Lord is grsat, and exceedingly to be praised." 15)
and again
for, first of all, it was your will that I confess to
you, my Lord God, because you are good, and your mercy
endures forever.16)
In such descriptions and discussions man engages in an aspect of his
most important function, praising and giving glory to God.
By con-
fessing aloud the words of faith and hope that are in the heart, one's
hope is increased even more and one cherishes more that which one has
faith in.
If allowed to remain in the depths of the heart, the words
often become obscured and fallen away from, but by bringing them up
one is strengthened and refreshed, for in His words are "the spirit and
the life."
Secondly, by discussing the words one makes reason a par-
ticipant in the mysteries of belief, thereby making belief more secure
and immune to rational attacks from non-believers.
What has been ten-
tative and confused in the mind, though the mind has been certain in
commitment, is dispelled and peace of mind replaces it.
Lastly we are
led away from what is base and turned toward the Image of which our
mind is the Image.
That which was meant to be subjected to man is
again restored to its proper position and man is freed from the tyranny
of created things.
Now we are ready to consider the first chapter of John.
15) The Confessions, Bk. XI, Ch. 1
16) ibid
This we do in
�77
the same spirit as St.
, ~xcludih~· ~11
Aug~stine,
not stating an opinion as true and
-~~~writing . wi~h
bthers;
f~i~ity ~nus,
the feat of
to grasp a portion of the truths present.
.'
hoping
For "God has ·adapted the
sacred w~ it.ings~ ta···meny ' men rs <.interp~e.ta .tions; where" . w'u1 be seen
iri
11) . Fi~a·l_ly we _, .proceed k.no.wing " that "in· no
.. ~h· l.ngs . true and divers.a."
other subj~ct is error mor~ dangerous, or , inquiry meta lab~rio~~~ or
di~coyery_
·: trye
;\'.
of truth
m~r~ ·p~ofi.table •.018 )
· <
~ '.
II
,, In di.s-~us~ing the implications of the Sbn · as Word there are· three necessary considerations:
( 1) in respect to the Godhead or -uarid the Word
"(2) .in respect to the made things
and with a~ t him was not any th.i ng made
was with God and ..the Word was God,"
o~- r ;;·all .-t~ings were
that · w~s . ma~e~" (3)
mad·e by him
in respect to his taki.ng on . manhood or ''and the
..
'
.
19)
f
:
'
W
ord was .made flesh and dwelt among us."
But be ore these can be
discu~seo
. th~~e is a preliminary discussion; and . that is whether we are
to consider the Word as a ptoper name cif
~ · person
in the Godhead, ·6r
as a me t~phor. · (Person ;will be explained in the section deal fog with
.;
re la ~ions hip_ ~n .th.a Go·dhead ~)
For
s·t. ' Thomas, 20 ) Word is . a personal ·and proper name · for the Son.
This itself is curious for why should the Son have any other n~m~ ' proper
to Him l:)eside Son.
an
As ·is pointed out by Aquinas himself i t "signifies
of the . intellect" 21 ) and thus the notion of be·gotten is
.em.~nation
trans f_err _ d fro,m son,"
e
in which · i t is essentif:ll, . to the· no ti.on of word, .
with alJ its necessary ·tonhotations.
metaphorical.
This process in one sense is
Secondly it -is said "wor,d" may . be used metaphorically i f
22)
it "makes something manifest as · word.'' .
Now .this is exactly what .i s
done · i~ th~ "
first ·chapter of John •. That which is bein~ . made manif~st
is God, . and
t~at
'"
which is manifested is
essenti~l
to God.
For in the
first case the :t"rinily in unity a.nd uni.ty .. fn trinity- is . in:iplie~, in the.
seco~d . God as . creator ·:i.s implied, . and Jn t~e· thircf
.\
':
17) The ..,Confessions, Bk. -XU, Ch. 31
18) St. Au~u~~inei . On :£he Trinit~, Bk. I' Ch.
19) John, Ch. I; 1,3,14
20) St. Thomas Aquinas, Q. 34. a. 1 and 2
21) St. Thomas Aquinas, Q. 34. a. 2
22) St. Thomas Aquinas, Q. 34. a. 1
3
"God ·a s the . end _and
�78
life of man.
In each case a sense or meaning of the word "word" is used
as will be shown.
Furthermore it is written
No man hath seen God at any time:
the only begotten Son
which is in the bosom of the Father, he hath declared him.23)
Again the metaphor of "speech" is used, and through it all three relationships are implicit.
For "in the bosom" tells us the Son is not alone,
but in God, and thus the first consideration is present.
Secondly, by
being the exemplar, He hath declared the glory of God in creation.
The
last sense is clear, for since no man hath -..s---~en God, the son must take
on manhood that man may again be brought to love God.
However the "personu being talked about in each case is the Son and
thus, if Word is taken as personal and belonging to the Son alone, we
are justified in calling it a name.
That is, there are not three dis-
tinct persons being referred to, only the Son.
That which the Word
represents is the Son and could be called a name, with theaddition
that the name is not arbitrary but in some way representative of the
nature of the Son.
.By calling the Word a metaphor we do not exclude
its being a personal and proper name, and we leave open the possibility
of truths being revealed by it.
We move on to the first consideration,
that of the Word's oneness and otherness as God.
This aspect is so difficult and so incomprehensible that ultimately the
only affirmative statement that can be made about.•it is that it is a
mystery.
Yet in trying to discover what is true we may discover what
is not true, thereby freeing ourselves from the worship of a false God.
I
Before discussing what relationship the
to the Godhead we must
W~tj /has
consider what the notion of relationship means in a simple and Supreme
Nature.
For notions of relationship among created things are derived
from quantity or quality and thus the things related are either not
one or they are different in essence.
If
w~
look to Aquinas we find
that relation in the Godhead is predicated essentially, and each per0
son is distinct and incommunicable substance. "
23) John 1 :18
24) St. Thomas Aquinas , Q. 29 . a . 4 .
24
)
So that personally
�79
the Father is the Father of the Son but not the Son.
then?
How are they one
Al though the person is incommunicable, " the mode itself of in-
communicable existence 1125 ) is common to the three.
Thus, since "in
26
God what . he is and that whereby he is are the same,u ) relation is
predicated essentially.
However this . is little more than saying, "He
is, through Himself, three and one, essentially three and subsisting
as o~e, eternal and unchanging."
enigmatic.
The mystery remains inexplicable and
No matter what words we use in trying to express this truth
we arrive at the same end.
Thus we must ask through what they are
other but not alone.
Again we must rely on St. Thomas.
27
)
Person is primarily derived from
the notion of origin, though this of course cannot be taken temporally.
first the Father is "from no one" and this includes nothing.
For if
we were to say he was from nothing, or non-being, then at one time he
would have not been, whereas he always is.
Father, begotten not made.
But the Son is from the
If He was made then He would have been made
from nothing, and again would have not been at some time, whereas He
always is,
~a-eternal
with the Father.
Thirdly the procession from the
Father of the Son is the Holy Ghost, being from both the Father .and the
Son.
However we must again be careful, for these notions are noticeably
similar to those of Plotinus and other Platonists who, we are told, have
no knowledge of the Trinity.
For in the One overflowing and producing
an exact image of itself, different essences are postulated, though they
are postulated perhaps with equal degrees of being.
If we consider the person of the Son, it is extremely fitting that the
Word should be identified with Him.
It is fitting because the origin
described is one of conception, and the notion of conception lends itself well to speech.
When the mind looks out to what is, the formula-
tion in the mind of what is, is a wbrd.
Though this conception is in
time f or us , that is , there is a time when the conception is not formed,
for God it always is.
Again, for us the truths signified by words of
the mind are many and diverse, while for God they are one and simple,
Himself, hence the Word.
25) St. Thomas Aquinas, Q. 30. a. 4
26) St. Thomas Aquinas, Q. 29. a. 4
27) St. Thomas Aquinas, Q. 29. a. 3
�80
~~~ sec~rd
case
~oo, _
the
of the Word to the creation is easily
~elation
seen · !n, a meaning or sense of the word, word.
pr.~dicated
Sut since creator is
of ·God ess.entially, and not personally, it perhaps is impro-
per to: -speak of the rela_
tionship a person in God has to something
commqn to all persons.
However if one takes the pronoun_ in the third
vers~.as ref,~ring to the Word, w~ich ~eem~·justifiable with the verses
'
.
't
,. '
' .
'
I
·•
that follow, .and understands the preposition "dia" as through, instead
' •
·'•
'
of by,
I,,
',
'
'
•
'.~
' ."
.. .
', '
-~his d~fficult~ _
','
''
'
can be easily
entire Godhead, through the Son, the
things from nothing.
explain~d.
Wisdo~
'
For God, that
and the Truth,
i~
the
made-~11
Similarly when man employs the mechanical arts he
makes after· the image that is implant.ed in his mind, what is properly
c·alled the
word~ ·
For instance, when a man sets out to draw a circle,
he represents with a mark in or on some thing, that idea he has of a
circle, the idea being also signified by the word circle.
the word is exemplar, and all perfection of
the word.
That is,
t~e represe~~ation
lies in
In so much as the made things contain any perfection at all
they contain it in Him.
Thus the created world cries out to St. Augus-
tine, "I am not he, but he has made me. 1128 )
In passing, one further comment should be made concerning the relation
of the created world to the Word.
For the Wisdom through which God
created, comprehends, but is not comprehended by creation.
For it
"shineth in the Darkness and the darkness comprehended it not."
By
this we are to understand that world only partakes of the wisdom to
a small Elegree.
This is a radical change from the meaning "logos" has
had in pagan contexts, where logos not only implied word, but that which
made thought and speech possible.
It signified an order, or sense, to
the temporal world, which man was capable of apprehending.
Now however,
we are all, in effect, asked the question that was put to Job.
Where wast thou when I laid the foundations of the earth?
declare if thou hast understanding.29)
So that which is paradoxical and unharmonious is not only present, but
inescapable to man as he lives in the temporal world.
But just as
the paradox is necessary, so is the belief that things which cannot be
28) The Confessions of St. Augustine, Bk.· X~ Ch. 6
29) Job 38:4
...
�81
reconciled with the natural reason are perfectly harmonious in the highest
order.
It is right then that Abraham should ·be- the ·
father · ·of · fait~, :
for
:ih ~ts c~s~ ihe .intellect was not only made to assent· t~ . what was not
apparent, but to that which was apparently not p·o ssible.
That is,
~~
believed: ..that tie u,Jas : to be the father · of generations·~ · and also believed
that he :'·.would ~ay.e ., to sacrifice his only hope for th~t pos.ifion ., ' ts·~~c.
. .
Thus it is belief in Him a~ Word that frees one : frdm ' ~~t~rial c~nceptions
. " >•
I
.
.
of God, . and prep.ares one for the supernatural end ... The Word . ·considered
with respect to qr_-a. ed things we move· on to consider ·the final case~ -.
e t
So much has been· said concerning the Word made f l.esh .that anything · said
here cannot be a new understanding of what this means.
Also, since there .
is so much to say_. concerning it, it is ~lmost i~b6~sible to know w~e~e :
to begin discu,s13ir1g
it . ~
For in these words
God sb ~ loved : the ~6r1d · that He gav~ His only begotten
Son, that whosoever believeth on Him sho~id not peri~h
but have everlasting life.30)
lies the whole ~asfs of Christianity.
But we have cqnstrained ourselves
to explicating the metaphor "word" and what is thereby
~anifested,
and
, :
• • J.
·- thus can only deal with a very small portion of what is contained in those
words just quoted.
However, because the position of man in those words
is so important and related to our discussion of word, we must clarify
what it is that distinguishes man.
That which differentiates ·man from other
mediately clear.
a question as to
is the Trinity,
cre~tures
is, on one
He is created in the image . of G6d.
whet~er
le~el
im-
But there ramains
he is created in the image ·of the Godhead, that
in :the likeness of one of th·e :·persons, the Son. For
31
the Son is personally and properly called the Image of God. ) Either
o~ .
seems acceptable but since it is said, "let us make man in our image,
after our likeness 1132 ) and since it is through the Son that we have life
everlasting, the latter seems preferable.
the image of what we are.
for that in which we are, is
If we truly are, then that whereby we are and
what we are is the same, one mind with Christ.
30) John 3:16
31) St. Thomas Aquinas, Q. XXXV
32) Genesis 1 :26
Finally, by belief in
�82
His name we will become sons of God and this seems to confirm our be
made in the
of the Son
If this is.the case then the Word made flesh corre
to the
ith a
n word.
seven more close
For the word
n is, as sound,
less than the internal word, but it proceeds from that internal word and
with it
exists
If we compare the sound to
Word made
flesh, it in turn becomes a procession from the Word
Since Christ is
born not
Ghost,
of the Vir
, but also of the
is seems
a
, when the sound rouses up the same internal
that it
from, the hearer is
the hearer
ifed with the internal
the
tal
or
is
and man is born
In conclusion
faith is near
s talked about in terms of speak
to see
apparent
the whole of the
is seen that
This is
, the Word is
For what we believe
Since Faith in time, precedes
the most instructive of all
the Godhead, the created world and man s
with God, is all contained within that s
to
Its understand
and see
Word is not
non-
It is then most appropriate that the basis for faith and the
and char
I have
as
natural for faith is of the th
basis for speech be the same, the Word.
rslationsh
or
in the be
d
me
ls the darkness
be made 1
is the be
The
�83
·DE .BELLIS. CA[ LESTIBUS
(vel a~s Sacram Scti~tu~am leg~ndi)
Pheme Perkins '66
Suadendo nob is ne ,contra
supE~!'r iores
nostros
be~lum
geramus' reverend issimus
doctor m~ Luthe~ non modu~ ~u6toritata : Sacrae S~r~pt~rae in tpistola ad .
Romanos, et in Libra Proverb.iorum, ·et in Evar:igelio seci.:fridam· Matthaeum et
'
'·
i .:
... .
in multi~ ; ~liis ~ locis ~~itui; sed · etiam _
nobis quinqLl~ argu~enta · dat •.. At
mentionem argum.enti gra0is.s1mi ; non facit, id ·es·t ·,' a.rgumenttJm · de c~elestibus
bellis·.
Pr.imum bellum
ex '"omnibu$ '.erat
in , c;:aelo cum Satanas ·-a Deq def.ecit •.
Hoc bellum erat ~er ta men · inferior is contra sL:Jper ibrem suuni, -re apse · cert·~me~ .
.
.
.
- -. .
...
: •
creaturae contra ~~eator~~ ~u~m •. Sic contr~ · superiores ' ~ostros non .·.
~i en"m contr·a ·s.uper. iore·~ · p~·gne~: ' S.a.tanam imitatur.•
i
.Chr i.st ia~u·s Clir istum: lmit~~ i st4d~·a t ~- 'sa tanam non imi ta tui;
.
certare : docemur.
Itaque 9qm
.
~
.
'
et
..
ergo numquam bellum co.ntra su·µe·riores su.os gar it. ·
Eddem mode de : bello inter aequales et de bello superiorum contra
inferi6i~~
disseram.u s •. . De. ill~ Sanctus Ioannes .in Apocalypsi nob is die it archa~geium
.
'
"'
Michael.um in nomine Dei contra archangelum Luciferum suum aequalem iu~te, · '
..
. '
certav isse. De _
hac idem apostolus ·in eva~ge_ lio suo nob is die it C_ r is,t.ym
h
'
suum infe~ io.rem, Satanain v .i.cisse.
'
I
~
Ergo sect..indum Sa: eras Sct·iptu.ras Chr istiario be·llum in nomine Qe ~ contr·a
' .
inf::er iores . ae'qu.alesqUe · iuste .gerere licet sad bellu-D. contra super fores
f
non licet.
Nihilom:inus reverend.iss imum doctorem
·m. · Luth.erem rogandi sumus cur Dews -
~ermi~e~it ut ·bella ca~lestia e~seh£~
..
.
sed sat superque
�84
"THE
LF AND THE SHEPHERD
(Lecture delivered
Robert
7' 1966
Reviewed
Aurthur
of any serious discussion is a glimpse.
The be
68
Now the person who
may recognise it for what it is, a shadow of an ob-
catches this
ject or a truth, or he may take it to be the truth itself.
But either
way, he wishes, because he has pride and desire to express his idea, to
talk.
If he understands the glimpse to be a shadow, he will be humble,
and will talk for the sake of learning through examination.
If he be-
. lieves he possesses the truth itself he will bluster, for he wishes others
to admit his superior
nee and wisdom.
in intell
When one sees
blackness, however, when one catches not even a
, he will have no
reason to talk, for he is certain of his blackness.
everyone else is a s
else and
E
to
, and he has no reason to
a dream ..
Characters in Platonic d
then, all have gl
to express in one way or another.
prideful~
s which
wish
in
Socrates is humble,
But because he has pride, because he wishes
him and admire him, he, with his self-truth of the superior
to
, is accessible.
of
beneath his
and argues unfair
He talks
and unfairness lies
and truth, or, as he would say, for precision.
and
for someth
So des
love knowledge. 11
Plato's d
s, but a perversion ..
for both
This, I think, is the thesis of
This is no total privation of truth in the
the
, for art
his
notions he is, after all, a friend of Socrates,
he and
11
villainsu of
For some reason each wants to talk,
because each has a conflict within him whether he knows i t or not.
' conflict is one between desire for precision and
and greed.
ins with a very equivocal definition of justice, "the
good of the
II
He
explains to Socrates that he is
of the ruler, the one who has the power.
him that mere obeisance on the
but
When Socrates shows
of the ruled, which Thra
�85
calls justice _becau~e it corre~p6nds t6 the ruler's will~ can~ be unjust
if the ruler· makes · · ~· mi~take . and . wills w
·hat is ·harmful to himself,
·.
·:·
·: :. ·,
Thrasymachus b~gins to sa~ ~ha~ he think~. · He claims to , hav~ ; be~Q
11
in the precise· ·sense 1 " that is, -the comp,~ete . and
supe~ior
rular, whq does not simply wield indiscriminate
speaking of the ruler
intellectually
power.
And this ruler "i.n
th- ~
precise( sense" makes"_ no mis:f:.akes.
One
begins to see what Thrasymachus admires, a~~ ·and i~fellect~ ' ·Socrates,
however, brings him to a
co.~tradiction
by arguing that . :the
~r.tls. t,
in-
sofar as he is an artist, works to imp~ov~ not himself b~t his material.
The doctor cures, and the ruler works for the good of the. sta·t~-.
Thrasymachus is flatly contradicted.
"Justice is the good of the weaker,"-
i f the rule·r is an artist·~ . · I.t is ~- t th'ls point that ThJ,'a_ymachus finally
s
becomes completely honest.
The ruler, he says, is lik~ a shepherd, not
taking care of ·his · flock for their sake but for his own advantage, fattening
them up to be slaughte~ed·. _ The ruler takes advantage of :the ru.l ed, defrauding them, · taking their. money and subverting the_ir will : t ·o · his, while
all the time mainta·iglng '~ reputation for justice . and " f:airne~~!" -
The
ruler: is greedy; .h_ is not satisfied with control over his city alone.
e
Why should he be, if he is completely unjust? . The w
·hole world· is his'{
if he has the
\.,
~bi~ity to . ~ake ad~antage
of
it~
~
i
· Nothing : l~ss than the whole world ~ in f~ct is the goal
_ of injustice ~nd · even that limit is merely accidental.
Greed recognizes no bound because i .t .. is grounded in no
need · .and recogniz~s no standard of what is · f'Hting. ·It ; ·
is unlimited by natur~: it alway~ seeks to get more and
yet more. Since there ar~ natural limits to most good~ · .
• • •. greed fastens on money as its goa l.
Inj us t i ce.
is good then 6ecause 'it ~ays in a literal sanse - ~nd pays
more the more compl_ tely . and p_ rfect1Y. it is practised.*
e
e
And becaus~ irijustic~ is a d~sirable thing it is good and leads to happiness.
Justice - is merely the fear of _
this good, a de~i~e ~y - which ' men
too weak to · su6ceed· at acquisition · s~c~re protectiqn f~om ~fronger m~n.
men may" t~ink "in the . secret places of :their hearts .tha:t. .
injustice pay!p, and pays well, but they continue· 'to· " ·' ·
reserve their praise for justice, for unselfishness and
al'truiSm a·s we put i.t, the .conce;rn for another's good.
·• ~ . • This pra. se· .. is only a. .roask of ··fear~ ' • ·• Justice
i
is no virtue ·but ' the craven ..r .enun_Ciafi:on" of the ·hO-pe of
happirie~s • . '
.
··
·
·
, .. , _
* This and all subsequent quotations are taken from mr. Bart's lecture.
�86
He sees in the world
machus' position
This is
possibilities
He sees these also in conversation.
for violence and
He
uses violence ''beciuse he pays no heed to what has been said, and fraud
because he does not say what he thinks."
s sees (himself and Socrates) as
unfair
over (each other) and come out
on
the figure of the contest dominates his view of
the discussion. What is
place for him is not so
much a conversation but a competition in which
violence
and fraud he can d
his powers in the stru
for
v
Further:
He revels in his own superior
foundations for him not in
• • • Speech has its
ion but in know
A conversation is mere
a contest between two rivals.
• • • In such a debate it is not the truth that is at
stake, but the success or defeat of the challenger.
Knowledge is hidden riddl
ic declarations
like
These
ize
the secret or private character of knowledge.
And this question, whether conversation and behavior in general are atand agreement, or relative superiority and wealth,
to find
causes the discord
himself.
ithin
cawse weakness.
admits can
integr
that
many of conv
11
Internal discord
requires e her-
True stre
, oneness
Thra-
11
And his discord
and his love of or commitment
is caused
the conflict between his
to art.
very presence in the conversation shows that he believes
that
in
ice as he understands it can be
in precise
terms, that it can be expressed as a positive attitude based on art and
intellect, and that it can be justified.
of an art of injustice.
He is committed to the idea
And the reason that he eventually falls, that he
blushes, is that he and Socrates do after all have a common ground for
iscussion, the admission of the
and univer
of ar
precision.
It is through the notion of art that Socrates reaches
for the
conflict in Thrasymachus. They may
differ radically about justice and what is
but
they have a common understanding of art. Perhaps the
th
in that idea that divides them is whether
it can be an
of
ice. Thrasymachus' claims
�87
for his own detinition ~how that he considers . it
excellent because it bears the marks of art. Art
is ~ist{riguished . from h~bit and experience by
universality and ptecision. He ·stresses that his ·
accoU"nt is univere.aL .. .
But this precfa{oh which
tice, victory.
victory.
h~
sd admires is ·at odds with the end .of injus-
Ty~anny ~annot
agr~emerit
prodyce
6r pie6~sion but only
"Unjust spee·ch can produce · only victor- and defeat.!' .And
y
Thrasymachus I t~ctic~ ,· intimidation ' and lying' '' are unjust.
They ·give
'·
no account. . To : give an account he must speak , : reasonably~
And.'. he does
wish' out of 'both pride o.f intellect and d~~ire ' for knowledge.' to give
.
an account.
.
.
.
:·
i'
~ .·
.
"He is perhaps always in conflict with himself, . f_or it is
subve~ts _
inconsistent to ask agr,e.eme,nt_ with a theor,Y. that. in: .i ,t self
the basis of agreement.
all
It seems that it cannot be consistent to try
to jUS.t ify a theory Of .injustice e II
This contradiction points to .the. greater contradiction that Socrates
leads to,: c;tnd Which . r1n.a11y destroy,s , Thrasymachus:
tice is not art at all, but stupidity.
Firstly, it is not an art in that
it does not improve its subject matter.
subject matter,
~nd
his "art" . of injus-
And it is knowledge of -fhe
a~d · possibilities,
the subject's definite · limitations
'
/ '
'
that gives art uhiversality and purpose • . ·The mµsioian tunes the strings
that ~hey might . be harmonious: · -- the herm~ny is the liinit - a consonance
is limited in conception; it cannot be improved
end, because it is pleasing and in tune.
upon~
-
. ~nd
the desired
But for Thrasymachus "(injustice)
is a good for the · ~rtist, conc~ived in the ~tritt sen~~ a~ · pure and- u~
limited gi~ed.''
~Md . so secondly~ injus~i6~ '- can by its nature achieve nti .
perfection or univer~ality; ·but only r·elativ~=: : dvantage".
a
urhe man who
ruled the whole . 'war ld would still be as greedy -as th· . ;novice ln injustice:
e
both are insatiable and know no limit."
is never fulfilled, n,evsr completed.
In terms o'f greed the · "artist" .
He· keeps 13·et ting ·more· bGt" never ·
e nough • . In true art there is agreement, for ·art "r. s.i.des iri the definite: ·
e
limits it imposes
on
the randomness .of ignorance' ~ II 'The 'artist Will not
compete with another attist: ·the musician · ~ill not co~pet• with t~s
musician i~ t~ning ~tri~gs,· ~~d · th~ just m~~ will not compete with the
just_ man, for both reco~nize the _same limits.
.
They will cdm~e~e · with
the unjust man, just · as the musician wiil compete with th~ hon-musici~n ,
,.· .
�88
who does not recognize ths limits or goal of the material.
If the unjust man is intelligent he will act like an
intelligent man. Now intelligent men are artists,
that is they acknowledge common limits or bounds and
only contend with the ignorant. But the unjust man who
has claimed to be intelligent and an artist contends
as much with other unjust men as with just men, for he
recognizes no limit to his greed whatsoever. On the
· other hand, the just man acknowledges the welfare of
other just men as a limit he respects and does not
quarrel with them but agrees with them in the law and
makes common cause with them against the unjust man.
The consequence is manifest: the unjust man does not
act like an intelligent man. Therefore he cannot be
intelligent.
Art, or law, cannot exist with respect to lawlessness.
This last argument causes Thrasymachus' blush.
"The lack of limit in-
trinsic to injustice shows that it is not an art."
The shepherd is not
an artist insofar as his eventual aim is the slaughter of his sheep,
but insofar as he cares for them and keeps them healthy.
Harm to the
material cannot exist in art.
The refutation of Thrasymachus is complete. He is
undone by his desire to unite knowledge and injustice.
Knowledge is no less crucial to Thrasymachus than to
Socrates, and he is tamed by the discovery that he
cannot maintain successfully the position that injustice
is the supreme art of intelligence.
Thrasymachus blushes not because he has been led to a contradiction that has happened before, and he has responded to it with a fresh
attack - but because he realizes that he is being stupid.
For him
stupidity, the contrary of the intelligence which he esteems, is intolerable.
But one must remember that in order to blush one must have
blood in one's body, and it is this blood, this pride and desire for
truth or
"pre~ision,"
that makes it possible for him to be a friend to
and a conversant with a man like Soqrates.
Always lurking in the back-
ground is the man with no blood, the man who has not even caught a
glimpse of light, who recognizes no precision and no knowledge. who has
no greed and no desire,
The opposite of white or light is black or
darkness, not some other color, ugly as it might be.
Perhaps that man
is perfectly unjust, or perhaps one cannot even apply the term justice
�89
to him.
But Thrasymachus, one finds, is on the wrong track.
For where
there is greed mixed with pride there is also embarrassment, and the unjust man cannot be embarrassed.
My chief starting point _
fot this lecture was a desire
a little b~ttet the reason underlying
Socrates' injunction to Adeimantus: 1 b~~'t stir up a
quarrel between Thrasymachus and meJ now that we have
·- . become friends; not that we were enemies before.'
· ~o ~ understand
Any man,
as he ..~ay ·be, who · desires the truth, who, however he
par~er~e
may boa~t ~nd bully, d~sires sincere agreemert with hi~ · truth~ is not an
enemy,
~hd ~~y
very . well be · a friend.
1.,
.
::
.
.
'
' ,·
. J,- .
'
:• ' I
. · !.:
· ! · ·.
.
~
.,,
..
.·
�90
MIDSUMffiER NIGHT'S DREAM
Margaret Rottner
is one of Shakespeare's most terr
of the world.
The apparent irrational
suffer a bewilderment
unredeemed
66
visions
of nature causes humans to
The
98
about passionate love, elemental nature, dreams and poe
is
darkness is
common to those themes because at the critical moments all our
tions are bound to fail.
The
is to surrender ourselves to exper
If we were to do the
in
them in th
way to
them
again, this is one of the most
ion I would like to see:
Hermia are left alone on stage,
s
sander and
in the first scene, when
talk about the fate of love.
says that i t is
•
moms
as a sound,
Swift as shadow, short as any dream,
Brief as the lightning in the collied night,
That, in a
, unfolds both heaven and earth,
And ere a man hath power to say 'behold',
The jaws of darkness do devour it up:
So quick br
th
come to
ion 11
11
Then he asks Hermia to meet him at midnight in the woods to run away
with him, and she swears that she will:
good Lysander!
to thee
Cu
s
st bow
By his best arrow with the golden head,
the simplic
of Venus' doves,
that which knitteth souls and prospers loves 11
•
..
•
I
11
At this moment, in the middle of her vow, the diction suddenly changes
from blank verse to
scene.
l
couplets and remains so to the end of the
We have entered the dream world
At this moment the
of the court ought to have begun to fade to an amber glow, with
the two lovers left in a pool of brightness.
If there is no sur-
render to the dream, there is no entering this world which
lover, the madman and the poet" apprehend.
"the
�. ~.
[
,
.. :J
·· ·
,
•• ,
-, .~
:
I
, ,
91
'
..
Although .Theseus and Hippolyta h~0& ' f~w of th~ t~~it~ of thei~~mytho
1
logical namesakes, those · very . na~es ~ive a hint about the ri~ture of the
world t.hey live in.
It .is·. pervaded with the ma·iancholy . un'c ertainty of
the world ~f Greek :· myths, .. and .re.igned hy supernatui:al beings. ·with no mora
than . human . judgment but · far ,more t~an hum~n powers~
are close co.unterparts . of . Zeus .and· Hera:
Oberon a~d Titania ..
Titania,. ~ike Hera, may have
considerable . charms but · there's, not much_.e lse good to be said for her;
Oberon, like Zeus, is a wise king but not above quarreling with his
c~r~
;
sort · bVeI;' a little human boy.
-
are·
J
~xtTemely
like the Greek gods, Ob.er on and Titania
'
affai~s.
interested in meddling wtth . human
.
That
~nterest
is ~om~times purely s~ifish, b~t when Ob~r~~ s~ts ~bout to sol~e the
16~~r's p~oblems it seems t6 b~ geouine bene0olence. ·
Puck is interested cin'ly in sport and uses mortah. . fm;. the butt _ ·his·
of
~ .joka.s; . when we think
c;if him it .
se!3m~ particularly , ironic to iri~oke · .those
... .. . ·.,··
.
. gods. ,for the purpose. of making :·s ,ense out of a se.emingly sense.less war ld.
At· its worst we sea·m to .be dqj;ng no more· than giving names · t~ ·blinq .
·fo.r.c e.s , as in the science. of Psychology when ,the. question "why · does that
fellow act like a madmaA?." gets. the answer "because} he is · psychotic."
It
might not see.m to be -= different to ask "why did Lysander suddenly ·f'all
.
in _-love. with Hermia?" · nd be answered,
a
·in his eyes~ II
.
.
1
.-beoause Puc.k put the love-juice
But sometimes . our lives se·em to .be full . of t'hat kind of
• q~estion and a~~wer~_
Either the apparent disorder is a tru~ ~ one, or
else we are only pushing the . problem to a higher level.
'.
This is in fact .what the play suggests w~ do:
for ~lthough we may imagine
..· ·· Ourselves as being ruled by ' the spite~ the caprice; : the passions of these
-.s upernatural beings,. we concl.ude ..that not even they ·are all-powerful:
·they are under the swa·y'. of everi . greater forces of nature.
In the Iliad
, ~.eus takes out the fatal scales to read which . ..way the w
.ar is to go; and
• ·.:.: SO
in A midsummer Night's Dream there are fm;·c~ .s Which dictate . to Obe l;' on.
· Jn . the midst of the quatrel tiver the changelin9
Oberon of
monstfd~s . icp~sponsibility
the whole world for this discord; the
sincie
~?Y'
Titania accuses
the _ ~lements ar~ ~unishing
seasona ~ th~ms~lves
quarrel:
II
the Spr fog' the SLJminer
The chiding autumn, angry winter, change
reflect . the
�92
Their wonted liveries, and the mazed world,
By their increase, now knows not which is which~
And this same progeny of evil comes
From our debate, from our dissension:
We are their parents and original .. 11
This suggestion of powers above the gods makes the working of nature
If they are to be understood in any way it
more mysterious than ever
will be in experiencing them:
perhaps in dreams.
If they are to be
explained in any way, it will be in setting down the experience - in
poetry..
Nick Bottom is a wise er itic of the play:
"man is but an ass
who goes ·about to expound this dream", he says, and we can take that as
both a warning and an
We should not confine the dream to the central portion of the play, since
are already
the play begins with
under the general bewitchment
quarrel.
s never
Oberon and Titania's
about
Demetrius to
any reason for
is his will.
sander as a son-in-law, except that
there is no reason to
As a matter of fact,
Demetrius; Lysander is as rich, as well
born, and he is beloved of Hermia.
Also, he is constant, while Demetrius
is charged with hav
wooed Helena, making her "dote to Idolatry" on
him, and then
her for love of Hermia.
have his dau
beloved.
the law than go against his will to marry her
This is strange behavior.
it happens every
It is nevertheless believable, since
A domineer
who insista that his love-
marry to suit her
over my dead
out of love with one
young man
another; a
Yet Egeus would rather
in love, seeing as her
marriage death or eternal
! II
;
8
1 and in love with
alternatives to a hateful
these strange things
happen to us, and how are we to explain this everyday madness?
Theseus is the ruler of a civilized socie
enact the law of Athens, since five unhappy people are ev
to find no solution to their problem outside of that law.
least to maintain political order
extravagant.
to
He has no choice
enforcing the law.
going
He has at
Oberon is more
He tries to bring about inward order and blessedness..
even his aid miscarries, for
a
But
sequence of blunders Lysander
�93
as well as Demetrius is mad.a· to fall in love with · He·lena·.
'Oberon · cannot
bring about any a~der until Titania amd .. himself .are i~co~cii~d ~nd · ~haotic
nature is restor~d tp harmony •. ,Bo~tom turn~ · out to be ·the solution :to
·,
all problems, and'; ' plays an even bigger . part than he eve,r dre.amed of. ; for
.
Titania is charmed ·into· so much lava for · hirn that she willingly · yields
up the changeling boy to Oberon, and once the fi~~l re~onciliatio~ ~f
their quarrel is acc·omplishad, -the .·fairy :magic finally
as it was meant ' to.
p~irs
th.a .lover .
s
Now, ·since they .. are. a.-t peace, at .. leas. t among them.
selves, Thes! u s ·overbears Egeus·1 wi,11,;
e.
.
.•
'
, ·.
to bind the ' couples in law, as Oberon usad his to bind them in
.
Theseus is
~he
·•
i· ,
•
.and uses his, kin.g ly .au.thority
lov~.
.
most sensible of all the humari beings in the 'play'; he ·
.
.
.
'
.
! '
'
doesn't believ~ a war~ of the strange things that the lovet~ tell him~
since he was safe and sane in t~~ brightly-Ii~ court whiie ~he lovers
were forced by their passions .· into th. heart of the dark forest. . "The
a
lovers, madmen· and· the poets," he says, . ~'are of imagination all compact 0
and to Theseus
imagin~tion
is the disease . of seeing
~hat
is
;
there.
~~t
Imaginatioh, · he says~· '.'apprehends/Mor.€3 than co. l reason aver comprehends",
a
and he means that ,if cool reason:_isn't able . to ..comprehe.nd it, it probably
does.n' t exist.
But those .wo-rd.s could mean ju.st the opposHe:
imagination· has powers· beyond
reason. ~
s; or·, .that
to experience and embrace more than reasrin ever
ima~ .ination
h~lps
th~t
allows us
.us to understand.
The mechanicals are sensible men too; they are neither lovers, madmen
nor poets ·and live very . close to the · war ld of thirigs, for they . a~e
weavers,"
carpenters~
tinkers, . tailors al)d.
bellow~~msnders.
They a re -
used to feeling that they subdue· na t.ure arid the elements to men's use.
1
They are also co~~unicative · ~en;
th~.y.
· manage . to talk to one another,
.
ask questions a·nd get ans111ers, better thf;ln the lovers do because t.hey
are extremely literal-minded.
Bottom may . be a prize ass, but he has
been thrust so completely into .the .dream of enchantment that when he
awakes he is almost a prophet:
"I have had a most rare vision. I have had a dream,
past the wit of man to say what dream it was: man is
but an ass, if he go about to expound his dream. Methought I was - there is no man can tell what. Methought I was - and me - thought I had, - but man is
but a patched fool, if he will offer to say what methought I had. The eye of man hath not heard, the
�94
ear of man hath not seen, man's hand is not able to
taste, his tongue to conceive, nor his heart to report, what my dre~m was. I will get Peter Quince to
write a ballad of this dream: it shall be called
Bottom's Dream, because it hath no bottom; and I will
sing it in the latter end of a play, before the Duke:
peradventure, to make it the more gracious, I shall
sing it at her death."
He cannot explain his dream, he begins and he stops.
He knows that it
is beyond explanation - "The eye of man hath not heard" is a distant
echo of Revelations.
"I will get Peter Quince to write a ballad of
this dream," is a stroke of genius, because a ballad will not explain
but portray in images and figures the experience itself.
And though
the images of a dream come from a deeply personal world, poetry can
move men to see another's personal images as their own.
The mechanicals bring a play to the court, the myth of Pyramus and
Thisbe; but they are not the men to let poetry speak for itself.
They
explain as they play, and they so much fear that the audience will
be upset by the
terro~
of it all that they honestly unmask their art
and assure the ladies that none of it is the least bit real.
may suffer, but there is still plenty to be learned.
The poetry
The lovers seem
to miss all of it, evidently not suffering a blush for the striking
resemblances between themselves in their own carrying-on in the woods
and the words of the mechanicals' star-crossed lovers.
Theseus tends to humor people less sensible than himself, wanting to
judge them only by their good intentions.
He probably smiles teasingly
at the lovers when he says, "To bed, 'tis almost fairy time."
But this
is the play's final gentle insistence that, deny it as you will, the
inner world of unknown causes does exist.
Once the court leaves the
stage, the lights are dimmed and the fairies appear by the dark and
drowsy fire:
dangerous and unknowable, but capable of blessing.
�95
I
.',
· .APOLLINAlRE:Js tE PONT n1IRAl:3EAU
1•.
Initially, upon
read~n_g
unity in the poem:
.
'\
.
•.
••
· oavid E. Long '66
.
felt a . lack of ·
Apollinaire's .le Pont fi1irabaau, .I
wha~ was . the. ·p·o et sa·ying?
Was ApoHinair_ . writing ·::.'.>'
e
about _ bridge, or the Sai11e, ,_,:i or :his own past ibve, or ~bout something . : ~ ,,
a
. ' .-·
altogE!the~ . . dif. .erent7
'
After . a first . reading it _ eemed
s
were the theme of our poet,
.
.
a~ ;thou·gh · he :·'wer·~· .st~nd~ng
'
~s
though · 1ove .
u.pon his .former .. ·
.
.
trysting p_act;i,. sadly r~membe-ring. his 1'6st . lover, and wat~h-ing t.he ·
l
Seine
f1ow···by. :
. In the first starua the·· authbr asks rather rhetorically ·
.
'
if his
pas~
loves could ever return to. him. ; In the second he recolle·c't.s
some of the' actual
belov~d.
But
mom~nts
som~t~in~
spent on le pant · Mirabeau .in the arms Gf :his
has happened to
deserted him for some reason.
But, for
t~is iove~ ~
~hatever
his lover died, or
reason, he is alone
no·w, for in the third stanza he comes·· to some general conclusions abou·t
his life and love:
love . fldWs awa~ lik~ the . ~unning ~aters .of the. Sein~.
:He seems to imply that whe·n · there is · no love, but ..~nly . hopes of ·love,
~
life itself becomes teoious, empty." ·· Finally, in the last ve·rse,
A o1.:.. ·..:
·
p
.. ... :
1
lina'ire answers ·. his opa.-ning question:... no, past, loves, like las temps
perdus, never return. i
~
.Superficially., this seems to be the
reading is complicated by the two
0
·story
lin~
0
of the poem.
.
However,. the
refrain:
Vfenne la nuit, sonne l'he~;~,
.· Les j.ours l? ' . en yont ~ . je dems_ re.
u
This app~ars aft~r ever.y stanza,- four ti··~es in all.
: It .i s as·' though the
author is indicating _to us here what the real point of h.;i.s poem may · be'·
as though he felt he should remind us after each
ve~$8
of what he means
us to understand by what he has just said.. . :.
.
;;
'.t ; .
What does the refrain te·11 . us?· The first . three imagE3l? ere pf ·some sort
of' motion': ·
nig~t
comes, the hour sounds., days .9.£• · Yet
.~he ·
author
' ·. ~·~.
remains; he does not move; he alone among . the shifting ·_ phantoms of time
remains static.
But what can this mean - je · demaure?
sense does he remain anywhere?
Where and in what
~
The threprpreceeding images are about.
> ••
• •
•
•
•
~
some sort of motion, ~fr1d especially about ~ . the · motions of · those phenofr1ena
�96
by which we regulate time.
The author seems to imply that his remaining
is with reference to time.
Time flows on, but he remains, somehow
unchanging among the continuous variations of nights, days, hours, weeks .
The question I find most difficult to ·answer is this:
concern of the poem with love or with time?
is the essential
That is, is the theme
essentially emotional, i.e., about love; or metaphysical, i.e., about
time and its relation to man?
I believe the poem is highly metaphysical.
The poet is expressing something about the nature of time.
is the poem in microcosm.
The refrain
Throughout we are confronted with various
descriptions of motion and with metaphors implying motion:
water flowing,
days passing, the tired wave, slow life, violent hope.
depicts love merely as another form of motion.
Apollinaire
It comes, persists awhile,
then goes away never to return.
Time is the measure of all these motion.s
Time measures the days, the
weeks, and with them the ebbing of love and the consequent monotony of
life.
The "eternals reqards" of the second verse is an ironic or even a
bitter reference to the feelings of the lovers on the bridge.
Looks of
love are perhaps the most fleeting of all transient occurrences, but
while they exist time stands still for those exchanging them.
Our poet
has at one time known these glances; he too has existed , for a time, i n
that timeless, motionless world of the lover.
paradox?
Perhaps, but so is love.
perfect to pass away?
In time, yet timeless - a
How is it possible for that which is
But the lover has not lived who would ·,have admitted
of the sli ghtes t f law in his perfect love .
Swa nn felt t hi s way towards
Odette; similarly Marcel, towards Gilberte.
But somehow, at the last,
when the motion (or
ennui.
~motion)
has run its course, there remains only -
Comma la vis est lente.
The passing of time may be likened to the flow of a great river; in this
case, the Seine.
Just as all the cr eeks a nd r ivulets arising from the
surrounding countryside merge and become one with the great river, so do
all the motions of hours and days, life and love, give themselves to
swell the Ultimate River, Time.
But wh~t is it that measures time?
Apollinaire has drawn t~e analogs
b~f~~~~ the flowings of time and of the Seine:
both eternally stream
�97
towards us, past us, away from us; eternally fluctuating, always different,
yet in some sense always the same.
With reference to the Seine (for the
purposes of the poem) le pant Mirabeau is the one fixed point, that to
which and from which the river is always flowing, although no part of
the river ever stays or fixes itself at the moment it passes the bridge.
The river is never "at" the bridge.
During every instant the water is
flowing ta the bridge, or from it, but there is never a time at which
the river may be said to be "at the bridge".
The mirabeau Bridge is
the focal point of the poem, not the Seine.
That the author intended
it so is even borne out by the title:
not after the river.
the poem is named after the bridge,
And the measure of time itself?
only by the human mind.
Time is measured
It is purely a subjective phenomenon.
As Saint
Augustine so beautifully demonstrates:
"It is in my own mind, then, that I measure time.
I
must not allow my mind to insist that time is something
objective • • • I say that I measure time in my mind.
For everything which happens leaves an impression on
it, and this impression remains after the thing itself
has ceased to be. 11 1)
We sea, then, that amidst the flux of time the only fixed point, as it
were, must be the author himself, his mind and memories.
Apollinaire
himself is the measure of time and thus in turn of the ever-changing
movement of the universe.
As the Mirabeau Bridge measures the Seine,
so does Apollinaire measure time.
the poet means by "je demaure".
It is now more clear, I hope, what
He has identified himself with the
bridge, as an unchanging point of reference.
He is, like the br i dge ,
"an ever-fixed mark" watching all things go by, never to return.
1) Confessions XI, 27
�
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The Collegian
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The Collegian, January-February 1966
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Santa Fe, NM
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Text
THE MUSIC OF .THE REPUBLIC
by
Eva ·Brann
ST. JOHN'S COLLEGIAN
Supplement
March 1966
�-1-
This study came about 1n the pursuit of ouestions raised
in a reading group formed by the Misses s. Manire, s. Rutzky,
D. Schwartz 2nd myself. A shortened version was given as a
Friday night lecture on March 18, 1966 at St. John!s College
in Annapolis.
THE COLLEGI"N
of St. John: 1 s College
and
Santa Fe, New Mexico
Susan Roberts •.....•......•...•.•••.•.•..••.. Editor
Sall R z
Y ut ky •••••••••• A.ssoc1ate Editor ·in Annapolis
Deborah Schwartz. • • • • •
ft
•
•
"
Vida Kazemi •••••••••••• Assoc 1 a t e E di tar in Santa Fe
~
P--aul Ollswang
~
·
····························~rt Editor
E va Brann
F
aculty Advisor
0
•
•
•
•
•
•. •
•
•
•
•
•
••
0
I.
A.
Mythos
Page
The Republic is composed of concentric rings encompassing a center.
1
• • • • • • • • • • -.
B.
SUPPLEPIENT
Jllarch 1966
The outer ring represents Socrates' descent into
the house of Pluto-Cephalus.
1. The oath •By the Dog"' is an appeal to Hermes
the Conductor of Souls.
2. Socrates assumes the role of Heracles, founder
of cities.
J. His longest labor is the bringing up of the
triple monster Cerberus - the soul.
4. His greatest labor is the release of a new
'Theseus.
II.
A.
2
3
4
4
Logos
The second ring represents the founding and degeneration of cities ttin speech" (Books III,IV . and VIII,
IX).
1.
2.
Four cities are founded: the city of demiurges
or craftsmen, of warriors, of guardians, and of
philosophers.
To these correspond four degenerate forms.
5
B.
These cities are "in speech" only, since they can be
neither generated or regenerated.
1. The Phoenician tale implies that men can be mined
as a public treasure.
6
2. The just city founders on the un-naturalness of
human nature and on the "f <mndlng paradox".
7
.3. The degenerate cities themselves are actual, but
the are;ument about them ls "detached~..
9
C.
In Polemarchus' house justice, defined as "doing
one's own business", is the craftsmen's specific
virtue.
···,, 8Ll.\0 ~E\~JL8l\€ 6LJ
···absque ph1losoph1a
O©Ob 116 ~Bn J L BLr&L -1 @6e o oc4~
c1v1tatem philosophicam express!
ebCD~O GL0 6 ~Gd@L l\G<lJ.
mortalibus!'
�-111-
-11-
Page
Page
1.
2.
J.
The "demiurge" is opposed to the 'panurge" in
all his forms.
The inner justice of the philosopher converts
the definition into 9 ki1.owing one's own soul~.
For the philosopher the argument that justice
is profitable fails.
III.
A.
B.
c.
D.
9
11
11
Ergon
In the center of the R.epublic Socrates founds the
philosopher's city •1n deed" (Books V-VII).
1. A. public vote forces Socrates to propose his
communal design~
·
2. Other works corroborate that the philosopher
city is not the· guardian city.
J. Socrates' city in the Timaeus is not that of
the Republic
3.
12
4.
13
14
B.
The paradoxical condition for bringing about the
city is that its founder must already live within
it.
1. Socrates· lives so as to fulfill this cond1 tion. 14
2. Glaucon has the qualifications of a young
ruler.
15
3. The bodily community of the guardian city is
replaced by a d1~log1c ~omrnunity.
16
Democracy, the exact inverse of the just city,
perversely proves to be the soil for the just
city.
The just city can be bro~ght to life by providing
a fl tting macrocosm, -as in the Tim_?-eus.
1. Temperance replaces justice 1n this city.
2. Antiquity in the Timaeus represents s~urious
actuality.
IV.
A.
2.
Glaucon's education in Books V-VII is Socratic
music.
1. The guardians' training is by purged traditional music (Books II and X).
a. Socrates corrects the myths of gods and
Hades but postpones the correction of
the myths of man.
b. The Republic itself exactly obeys the
stylistic requirements of •purged music•.
c. This music is explicitly excluded from
the plan of the philosophers' education.
19
C.
D.
21
21
22
22
22
22
23
23
23
24
25
26
11
18
20
The discovery of op1n1on . (doxa) is Glaucon's introduction to philosophy.
.
1. The outer dialogue requires the "helmet of HadAa•
which excludes •good opinion• (Books I I and X1~
but the central conversation ls governed by •true
opinion.•
2. Siimmary of. 474-480 (Book V). As becom1ng''1s between being and non-being, so •opinion• 1s between 1€e?tOre..n ce and knowing.
3. "Opinion corresponds to "sp1r1 t •, tr.a mean between "reasoning"(logistiko~) , and "desire• in
the tripartite soul. ·
4. The log1st1kon, properly called the •calculating power•, ls a lesser faculty than •mowing".
5. After the new division of the soul as· an •1nstrument of learning• the terms of the "lower"
tripartite soul designate· desires.
6. The finer division of the soul by finding ~the
middle• ls the dialogue's main pre-dialectical
exercise.
1
17
Music
Socrates' music is •philosophical music•.
a. Socrates has spent his life making music.
b. Socratic mimeses of truth are images rather
than myths.
c. Such images are sketched in the soul by
long reflection.
d. Socratic images induce a logos while myths
are nreceded by one.
e. Socrates fulfills his own requirement that
all poets make an •tmage of the Good".
f.
Socrates corrects the Promethean Myth of
Man in the Cave Image.
His plan for the philosophical education is
presented musically as the •prelud·e • of mathematics and the ~hymn• of . dialectic.
The central dialogue is a symmetric texture of
images and their explications and correlations.
26
27
28
29
The orator Socrates is elected to defend philosophy
before the democracy (487-505~ Book VI).
·
1. Adeimantus is the expert on corruption.
2.
Socrates by his images persuades the many to
accept philosophers as kings.
3. He refuses A.deimantus access to the "highest
study•, the Good.
Jl
Socrates tells Glaucon of the Good in a •true image',
the "s'm image".
1. Summary and tables of 506-511 (Book VI). The sun
image is explicated by the Divided Line.
32
29
JO
�-iv-
2.
3.
The image requires Glaucon to exercise .the two
lower, •doxast1c• powers of the soul
a. The lower of these\ likeness-making and recogn1Z1ng (eikasia~ known to Glaucon as a
game, is Socrates' chief instrument in
this context. The image itself forces
Glaucon to recognize the visible world as
a mere-image.
b. His trust (pistls) in the visible world
is· shaken and a belief in. tne rule of the
' Good is substituted.
c. Socrates' non-dialectical or •doxast1c"
presentation of the-Good serves to avoid
misunderstanding and to instill a kind of
artificial recollection in Glaucon.
The Divided Line, a figure for knowledge, pro. vides training for Giaucon's power of •thinking ".
4.
!, • ' • -
•" ':
1 ---- :i
-v-
P_age
5.
J4
35
35
7
a. • Dianoia-,- - -thinking things through•, involves a htgher eikasia in two ways:
natural -objects are here regarded as image~ and also analogies are to be made by
recognizing likenesses.
b.- The mathematical faculty characteristic of
Glaucon, diano1a, is discovered by him as
a ''mean'!
c. Socrates particularly invites Glaucon to e
dialogue on number; · this passage is the only
approach to dialectic ih the Republic.
d. D1alegestha1 has - three meanings: conversation among the many, - dialo~e between a
knower and a learner, and ialectlc, the
movement of the soul within 1 ts elf '
The mathematical model of proportion (~nalogia)
is fully exploited.
a. The Good ls not really a •study•.
b. The absence of dialectical accounts (logo!)
of being is expressed by the absence of
defin1 te ratios (logo!_ between the line
)
sections.
c. Socrates forms four propo- t1ons ' from the
r
_ Divided Line, showing Glau con how sameness of relation runs through the .whole
before he knows the parts themselves.
d. This induces him to trust the bond of similar! ty (homoi.otes) required for _dianoetic
ascent, which is by likenesses.
e. The Good, by exercising a downward e1kas1a
and likening things to itself, makes this
ascent possible.
f. The mimetic arts are condemned for usurping
the power of the Good (Book X).
36
1?
_
37
38
39
40
41
42
43
43
E.
Page
The image of the Good 1mpl1c1tly introduces
Glaucon to the fundamental problems of dialectic.
a. The Good has three capacities: as progenitor
it fathers the sun; it is the responsible
cause (ait1a) of knowing; it is the ruling
source (arche)of being. These are presented
in reverse order of "poll ticat' importance:
43
b. A diagram shows how being is articulated in
doubles by the Good, and particularly why
becoming is doubly apprehended, in sense nerCe.Jltion and opinion.
44
c. The Good ls not really a differentiating but
a binding source complimented, as the image
implies, by a secondary •dye.die• sour·c e.
45
d. "Likeness", which fails to account for ~parti
cipation !t w1 thin the real"1 of being, takes the
place of ~otherness• beyond being. It is that
•bond," by which the whole becomes onf? which the
three-term proportion of the Divided Line expresses.
46
e. In the dialectic progress from •what each _ts•
to •1what the Good ls• the latter is revealed as
•the whole•, and thus as the pattern of all
political community.
47
f. The Myth of Er contains the mythical counterpart of the sun image - a model of the world
within the world.
48
Socrates tells Glaucon of evil in a second •true imagen,
the •cave image".
1. Summary and table of 514-517 (Book VII). - '!'he cave
is to the upper world as the place of v1s1b111ty ls
_
to the place of thought.
48
2. While 1n the sun image the places prepared by the
Good for the soul are shown, the cave image shows
the actual dwelling of men; thus the oave image
explicitly includes ignorance and even deceit.
Igiiorance, however, corresponds to non-being.
50
J~
Therefore a different correlation o.f the images
is implicit:
_sun image '
_
cave image
being~ intellectual realm
·
becoming: sensible realm - - - -- non-being!
underground realm 51
4. Non-being is the mother corresponding to the Good
as father.
a. Politics as the dissembling art of managing
human stupidity has a special place in the cave
image.
51
b. The cave. as womb is a figure for non-being,
to wh1ch15 opposed the reaim of being under the
sun; between them lies the road along which 'bomtng into being" takes place~
52
t
�-1-
-v1-
c.
d.
F.
Socrates identifies the cave as the mortal
Hades, the •sightless place". The backward
position of the prisoners signifies human
perTersion, which is corrected by the
Socratic •conversion•.
Socrates alludes to Pythagoras' descent into
Hades; 1n fact the dialogue itself has the
form of a Pythagorean •recollection exercise
Page
I.
Myth
52
11
•
5J
Socrates recites the nhymn of dialectic• for Glaucon.
1. · The ascent from the cave represents the road of
learning1 which has three parts:
a. •conversionn is not within the formal plan
because it .is, in effect, now being accomplished.
·
53
b. The "haul upwards• is effected by the building of an 1ntell1glble cosmos according to
a purified Pythagorean mathematical currlculua. Socratic mathematics as a •propaldeut1e • study ls •1nYerse• or 9 dream1ng• dialectic.54
c.. Dialectic 1 tself ls withheld from Glaucon as
accessible only by the path of study; instead
its praises are sung in a ~hymn•.
·55
d. Having h~ard the plan, Glaucon, as an initiate
of. the ~steries of learning, becomes a fellow
law-giver.
55
2. The ages for study and practice are set as in a
formal curriculum.
a. · The education of the rulers always leads out
of the city which contains nothing •fair"
.
for them; 1n · 1 t geometry is subs ti tu.ted for
;ros~
·
·
56
b•
ecause of' the hypothetical character of
•patterns~, the rulers 1~ the Constitution
do. ·not study constitutions, but learn to
rule 8 1n the light of the whole~.
57
c. Socrates introduces the dead philosophers as ·
···
58
•new di vlni ties•.
d. So~rates has brought up his Theseus.
58
At the center ot Plato's second longest dialogue, the
Const1tut1on,(Politeiah usually called the Republic, there
is en ergon, a deed or accomplishment. In order to find
th1s center 1t is necessary to establish the periphery. The
Republic is composed on the plan or concentric rings; the
themes on· the diameter reappear in reverse order as if they
were reflected through the central axis. The outermost
periphery ls a setting of myth. A broad i nner r i ng oons1sts
of t he construc ti on and destructi on of the successive forms
of a pa ttern city in •speech•, logos . The themes of this
ring, for in~ t ance the attack on the poets, are also symmetrical with respect to the center. This center itself, clearly defined as such by the plan· of the dialogue, presents the
actual founding of a city in 9 deed•, ergon.
B.
1. Anyone who has used an annotated edition of the
Repub11clJ will have read the curious anecdote told by
Diogenes Laertius and Dionysius of Halicarnassus about the
beginning of the work. The latter reports that many stories
about the care Plato took to •comb and curl• his dialogues
were current and especially one about a tablet fotmd at his
death which contained •that beginning of the Republic which
goes 'I went down yesterday to Pe1raeus With Glaucon the
son of Ar1ston', transposed with subtle variety.• We may
infer that some special meaning was tn be conveyed by the
beginning. Indeed there ls someth1~ curious about its
style: ancient as well as modern i\-t\i rnHAm,when they visit
their harbor:; do not go •to Peir a eus• but •to the Peiraeus•
(e.g.) Thuoy<j±des VIII, 92 ,,11 ); thi s ls Cephalus'Own usage
(J88 c 6), 2 ) and since he lives t here he ought to lal.ow. The
phrase els TTe .../' a..c...2. 1s to be heard 1n a speci al way. Now 1 t
h appens that the Athenians heard a certain meaning in this
name . - it meant t he •beyond- land•, v' Tr~ra.., the land beyond
t he river which was t hought one~ to have separated t he
Pe1r a1 c .pen1nsula from Att1ca.3J Therefore let us try r ead!ng : •1 descended yes t erday to the land beyond the river together with Glaucon the son of Ariston, •.• in order t o offer
my devotions,• he goes on, •to the goddess •••• • The goddess,
we learn at the end of the first book (354 a 11), is Bendis,
a Thracian stranger identified with Hecate,4) the guardian
deity of the tmderworld. Socrates is on his way back UP to
�-2-
town when Polem~chus with his companions detains him and
presses him to come to his house, where they find Cephalus
Polemarchua' rich old father, sitting in state. He is on '
that •threshold· [to Hade!J which is old age• (J28 e 6). 5)
As he himself explains, he scarcely has a body anymore·
He is, as his name signifies, a mere 9head• - as Socrates
slyly points out, he sits on a head rest, a proscephalaion
( J28 c l). His riches, ploutos, (.331 b 7), Socrates suspects, are his great comfort. A strange light is thrown
on him and his house by an ancient source which reports
him oTer thirty years dead at the dramatic date of the
dialogu~ which is between 411 and 405 B.C.; his son himself has only a few more years to 11ve before his death
at the hands of the Thirty Tyrants. 6 ) We are in 1\1.< city
of shad.ea, in the house of Pluto.
- Socrates occasionally refers to this situation throughout the dialogue, for instance when he declares to Thre--symachua and the others who are ther~ in solemnly ambiguous
language, that he will not cease his efforts until he has
prepared them •against that other life •hen, born again,
they may happen to hold such discourse• (498 d J-4). And
the very figure for the yoUilg guardians of the city which
he builds for his audience is a reminder of the setting:
they are to be like watchdogs who, as true lovers of wisdom, determine their friends and their enemies by the test
of their .knowledge or ignorance of them. The perverse
pattern of such dogs 1s Hesiod's hound of Hades who pcsseses
the •evil art• (Theogonr, 7?0) of fawning on strangers and
devouring those at home in Hades.
2. What is Socrates' business down there? To detect
the myth that provides the venerable setting for Socrates•
descent it ls necessary to go rather far afield for a
moment.
On certain occasions Socrates uses an oath which was
evidently considered 1n antiquity to be his very own: •By
the dog!•, and in the Gorgias (482 b 9) more explicitly:
•By the dog, the Egyptian godi•.?) Socrates uses the oath
several times 1n the Republic and often 1n characteristic
contexts, that is, in rhetorical passages and particularly
1n those concerned with the philosopher's part in politics
(J99 e 5,· 592 a ?). Who is the Egyptian dog god whom
Socrates calls on? Plutarch (On Isis and Osiris 368 e-f)
describes him: he is born of an underworld mother but
nursed by a heavenly goddess and thus belongs to both
realms; he can see his way both by light and by dark and
therefore has the office of mediating between the upper
and the lower world. His Egyptian name is J4.nub1s, bit to
the Greeks he is Hermes, the Interpreter, the •psychagogue•
who conducts the souls of the dead and guides those who
must descend into Hades while yet alive (cf. Diogenes
Laertius Vl!l,31). He is also the bringer of political
-3-
wisdom to men (Protagoras, 322 c 2). In particular, Hermes
1s known as the guide of the hero Heracles in his famous descent into Hades (Odyssey XI,626) and is often so represented
on vases.
8)
Heracles himself is a most versatile hero.
He is the
chief founder of cities - witness the many cities c~lled
Heracle1a
He ls the great civilizer, •using music - at
which he is proficient - in this task. He is the guardian of
boys' education, the guardian of the palaestra, and the boys
devote their hair to him. He teaches men letters; Plutarch
jokingly calls him •most dialectical• (~ E l!t, Delphi, 38? d).
He ls a partisan of virtue, hav1ng~accord1ng to a story told
by Socrates (Xenophon, Memorabilia II,i,21; cf. SYI11poslum
177 bh chosen to follow Virtue as ~ teacher rather than Vice
because of the happlness~(eudaimonl~) she promised. But
Heracles' greatest fame derives from the deeds or labors imposed on him by the unjust king Eurystheus. These include
the killing of the snake-headed Hyd.rla and of the/Nemean Lion,
but his most awesome deed is his descent, his katabasis, into
Hades. His task there is to bring up to the light of day the
triple monster Cerberus. He has Hades' permission to do this,
but he is to gentle and persuade the beast and not to hurt it.
On his way into Hades, so the story goes, he at first forgets
his business and allows the shades to detain him 1n conversation. Before returning, he performs an incidental labor, · a
.
parer,gon, 1n releasing Theseus, his emulator and the founder Q.,~ \.o.~,vU"
of Athens, who is chained down in Hades, though he fails to
free Theseus' companion Peir1thous. While in Hades he is
nearly washed away by the underworld river.
This hero is, as it were, made for Socrate~ and he himself
makes the comparison. In the A.pology, speaking of his search
for a wise man,he says to the court: •Jind by the dog, men of
Athens - for I must speak the truth to you - those who had
the greatest reputation seemed to me nearly the most deficient •••
so I must show you how I wandered as if performing certain
labors ••• • (22 a 1). Every Athenian would of course recognize
the allusion· most translators put 1t into the text. Again,
in an 1nterl~de in the Phaedo, Socrates, playing with Phaedrus'
hair, which, if he ls Heracles, is his due, explicitly consents to take that role in the battle of argument, with Phaedo
playing Iolaus (89 b-c).
·
There are certain signs and indications that Socrates plays
this same role in the Republic. He •descends' to the land
beyond, is caught in conversation 1n the house of Pluto and,
like the phantom Heracles whom Odysseus meets on his own visit
to the shades - the true Heracles is among the gods - he tells
down there the story of his own descent (Odyssey XI,601). He
first fights the s9phist Thrasymachus, who comes at him •1ike
beast• (JJ6 b 5),J and With Whom he says he would as Soon
auibble as •shave a lion• ( 341 c 1). A 11 ttle later Thrasy~achus, laughing~~l°~~vLo~ "like one doomed• as the scholiast
explains the word, adresses him •o Heracles! this is that
wanted dissembling of Socrates• (337 a 4), which 1s, of course,
a
�-5-
-4-
nothing but a popular exclamation of wonder, but which
sounds almos t like the lion's roar of recognition - by the
end of the first book the lion 1s subdued. · At one point
Soc rates refers to the wrong way to kill the Hydria; implying that he knows the better way (426 e 8).
3-4. But .the longest labor begins after the •prelude•
(357 a 2) of the first book. In the nine books following ,
the running motif w111 be that Heraelean theme, the relation of virtue to happiness, ever recalled, even in the
mi dst of ye t greater matters which a re curtailed in its
favor (e.g., 445 a, 580 b, 608 c); this relation is to be
examined 1n a man who is wearing the Ring of Gyges (359 c
6) and 1 as Socrates adds, the Helmet of Hades too (612 b 5 ) ,
a magic cap which deprives him 1n life of a11 appearance
and reputation and puts him on a level with the bare stript
souls in Ba.des (cf. Gorgias, 523 c). In the course ~f this
argument Socrates will indeed teach his audience letters,
using the great text of the city to teach them t he small
letters of the soul {)68 d, er. 402 a 7). He will 1 as we
ehall see, found a city. By. the 9psyeh.agogurry• of his
rhet~~1ca1 music (Ph.aedrus 261 a, Aristophanes Birds
1553 J) he will release his Theseus, blameles~ly confined to Hades (391 c 8). But his longest effort will drag
to light a triple monster haTing, like Cerberus himself , a
bush of snakes for its lower part (590 b 1). Having plumbed 1n argum~t the remote depths of the tyrant's life>
Socrates recalls once more •those first words because of
which we came here• (588 b 1), namely Thrasymachus' cl aim
that injustice under the reputation of justice is profitable. To conclude the oase against him they "model an
image of the soul in words• (588 b 10). It will , Socrates
says, be a creature such as is found 1n ancient myth, a
Chiaaera or Scylla or a Cerberus, whose nature it i s to
haTe •many forms grown together into one• (588 c 4 ) under
the outw~rd guise of a man's shape. When they ha ve brought
up the soul and cl eans ed it of accretions (6ll)"we have~
Socrates says, •discharged ourselves of the argument• (61 2
a 8). · Heracles has delivered Hades of its mans t er.
Having ceased to enact a myth, Socrates closes the dialogue by telling one, a recollectlon of one of t hose "myths
which are told about those in Hades• which keep tormenting
Cephalus who is so close to these things (JJO d 7 ). In
this myth, Er, the Pamphylian or •A.11-tribesman• (614 b 4 )
ls charged by the soul s t o carry back t o the liv ing the
long tale of their thousand-year journey, of the ascent or
descent which is their reward or punishment. He actually
tells only of the end of these journeys since, as Socrates
s1gn.1fican.tly observes to Glaucon, the story itsel f would
take •a very long time to go through• (615 a 5). Socrates
ends the dialogue by urging Glaucon to hold fast t o the
•upward way• (cf. 514 b 4), so that they may do well in the
.
(
(.\
thousand-year journey "which we have just gone through
1"\v
~Le:AGe~v, 621 d 1). He means the ascent of the dialogue
itself (e.g., 473 a 5, 544 c 9).
This then 1s the setting of the Republic: Hades with its
tales and a deliverer willing to go down and able to come up a most appropriate setting, for down there, so all)the tales
go, Justice 1s close at hand (330 d 8, 614 c J).11
II.
Logos
A.
1-2. We come now to the arguments, logo1, which form the
broad middle ring encircling the center. .1.s the question
concerning the connection of justice to happiness 1s answered by bring1ng to light the human soul, so the soul itself is
disco•ered by raising and taking down cities . This is done
•1n speech. ( x~ y £& t and not, to use a pervading Greek OP{>Oe1 t1on, •in deed• (£/'Y'i · e.g., 382 e 8, 383 a 5, 498 e 4).
Let us first follow these city constructions.
At the beginning of the enterprise Socrates says: •come ~
then let us make a city from the beginning 1n argument• (1tt:'
>-.6y'w, 369 c 9, cf. also 369 a 5, 472 e 1, 592 a 11). The
obJect is to find the nature of justice by looking at the
largest context to which it ls applicable - hence the city
founded in speech will have to be just. They first found a
community of craftsmen, workers collected to ply their own
trades so as to supply eaoh others' WE:Ulte, making the city as
a whole self-sufficient (369 b). In this city the full pol1t1.cal weight of the Greek name for craftsmen, dem1ourgo1 {S?p..L...0~ yo~, J70 d 6) •public workers•, is realized. This, as we
will see 1s the most literal model from which to read off the
definiti~n of Justice which runs through the Republic, but
just as Socrates is about to do thtlt, Glaucon stops him. rn;i1s,
he says, 1s a c1 ty of pi~s {372 d 4). He means that the ci · 1izens' whole being, like ·that of pigs, ls absorbed 1n oonsum1ng and being consumed - there is no place or ·. lei sure for honor
and pride. Socrates, though still maintaining that this city
is the •true• and 9healthy• city (372 e 6), yields to Glaucon
and changes the •first city• (373 c 5, Aristotle, Politics
1291 a 18) by the addition of luxury and that soldier element.
which will procure wealth and maintain safety. He assents to.
the construction of this •revered• city because in 1t one might
see •how justice and injustice grow up in cities• (372 e 5);
this city, then, illl contain the. seeds of injustice also. He
describes the natures and the training of the soldiers or
guardians (<f0Ao...¥<£J), a subject to which we must return. At
�-6-
the end of this long argument (375-414) Socrates again reorganizes the eity, this time by division, namely of the
guardians into guardians proper older men who rule and
the 8UXill1arieS ciTTL-kOVpouj KO:i: /Jo'?'f}oVJ 414 b 5)' the
younger fighting men. This third, tripartite, city'suffices to read off the similar constitution of the soul and
to show conclusively. that, as in the city, so in the soul
justice must be profitable. Socrates now considers the
positive half of his task finished and ls about to go on to
investigate how injustice comes about in cities and souls
(445-449, Book IV). He ls interrupted. Three whole books
(V-VII) intervene in which a fourth and very different city
is founded. Not until Book VIII does he return to the
argument. In Glaucon's figure, 9 l1ke a wrestler he assume s
again the same position• (545 b 5 ) and goes on t o account
1n order for the four degenerate c i ties C.544-59 2) . W
hen
this argument , t he complement to the genes is of cities 1s
done, Glaueon once again refers to •the c ity which we have
Just been founding and which is preserved in speech only
for I do not think that it i s anywhere on ea rth• (592 a io).
B.
. 1. Now what is the meaning of the claim that the genesis of the city, or the ci ty i ts elf, is only •in speech•?
It means of · course first of all t hat no actual cit of
living men comes into being whi le they speak or as a consequence of their discourse. But that is mere fact. What
is more interesting is that no such city can come to be now
or later, .QI. the design and intent of the--argument itself.
These word constructions are n ot •constitution
the practical _ patterns for working ci ti e s s uch as Plato and his
pupils were invited to write f or Greek cities 12) The
dialogue conveys this in one as t oundi ng fact:.no human
bei ng i s ever born i nto any of the three c1t1e - they cannot regenerate themselves ; they are unna tural. The first
city is constituted by collection t he second by addition
the third by division. No less strange is t he original '
physical settlement of the third city which i s first said to
begin with the exodus of the guardians to a camp outside
the old city (415 d 6), but later with the expulsi on of
all souls over ten years old (.540 e 5 ) . The citizens
are to accept this curious fashion of founding a community
because of the "Phoenician myth•, the one noble lie (414
b 9) which they are told (414; cf. 489 c 8): that their
youth and education was a · dream; that they were reall y
~armed like metals in the womb of the earth their mothe r
who sent them up fully formed, that they are theref ore ai l
brothers, though of different metal. Those who have an
admixture of gold must rule and those of silver must assis t
-7-
for, as an oracle foretells, the city will fall when a man of
brass or iron rules. The purity of the metals must be carefully preserved, and if a gold or silver parent has a child
with an admixture of brass or iron he must consent to see it
put into a lower class.
The •11e• in this myth 1s not that . men are of different
metals or that the city caIUlot survive the wrong kind of
ruler - all that is true - but rather the claim that the
citizens have no proper natural birth and no privacy of soul.
Under their flattering epithet •earth-born• (415 d ?), which
intimates that they are Giants, is hidden the claim that they
are natural bastards who have a mother but no father and that
their soul can be accurately assayed like any ore. So too
the continuation of the city depends on the citizens' belief
that each generation is newly mined, like a public treasure,13)
from the earthly element on which the city rests.
But the curious character of this 'needful 11e • (414 b 9)
is that the joke ls, so to speak, on the guardians. The myth
must not only be believed to be true - it ought in fact to be
so, if the city ls to breed true. For if men are not born
from a common parent at the rib ht time and with pure souls
easily assayed, the guardians cannot control the new generation and insure the stability of the city.
2. The community , (ko1non1a) of women and children, the
•source of the greatest good to the city• (464 b 5) is intended to· achieve exactly this community of birth. All children born in the same year are to be ignorant of their parents
and are to be called brothers and sisters, although this ignorance may eventually lead t o incest (461 e 2). These children of the city will be tested all the time, but one of the
conditions for stability is beyond the guardians' control: the
timing of the mating. For as Glaucon wisely observes, the
best are drawn by necessity to have intercourse with the best,
but this necessity is "not geometric but erotic• (458 d 5).
Yet the guardians' control of breeding is to be precisely
•geometric". The Phoenician myth, in accord with Phoenician
greed (4J6 a. 2), makes of men a Pluton1c treasure to be dug up
and refined at will; the scientific counterpart of this is to
consider them a crop to be sowed and harvested in accordance
with the heavenly motions ..
The geometry of these motions as they affect breeding is,
however, not lalown to the rulers. In Book VIII Socrates has
just resumed the discussion of the degenerate cities when he
stops himself and prays to the Muses to tell him •how discord
first arose•, an allusion to the Iliad (I,6; XVI,112) and the
fall of the city of Troy. The Muses' response is a mathematical myth. A city so constituted as his, they say, can hardly
be moved C.546 a 1), but since everything which has a genesis
also has a degeneration, the city will not last forever - note
that in the order of argument the decline in fact follows
immediately upon the beginning. It must come because the
�-8-
the rulers' reasoJ'\.\.V\'J lt or rather their calculating power
mixed With sense l ..\oyt..~4? µeT) o....la·Bf a- E u15) b 1) as it 1 ~,
will not be able to apprehend the •geometric number• which
governs births. The ~uses recite this fabulous number,
which is indeed not to · be understood. Thus the generation
of rulers is corrupted and as a final consequence of their
baser metal they neglect the study of music and lose the
power of testing souls. This is how the decline of
Hesiod's ages, from gold down to iron begins.
Human generation is thus an impenetrable mystery, and
the city founders on the rock of the fact of bisexual generation. The human being, considered as that unstable union
of body and soul, does not run true to ~ as does a
plant. Human nature is un-natural. This ls the insuperable problem which is again attacked in the Statesman
( _ 71 ), where the Golden Age, the age of the direct divine
2
rule of Cronos, is characterized exactly by this - that
men grow directly from the earth and hav~ no human birth.
Later on Socrates quotes an old phrase\4J to contrast the
city with non-human nature: •You do not think,• he says,
•that constitutions come out of 'oaks and rocks' and not
out of the characters of those in the city?• (544 d 8).
Very nearly the same figure is used by Vergil for the
human race of the Golden Age of Saturn; they are sprung
from •trunks of trees or rugged oaks• (Aeneid VIII,314).
The Golden Age 1 s the age when men gi-ow n:a turall~.
The dialogue itself tacitly underscores the 1mposs1- bility of genetic contro~ both at the very beginning and
at the very ·end. For of those said to be nresent in
Cephalus' house, five are full brothers, two of them
Glaucon and Ade1mantus, sons of Ariston, and the three
others Polemarehus, Lysias, and Euthydemus, the host's
sons. The conversation itself will show how the sons of
the •Best• - Socrates often alludes to the meaning of the
father's name (e.g., 327 a 1, J68 a 4) - differ profoundly, and something similar was known of Polemarchus and ·
Lys1as (Phaedrus 257 b). And the Myth of Er which concludes the conversa t1on shows why genera tlon is 1ntra.ctable; human nature is not determined on the hither side
of life by others, but in the •divine place• beyond by
each sour_:itself (617 d 6). The coming to be of the
city is therefore not in accord with the coming to be of
human beings.
The enigma of regeneration is, however, only secondary to the paradox of the city's foundation itself. For,
it turns out, only those will be content to accept this
constitution who have accepted the'\dye 11 of its laws (4Jo
a 3). The just city can only be realized by its own
children; to begin it must have already begun. We eee
why the act of settlement itself is so lndeflnite, amounting once to the emigration of a11 rulers and another time
to the removal of all adults who leave behind a city of
children. This is what is meant by claiming that the
-9-
three constructed cities are cities in speech only. They are
the kind of city that the dialogue's most knowing reader was
to call a -No-place•, a Utopia.
J. The degenerate cities which are symmetrical with the
three constructed cities are, on the other hand, all too realizable - indeed they exist. Socrates underscores this by
mentioning, 1n this context alone, actu21 Greek cities, namely
Crete and Sparta, the t1mocrac1es (544 c J). Yet here too,
in a different way, the argument is remote from the deed.
The argument that Socrates returns to 1n the eighth book
had just been initiated at the end of the fourth. Of the
five •bends• (T/'o~o~) of the soul, one alone is good while the
other four illustrate the multifariousness of evil; to these
latter correspond four cities. They have •so far ascended
in argument• (445 c 5) as to stand on a look-out tower whence
to view the manyness of vice. This discussion of vice, when
picked up three books later, continues to rise above its subject until having traversed timocracy, oligarchy, and democracy, they finally look down on th~ sink of tyranny and the
abyss of the tyrant's misery which ls 729 days, that is two
years of continual travel, beneath them (587 ). This is what
characterizes all serious discussions of .vi c e - they must
certainly not bring about that of which they speak, but rather
become more detached the closer they come to the tnith, just
as the best judge of criminals should have the least experience of crime (409 a). The effect of this •remoteness• on
the argument itself is that the degeneration of cities is presented as an inevitable downward progression. Here the argument takes account, as it were, . of its own impotence - the
situation is in actual fact desperate and in a few years a
fierce battle between the democratic faction and not one but
Thirty Tyrants will be raging about the sanctuary of the very
goddess whose feast is now being celebrated (Xenophon,
Hellen1ca, II,4,11), and the tyranny will have destroyed the
host's family, while a few years later a temporarily restored democracy will have murdered Socrates (399 B. c . ).
c.
1. The facts of the host. : family's condition and politics
determine the conversation in yet another and pervas1~e way.
The family runs a prosperous shield manufacturing and selling
business, and both Polemarchus and Lysias are known to have
democratic leanings though, we may suppose, of a decent and
moderate sort. This is the clue to the peculiar treatment of
the virtue which Tater gave the subtitle •on Justice• to the
dialogue. It is not usually Socrates' way to inquire whether
a thing is profitable or unprofitable before having inquired
�-10-
-11-
-What it 1s• (e.g., Meno 71 b), but this is just what happen.a wi~h respect to justice in the Republic. From the
second book to the end the question is: Is justice profitable? What justice 1s,1s assumed. As Socrates, somewhat to Glaucon's annoyance, insists (432 e 8), when they
come to find justice in the city they have constructed they
find there nothing more than they put in· the city is just
because they have made 1 t that way {4JJ ~ 1 443 b ·?)
The
working definition that is not the result b~t the ass~p
.1!.Qn · of the argument is that justice ls •doing one's own
b~siness and not meddling it {To "T~ o.t,'To ~ 7TfJ~T-'f£L" Ko..\:
IL'? no>." rr_pa.y
~ovs.'lv, 4JJ a 8), a def 1n1 ti on they have
heard from many others and . have themselves often given
Justice so conceived is, to begin with, simply the •
opposite of the literal understanding of the names for
various degrees of wrong-doing. '!'here is rro~orrpo-.y/lAoV£-'(v
(4JJ a 9, 44) d 2, 444 b 2), literally ~muoh-doing• or
being a •addling busy-body nO:v"To... rro c...t..'Lv . ( 596 c 2}
·d o i ng every th"
· ~ or being a jack- of- all- trades - Socrates'
favorite description of the sophists' easy expertise (cf
397, 596\ cf. Sophist 2JJ d 9) and worst of all rro...vol/,/Oy£'2v
(409 c 5J, •being up to anything• or simple sha~eless wickedness, the behavior of the man who takes full advantage
of the impunity given by Adeimantus' Ring of Gyges
Positively, justice is acting in accordance with that.conveniently ambiguous phrase
7TJ'>Ci \IELV e1 ther •doing right•
or 9being we11•, with which . the Republic ends (46) e 4
519 e 1, 621 d 1).
'
From this·point of view the most simply just city is as
Socrates himself says, the first, the self-sufficient city
of demiurges or craftsmen who both know and do their own
business iJ73 e 6, 428 b 12). In them virtue is indeed wisdom (o-oq>t.Cl.}, in the good old-fashioned sense in which sophia
means what in English used to be meant by •cunning• namely
craft end skill, and arete means the power to do wo~k the
•v1rtue• .of an agent (er. 350 c 4, 353 e 1).
'
. We may well ask how a view so practical almost pat
comes to underlie the dialogue. It is nec~seary here to
recall that justice in the city. is exposed by finding and
analyzing out the other virtues and considering the remainder (427 e 13). Thus wisdom is found to be the rulers'
virtue, courage that of the warriors temperance the agreement of all on who shall rule (4)2 a~. Justice is then
found in each class as that virtue by which 1t does its own
work and nothing else. Now clearly in this context temperance 1s somewhat redundant. In fact, when Socrates turns
from the city to the soul he makes no distinction between
.justice and temperance (443 d 4, cf. Laws 696 d 11, where
temperance is called a mere •appendage• Trf'oa'/9 7~ o.. and
Charm1des 161 b 6, where Cr1t1as very idiowingly a~ he
thinks, proposes the present definition of justice as a
definition of temperance). We may therefore say that justice is that special virtue which all three classes possess
ftlll'.
'
·'
eu
,
and consequently a unique and special virtue for .the crafts-
men, •the popular and cl tizen virtue• (-rVj'I 'S9)-loTL1<.~-..t Ka~t
Ph_?-edo 82 a 11). It is the virtue by
11 0.Al-ru·o?v
¥£T9vJ
reason of which each performs •that to which his own nature
J
<.."\
)
"""
(
,,.,
)
"
,.,
is most fitted • ( £LS o o...,JTou "7 <jJUc:r'-S eTTL.T?oe~ aTa..-rp
rrc.cpuKvi:.o... t-.r'? >
433 a 5), . by which, we might almost
say, a human being is ever himself. In some cases this means
quite simply •minding one's own business•, as must the lover
of wisdom~ for instance, in a city not fitted to his nature
(496 d 6). Justice might therefore be termed the private
public virtue which turns particular natures to the general
account. This is why its presence is the greatest good and
its absence the greatest ruin to cities (433 c 4 - 444 b 7).
This virtue, in essence decent self-respect, is therefore
quite naturally discussed under the roof of people who would
constitute the multitude of the merchant and artisan class
of the third city, supplying young warriors like the sons of
Ariston with their armor and occasionally sending a philosophically disposed son like Polemarchus (cf. Phaedrus 257
b 4) up into the ruling class.
2.
But Socrates never allows us to forget that this third
citv is a dialogical phantom and that the justice. in it is,
for .. all 1 ts apparent practical! ty, a mere •1do1 • (£lSSw~O'v ''4JJ c 4), since the true virtue does not lie in deeds concerned
with the outside but in the inner disposition of the classes
( y£v? d J) of the soul and their ordering. We will see that
in th~ case of the true ruler, that is, of one so •constituted•
as to be able first of all to rule himself, the distinction
between •his own affairs• and •others' business• vanishes.
For him that which is most common is also most his own •and
with his orivate affairs he will preserve the common business•
\<o.."\. _A~m =Twv l~wv ,..~ ¥--OLVO:: O""~cre:...~)
497 d 5). In him,
•doing his own business• will be turned into •kn.owing himself",
which means •1ooking ••• at myself, whether I happen to be some
beast more complicated than Typhon leerberus' father, Theogony
Jll] or a gentler and simpler animal• (Phaedrus 230 a) . True
justice is concerned with that 1~ m~n wh~ch is :'t~ly ~bout_
himself and his own business• ( w..s °'-A'<J8w5 n£pL- ca..u1ov ~o..L
•\O:. eo-\J"TOG', 443 d 1). This is the reason why, as we s~c;Ul see
below, the soul is the one single subject of the dialectical
method in the Republic.
3. This •inversion• of justice in the case of the true
ruler, that is, in the philosopher king, leads to a curious
suspension of the main argument in the central three books.
If for the guardian rulers justice can only with difficulty
be proved to be profitable because of the hard life they lead
(419 a, 465 e 4), for the philosopher kings it is altogether
1mooss1ble. For those who already consider themselves to be
living in the Isles of the Blessed (519 c 5) the descent into
�-12-
the city to take office cannot be made to seem like happiness {519 d 8) nor can it possibly improve the .tone of their
souls. They must be made to enter politics "forcibly• ( i rr'
6..~~yl'<a'L oY) 520 e 1); in fact .their reluctance is a guarantee of their suitability (e 4). Glaucon sees immediately
that the main point of the outer rings of the argument has
been lost and wants to know if the philosopher rulers are
not being treated unjustly (519 d 8). Socrates' a~wer is
an evasion; it is not their happiness but that of the whole
city which is to be considered. When all is said and done
the true rulers of the Republic enter politics only out of
pity, gratitude and simple decency (516 c, 520 a-e). ·
III.
Ergon
A•
1. Socrates ls about to go on with the in~estigat1on of
the unjust ei ties when he 1& again restrained,· as once before on his way up to Athens (327), by a conspiracy of Polemarchus and Adeimantus {449). After some whispering a vote
is taken and the decree which has been passed ls announced
by Thrasymachus (450 a 3): Socrates must expand and defend
a principle mentioned before with conspicuous briefness which
ls to give the city unanimity or better, perfect publicity:
•Friends own what ls common• ( Koc..v~ -rci: 1wv cp~ ~ w v,
449 c 5), a new political reading of a current phrase (cf.
L1s1as 207 c, Phaedrus 739 c), which may mean, significantly,
two things: 8wha.t a friend owns is at the service of his
friends", or "what friends own insofar as they are friends
is communal by nature•. They particularly want to know ·
about the equality of education for men and women (451 b)
and the community of wives and children (457 b). Socrates
reluctantly complies and . faces the first two of the three
waves threatening to overwhelm him (47J b 6). He has gone on
to describe such a c1ty 1 s relation to other Greek cities when
Glaucon erupts:
•But it seems to me, Socrates, that if one were to allow
you to talk about such matters you would never remember what
it is you pushed aside in saying all this, namely this - is
such a constitution capable of coming into being and in what
way is 1 t possible?" (471 c). And he 1ns1s ts on this question although Socrates stalls by getting him to admit that
the object of their discourse was the discovery of justice
and injustice and their respective merits, and that the •c1ty
1n speech•, having served that purpose is none the worse for
being impractical (473 a 1). But since Glaucon insists1 he
-lJ-
must not not force Socrates to show that •what they went
_
through in speech (T'2 '>.o 'I l.J.!) can completely be in deed• ( .,-~·
¥!"' y Lt' ) ; he must content himself w1 th as close an approximation as is nossible (a 1). This approximation will be reRched by mrkin~ the least number of chanc'.;eS in things now done
badly in cities such that they may be founded according to
their constitution, whether there be one or two or others, but
as few as possible (b 4).
So Socr~tes, like Odysseus, meets that third wave which will
carry him to his PhReacia (OdyssEZ.X V,Jl3,JJ6,425). The one
thing that must be changed, he announces solemnly (b 8) is this:
•Unless either nhilosophers rule in the cities or those who are
now called kings a.nd dynasts philosophize genuinely and sufficiently and these two coincide, namely political power and
philosophy, and the many natures of those who now pursue either
way separately have been excluded by necessity there is no end
of evils, my dear Glaucon, in cities or, in my opinion, in the
human race• (c 11). He adds that he cannot see how any other
city can be happy in public or in private.
Together with Glaucon he now prepares the ground.for a new
city. It ls necessary to show why this •one change may be
said to produce a new city - is it not merely the guardian
constitution put into effect? Both Socrates and Glaucon, at
least seem to regard these two as different; he calls the
latte~ •the first selection• (536 c 8) and Glaucon refers to
the former as the •better• city (54) d 1). And then, as
Socrates himself says, an actual city is never the same as
its pattern, its par&de!gma, (472 d 9, 473 a). The guardian
city and the philosopher city differ, then, as does a reali~
ration from its pattern. The discourse on the possible city
will be, among other things, e subtle consideration of the
relation of pattern to product, of •theory• to •practice•.
The addition of that which makes the pattern possible will
prove to be thet which makes it superfluous.
. 2.
The philosopher kings can certainly not be regarded as
part of the constitution of that just city which must have
been known generally as •socrates' city". Aristotle, in his
critique of the Republic, mentions as its salient features
the warrior class and the community of women, children and
goods but omits all mention of the nhilosopher kings (Politics
i291 a 20, 1261 a 4). Aristophanes in The Ferne.le Parliament.
(427), where the community of goods and women becomes the law
of,Athens, falls to seize the comic opportunity inherent in
the subject of female philosophers. It is likely that this
play was written before the Renublic and we may infer that
people - Socrates in particular - were talking about such a
c1 ty. In the dic.tlof' Ue there are enough passages parellel to
the playl5) to constitute an acknowledgement to posterity that
the women's city is a parody of Socrates' notorious city. In
fact, the nod ls nearly explicit, for in facing his first
wave Socrates remarks that after the men's part has been play1
�-13-14-
ed out it is only right to recite •the women's drama ( To
yu~~~K£~ov ~~~~)451 c 2), and in going to meet his third
wave he says, as if speaking from experience , that •it
might overwhelm him with laughter and disrepute• (473 b 8 ).
3. Last and most weighty is the account Socrates hi ms elf gives of his city in the Timaeus when he recapltulates
the constitution which he had presented to his friends in a
discourse on the previous day. There is no reason whatever
to conclude that the Republic is that discourse . In fac t,
while the Republic ls spoken on the day after the Bend1d1a,
the Timaeus, quite appropriately, takes place on the Lesser
Panathenaea, a festival which occurred two months later
also in the Peiraeus (26 e), and during which a gown wa~
sent up to Athena •on which the Athenians, her nurslings,
could be seen winning the war against the people of Atlantis• (Schol1ast on Republic 327 a). Al.so the dramatic
year of t~e Timaeus seems to be earlier than that of the
Republicl ) The city Socrates recapitulates is not the
city of the central books of the ReTubl1c, for, although
his account is said to be complete19 a 7), the' philosopher
kings are omitted; it is rather the •third city• with e.11
its notorious features. We may infer that Socrates proposed
this city on various occasions and that it was known as h is.
This guardian city therefore differs from the philosopher
city and differs as the impossible differs from the possible.
Soc r a te s h 1m~ el f expla ins to Adeimantus, when he asks whethe r
this guardian city t hey have founded is the city suited to
ph ilosophy, that 1 t is that city in many ways but that th ere ''v.10..,1d
a..\w~"t5i \le
n eeded s omeone understanding the reasoning (logos )
behind t he constitution - that same on e who guided you when
as a law-giver you laid down the laws• (497 c 7). The
difference between the cities is therefore not consti tutional, for the older guardians will still rule and rule
so as to achieve the most harmonious community possible.
The dif f erenc e i s rather in the rulers themselves, in what
they Will look to, in their education. We will see whether
this may not outwei {:h any more externally obvious difference.
B.
1. But the claim is not that the fourth city is a
possible city but that it is actual, that it comes into
being while Glaucon and Socrates converse, that it is a
city •1n deed•, ergo1. According to what has been said,
this could happen only if one paradoxical oondition were
fulfilled: if there were some one adult who actually lives
in the just city, who, as a living citizen of the city, can
?ring up another within it. 'rh1s must be the case not only
must not not force Socrates to show that •what they went
~
through 1n spee ch (Tc? Xo y ~) can compl e tely be in deed• ( ,...~
~l"'°Y~ ) ; he mus t content himself wl th as close an approximation as 1s pos s ible (a 1). This approxima tion will be reached by me.king the l east number of cha.!l6e s in things now done
ba dly in c itie s such tha t they m y be founded according to
a
t he ir con stitution, wheth er there be one or two or others, but
as f ew as possible (b 4).
So Soc r ate s, l i ke Odysseu s , mee t s t h at third wave which will
carry him to h i s Phaeacia (Odyssey V, Jl J,3 36 , 425 ) . The ~
thing that must be changed , he announces solemnly (b 8 ) ls this:
•ttn1es s e i t h e r phil osophers rule in the cities or those wh o a.re
now called ki ngs and dynasts philosophi z e genuinel y and suffi ciently -and these two coincide, namel y political powe r and
ph ilosophy, and the many natures of those who now pursu e either
way separately have been excluded by neo~ss i t y there is no end
of evils, my d ear Glau con, in citi e s or , 1n my opinion, in the
human rac e • (c 11). He adds that he cannot see how any other
city can be h a pp y in public or 1n private.
Tog e ther with Glaucon he now prepares the ground for a new
city. It is n ecessary to show why this •one change• may be
said to produce a new city - ls it not merely the guardian
c onstitution put into effect? Both Socrates and Glaucon, at
lea st, s eem to regard these two as di f ferent; he calls the
l at ter •the fi r st selection• (536 c 8) and Glaucon refers to
the former as the •better• oity (543 d 1). And then, as
Soc r ates him self says, an a ctual city is never the same as
lts patte rn, its parade1gma, (472 d 9, 473 a). The guardian
city and the philosophe r city di ff er, th en, a s does a real1~
lation from its pattern. The discourse on the possible city
will be, among other things, a subtle consideration of the
relation of pattern to product, of •the ory• to llpractice•.
The . addition of that which makes the pa ttern possib l e will
prove to be that which makes it superf luous.
, 2. The philosopher kings can certa inly not be regarded as
part of the constitution of that just city which must have
been known g ene rally as •socra tes' c ity•. Aristotle, in his
critique of the Republic, mentions a s it s s a lient features
the warrior class and the community of women, children and
goods but omits all mention of the philosopher kings {Politics
1291 a 20, 1261a4 ). Aristophanes in The Female Parliament
(427), where the community of goods and women becomes the law
of,Athens, fails to seize the comic opportunity inherent in
the subject of female philosophers. It is likely that thi s
play was written before the Renublic and we may infer that
people - Socrates in particular - were talking about such a
city. In the dialogue there are enough pass ages parallel to
the playl5) to constitute an acknowledgement to posterity that
the women•s city is a parody of Socrates' notorious city. In
fact, the nod is nearly explicit, for in f a cing his first
wave Socrates remarks that after the men's part has been play-
�-17-
-14-
ed out it is only right to recite •the women's drama (To
yu"c:U-KE.'L-ov '..P~a..) 451 c 2), and in going to meet his third
wave·he says, as 1f speaking from experience, that •1t
might overwhelm him with laughter and disrepute• (473 b 8).
J. Last and most weighty is the account Socrates himself gives of his city in the Timaeus when he recap~tulates
the constitution which he had presented to his friends 1n a
discourse on the previous day. There is no reason whatever
to conclude that the Republic 18 that discourse. In fact,
while the Republic i8 spoken on the day after the Bend1d1a,
the Timaeus, quite appropriately, takes place on the Lesser
Panathenaea, a festival which occurred two months later,
also in the Peiraeus (26 e), and during Which a gown was
sent up to Athena •on which the Athenians, her nurslings,
could be seen winning the war against the people of Atlantis• (&choliast on Republic 32? a). Al.so the dramatic
year of the Timaeus seems to be earlier than that of the
Republicl6) The city Socrates recapitulates is not the
city of the central books of the ReTublic, for, although
his account 1s said to be completel9 a ?), the· philosopher
kings are omitted; it ls rather the •third city• with all
its notorious featilres. We may infer that Socrates proposed
this city on various occasions and that it was known as his.
This guardian city therefore differs from the philosopher
city and differs as the impossible differs from the possible.
Socrates him~elf explains to Adelmantus, when he asks whether
this guardian city they have founded is the city suited to
philosophy, that 1 t is that cl ty ·1n many ways but that there ~'wov\d
a.\ -~be . needed someone understanding the reasoning (logos)
behind the constl.t utlon - that same one who guided you when
as a law-g1 ver you laid down the laws• (497 c 7). The
difference between the cities is therefore not constitutional, for the older guardians will still rule and rule
so as to achieve the most harmonious community possible • .
The difference ls rather 1n the nilers themselves, in what
they will look to, ln their education. We will see whether
this may not outwel~h any more externally obvious difference.
1. But the claim ls not that the fourth city is a
possible city but that it 1s actual, that it comes into
belng while Glaucon and Socrates converse, that it is a
city •in deed•, ergo!. According to what has been said,
this could happen only 1f one paradoxical condition were
fulfilled: lf there were some one adult who actually lives
1n the just city, who, as a living citizen of the city, can
~ring up another within 1t.
This must be the case not only
I
source. There is, as we will see, no eidos, no idea of a city,
while the communl t ,1.· which underlieE dialor:;ic communicc~tion is
orecisel:v eidP.tic, and, unlike the r:,uC:;,rdia.n 's communi t:y of
bodily ~: ~ads (416 d), indestructible, for th~ eidos which un~er
lies sp~ech is not a delicate adjustment of one out of many
but c.n 1nd1 vis1 ble one ~Y 1 ts elf• ana. opposed to all me..nyness
(e.g., 479). This is the •common thint. w which belongs to
friends. The foundation of the fourth city consists in beginning the dialogue with which an education begin~. We will
see exo.ctly how Socrates goes about this founding v.ct.
c.
But first lt is necessary to see where and under what
clrcumste.nces his foundation takes place.
The conversation of the RenubliQ is held in the Peiraeus,
the harbor of Athens, on the day of the Bendidea. In the
mythical dimension this place is revealed as Hades~ in fact
it is a turbulent center of Athenian democracy. Th e cult of
Bendis, a new Thracian import, is itself a sym~tom of dissolutlon •a new workshop of turbulent revelr y as a comic
wr1terl8~ seems to have described it. Its celebration 1s to
culminate that night in a torch-race and an •a11-nighter•
(rro..vvuxrJ> J28 a 8), an orgiastic affair which the young men
are clearly waiting to join.
Socrates and Glaucon, both citizens of this democracy, will
hold the conversation which occupies the central books of the
Republic within this setting. It is, in a strange way, the
right setting, as the dialogue itself intimates. To show this
let us look at the degenerating cities and citizen souls of
Books VIII and IX.
There are four of them, in downward order: timocracy,
oligarchy, democracy, and tyranny (544 c). But exactly as
in the case of the just city the monarchy and aristocracy
are regarded as b e ing two names but one constitution (445
d 4), a c.s.se may be made for taking democracy and 1 ts 1nev1 table cansequence, tyranny, together. For not only do they
in fact alternate with each .other in Athens at this time,
but within Socrates' scheme they have this important trait
in common, that they sre both less than cities, almost nonconstitutions, to which no definite kind of soul corresponds
(557 c 1). This bracketing gives us the following scheme:
). monarchy - a.ristocracy A-I
2. warrior city
1. craftsmen city
l
1
o.
timocracy
oligarchy
democracy - tyranny,
1
~
which conveys a kind of inverse correspondence between the
best and the worst. This correspondence of opposites is
�-19-
-18-
evident in a number of ways: the just rulers, especially
when the elders of the third city become the philosophers
of the fourth, make no difference between t~ilr own and the
public business (497 a 5), and in a perverted way, neither
does the tyran~ whose rule is a private nightmare publicly
staged (573, 576 b 5) - for in ·private the tyrant is himself, like his city, most absolutely tyrannized. As does
the just oonst1tut1on, the democracy cCG'ltains three classes
which again correspond inversely: the have-nothings in the
latter form the lowest and largest class and the most eager
for revolution, while 1n the former they are the highest
and least class (428 e 7), most careful to preserve the city.
And again: the ruling class in the democracy cannot fight
because of its luxuriousness (556 c 8) while those who have
that strength and should be the watchdogs become wolves to
the human fold (415 a, 566 a 4). These cities then are
related .by Socrates as extreme opposites (576 d), and he
even . describes them by the same term: the Just city is
called 8 the city of beauty• (~o.~kt-mi~~.J > 52? c 2) and,
the democracy too is called, bitterly, the 9most beautiful•
of constitutions (K~~aT?> 557 c 4) for the colorful
variety of constitutions to be found within it. All the
other characteristics contribute toward putting the citizen
of a de111oel'acy 1-nto a perverse li>11t -peeu'.11ar re1at1~<~~~uythe
just city, but it 1s this last which makes democraoy~£ne
best base for Socrates' enterprise. For as he tells Ade1mantus, it plays host to so many constitutions that •he who
happens to want to formd a city, ~ ~ ~ nQ!! doing, must
go to a democratic city•, and having picked a constitution
he likes he may proceed to settle his city (557 d). This
is precisely what Socrates does, who, as he himself points
out never considered leaving a perverse Athenian democracy
for' a dully decent t1mocracy like that of Sparta or Crete
(Cr1to 52 e 5). The dialogic community is one of the many
Athenian constitutions.
D.
1. One point remains to be made which will bring out
the full force of Socrates' founding act. As we have shown,
two things are required to bring the best city into being~
that the breeding of the citizens should be founded in nature and that the vicious circle by which the established
order makes citizens in its own image _
should somehow be
broken. These same conditions are fulfilled in another
dialogue in a totally different way.
Al.though the guardian city and its institutions are
said at various times to be according to nature (e.g.,
428 e 9 1 456 c 1), it is the nature of the soul which is
meant, a most un-natural nature, as wes\l~11 see. The
conseauence of this is that the city no sooner ceases to be
regarded as a mere pattern but begins to have corporeal life
than it enters its road of dissolution. For i~ change or
•motion• ( Kt'v,a"Lf) is "discord,. (o-mo-~5, 546 d) "A> co~sti tut ion in agreement with itself cannot be changed• (o..~ u"o...To"
Ktv9G9vc1.1.. d 1) · for 1 t the question ..how ••• then does our city
come to h~ve ch~nged~"(d 5) is answered by the inaccessible
mystery of the mathematics of birth-governing celestial cycles
(546). Now in the Timaeus Socrates expresse~precisely this
wish - to see his city put into motion (K\.\/o~£Va..> 19 b 8),
like a person who sees some fine animals painted or resting
and feels a desire to stir them. His hosts therefore must find
a way to •move• his city without dissolving it. Timaeus',
Critias' and Hermocrates' entertainment of Socrates on the
Panathenaea (17 a 1, 26 e 2), unlike the bitter feast Thrasymachus serves him on the Bend1dea {354 e 10, 357 a 2 )_, is truly
amusing for him. They present to him the frame of his picture,
as it were, by providing that mathematically moving macrocosm
into which the harmony of his animated city will fit consonantly - in the Republic the largest context, and that one of
strife had been Bellas (496 b 5); now it lstti(numbered
'
heavens. Where in the latter the city was a soul writ large,
in the Timaeus the city is as a cosmos writ small {27 a, 41
d 4, 69 b 1, cf. Republic 506 a 9). Obviously in this setting
the main political virtue would not be what might be called
the •substantial• virtue of justice but rather the •relational•
virtue of temperance. so strangely dim in the Republic, for as
Socrates says-there (430 e 6), •temperance is a sort of cosmos•~
an interior cosmos.
2. The city itself they animate by translating it into
history. Its citizens are indeed earth-born, sown by the
twin gods Hephaestus and Athena, she the goddess of wlsdoa
and war and he the patron of the craftsmen of the city. To
this •natural• genesis corresponds a natural end; the city
sinks out of sight in a cataclysmic earth-quake (25 c 7).
Socrates had presented them with a myth (26 b 4, c 8) and a
living myth, a tale of antiquity, is the gift they return.
The city of the Republic, on the other hand, is only as
old as •yesterda7•. It too has a source beyond itself, but
this source is not within nature, visible or intelligible,
but beyond it (540 a
The true ruler must be in touch
with this source - this, the fulfilled love of wisdom, is
what is meant
this dialogue by philosophy; Glaucon's
question about"genes1s of the best city turns into a question
of the genesis of a philosopher (504 b). Socrates answers
this question with a demonstration.
ST.
ln
�-21-
-20-
IV.
Music
A.
la. We shall now show that, like Heracles Socrates
uses music to •civilize• his young guardian. 'it is not
the traditional music of the poets which he uses but his
own r~storat1on of true music, for he takes seriously
Damon s thesis that a change in the character of a city's
music produces a change in the fundamental laws (424 c 5)
Socratic mus1o ls, as weS\i\bl.l see, philosophical music, •
the music of truth. Its special force will 11e in this
that its logo! are at the same time erga, this heing pr~
c1sely what the poets cannot achieve, so that they leave
no true 8wor~s • behind at all ( 599 b 3}.
By 9muslc the Greeks mean whatever activity is under
the care of the "uses - that tradition consisting of arts
and skills which we call •arts and letters• and among
these espee1a111 poetry and melodic music. 'To be •amusica1•
is to be an uneducated boor. Accordingly the upbringing
of the· guardians of the third city, described in Book III,
1s to be •that discovered oyer a long period of time•,
namely gymnastic to strengthen the bod.y and music for the
I0\11 (~?6 e 1), to make it gentle and "well-arranged•
CeUo-x7)J-- 0 '-'°'-> 401 d 8). But this available music will
have to be purged. Now music 1s understood to be altogether •11!.age-making and imitative•, mimetic (E..t\'\o...o-...,..L.K~v--)LL)'A--£."T'- t<."'}" >
Laws 668 a 6), so that the purging consists
of condemning the poet's false and deteriorating represen~
tat1ons especially of gods and heroes and of expung1~ _
the ~ass~es whxre he •1mages badly in his logos• CE.LKQ.)!)
ka..~wf T'f? A.o Y 't;' >
J?7 e 1). Children will then be told
myths which will be, on the whole, lies, though harmless
ones, and which 111 contain some truths ( J?? a 4). · Soc~
rates g!-v-es a practical demonstration of this purgation
1n reviewing passages containing myths - as Aristotle cl'l d
later he regards poets primarily as myth-makers ()A.v901T0Lo~>
J?7 b 11, cf. Poetics IX,9) - harmful to the tone of the
soul. When: he has criticized the myths, particularly the
Homeric ones, •about gods ••• and demigods as well as heroes
and about those ln Hades• (J92 a 5), among them the slanders concerning Theseus' presence in Hades (391 c 8) he
declines for the moment to go on to correct the myth~ concerning men. For these are worst told by the poets nor can
we correct them until we know how justice works (392 b).
We may, accordingly expect such a correction of the myths
of man later on. Socrates concludes by requiring not only
the poets but all imitative artists to make in their works
•the image of the Good. (Ti}v TOO J .. y 0.. e 0 J e-L \..-,.() v o..
401 b 1).
>
lb. Not only the stories of the poets, their togoi (J9?
c 6), are purged but their mode of speech, lexis ibid.)> · . .
which corresponds in them to the modes of melodic music, oJso
comes under Socrates' review. His remarks make the dialogue
itself the vehicle of a most fundamental reflection on the
dialogic mode, for the form of the Reuublic is a subtle but
precise example of the approved mode. Socrates distinguishes
two basic poetic modes. The first of these is straight narration in which the poet himself 1s speaking directly while
his characters speak in indirect discourse. In the second mode
the narrator drops out entirely and the characters speak in
their own persons, as in all drama (392 d 5). Epic represents
a mixture of these two basic styles (394 c 4). The first
mode is honest, but the second mode ls censured because in
1 t the poet> by hiding himsel~ hides the fictional nature of
his work and slides out of all responsibility for its truth,
while the ~:tctor or rec.der is caught in an unwitting imitation.
For he becomes, as it were, the character - all too often
reprehensible - whose direct speech he declaims, while the
guardians should be allowed to imitate only good men (394
d 1)
0
The Republic itself has th.at form wh1ch is exactly designed to provide at once the most complete poetic responolbili ty, the greatest mimetic force, and the most beneficial
imitation. For the narrator, Socrates himself, is ever present and responsible and he keeps himself before us with the
ever recurring phrases "he said' and •1 said• (J9J c 11, contrast Theaetetus 143 c). What is more, he is not an anonymous mouthpiece, whose work one reads, as one does the Homeric
epics, without ever learning who the poet was. (We see here,
incidentally, one reason why Hesiod, who not only identifies
himself but even warns the reader that his source, the Muses,
will sometimes lie, Theogony 22,27, is, if less loved, yet
more acceptable, 5~6 e 1, 607 c 8). The teller 1s Socrates,
backing his own words with the acts of his own life. A.t the
same time these words and arguments are direct and dramatic,
in the sense that one may rehearse them in one's own soul and
try them out for trut.h, thereby letting the logos turn into
an ergon. And finally, the Republic as a whole is an imitation of the activity of the 9 best of men• (Phaedo 118 a 17};~\ \~
Plato's 1m1t&t1on nf Socrat~s.
le. Nevertheless in Book VII, when Socrates revises the
guardian education for the philosopher c1 ty, music is expli ~
Ci tl v and empha. 1cally excluded from the formal plan of educ~t
.,
,
> C·/
tion as "no learning matter• (~cr..97fAo.._ ou 6~"",
522 a 3, 537,
cf. 504 d 1). For such music is a habituation of the soul,
but it does not lead to knowledge; it is a training but no-t
an educationt a conditioning but not a journey to the source,
for •the dialectic pursuit alone travels in this way• { .Jl
~ l..~).SK TtA-. Q' /u~ Qo~o) ./.v._~v7 '°'·<)TVJ nof=>E-U £ 'TU..\...)
5JJ b 7).
Consequently the musical training is completed very early and
culminates in gymnastics (376 e 6, 546 d 7, 591 c 5).
�-23-22-
2a. We know from the dialogues, however that there is
a music yet different from both the trad1t1~nal and the
~urged music, the phi:osophloa1 ·music mentioned above
videntl y it was Pyth~goras who first approprtated the oldest of the Muses, Calliope, for philosophy.19} Socrates
gives er, t ogether with the next sister Urania this same
office i n the Phaedrus.where the latter ~atches ~ver those
who make stories about the heavens and the gods while the
former ::;[.es for those who compose •human stori~s• (A~your
~"9.PW '-'1ou5 · ). And in the Phaedo Socrates tells of a
ream that has come to him often and in various shapes but
always With the same message: wo Socrates make mus1c' and
let that be your work" (p.ovcn.. k.YJv 7Tol.£L 'Kn.°L £_,,oy~~ou
60 e 5)~ Which he has always taken to mean that he sr?ould
pursue philosophy, that being •the greatest music (_µ.€~ 1
'(LCT ?5 ,µ.ou o'L ~?s > 61 a 4, Cf. Republic 499 d 4, 548 b a).
0
2b. What then is this philosophical music this •in~
quirer's imitation• (to--..,-o_...PLK'Jv ~Y..,..?cr'-Y.> S~phist 267
e 2)? In the passage of the Phaedo quoted above Socrates
s~ys ~f himself tha} he himself is not a myth-teller (~0Tci
ouK ·1 /'l-UGo)\oyL.Ko5,
61 b .5L This is literally true
·
for he ls not one who makes imitations of what never wa~
nor Will be, but one who makes images of what ls
WeliiUst
immediately mention an almost paradox1ca1---eiCeption to this _
the logos of the cities built 00 in speech• is as it
Socrates' own myth: he speaks of mthe constitution w~~~~pwe
tg_ld ~ a ~ in speech• (
7ToA~TE:°La... ry~ µu$o>..o yc'U_;u.€.v
>..oy'f!, 501 e 4). But otherwise Socrates avoids telling
11yths of his own making; the •noble lie• of the ;;::uardlans
1s a myth attributed to the Phoenicians {414 c); ···that
ant1~Homer1c Nekvi~ or Descent to Hades, Socrates' substit(ute for Odysseus false and tedious tale to Alcinous
cf. scholion on 614 b 1) which closes the dialogue is
attributed to Er and only •saved by Socrates (621
·8)
and in other ~ialogues too Socrates avoids responsibility
for myths (e.g., Gorgias 49J, Phaedru.s 244 Meno 81)
·
Imagesp on the other hand, are his very · owli mode; as Adeimantus lmowlngly remarks at one point ~'It isn't the usual
thing, I suppose, for you to speak through images~ (487 e 6)
5
vl
b
0
0
2c. An account of how . such images as Socrates makes are
formed ls given in the Philebus {J8 e)
When someone goes
about reflecting (~Lcx"ooG.;U-t..VoJ ) much by himself p man · true
opinions and accounts become written into his soul as ~Yan
inner scribe. This scribe is_ succeeded by a painter who
draws images illustrating these inner accounts and if the
accounts are true, then so are these images. ~
,
0
2do
Socratic im~ges therefore differ from myths in bein
the direct consequence of an inner argument and not the
g
persuasive counterpart of a public convers1;n
In their
presentation myths a.re thus preceded by an argument, as
nearly the whole Republic precedes the Myth of Er, and as dialogic passages precede the myths, for instance, of the Phaedo,
the Phaedrus, the Symposium, the Gorg1as; images, on the other
hand, are either actually followed by an explication which
draws out the argument which went into their making, or they
themselves give plain hints how the participant in the dialogue should reflect on them. This · reflection is of a very
peculiar kind and :ln inducing it lies the special strength of
the Socratic image: each such effort is accompanied by a reflection on itself, for to study a Socratic image means to
study not only its content but the nature of ~ and imaging
itself. The st~dy of Socratic imagery is then exactly what
Socrates himself says music ought to be: the study of true
being and its images, and, as he repeats twice, this is the
same art and effort (402 b 7, c 7). In Aristotle's opinion the
making of such images, which are, as we shall see, based on
analogy, the chief sort of metaphor (Poetics 1457 b 11), demands by far the greatest poetic gift, for it demei.nds •the,
ability to see what is like" (1459 a 17). We shall see that
this is also the philosophical gift. In Socrates' images the
•ancient difference between philosophy and poetry• (607 b 5)
is composed.
2e-f. Socrates himself fulfills the demand he makes of
all poets, to ~ake an image of the Good• (401 b 1). ,His
image of the Good is the sun •image• or 'likeness• (£~K6va..,
509 a 9, ~'.Ai...ov ~oL.b--r~To.. > 509 c 6), which dominates the center of the dialogue. It is followed by that example of a
"corrected 11 Myth of Man which Socrates had before omitted
(392 a 8). The myth which he chooses to correct, tacitly
but devastatingly, is indeed themost crucial of a11 stories
concerning humans. It is the one told by Aeschylus in the
tragedy of Prometheus Bound, which tells how the treasonous
immortal Prometheus gave men fire (2~), how he opened their
eyes (447) and made them see, and how he made them come out
of the caves they had been, antlike, inhabiting (452) into
the light of day to see the heavens and to become wise (476).
As Socrates re-tells this myth in his •1mage of the cave•
(Republic, 514), it turns out that the fire Prometheus .brought
was a counterfeit light (bl); those few who know how to use
it only abuse it, allowing it to project deceptions (b 8);
men's eyes are as blind as ·ever (.515 c 9); they yet live deep
in a cave and their wisdom is worthless (516 c ?). We might
add here as a note for the future that in the Ph1lebus
Socrates intimates that the true Prometh~us is Pythagoras
(16 c), and that in the Protagoras the sophist himself, while
crediting Prometheus with having brought the other arts to
men, claims that he omitted the political art, which Hermes
)
brought later directly from Zeus to all men alike (320 c 8).20
J. Socrates' music in the · Republic, as contrasted wLfn the
battering ram of his rhetoric in the Gorgias, ls intended to
�-25-
-24-
work a gentle and orderly conversion of the soul to the
love of wisdom; 1t is what Socrates once refers to as the
•art of conversion• (1fxv'?···'?J m:_pc...C\.ywyl]5, 518 d J).
According to the formal plan .of the philosophers' education, at twenty those chosen to study begin a formal sequence of . mathematics culminating in a •synopsis• (c 2) •
.At thirty, after another selection, the young philosophers
enter upon the long road of dialectic, which again culminates in a vision, that of the Good itself (_540 a 8) •
.l.s Socrates had before introduced Glaucon to the Good as
the •greatest study• poetically, by an image_ so he now
,
sets out the plan of study which Will prepare Glaucon to
reach it in a •hymn•: "Don't we know," he says, speaking
of the mathematical studies they have just surveyed, •that
all these things are only the preludes ("o/o or.,..u.~o... ) of
the .Dl:!m ( vof"-ou ) which we must study?• ( 531 d 7 ·. , cf.
Ti.aeus 29 d 5; Laws 7 22 c 6). And a little later, playing on the double mean.illg of nomos, law or song, he speaks
of the 81.aw which the activity of dialectic fulfills• or
the •song which it performs• ( ~ vo_µ.05 6''....t r~ ~t.o..)\.f.yc:a-e~(..
TTe.pa:t:..~t..t...J . 532 a 1). - Socrates will not turn this song
1ntoo.i,llllla\"\SJsl.wtce -9no longer, dear Glaucon, will you be able
to follow· me ••• for you would no longer be seeing an image
of what we are discussing but the truth itself, as it
appears to me 8 (533 a 1). Socrates ' music, ae the art of
conversion, is nothing but the poetic synopsis of the end
and the ..,.oa..d. of the philosophical education itself, designed to turn Glaucon into the right course. That was
the significance of the omission of music from this plan its very presentation itself was to be the overture to
learning. We w111 see that when the end of study 1s t.he
9highest study• the images and songs in which it is previewed demand the highest art.
4. Books V-VII, which contains the central images, are
again, like the •outer• books, roughly symmetrical about
the center. On the completion of the just city culminating in the discussion of the community of women and children (V,449-471: VIII,543 a) follows Glaucon's question
concerning the possibility of this city with Socrates '
answe~ about the philosopher kings; this question and 1ts
answer frame the center of the dialogue (V,471 c - 473;
VII,.540 d). The next inner theme is the definition and here ~e1mantus interposes - the defense, temperament and
proper f!lge of the philosopher (V,474 b -·VI,502: VII,
535-540). ~t the very innermost core is Socrates ' initiation of Glaucon into the philosophical education, effected by two great images, the \\sun image'' and the '·cave image'~
Tbese are interwoven with explications and with each
other as shown in the table:
507 a sun image
509 d ( ,explication of the sun image
514
517
522
a
533
a
b
a
by the •n1vided Line•
cave image
rcorrelation of the two images
explication of cave image in the •plan of studies•
lcorrelation of the explications
l
We ha ve before us a composition of intricate but clear texture.
B.,
1.
Gleucon's introduction to philosophy will itself have
a prelude - he will discover for himself the meaning of
•opinion•, doxa.
Opinion with its various meanings and its absence or pre .~ence deter~ines the key of the different parts of the dialogue.
The outer ring of logoi is explicitly spoken in a. signature
appropriate to the absence of the •good opinion• of mankind and
its homonymous consequence .. reputation., (~~5<1.. ). Adeimantus
has stipulated at the beginning (Book II) that the argument
abou~ justice must "remove reputations'' {"10-5 8~ 1;6'!}0-5
)
21
o....<p°'-'-P£'--; 367 b 5) and ha.s provided the magic Ring of Uyges,
which will allow the wearer to do anything, that is, to be a
complete panourtws. wl thout being seen or blamed. At the end
of the argument (Book X) the ring and also the concealing
Helmet of Hades which the argument had been wearing can be
removed (612 b 5), for even on the supposition that the opinion
of men has no weight, justice has been proved profitable.- At
the center of the dialogue, however, where an ergon is set
into the logos, the opinion of mankind cannot be supposed
away, for the many will have to be won to the acceptance of
philosophy if anything is to be done.
But 1t is really the inner source of this public opinion,
the faculty of the soul Glaucon will soon learn to call doxa,
which is of overwhelming importance at the center, both for
the older and the ymmger lover of wisdom. For about the
~greatest study" Socrates himself has, as he repeatedly says,
only opinion (506 c 4, e .2,· 509 c J, 517 b 7, 533 a 4), although
opinion so well founded that Glaucon · will not be able to follow
him without a long course of study. So also the •1nterest• on
the capital good, its child - Socrates plays on the double
/
meaning of T0Ko5 : child and interest, as in our phrase •bearing interest
which he 61 ves to Glaucon will provide him only
with opinion, but as the interest is not paid in counterfeit
coin and the child is no bastard (507 b 5) so, we may infer,
will Glaucon conceive not false but "true opinion'', and this
is the beginning required for learning. But throughou~ the
one thing which everyone wants in truth and not merely in reputation (rjj 'b£. csc;;G-v 505 b 8) Will have to be approached by
opinion.
1
'
-
�-27-
-26-
2. As so often in the ~epublic, the conversation ma.kes
its own medium the object of reflection, in the case of
doxa at its very inception.
The "third wave,. has just closed in on Socrates (Book V,
47J c 6). He and Glaucon must now define the philosopher
(474 b 5). Just as there are some who desire love, he
says, and some who desire honor, there are some who desire
wisdom, and all of it. Glaucon asks whether the lovers
of wisdom then include lovers of sights and sounds. Socrates answers with a distinction to which he would have
difficulty in getting anyone but Glaucon to ageee (475 e
6): The just and the unjust, the good and the bad,, are each
one by itself but ftin communion with deeds and bodies and
one another they are imagined in every way and Hppear each
to be many• (476 a 4). Now lovers of sights love - and
apprehend - beauty in its manyness and are asleep with
respect to true beauty itse1f, being unable to distinguish
this one from the many, but the philosopher loves true
beaut~ The thinking (~ <adi."'o Ln... ) of the latter is
knowing and is to be called knowledge, gn~4e, while the
former only opines and has opinion, d6xa
76 d 5).
Furthermore knowledge must be of something which is and
is •that which ls completely .. (T~ rro..'-'•E-Xw) ~/v ) ,wnich
is COm_Rletely "to be known•, gnost6n, While "'what is not,.
(fJ-i' ~{v ) is entirely "unknowable", Sgnosto!! (477 a 1).
Now if there is something "between• (,...<.t.£ ra.~u ) complete
being and complete non-being,~then, as knowledge belonged
to being and ignorance (agnosia)to non-being, so to this
.ithing between" (To./-'-£TO...~u
) must correspond something which 1s itself •between ignorance
o..V'td..
knowledge• (epist~me, a 10). This 1s found to be
opinion, having an object and a power (~OYU:-.)...t-LJ) different
from either knowledge or ignorance (b 12). If he and
Glaucon can discover what it is that, being more shadowy
than the former but brighter than the latter, lies between them, they will have found ~that ~h1ch is to be
opined~, the doxast6n (478 e J), and so they will name
it, "assigning extremes to extremes and means to means"
(e 4). They will appeal to the lover of beauty in manyness and ask him if all these things are not also sometimes ugly, and 1f the same is not true of things just,
great, or heavy - that they will all be fmmd at some
time to be the opposite, so that they cannot be said to
be or not to be one thing or another and are tossed about
in between being and non-being. A lover of such things
should be called a "lover of opinionn and not e •1over of
wisdom• ( g'L.'Ao~o5ou5 > q>1....>-.oo-O'lpoU)
480 a 13). So
ends Book V; becoming, genesis, the "in-between thing:• has
not been expl1c1tly named.
1
J. This foregoing argument cannot help but remind
Glaucon of an earlier one (Book IV), in which it had been
- concluded that cities derive their constitutions from the
individual constitutions of their citizens. 22 ) Socrates had
then asked whether the three powers of the soul, those of des ire, of spiritedness, and of reasoning, belnng to three parts
or whet.her we do each of these with the whole soul (436 a 8).
To show that there are indeed three separate parts they posit
a strict correspondence between desires and their objects. If
a man wants at the same time to d·rink and not to drink because
he knows that he ought not to, then his soul must conta1E two
opposing parts: a ~'bidding" and a ur or bidding u part ( To
KE.A&uov, r() ~w,\Do~4J9 c 7). There are then these parts: the
rational part or logistikOn with which he oalculat~s ( ~
'Aoy'ffc__To-t- ) and the desiring part or epithymetikon ~hich is
unreasoning (0..AoyLcrrLkbv) and where desire . (ep1thym1a) sits
(4J?r d). Between these two, the forms usually recognized
(£>L~!?>
e 2), Socrates inserts a third part, the spirited
part or thymoeid~s, which Glaucon, obviously listening to the
name thinks more akin to desire, but which, as Socrates points
out, 'can be an "aux1111ary" of the /easoning part ( e 3 )J making
us feel high-minded anger or thymos (440 e). Finally, these
three parts are arraniJtd wi thin . . .us !_!S the,, 0 three terms of a
.
musical proportion" (o,.r>ou5 Tp£t..5 ¥,µ.ov. . .t...a..5 >
,,44J d ....6) and
thymes becomes •the in-between power• (1~ j.J-E. •o..5 v 'e u v~&L..,
479 d 8).
Glaucon has therefore been asked once before to distinguish
the parts of the soul by means of their relative object and
to understand one of these parts as a mean between two extremes.
If we juxtapose the results- of both exercises we get the following result~
gnos1s
loglstikon
doxa
thymoeid.es
epithymetikon
~Si~.
For the middle parts this correlation ls, in fact, tacitly
but unmistakably made in the dialogue. For instance, a chief
characteristic of the warriors, who as a class of the just
city correspond to the spirited uart of(th;~sou\, i~ the
11 preservation of law-abiding opinions•
~ o 7 '?S £.VVo~ov
cr-WTt-;,Plo...J 433 c 7) within them.
ll:lso in a timocracy, which
renresents spiritedness among the degenerating cities and is
emphasized as lying 1'between'~ aristocracy and oligarchy (527
c 6, d 1), the chief characteristic of citizens is love of
honor (548 c 6), which implies a connection of thymos with the
external doxa called reputation.
4. The logistikon, on the other hand, is not quite coextensive with-gnosis. Here we must stop to observe the name
itself. In the traditional double division of the soul into
a rational and an irrational part, the first as having •reason",
logos, that is, the power of giving accounts (Aristotle,
N~Gomachean Ethic~, 1102 a JO) was quite properl~)called
logikon, evidently already by the Pythagoreans.2J
Why then
does Socrates call it the lofjistikon, connecting it explicitly
���3
�-34-
-35-
source of the whole
truth
ideas
intelligible
things
clarity
: ~thought 01
. lknowledge
- as exercised
in dialectic
hypotheses
things of
sight and
opinion
trust
reflections
recognition
and making
of images
1ntell1g1bles~
thinking as
exercised in
mathematics
natural and
made objects
place of
being
place of visibles:
becoming
2a. In presenting the sun image to Glaucon Socrates
ls requiring him to exercise his doxa.
Of the two _.doxastic" powers, the lower, whose pregnant
name is e1kas1a, thrown in at the very end with conscious
nonchalance, will prove to be the most pervasive of the
four ..affections".
Ordinarily the verb e1kaze1n means to '1 1magine" both in
the sense of making an image and likeness) and of discovering a likeness or likelihood, 1. e., to compare or conjecture,
while eikas1a is both the ability to make or see images and
likelihoods, and the image and likelihood or conjecture itself. To Glaucon the word would particularly call to mind
a witty and malicious amusement with which clever peop~g)
spiced their symposia, called ~likenesses• or e1kasiai..
It consisted of representing someone in a.n image, whereupon
the victim mi~ht retaliate by mak~ng a ')counter-image" or by refusing to play. So Meno t~lls ~aerates that he
appears to him to be "most like .. (op.ol.oT<>...TQ.5 80 a 5) a.
torpedo fish, and &lcibiades, in the one t~1e'triumph of
his life, appearing in the Symposium as the god Dionysius
himself, speaks of Socrates "through images'' and compares
him to one of the Sileni in his train, except that - since
his image is "for the sake of truth .. (215 a 6) - this
Silenus ls more sober and far more divine than the iOd
himself. And in Xenophon's Symposium (VI,B) Socrates curtly forbids the game when the eikaslai threaten to become
injurious and false. Now Socrates is in the habit of introducing great matters under the image of a game or riddle (cf. 1 479 b 11, 521 c 5), and Gla.ucon will soon see
that the game of images 11 1tself ls no mere image.
In the meantime it must startle him to hear ttconjectur1ng" elevated into a ~power~ in a direct line with thought
1 ts elf. But as the meanl!lf'; of ~aerates' central image penetrates he must notice that it itself requires a peculiar
application of his ~bllity to see imates - for he is~on the
one hand> intended to ima~ine by meRns of the 1ma£e what the
Good is ''like'•, but he is also, on the other hand, to reco~
nize that the sun's world is but a likeness, t~lt his own
visible -world ls a count'erfeit of-}?~. Socrates had 1n
fact prepRred Glaucon for the fundamental importance of this
power to recognize an image ~ an image. To fail to possess
it is to be permanently asleep to being: .,Look, isn't that
just what dreaming is - when someone either in his sleep or
while awake re ~ ards that which is like to something not as
like but as the same a.s tha.t to which it is lil<e?,. (47b c 4).
In absorbing the sun image, Glaucon then learns to use his
eikasla in both of the fundamental senses which Socrates, as
the savior of the t~1e meaning of words, has restored to it.
2b.
So also the next power, pistis or trust, comes into
play. For as in seeing the sun's world as an image, Glaucon
has been forced to lose trust in the visible world, so in
s~elng the sun,as a.n image of the Q.QQg. a.nd most like to it
(o_µoL.oTo..."Tt>J eKe-Cv't", 506 e 4) he acquires a better doxa
of this world, a trust that life and government 1n the image
of the Good are no~sible here. This trust ls the ~eikasttc•
counterpart of the nersuasion exercised in myth-telling {cf
6?1 o 1,3). In this use of the image we wee why the question
"whatever is the Good 1 ts elf?,. is ''bid goodbye for now•• ( .506
e 1), why no explicit 1'diE1lectical" acco1.lnt of the Good ls
given at all: the Good appears here only as the end or incentive to learning e.nd doiJlb, as tithat which every soul pursues and on account of which it does everything, having a
presentiment that there is s0me such thlntft (505 d 11). It
is that one same thing which all human action, be it for
show or i",enulne, intends for the actor not in seemine·, but in
heing, and the difference between attaininL it or missing it
is precisely knowledge or lack of it (e 2).
In that sense
it is the "greatest studytt, for, as we will see, in another
sense 1 t ls n0 'J'leB-rning matter" ht all. The overt treatment
of the Good in the .H.e1)ubliQ consists simply in maintaining
lJoth that there is one r-,ennlne enc1 of all human effort which
is at the same time 1 ts sour<;'e, and thc.t 1 t is necessary to
hold t11is opinion.
D
2c
Yet the absence of some explicit reflection on the
nature of the Good seems in want of further explanation.
kl Aristotelian anecdot.e about the audience's reaction to
Plcto's lecture on the Good, related by ~ristoxenus in his
Ha:r.!Tlon1c E_lemen ts {II, 30), is pertinent here: '''rhey came,
every one of _them, expect1Ilt, to get some one of the goods
considered human, .• but when his reasonings appeared to be
of Rtu~ies and numbers and ~eometry and astronof9.Y and of
the limit - t1lat as a limit Good is one (TO' rre/' a..5 Cf1L.
~yo..e~v icrTl..V ~v ) , I think it seemed to them irery stra.nge
0
�-36-
indeed, and then some sneered at it and others criticized
i t . Now what was the reason for this? That theY. knew no>
')
thing beforehand, but just like intellectuals (£,P~~rl~o~
were present to lap it up on the strength of the word itself.• Now Socrates himself had several such "eris tics''
on his hands - one of them Adeimantus} to whom he ls careful to mention the •1dea of the Good ft as something ~dei
mantus has often heard before, as something which is a
cause of usefulness ~d profit and without which a man
•cannot have the sent1m.e nts of a gentleman" (Ko.Xe"' ~£
ko..'t ctyo..eci-v ,,u.?8e"' cp?c:>-...JE,cv
505 b 2), to which Adeimantus reacts with a pat, erlstic question worthy of a
Meno: "But yo1 Soc~ates, do you think the Good is k:nowledc;e or pleas· ire or some other thing besides these?"
( 506 b 1), clei .rly a standard question about ''the Good"
(cf . Philebus : 9 c). Here Plato nobly shows Socrates as
wiser in p r act: c e t han he himself was - in the t wo di al ogues dealing with the Good, the Republic and t he
Philebus , Socrates f inds tactful ways to choo s e h is i n terlocutor and to b ring him a l ong . In the p r esent 41alogue he silences ~de 1 mantu s by s ugg e st i ng to h i m tha t
he has heard it all before - t he ri tual -like u se of the
term •1dea of the Good • (505 a , 505 e , 517 b , 526 e ,
534 b),when the Good is not an eidos at all , sounds like
a soothing allusion to current d 1scu ~ s 1 ons (c f . Epicharm s
u
in Diogenes Laert1us III, 14) - wh il~':b ring 1ng Gl au co n
with a light hand to the •awe-inspiring enorml ty• ( ~o... '-
µov'C.0...5 u-rr£,P/icA'?5, 509 c) of this So era tic Good.
But Socrates' indirection is not on ly a mat ter of avoiding public misunderstanding; it als o has a posi t ive peda gogic aspect. In providing Glaucon with imag e s to r ef l ect
o~Socrates instills in him a kind of artificia l "recoll e ction" {cf. Meno 81 c) which will enable him to •)ecognize •
the logos he might after reflect i on c ome upon. 2 7
This 1 ~
after al~ what an interpretati on of an image is - a
recognition of its meaning. The r e f ore in some way a
d i a l ectical account of th~ Good li ke t hat severely arithmetical one given hy Plato in t h~ famous lecture on the
Good mentioned above _ or in ~is oth er ~unwritten teachings•, must be latent here. 2 ) We shall try to find it.
Ja. When SocratP-£ has deli v ere d hi s s un image Glaucon
asks him to go once more t hrough t.he "li kenes s of the sun"
"
.....
ltl'\
'
5 09 c b to f 111 i n
/)
TT£f"- TOV V]" c...oY O_Aot.. /oT?TCL )
( ' T~ v
whateve r had been omitted before . Socra t es ' answer t o
this request is the dividing of the line.
The Divided Line is the mathematical figure fo r the
implicit logos and the possibility of learning what is
yet unknown. The choice of a linear figure is itself
meaningful, for the line, as the unique connP-c ti on of two 1l10nd\'points, stands for that closest of all relationships of
like to like of which the knower and the known are the
-37-
paradigm (cf. ~.\ristotle, On~ Soul, 404 b 5 citing Plato;
Metaphvsics 1036 b 8, the Pythagoreans). In understanding
this explication of the sun image, Glaucon exercises his
dlanola.
The word dianoia is used quite generally of what we would
call •mental activity... For instance Socrates himself says
(4~6 d 5): !'fWhy may we not call the mental activity (TYjv
~ L~ "o L"'-"' cf. Sophi st 26 3 d) of one who knows, 'gnome,. s.nd of
one who opines, 'doxa '? • This word too is "restored" by Socrates. The d1ano1a whir.h goes with the third section from
the bottom is the power used in thinking or as the phrase
goes, in :Mthlnklng things thr .1ugh" ; it mean~ attending to or
searching for that in them which can be grasped 1n thoughtful words, which the Greeks call logo1 . This involves a
h i g~e~ ~1n~erR&~eikas1a which may be terme d "d1anoet1c eikas la , 9 ) for~ tn in gs wh en caught i n speech reveal themselves
as mere 1m1 tat~ ons of some thing which. t h e logos is truly
about, as t he visibl~ a spects • (hor6mena e1d e 510 d 5) of
the true •1ooks" (eide) of the thing 1tse1r:--(so in the
Pha edo _. 99 d) Socrates intimates that in a c ertain way logo1
deal with imitations,i~not 1n truth.) The objects of
the dianoia are therefor~ described primarily as •1mages••
in the dlanoetlc section the soul preceeds by teus1ng the '
things then imitated [J.e. the natural objects which were
imitated in the lowest sec ti or!) as images•• ( 510 b 4 511
a 7 ) • By "suppos lng" these, 1. e. J using these as hyp~thes es
distinctions can be made and conclusions reached. The ref e~
ents of .geometric drawings are such figurative hypotheses
while the great arithmetical hypotheses are those recomme~ded
by Parmenldes himself as a pre-dialectical study, the hypotheses about the "'one''; that it ls or is not (Parmenldes 1J5
c 8).
Jb. If from Soc.r ates' point of vi ew the fundamental
nature of the present discourse is eikastic, for Glaucon
it is dianoetic. Summarizing in his own words, but accurately , what he has learned from the di vision o·f the line
he brings out a central fact only implicit in Socrate s ' w~rds
namely that the objects of the dianoia are the same as the
'
noeta of the uppermost part, that they are these-n0~ta with~
out a full logos, and ends by treating the faculty as that
which the division was intended to define. For observing
that the very name of dia-noia suggests a mean, he defines
it, analo§ously to doxa before, a s "something between
C,,,l.(..t.Ta..~ u ) doxa and nm!§. [thought\ '' ( 511 d 4), as the
naturalfy intermediate faculty (cf. Sympo sium 202 where
Eros as dalmon is the corres p ondi ng intermediary )'.
J c. Soc rate s of cours e depends on the mathematical pred i spos l tion of his young philosopher - mathematics being
after all the young r u lers ' childhood amusement - in 1ntrodu e :\ ng him (cf. 508 c 4, 509 d 1) to the exercise of the
�-38-39·1 0 wer noetic faculty. In Book VII, in the very act of beginning the long description of that formal mathematical
education which 1s the "prelude" to dialectic (~31 d 7), ,.
Socrates actually engages Glaucon in a serious methodical
dianoetlc exercise. When Glaucon, accurately recalling
the musical education of the guardians, perceptively concludes that this cannot be the study the future philosophers need, Socrates asks him: 110 my marvelou~ Glaucon,
which would be such a study ••• ?" Glaucon eager~y interrupts to ask what study indeed might be left (522 b 3).
Socrates now 1nv1 tes l;_im pointedly to become his •fellow. '\ .
1nqu,1rer• (o-vve~a.Try5J 52)
85S he '~akes divisions \N\~·~w: ~ ;·)i1mse1r• (8 L°'-"-/'oD_).'-o-\... rr¥ ~a..~""{'~) ab~ut w~at
studies lead toward be1pg~ and to say I agree or I
dlaagree • • (o-~~9t... t} b ..:rr e:. L. 77 e), being careful to see
that Socrates ls Norac11ng• correctly. The discussion
which follows shows that arithmetic is precisely the study_
wanted, since it is •1nv1 ting to the dianoia "(1Tt:y>a..~A?Tt..~a~
"
~ '-o--vof..a...Ji 524 d J) and •arousing to noesis • (c:.ye:,:PTLKQ..
. ~5 "VO .,,. o-ew5 d.> 5). Socrates proceeds to begin with Glaucon
th~ stJdy of' uthe one and the two and th·e three'-' ( 522 c 526 c) and this is Glaucon's first and only step on the
d1alect1ca1 way; here and nowhere else in the Re~ublic is
there undisguised direct philosophical work - a huge
)
work•, as Glaucon has begun to realize (511 c 3, 531 d 5 •
a?»
Jd
But why should Glaucon need to be especially invited. to this dialogue, since they are already in the midst
· 0 r one and have indeed come
as Polemarchus says in the
beginning to converse (~ l.O.~~~ 6~e.$o..J328 a 9 H- Evidently
there are' various ways to converse. In fact three meanings
of dialegesthai can be distinguished in this dialogue.
First it can mean a conversation 1n which anyone may
take part
This desoite Thrasymachus' efforts to stage an
exclusive.rhetorical display, is its meaning ln the .,prelude~
(357 a 2) of the dialogue, Boo~ I. It _ca.!1 also ,.be that .
"power of dialectic .. proper C3vv0-~L..5 rou <81..0....)\e.yc:.o-&Q;l...-,
511 b 4, 532 d 8, 533 a 8) in which the logos, the accountg1v1ng power, by itself, leaving all sense perception behind moves "by the e1de themselves, through them and into
them~ (511 c 1). This power is imitated by sight (531 a
2)
as the eye sees things at once distinct and together,
80 the soul ranges over the noetic •sights", as the name
eidos, •sight, look, aspect- indicates. It is clear that
Socrates regards the soul as truly moving (cf. Timaeus
36 e 1) both upward and downward> only in dialectic, which
1s thus' repeatedly called a "way If, a •pu~sui t or a method •1,
a "journey• ca-~~5, 533 b 3, 532 e l,3;;-<-€.9o'O.:l.) 533 b 2,
c 7; 770/'e-f:o..J 532 e 3), while the conclusive motion of the
d1ano1a 1s downward (510 b 6, d 2) as in deduction, and
that of the' lowest two powers is back and forth as in comparisons. In the us~f its lower powers the sou; is said
to be bogged down ana:-s1uggish (533 d 1, 611 c) bJ its
J
association with the body; the soul is never quick with bodily
life but only With the l)gos. But dialectic is only praised
in the Republic (532 a 1 ; its 1ctua1 exercise 1~ impossible
to one wh o i s not "practiced•• (£,P-7TEL,Pt.t/ > 533 a 9) in dianoet1 c studies. ~d indeed those 7'propaedeutic1l' (536 d 6)
mathemati cal s tudies are c&refully trimmed not only of all
•banaus 1c~ , ioe, applied, elements, but also of aJ.l explicit
•eidetic" admixture - for instance nothing is said of the
"eidetic numbers (cf. ~istotle, Metaphysics XIII,6) - although allusions to dialectical terms abound
There remains a middle dialegestha!_,which is characteristic of this central cor.vers&tion. This is speech between two
souls Which must have a sensl ble clothing of sound, the a.udible dialogue. Such dialogue is strongly distinguished from
myth-telling (e.go Protggoras 320 c, 324 d, Gorgias 523 a,
Timaeus .26 c) , which appeals to trust and imaginationp because
1 t involves primarily the dianoia Which supervenes as soon as
sense perception when expressed ln wor(ls gives rise as it
inevitably Will, to dilemmas, for instance self-contradiction
(524 e J). In supplying hypotheses to solve these dilemmas
it brings in noeta and invites the uppermost faculty of
·
thought, noes is ( 523). In 1 ts elf it is the faculty of di f- ferences, distinctions and contradiction~which ever ranges
be~wixt an~ between and which unguided, can be an aporetic
or waylesd affection (524 a 7~. Therefore in such a dialogue
one of the interlocutors must know somewhat more than the
other, . must have advanced into dialectic so that he will be
able ''tn ask and answer most knowledgeably" ( 534 n
Here
With Glaucon, Socrates exercises this superiority more even '
than usual , since their conversation is · ''synoptic .. and requires a large fore-knowledge. The introduction to arithmetic
mentioned above displays precisely the required relation of
the interlocutors: Socrates makes dialectical di vis ions •wt.ihtn
himself" (523 a 6), which he !'shows•' to Glaucon (a 9) while
Glaucon is to look on with him and to agree or disagr~e. But
most of all . this dialog1c superiority is evident in the very
n aming of the powers of the soul With which Book VI closes
for they are, as it were, named from above. Anyone who ha~
not left the first three sections ca1Ulot possibly know their
true names: doxaJas used ordinarily, means the faculty of
jud~ment; people.rarely think that they have what to Socrates
is mere opinion but rather that they Y.now what they are
talking Hhout, while the various provinces of the dianoia,
n~Iriely the arts and mathematics ( 511 c 6, d J) i are regarded
by their devotees as producing •'knowledge •·1 ( 533 d 4).
1
'
0
9).
4ao We return to the 1nv1t&t1on extended to Glaucon bv the
sectioni~g of the realms ~as if" they were a llneo AS was said.
the Renuolic has no dialectical treA.tment either of the Good
or of the eide~ but this missing logos is absent in a different way for each:
The Good has no ~place" Within the realm of being, for it
�-40-
-41-
is 9beyond being• {En{KtlVO... ·1-S) 000-<:"a...5>
509 b 9).
Since it is that which is 9un-hypothesized• it cannot be
traversed in the way in which are the •hypotheses to
being•, the stepping stQnes of the logos {511 b 8).
Consequeritly th~re is no power of the soul which corresponds
to it, as is signified by the fact that it is off the
Divided Line. Althou6h within the context of the imaGery
of sight, the eye of the saul is s5,id to look at~ it, a
distinction between movement 1tamong • and "through,, the
eide {o..vTol...5 £l/~~O'"l. ~ . . .,o..0-rwvJ,.... 510 b ~ ,.511 C 2) and
movement •u_p u.nto,• the C!_ood (~£(P!- 1ov ., o..~... uTTo.?£\CJu . .
trrl: 1ryv IOV rro..vTOJ ci?XVJVJ .511 b ; t.:n~~'{'YJV' TtJV O:...~;(?V'_,;
533 c 8) is maintained; the latter has~something ta~en
tl.o..\ and momentary - the sight is scarcely (~o Y'-5 517
b 9) achieved. Furthermore this beholding ls not knowing in the dialectical sense, for the •1dea of the Good•
is the result not of "intuition" but of "abstracting"
( d.Cf'e 'A~ v
) and 111 defining in a logos'' ( 534 b 9). Socrates reneats this several times: the Good as responsible
source
known onl ...,. after the vision, on the downward
return,. so to speak, by a syllogim~..°s OJ' ~C?}le~/tion of
logoi, a logos of logoi ( ~o..\:: .1"'-t.\O To..VT O.Y YJ S? cru~.Aoyt'.:~oLIO .... ~Tt- ~t-rL..o5» 516 b j; ~<pe£'2cro... o-u.A).0
Lo-Teo.. £L~o.'- ~5. - .o..~Tro...._, 517 c 1).
The Good{ the
-~g/eatest study•, 1s not really a "learning matter•, a
mathema at all.
1s·
4b. For those realms, however, which are on the Divided Line, the absence of logoi takes on a different significance and form. It is essential to the following
discussion to recall that the word logos means not only
account- or reasoning but also the mathematical relation
of ratio, a double .meaning of great importance partlculRrly in "Pythagorean" contexts ( e.f',. Epinomis 977 c J). Now
we are told that each of the unequal main sections ....... the
of
.......
line is again to be cut in the same ratio ( o.. v a.. ·1 o v
CA.\}\o '1 '>...oy o v,) 509 d 7), but we are Liven neither the
ratio itself, be it numerical or irrational, nor a re we
told whether the great~r or the less of the unequal segments is to be the upper one. We can conclude nothing
except that the two middle segments must be equal, ioea,
that ,nJ.st1s and dianoia are in some way coextensive, as
is indeed necessary since the die.noie uses natural ob~cts as 1mages.30J This absence of definite ratios ls
the--more noteworthy, as for the earlier tripartite soul
th~ numerical rat:1.os of the parts are, playfully, given:
111
they form the musical progrAssion of the "•high .. , u1ow ,
and ·~iddlefl notes, tbat is, 3i)pr1me:fourth:octave,
which are as 3:4:6 1443 d 6).
&1t if the logo1 themselves are absent, this much
a.bout them is given: th8y, are the -~'ilf: throughout, for
that is what defines a proportion, Em analogia. How is
Gleucon to interpret this mathematical fact which is
presented to his dianoia?
")
4c. Immediately after the fundamental division of the
line and the description of the lower subsections, Socrates
reads off a first proportion (510 a 9):
·
doxaston : gnoston
images : imaged object,
.
>
this announces that the internal relations of the lowest
realms are the same as those of the whole, that the whole
is mirrored in even its lowest parts. At the very end of
the Divided Line passage he reads off another proportion
( 511 e 3):
segments of line : truth
affections of soul : clarity,
which means, in m&thematlcal terms: the affections of the soul
are the correspondents (Euclid V. Def. 11, given a:b;:c:d, a
is said to correspond to Q and Q to g) of the realms of beilig
which the line segments represent. Or, using analogical
reasoning, that is, inferring the likeness of correspondents
{cf. Aristotle, Metaphysics 1016 b 34, 1093 b 18; Topics
108 a 7);we may conclude: lmown and knower are alike (cf
Aristotle, On th~ Soul, 404 b 18). Here the analogical •
method brings ~ut the bond whic~ •yokes together with the
strongest yoke (.508 a 1), the linking of known and knower
by the light of truth, which can bind them precisely because
they ar~ both •1ike the Good• ( 509 a 3), that •ruling source•
of the comiinlnity• of knowns and knowers (cf. Sophist 248 a
11) • . And finally, in concluding the ex'Plication of both the
sun and th~ cave image, he forms two more proportions (5~4
a 3):
J
being
becoming . . noesis : doxa ·
noes1s : doxa : : episteme : p1S't'is
d1ano1a : e1kasia,
the first of which signifies that the degrees of lmowing are
the same as those of being. The laet displays particularly
well the force of the mathematical form Socrates has chosen
For Rince the affections of the soul are coordinated with ·
linear magnitudes they may be "alternated' (Euclid V, Defs.
13,J) so that the first is to tne third as the second to the
fourth, and this is exactly what Socrates has done here. This
form draws attention to the close relation of each faculty
in one main segment to the corresponding faculty 1n the other,
a relation which is the same as that of the main faculties
and again as that of the realms of being. The last ratio
given particularly justifies the notion of a •d1anoetic eikas1e•,
while the ratio before that shows a certain special relation
between lmowledge and trust; this con;ies out clearly in that
unassailable finality, on a low level. not unlike the selfsufficiency of knowledge, whic~ certain sense perceptions
possess {523 a 11).
Obviously by using the various Euclidean oper&tions {V,
�-42-
Defs. 11-18) on these proportions, and by attending either
to the sameness of the ratio relation or to the likeness of
the correspondents in the new proportians1 it is possible to
obtain a variety of illuminating remJlts. .All of these are,
however, only the expression of two fundamental similarities: that of the knower and the mown, mentioned above,
which leads Socrates to tell Glaucon to •order them [1he
affections of the sou:ij analogously• (511 e 2) to the realms
of being, and secondly> that really prior similarity of each
degree of being ·to the one next higher) by reason of which
these deg~ees are described in ·turn as •that which is made
similar''{~o'-welv ), "that "Co which it is made similar",
•that which was before copied now treated as a likeness•
(~(\<.WV, ¢f.(510 a 10, b 4, 511 a 7), while the~ themselves are agathoe1de (509 a ?.), forms '"well-formedft or
formed in the likeness of the Good.
This four-stepped ladder of similars is what makes upward
transition, 1.e., the dialectical road, possible. It 1s, we
should note, first articulated in the Divided Line: the sun
image has only two undifferentiated realms, the intelligible.
and the visible. The Divided L1ne in a certain way preserves
this original homogeneousness of the larger realms; images
and natural bodies are not differently constituted, that is,
made of something different, for.both are sensibles (510 a
1 :1; note that reflections are •1n water" and •on smooth
bodies•, 1.e.> the difference is not that of the visible to
the palpable), and hypotheses and eide are both 1ntellig1bles.
What differentiates the realms internally is rather the
•reflective• distinction of like to likened, by which the
parts reflect the imaging relations of the sun to the Good.
4d
Glaucon must then see that the logoi relating certain ~spects of the whole are one and the same tl_!roughout,
that on account of similarity or likeness (homoiotesJ
there is one logos pervading the whole. In presenting
this to Glaucon mathematically, Socrates is in fact presenting him with such hypotheses about being and becoming as
will make thinking itself, namely thinking consistently,
i.e.) "preserving a sameness of logos 11 (o,.µ-o)\.oyov,...u-fvtJJS,
510 d 2) possible. For if the characteristic dianoetic
direction is downward to conclusions by deductions which
win agreement (homologia), the inventive or discovering
d1anoia moves upward by an analogia; it is this latter
use which is chiefly required of Glaucon in this dialogue:
•Make an analogy ••• ,. (524 d 8, cf. 509 b 2). A sober
application of this me&ns . of learning is· examined in the
Statesman: when something about which the learner has
right opinion is used as an example, a parg-deigma, something "to be shown beside• some unknown, then this unknown
may become known to him by the recognition of the analogy
( 277 d 9; Socrates in his characteristic refle ,)C· l ve mode,
explains "example,. by an example, just as in the Rep@_lic
-43-
he explains "image" by an image). The sun 1mag e is just s ch
an "example•.
u
We m~y say that the Divided Line tells the story of •recollection ma.th~matically by presenting through proportions
tha.t faffinity of all nature (cf. Meno 81 d 1) which makes it
possible to move with recognitl0n in unknown places.
4e. The first ~nd 0rlginal affinity, the sun image implies
is that which the Good as progenitor gives to the sun as an
'
offspring made in its image. In other words, the Good itself
possesses an image-making power which it nasses down to the
eide ~nd which they pa~s on in turn (cf. Phaedrus 250 a 6)
This downward e1kas1a , as it might be called, is originaily
responsible for our own ability to recognize likenesses or
to make .analogies, for m1r •upward e1kas1a• and the pleasure
of recognition which it gives us (cf. Aristotle Poetics
1448 b 1), a power so fundamental that without it we would
not know the looks, the eidos, of our own face!
4f. We can now see why the criticism of ~o~try in Book
III turns into the radical •ancient quarrel~)?} between
philosophy and poetry• (607 b 5) in Book X. In the light of
the sun image poets are usurpers ~ perverters Qi the power
of the Good. They &re more despicable even than that char~atan who by car;;y1ng a mirror through the world claims to · have
made everything (596 c l)>when he has only borrowed the lowest '" effects of the power of the Good, for they make artificial
ima.ges,ttusing a.perverted power of elkasia, a •1ow generation•
called mimetic or imitative (602 b 4), which produces images
indiscriminately of good .ana bad (604 e 1, cf. Soohist 233 c)
and distracts the hearers from true baing (605 a 9). Mimetic
products are not natural likenesses (cf. the phrase in Gorgias
51) b 4) but are separated from the true source of images· by
~~~ 19~e~pos1t1on of a human maker, who •makes images vilely•
£\...\<..~,TI - - - ¥:.o....f w)s, 377 e 1).
Poetic mimesis makes art1f1c1al 1mitat1onsr 3 while Socratic e1kas1a make~ likenesses
in the sense of observing those which are already there by
nature, clothing them in figures and putting these in words.
5a. We must n~w see what conjectures about the Good the
sun image allows Glaucon to make on reflection even though e
logos must be absent.
>
In the ~IDA6~ the Good is presented in three successive capacities, u triplet proved fundamental by its recurrence in
;~et~~ilebus (20 b 8). It is presented first as the father
- ~ -,_ · s.un ( 508 ~ 12), then A.s that which is resyonsibl~ for
!ffio\'Jledge (e 6) and last ?s the source of being b 7 )_J4 J ~hP first of these might oe called its cosmo~t enetic function
Y Which the potent male Good t;enerates the
as a male
'
offspring to be lord of the visible world and a secondarv
(5~ac: 4nalogous to itself us ruler of the world of thought
· , 517 c 3)a The obvious question here is whether the
sun
�-47-
Correla ti ·ve eide of the Same and the Other which extend throughout being, for by being one and the same with itself each
eidos remains integral and independent, while by being other
th~n another 1 t becomes the same w1 th that other, 1. e.> another
''other", and capable of participating in 1 t ( 256 a 10).
Now if the point of view taken is not within but ('beyond
being", Likeness and Difference perform just such a function
as Sameness and Otherness did within being, and, in a way, more
adequately. For within being 1 the secondary, reflexive e1dos
of the Other was the source Qf _community, while the primary
Same was responsible for separate and independent oneness.
Rut the bonding of the whole is achieved precisely because of
the Likeness of each thing within it to a pattern beyond and
so to each other thing, while Difference ls resoonsible for
the separb.teness of each single thing. The fact is that
Parmenldes' objection fails if only the pattern is beyond
reach, as the Good indeed is: "~ •• it is right to deem both
of these Cknowledge and trut1!] like the Good, while not right
to consider either of them tne Goo~ rather the condition of
the Good is yet more honorable. • . L_and furthermore] the Good
is not beine but :-'et beyond being in seniority and exceeding
it in power• (509 a 3, b 8).
It is precisely this bond by which the G')od makes everything one which, when mathematically expressed, takes the
form of a proportion: '"and the most beautiful of bonds (&·E'.~~v)
is that whlch_makes itself and the things bound togeth~ es
much as possible into one. Proportion accomplishes this most
beA.utifully. For when the middle term of three numbers ••• is
such that as the first is to it, so 1t itself is to the last, •••
then necessarily all will turn out to be the same. They will
all become~ with each other• (Tim.?~ 31 c 2). We can now
see a second. reason for the equality of the middle sections
of the Divided Line - it is the three-term proportion (i.e.
a: b:: b: c) which "'makes one••, and herein lies the power of the
"in-between••, the metax_.Y.
sun also has a mother - the cave image will deal with ~hat.
In its second capacity the Good is several times callen the
aitia the •responsible cause" (508 e 3, 517 c 2), and
aitlo~ nthat which is to be called to account" (516 c ?)
both f~r the pass1 ve state of noo\imena, •1beings known" ( 508
e 1, 509 b 6, d. 8) and for the activa knower (508 e 2), that
ls for the soul in 1 ts 11state of 1mow1ng• ( 509 b 6) ~an
ait1a more beautiful and more honorable than its e1fects.
In 1 ts third capac1 tv the Good is called king ( 509 d 2,
51? c 4) and arche)~~ling source 11 (510 b 7, 511 b 7) of the
whole ··. or •arohe 1 tself'• (533 c 8 ), •1n power and seruori ty
exceeding the nature of being• ( 5~ b 9), which gives th~ngs
both their "state of bein~· (To t:Cvo...L
) and their ousla,
their "'nature as beings" (b 5). The latter two ca.paci ties
are duplicated by the sun as source of sight and hecoming.
Socrates presents these functions in the order which will
bring Glaucon up by analogy from the visible many to the invisible one (507 b 1). In the order of logical generation,
however the listing should clearly be reversed, since being
itself ~ust precede the confrontation of active and nBss1ve
beings and this split must 1n turn come before the birth of
a perceptible world. The grandest, most "poli ti'cally ' relevant furtction of the Good ls therefore its rule over being,
next 1t acts as the "answerable cause" (aitla) for teachers
and learners while its most private fu_YJ.ction is that of H
father. But' in truth neither order holds, for the Good itself 1s not ordered, being itself the source of all order,
arche itse\f (533 c 8).
1
Sb. The diagram below shows the pRrts of this order.
A.11 the terms but one are taken from the text:
I
arche
ousia
ait1a
~ooumene
noeta
--~..
tnith
genesis
doxaston
noesis
,~
~
horaton
,........_
clarl ty
/ ' >~~~' -, -,,
genesis
',
. . si£;.hts.
sivht_ dop;matfl
~
)
do~
5e. Socrates had introduced the sun image with a reference
to 'the things said earlier ~f. 47Q}and often spokenof at
other timesn (507 b 8), namely the many and how they participate in the one idea which is "what 1s• in these many things
( 476 a 7, d 1, 507 h 5). In the sun image he leaps from this
beginning to that highest point of view, the way· to which is
sung in the "hymn of dialectic": lfwhen someone leaves behind
all sense l?erce~t~o32 t9 set ..gut upon the.t. its elf which each
thing is (<::11.) O..\r\O o' .ocr·nv €.~a..o--ro v
1 and does not leave
off before)he c:;rasps by thought that itself which is the Good
o" t.,#o 'I<- v ct'/ o.. f9 ov
) , ~then he TS'at the very end of
the knowable•• (.532 a 7, cf. 507 h 5,7). Now the repetition
of the phrase in which~he Good, is substituted for "each
thing" ls Clearly meant to catch Glaucon'R attention and to
convey to him sornethi!l(.>; - actually the one most expl1ci t thing
in the dielogue - about the nature of the Good. For upon
(o..v·To
�-48-47having grasped what •each thiris;w is in itself, one would
expect to learn what 'all things•• are together, and 1 t is
in place of this expected phrese that •the Good• occurs.
This sentence then hints how the Good as the-Bource of
the whole• (511 a 7) will have to be understood: it is not
a separable and different being but precisely the oneness
of all beings, the All as that Ylhole which all wholes within mirror (cf. Theaetetus 205 a). As such the Good 1s indeed the fit pattern of all community . and in the Republic
especially of the political commun1 ty: ••using ,t t as A. .
pattern"' (1\¥0... ~Gty_µ.o..TL), the rulers are to order the. city
and private men and themselves" .(540 a 9). tlnd finally, it
is to be noted that all &he terms mentioned above come into
their own in di&lectic.J )
5f. One additional observation: What is characteristically
Socratic about the sun image ls that it is reflexive, an image of imaging which shows how images are possible. But
more than that, as an image of the whole, lt also shows how
such images are poss ible, how the whole can reappear within
itself, how we can •see• the Good. This aspect of the Good
is reflected 1n the central visual image in the closing
myth of the Republic:
The place in the Myth of Er where the souls choose their
lives (616 b) is not easy to imagine. There seem: to be two
irreconcilable 1mages;37J the first one consists of the
whole heatrens which have a aha.ft of light passing through bol'n
them and the earth (b 5): the second consists of Necessity
sitting at · the earth's pol• -whlrling a spindle whose whirl
is a planetary system and which hangs on chains let down
from the heavenly light encircling the whole (c 4). Now
1f we recall what a spinning woman actually looks like
these .two images become one. Between her kneee she has
a long distaff.- at the top of which a cloud of white wool
is fastened which feeds into the thread she is spinning.
This thread is twisted into yarn by the whirling of the
spindle, which hangs at the end and onto which the finished
yarn ls wound; this spindle is weighted with a whirl. In
the figure of the myth the shaft of light which is the
world's axis represents the distaff, the chain of heaven
is the thread being spun, and the whirl of the spindle of
Necessity itself is a miniature planetary system , an
orrery , a·model of the whole, within the sight of which
the souls choose their lives.
E.
1.
Book VII begins with this invitation to Glaucon:
after this, _liken our nature, as far as educstion and
the lack of education is concerned, to the follow1116 sort
~•Now,
o!
Correl~ t.1 ve eide
the Same and t he Other which extend throughout being, for by oeinc.. one and the sam~ wi tri 1 ts elf e2ch
e_idos remains integral and lndepencl~nt, while by being other
~!l- ano_t_})~l: 1 t becomes the sa.rne with that other i e another
.. ~ o .th er ,, , 0. . . n d capa b le of p&rticlpating in it (25b ' a 10)
-.
.
"
• •)
Now if the point of view taken is not wi thtn but ('h~yond
being", Likeness and Difference perform just such a function
~s Sameness and Otherness did within being, and, in a way, more
c.dequa tely.
For w 1 thin belrJ6 the secondary, reflex! ve ei.dos
o'!_' the Other was the sour_Q_? Q_f _ c~11muni_.t,y, while the pr1 0 ary
Sa~e was responsible for separate and independent oneness
But the bondi&: of _the wholP is c..chieved precisely becaus~ of
the ~iken~_~s of each thing within 1 t to a patt e rn beyond and
so to each other thin~, while Diff erence ls resoonsibl e for
the separ~teness of each s111f~le thing. The f a ct is that
Parmenldes' objection falls if only the 8<-'Jtt e rn is beyond
~ch, as the Good indeed is; " ••• 1 t is rit;ht to d e em both
of these [knowledge and trutli] like the Good, while not right
to c~nsider either of them the Good· rather the condition of
the C.rood is yet more honor~ble ••. [?.nd furthermore] the Good
is not beine; hut ;.·et beyon) being i~ seniority and exceeding
1
it in powerff (509 a 3, b 8 .
I~ is oreciscl~ this bond by which the Gnod ~akes everything one Which, when mathemeticallv expressed , takes the
f
f'
.,
"
.
orm o_ 2 proportton: and the most heeutifu1 of bonds (S·e:~wv)
is that which _ma_~es itself and the things bound tovether &.s
:nuch as poss1 h~e intq g_n~. Proportion Accorr1:P1is~~e~-- t'tiis most
benutifully. .ror when the middle term of three numbers
is
such that As the first is to it, so it itself is to the·i~st,.
then necessF.irily B.11 will turn out to be the sP-me
They will •·
&11 become one With ea.ch othertt (Til1l_?.eus 31 c 2) .. We can ;;,ow
see a second reaRon for the equality of the middle sections
of. the Divided Line - it is the three-term proportion (i c
a:o:~:b:c) Which 0 mE.kes one'', end herein lies the power of the
''in-oetween u, the metaxf.
~eo S?crates had introfu1ced the s1m imag~ with a reference
the tni~gs said e2.rlier [gr. 47'{]] and of ten spoken of et
other times {507 b 8) • namely the m2ny and how they participate in the one id:a which is "what is~ in these many things
( 47? a 7, d 1, 507 n 5). · In the sun image he leaps from this
beg,innint, to tf that highest point of view, the wc..:1
which is
sung in the hymn of dialectic~: ~hen someone leaves behind
811 sense 17erception t9 set out upon thB.t 1 ts elf which each
thing ~ (~-rrJ c...J·10 o' EcrTL.Y fKo...C1"TO V - J and does not leave
oft: b~~re,re.,_,he c;ra~ps by ,thought "thBt itself. whic~ is the Geed
( o...vTu o
t.alLV c...'10..'9ov
) then he is at thA - - -d f
t·
kr . •":lb, 1, ( ?
,.
'
,
.. very en
o
ne now~~ .... e .5_,.?_ a. 7,1 cfo 507 tJ 5,?)o Now the repetition
of th~ pnrA.se in wnich 'the Good" is suhsti tvted for neach
thing· ls clearly neant to catch Glaucon 's attention and to
convey to him sornethinp; - cJctually the one . rwst explicit thine;
in the diPloc!,11.8 - 2bout the neture of the Good. For upon
to
to
�-49-
-48-
having t:.rasped what '9~_ach thi~" is in 1 ts elf, one would
expect to learn what "all tlling§_~' are toGether, and 1 t is
in place of th1 s expec tecc phrs.s e that •the Gooc\ • occurs.
This sentence then hints how the Good as the •s'.)1.1rce of
the whole,. (511 a 7) will have to be understood: it is not
a separable and different being but precisely the oneness
of all beings, the All as that 'Whole which 2.11 ~holes within mirror (cf. TheHetetus ?05 a). As such the Good is indeed the fit pattern of all community c;.nd in the Republic
especially of the political community: '~sing it as H ·
pattern" (\\o..._,P~ '2,c.L.y~o.:n. ), the rulers are to order the. city
and pri v& te men and- th ems elves" ( 540 & 9). Anr1 fin.ally, l t
is t6 be noted that all the terms mentioned above come into
their own in di&lectic.36)
5f
One additional observation: What is characteristically
Socratic about the sun image ls that it is refleYive, an image of imaging which shows how images are :possible. But
·
more than that, as an image of the whole, it also shows how
such images are possible, how the whole can reappear within
itself how we can "seei.1 the Good. This aspect of the Good
is refiected in the central visual image in the closing
myth of the Republic:
,
The nlace in the Myth of Er where the souls choose tneir
lives (616 b) is not easy to imagine. There seem to be two
irreconcilable images;371 the first one consists of the
.
whole heavens which have a shaft of light passing through b cl:r\
them and the earth (b 5); thP. second consists of Necessity
si tti.ng at 't he earth's pole whirling a spindle whose whirl
1s a planetary system and which hants on chains let down
from the heavenly light encircling the whole (c 4) . Now
if we recall what a spinning woman &ctually looks like
these two images become one. Between her kneee she has
a long dis ta ff . at the top of which a cloud of
te wool
is fastened which feeds into the thread she is sp~nning.
This thread is twisted into yarn by the whirling of the
spindle. which hangs at the end Hnd onto which the finished
yarn is wound; this spindle ls we 1ght ed~w1th a whirl . I n
the figure of the myth the shaft of ll ~ n t whi ch i s the
world's axis represents the distaff , the chai n o f heaven
is the thread being spun, and the whirl o f the sp indl e of
Necessity itself is a miniature planeta r y system , Pn
orrery, a · model af the whole, within the sie .ht of wh ich
the souls choose~heir lives.
0
wh;
1
E.
1. Book VII be g inf> with t h is in vi ta ti on t o Glaucon;
~'Now, after this liken our nRture, c.s f t..;, r a s ed.11c~. t 1on and
the lack of educ~ti oni"s concerned, t o the f ollowi11S sor t
of s t~1 t e • , ( ..U.€. \ o.._ 'Q..G 10,,,.i\6-8t.L \Y)V '? JJ..€..Tc,po,,V
514 a 1).
The sentence is drarnc-~tic.
•J.fter thi8° indicPtes that
what h&s imrediately preneded, thRt !~Socrates' naming of
the pathemata of the soul the lbst of which is eikas1e
(cf. also 511 a 7 for £.12_eikazein), is the necessary-prelude
;:-o what is no~ to come; the word Q_a_t_hos has a trRgic flavor,
ci.nd the position of the preposition perfr after 1 ts noun ls
poetic (cf. Aristotle, PoetJg§ 1458 b 1 ). Glaucon ts now
to use his power of elkasia. to se~ (a ?) the dark drama of
human nature under an image. This lmA[,e will show what
human beings are and do within the whole
Behold1 t;._e says, men as "in a cavelike ·underground habitation (oLK 1crc. LJ a J) with a wide entrance turned toward
daylit:~ht.
From childhood on their lee:,s :=md necks are fettered so that they can only see str&ight ahead but are unable to tu:r-n (1n:;n6-yc-Lv ). Their light comes from a fire
bt•.rning behind them. Between this fire and th ems elves runs
a roa~ alont,sid~ of which a screen wall has been built. Behind this wall men pass back and forth carrying artificial
o~)ects.
To Glaucon 's exclci.metion "VJhat an out-of-the-way
(0...10-rrov ) image and what out-of-the-wai prisoners" (515 a
3) Socrates replies quietly; •Like us• (Qµc[ov; ~f>.~vJ 515
a 6). And, . he goes on, these prisoners see only their own
and each others' shadows which are thrown on the wall they
face . together with the shadows of the things carried about
behind the wall.
If they converse it is about these shadows
which are s.s truth to them; the echo of words spoken behind )
the screen wall seems to them to be the speech of these shadows. Now suppose a prisoner were released and ~ o reed ·
stand · up and turn around, a.nd were compelled to answer questions nbout th~ things formerly behind him, he would be uerplexed (d. Tro,PE-<-V' ) 1 his eyes Would hurt, and he Would regard
the shadows as having mo:ttp being than the things oeforehim. ~
And 1 f someone dragged { £ ")... \<. oc) e ·6) him up the steep roa.d
out of the cave by force to look at the light of the sun his
e yes would be SJ) pained tha.t at first he co"tAld se~ nothing .
But after a w11ile he would be ·able to see first (TTpw To"" )
shadows, after that (}.A-~""5~ 10~10) imabes (E:· 'L~wAo..) of things
~p water, an1' at lF.ts t,.. ( Lio-lf..;r> o-v, ) the things themselves.
rtrom these { E'f:.. ~~ Tov-rwv) he could raise his eyes to see the
moon and the st~rs at.... night, when the sun itself is absent.
kid finally (\~A.e·~-ro...l.ov ) he would see the sun in 1 ts own
place; Hfter that (,)Anti: Tc°U'"ra) ~e would infer (cruAkoyC~o.;...10 )
that the sun was responsible (~\.1t..oj) 516 c 2) for the seasons
and year s and was car etaker 0f everything. Then if he recalled
hi~ for~erfhabltation he would feel that he was now happy
(£u~o.'-flov>;J£'-·.../
).
The honors t,1ven down there to those who
w~re ~ood at o?servi~, . remembering and oracling (c 8) about
snadows would oe notning to him r-.tnd he would do anything
rather than live like that (e 2). But if he had to join
the competition, his eyes being st111 full of darkness from
(.
to
�-50-
-51-
his s11dden descent , he would make himself ridiculous. )/ Men )
...
( ')
f:J.....
would then say that by •ascending upWEi.rds • o.vo..//~ 5 a...v w
he had ruined his eyes and that it was not right to attempt
to go up. And as for anyone who tried to release another,
if they could ca \ch h,im / they would kill him ( 517 a. 6).
This image (T"7v £L\.C.OVQ..J 517 a 8) must now be attached
(1rpoc::r'o..TfTi°ov) to what has been said before: Glaucon is
to J 1ken (0.cp~oLou~"lo.. ) the '1seat which appears .. through
sight" ("Try-v /'4AE:." bL' O'(IJEWJ <fb-LVC)A.€¥? i~po.V
) to the
cave-like habitation, the power of the stm to the light of
the fire, the f6rced climb of the prisoner into the light
of day to the ascent of the soul and its vision in the place
of thought. In a table:
diale~tio {~~ht sky
~
natural objects
~
place of thought
.
\shadows and image
dragging up .
conversion
~~~:en
wall
{prisoner
shadows
}
~
place of sight
2
This correlation of the sun and the cave images seems,
though brief, explicit enough, from the conjecturing about
shadows at the bottom up to the lively motion of the soul in
the upper realm. Yet a certf71n reservation is expressed. If
you interpret the ascent (anabasis) in the former ~o be the
upward way (~nodes) in the latter, Socrates says, you will
not fell to fulfill my expectations. But perh8ps only god
knows if that is what truly is" ( 517 b 4).
Let us look independently at the interrelation of the two
images. The sun image shows how the Good has everywhere prepared places for the soul's kn.owing. There is motion within
these ulaces but not straight ascent - the word anabasis ls
never mentioned. The cave image, on the other hand, deals
with the actual habitation of humRn nature, that 1s of the.embodied soul, and with the painful steps of its slow ascen-c:;
Furthermore, in the first the Good itself is not ec:ually
represented but is to be caught by analogy, while ~n the
second the sun represents the Good and an underground fire
is in turn contrived to represent the sun. This means that
in the given correlation of the images our visible world
comes, curiously, to occupy different levels:
sun image
~ image
being : 1ntell1g1ble realm
~sensible world
becoming : sensible world~
imdergrotmd realm
Still later in Book VII, after the detailed discussion of
the mathematical ..arts,. which are to '~aul .,. the soul towara
being, Socrates himself blurs this correletion and. seems
to match the upward trek of the soul into the sun's world
with the raising of the bodily eie, the world outside the
cave with the place of sleht (53?. b 6). Purthermore in the
sun image the Good is beyond the realms of being and be·
coming, while in the cave image its representative, the sun,
is, of course, wi_thin and part of the · world. 1'nd finally,
while the sun 1maf':,e, c..s explicBted by the Divided Line,
refers only to different capacities of learning _ but not to
the incapacity of 1£Snorance (cf. 585 b J), the cave image
is explicitly about both education and lack of education
( 514 a 2) and is ve;y much concerned not only w1 th "'mindlessness n ( d..·cp,? 0 cru v'? 515 c 5) and "h2.nt of lmowl edge •
( ~ o...SC.o.., 518 a ? ) "6ut even with positive deceit.
For
those who ce.rry •idols" bq.ck and forth ·.as puppeteers do
their 'fmc.rvels 111 ( thaumata, 514 b 6 - Socrates plays on the
double meaning ttpuppets : marvels•) are indeed elljsaging in
that complex form of dissembling which the orator shares
with the sophist (Sophist 268 b, cf. 260 c 8).
3. ·Now at the very bef~lnning of their converse.tion
Socrates and Glaucon had determined that ignorance ( e.gnoia)
must necessarily be assigned to non-heing, knowing (gnos1s)
to heing (478 c 2), and opinion (doxa) to an un-named intermediate partaking of both and later identified as becoming. It is to recall this scheme that the main segments
of the Divided Line are at one point named gnoston and
doxaston. Thus it is obvious that wherever becoming occurs
!!Q!!:-belng is implied. But since non~being is not explicitly
named in el ther of the images, G_aucon should conjecture
l
that it is present s omewh ere somehow> in a manner appronriate
to "that which is not'! The following new correlation, ln
which the levels of the ~sensible world~ are made to coincide, does reveal it:
sun image
cave image
being : intelligible realm
becoming : sensible world -(-~:> sensible world
mm-being
underground realm
4a. To put in a word the effect of seeing the cave
image in this new juxtaposition With the sun 1ma.ge: the
cave lmage takes into -a.ccount human badness _ in al 1 1 ts
organized obtuseness. rh1s is why it ends with a brusque
reference to that most telling.crime, the legal murder
of Socrates (517 a 6). The introduction of this factor
and its management, which is called politics, comes out
clearly in the table outlining the cave 1mage~50~Asoppos
ed to the main se~ments of the Divided Line with thelr two
subsections, each realm here has a third part, the screen
1
�-53-
-52-
wall w1 th its puppeteers in the lower realm and the stcnr~
night sky with its moon, bright with reflected solar
light (cf. 617 a 1), in the world above. We may interpret the fonner as representing· the politicians with
their laws and ordinances, their dogm~ - we must rec&ll
that political deceit is still to be practiced in the
just city, only •nobly" {414 b 8, cf. 382 d). The latter
will then be their cosmic counterparts, the~laws of nature•
(Tiinaeus 8J e 5) which are best studied in the nocturnal
sky- although better yet not studied at all (529 a).
:
4b. When Socrates first introduced the source of the
visible world as a son, Glaucon had immediately inf erred
that as a parent the Good was a fatner (506 e 6). The
cave image now provides the answer to the obvious question: who is the mother? It is non-being, whose human form
ls w1llf1ll ignorance. It is not easy to imagine, for in
its elusiveness (Sophist 237 b 10) it is experienced only
as a bewilderment of the eye, that positive apprehension
of darkness which 1s experienced after the descent into
that 1nfin1 ty of tttiuman evil .. ("r~ O-v9pW' 7TC:Lo... ~o..~<L >
517 d 5, cf. 445 c 6) which ls so feelingly described by
Socrates (517 e J). The cave represents non-beine; under i.'ne
guise of a womb where, as ln the Phoenician myth (414 c)
the l•earth-born t• race gestates. From the point of view
of the hu~an soul struggling with a body and with otheT'
men J the ~ood is not at work throughout the whole, for its
light never penetrates into the cave - to the realm of
being which it shines on, there ls opposed a dark realm of
non-being and between these realms is the steep road
along whi~h men ,.come into being~" the road of genesis
or birth.
4c. Socrates has a figure of his O"'-"n for such life
as goes on in the cave, That slander against the underworld which he forb~de the poets he commits himself
against our earth. Earlier he had struck a. line from the
Odyssey (IX, 489), }l{~1 one in which 4chillebs a~, a shafde
th
among shades lamen~sJ,_~ha.t he would rather e ' G. ser on eaT
slaving for another portionless man" (386 c J), but now
he himself outs this very line into the mouth of the man
forced to descend into the cave (516 d 5)~
Just as in the Phaedo there is proposed ci. place rather
to ·be taken uas truly the earthw than the hollow 1n which
we live (110 a 1), so in the Renublic Socrates points to
a true Hades, truly blind and obscure (508 c, 517 a,d) ;
for the "invisible Hades•, the .Aide_g_ a-ides of after-life,
is invisible rather as a place pure of all bodily sight
(cf. Phaedo 79 b 7, 80 d 5, CratJlos 404 b 1), a "divine
place" (topos daimon1os, 614 c 1 • Taken as e place for
the 11 ving soul, the t·•mortal Hades" thus adds to the
·n1ntell1g1ble• and the nvisible" a third, the "sightlessn
place. Its inhabitants live in a dream~like isolation
(5JJ b 8, cf. 476 c 4) reminiscent of the mindless flittings
of the shades in Hades; like the shades in Hades they are inCApable of touchint each other (Odyssey :X., 494; XI, 204), O.V\d
soW'le go completely to sleep, havine as Socrates puts 1 t
~arrived in Hades before they have ~oken up here• (534 c ?).
\~hat is characteristic of the mortal Hades is the wilfulness of its inhabitants - the Good has oreuared other and
better nlaces for the soul; it is not necessary to sit below. Perhaps the most important 2spect of the cave is that
it 1S not~ natural £,?Ve~n but a flcavel1ke underg,round chamber" (~a J), clearly an art.ifi~iRl prison made by men for
men. The :position of the prisoners itself indicates stubborn
perversity; they are fs.clng the wrong way round and have a
perverted view - that is why they must first of all be"convertedn (518 c 8), or that failing, must be <lealt with by
"persuo.sion a.swell as necessity" (519 e 4).
4d. Glaucon should have no dlff'iculty ln recognizing
the place. He lm.ows something of Pythagorean doctTine
(5Jl a 4), and the notion of the world as a urison and life
as a living de&th are both well known Pythagorean teachings
(cf. Gor51as 493 a, Phaedo 61 d); so is that of the •descent
into Hades". For Pytha~oras himself is said to have ntold
how he o escended ( Ko.\0~6:.5 ) to look on the way of life of
those who have gone below, to see how entirely different
were the live~ of t~) Pythagoreans" (Aristophon in Diogenes
Laert.JJJ.§. VIII,J8).j
In fact, the whole dialogue has A
Pythagorean undertone, for the J.ectures of Pythagoras were
said to have taken placP- by night (Diogenes VIII,15, cf. the
•nocturnal council" of the Laws, 961) and it_must be well
into the night when the central part of the Henublic is
spoken; and what is ~ore, its v~ry form seems to be that of
a Pythagorean exercise - 1t was evidently part of the discipline of a Pythagorean to attempt, before starting the
day, to "recollect~ within himself what~~~r conversation he
had had the day before in its entlrety.J~J This would explain both why the dialogue ls told as having taken place
not just recently, but 'yesterday" (327 a 1 )) and why Socrates
addresses it to no one named at all - he speaks it within
hirlSelf: Plato). even more truly than Alcibiades can "open up·"
Socrates (Symposl~~ 216 d S)~ Certainly the r~call of a
conversation which lasted the better part of a day and a
night in s prodigious fea~ only to be accounted for by the
mastery of a special discipline.
1
F.
la. After the cave image Socrates considers with Glaucon
the actual educe.tion of the philosophers. He begins signi :.__
�-.54-
f1cantiy: ~ould you like now to see in what way such men
will come to be born [!n the c1 t~ and how one will ia8Q...
them up into the light, just as some ~.g., Heracles Jj
are said to have ascended up among the gods?" (521 c 1).
The sequence of learning, which follows closely the
•pathos" of the cave drama has three stages: ''conversion"
tiiE.f'Lo.yw Y f J
.51.5 c 7, 518 c 8, d 4, 521 c 6), ~he 11 haul •
toward being effected by mathematical studies (E~ K.€&..V,
µ{S'?f4·o. ~>.tc:6v, 515 e 8, 521 d 3, 527 b 9, 533 d 1),
and the "divine .sights" of dialectic (St:~a...t.. B£w.13'La..'-,
517 c 4).
• conversion" is what we are witnessing i n the dialogue
itself. Since it precedes all education and depends more
on a man than on a study, it is not part of the explicit
plan. Nevertheless there is an "art of conversion• (518
i J ) which , s inc e this first act is lar6ely a matter of
making the soul recognize the shadows 0n the wall ~ mere
shadows, is clearly an eikastic art - namely Socratic
music, the persuasive imagery of truth . I t may be said
to take the place of that traditional m ic s o emphatus
ically excluded from t he philosophical education (522 ).
lb. The long •haul• into t he light of day i s accomplished chiefly by the "hauling study w of mathemati c s
(522 c 5 - 531 d 6). Tbe program ls that of Pythagorean
physical mathemat1cs.41J In a r i thmetic the on e a nd the
two and the other numbers are distingui sh ed, i n plane
geometry the surfaces of bodies, in solid geomet r y t he
bodies themselves, in astronomy bodies are put·in motion,
and finally, harmonics studies the audibl e rela tions of
moving bodies. In this way the cosmos imaged in the Myth
of Er, with 1 ts heavenly bodies g i vi ng out a harmony a.s
they revolve, is constructed . There is only on e difference
between this Pythagorean cosmos and t he Socratic study, bvtoV\eso
deep that it is very hard for Glaucon , who loves the se
studies especially astronomy, to g rasp. He immedi a tely
ident:tfies Socrates' J(hrase about .,see l~ the things ahove"
(10: ~vw d't.JJc.o-ea.~ ) ..Jtth "looking into ~he skYJ above"'
(.s:.'L.~ ..,..c l:f...vw o_.,oCi.v >
529 a 2), and Soc r ates has to rebuke
him: that kind of astronomy really ma kes its ~tudents
"look downward al together!• (a 7 ) . So era t es der!l ands tha t
in the serious s~1dy of this paradl~m of every • s tu dy~, of
every mathema, not only all practical consider~tions 1
but even every admixture of sense exnerience should be
put by, and only those true motions and numbers and f igu res which ere ~rasped by the logos and the diano i a alone
should be studied (529 b). Glaucon, who f oll ollls the
early part of the discuss1on,the demonstration of the
d1anoet1c power of ar1thrnet1c, very well, is somewhat
puzzled by-· what follows ( 522 d) ~ For indeed 1 t is the
effort of mathematics itself which is needed to complete
the conYersion from sense (533 d J), a:na. this ls still
before him.
-55-
What is this purg ed mathematics of Socrates? It ls, in
fact, a kind of inverse dialectic. It beg ins with an investigation ~hich in dialectic is the la~t and greatest, the
•study concerning . the one" (rln~pL \~ e.v)AO...S1or'-) 1
525 a 2), which asks after the "one itself" (524 e 6) and 1ti;vest1gates 0 the one and the ~anifoldl two and three !t { ..,.c)
Ko..'t ,G:. ~ uo '<-o...t ,0;: 'I' Ca..,
522 c 51, a study ·Which is "that
whichis in commo~ ( 10' \<..o'- vov, c 1) to all others and of
which they "partake " (,.,.u.e 1ox 0 5 yt. yvf. o--B a...'- ) ·
c 8). It
is called !•an ordinary 11 ttle thing !7 ( -,.o- cp o...OAo v,
c 5 42 )
but it di scovers the great dialecti cal archai of •the Great N
and "the Small" and ,. the Infinite " ( 523' e J , c f. Aristotle,
M
etaphys ics 987 b 19, Philebus 16 d ). The f inal m
athematical
subject, on t he other hand, ls ha rmonics) -which :oresumably
deals with such matters as the "marriage number" (546 d 5),
a number told by the Muses and.built on "agreeable 4 number
relat1ons;t~'t:nmt\:F,,although not apprehensible by any reasoning
mixed with sense perception, yet rules breeding and birth ,
and is , i n short, c oncerned with the mos t concrete and intractable m
ultipl ic i ty, with the l owest ma t ters. The cosmos
bui lt with purified ma t hemati cs i s t hus, t o be sure , n ot a
model of our sens ible world but a •noe tic cosmos", and yet,
in acc ordance wi t h the downwa r d moti on of the dian ola, it
become s progress ively more"palpa ble " in t he process of construc tion. To put it another way , this intelligible world
1s built up f r om the least el ement; the non-dimens ional one,
geometrically considered as a Eoint, to a •community~ and
"affinity" {KO"-'lwvl:.o.'-'· ... KOi.\. cruyy£'Vc.La.~5Jl d 1) gener ated by dimensional growth, while in dialectic the One is the
end of all studies, that which is beyond the sum of things,
the whole. It is this inverse relation to dialectic which
makes mathematics the "pro:oa1deut1c" study {536 d 6).
One might add that when this mathematical cosmos ceases
to be regarded as a mere pattern (pa r adeigma) and is elevated into an eidos, a source of b e ing, dialectic yi e lds
to mathematics as the science of bei ng, and something ofJ)
this sort indeed seems to have happened in the Academy.q.
But as long as Socrates is convers ing,a mathematical argument r ema i n s hypothetical, or as in the Tima eus, -. mythicfl.l.
(29 d 2). This is s t i l l t he case even in the Philebus,
where i n the course of the inyestigation of the Good a
•bodiless cosmos" ls buil t (64 c) from mathematical principles such as the One, the More and Less , and Number ( 2)
c ) , which principles all come to Sotm~l.n ~ myth or f rom a
god (16 c, 18 c 25 b ) or in a dr eam (20 b ) - and tha t , as
he says in the Republic , is p re cisely the way t hings come
to mathematicians : ~They dream about beingn (533 b 8), just
as he hims elf ~speaks oracl e s • {523 a 8 ) on t he s ubje ct .
t:v
»
lc-d. Di a l ectic itself i s no longer accessi ble t o
Glaucon; to se t out on thi s road would be t o see •no longe r an 1rnage .• . bu t the t rue it self ~ (533 a J ). Instead Soc ra tes sings h i s ~hymnft in praise of dial ectic (531 d 6))
�-56-
-57-
and with that Glaucon must be content. He has now been
a preliminary synopsis of the synoptic studies which
the young rulers are to engage in first {537 c). After
this Socrates add,J'esses him as a fellow · law~g1ver; while he
rehearses with him what he would do n1f he were ever to
nurture 1n deed those whom he is now nurturing and ecucating in speeeh • ( 534 d J, 8, 535 a 3, 537 c 9 ); that is, what
Glaucon will do once he himself becomes a teacher of rulers.
Here it is interesting to note that Theon, elaborating in
great detail Socrates' allusion to philosophy as an initiation into the mysteries (Phaedrus 250 c), makes the
fourth stage of the initiation, (the stage following the
full vision) that which authorizes the initiate to transmit his knowledge to others (Mathematical Matters UsefUl
for Readitig Pla.to, Introduction).
- Together they review once more the virtues necessary 1n
the nature of the future ph-ilosophers and the danger to
the "puppies• (539 b 6) in taking up c;l1alect1c too early.
In the last image of this conversation Socrates likens
_ them _to a son who on growing~dlecovers that his alleged
parents are not his true parents and , consertuently,. losing
trust, begins to ask questions about the traditions 1n an
"· ristic• way and to scorn the laws ( 538 c 5). Note that
e
the source of disillusionment of the precocious dialect1c1an in -the image is precisely the content of the Phoen1o1an my~h (414 c 4) which is told the dog-guardians to make
them conform!
g1~n
2a. Row they have come to the final question) which
·socrates clearly considers of acute importance in the
aer1ous execution of his program - this is the matter
over which he had before become angry (B"~w8£f..s,
536 c 4). It is the question of age, ,the fitting of the
progress of study and .practice to human growth. The ages
Socrates assigns to each stage is best seen in a chart
(539 d 8} fitting them to the ascent of the cave image:
outside
.inside
natural objects dialectic ---~~-----~~-!hadow~_ _
_ _____maQiemB:_tI_~~ ----- - --
___
WI
cleo.~
r~r:z~e;11
L ------··--------·
After fifty, Socrates says, the time has come for the
philosophers to "behold" the Good itself an~us1ng it ~s
a "pattern• (-rra..po.. ~·i.L yµa.1LJ 540 a 9 )J to order ( Ko~e~ v
b 1) the city and to educate others to live in the city as
its guardians. Thereafter they will spend their liveR in
philosophy whenever possible, but when their turn comes
they will descend and govern, ~nns1dering it "not as sqmething fair but as necessary'' ( 0 \) X ~ \<O. )..oy TL. d_).).. > .fJ5
Q"lo.. y Ko..'~ov, b 4).
·
The last phrase recalls one last time that for the nh1losophers the chief thesis of the dialogue, that just1ce'brings
happiness, ls suspended - they are just out of mere necess1 ty.
It also shows why this is: the "fair city~, the kallipolis, has nothing fair for which a philosonher might w11.__
lingly descend - witness the fact that 1 t ls so called insofar
as its citizens study solid geometry (527 c 1). In this
city geometric is substituted for erotic necessity (546 cf
458 d 5 )) and •1ove" means primarily love of truth - hu~an •
eras plays a purely utilitarian part in it (459, 460),
though such eros alone might bring the nhilosopher down
willingly. It is necessary that love should be absent here,
where the dialogic community is to be displayed as the
fundamental political community, but Glaucon receives compensation at another time: it is to him that the speP.ches
Illade about eros at that famous symposium are recounted.
he hears them •going up from Phalerum 9 Athen's second'
harbor (Symposium 172 a 2, c 3).
'
r
2b. What is.most remarkable about the age chart itself
is that the rulers• education, al though i.hl.t\o..l\y founded «nn
the city, always leads them straight out of it and beyond.
Practical experience cornea to them late. In terms of the
cave, it is conspicuous that no mention ls made of a "look
behind the scenes• of the puppet theatre) of something which
might be construed as a political apprent1ce~h1p. The
counterpart of this lack of practical training is the absence
of all Political theory from their studies, that ls, of· such
formulations as are abstractions from practical politicB .
in the dialogue called the "Constitution~ the study of constitutions is not advocated. The reason for this ls 1n the
nature of such patterns: the pattern of the just city is
not an eidos, a being responsible for what ls but an ideal
significantly located not in the •hypercelestlal place"
'
{Ph~edrus 247 c 2) with the eide but in the sky (592 b 1)
with Cloudcuckooland. A parade1gma is only a •hypothetical
e1dos~ (Timeeue 48 e 6), not an object of study or know- ·
ledge. Were it otherwiseJnothing would be necessary for
the young · rulers but to study the best constitution - this stud..'j
would be what is called ideology. Instead they are to look
to the one effective pattern which is that beyond being:
the political wisdom of the Aepublic demands that governing
be learned by looking, so to speak, in the other direction;
in practice the rulers will literally look at affairs "in
the light of the whole~ ho n~o-"" cp~5 no.._pfxov, 540 a 8).
The ab111 ty to do this, 1rrepla.ceab1e by any technique or
formula, is called human wisdom, phronesi! (521 b 8), the
~irtue containing the political virtues (~ymposium 209 a 6),
and of all the virtues the loveliest (Phaedrus 250 d 5).
�·-58-
-59Notes
-The image of such a man at work, which might be called
•Socrates in the city," ls found in Xenophon's Memorabilia.
2c. Having come to the end of iife,, the philosopher kings
will at last be allowed to depart permanently to the Isles
of the Blessed, and the city will honor them with memorials
and sacrifices; 1f the Pythia permits, as divinities (daimosi),
otherwise as happy men (euda1mos1, 540 c 1). Socrates is
ending the conversation with a sly reference to himself: he
has indeed advocated - w1th the permission of the friendly
Delphic oracle, to be sure - the introduction of •other new
divinities" into. the city, exactly as the indictment against
him was to state (A.pology 24 c 1, cf. 21 a 6; he was also,
incidentally, honored 1n Athens after-his own death very
nearly as he here prescribes, e.g., Diogenes Laertius, II,43).
2d. And now Socrates and Glaucon are emerging from their
deeply publi_c private dialogue back into the context of the
~city in speech•, the guardian city.
Socrates himself recalls
1 t with a smiling rejoinder to Glaucon' ~ perceptive; praise of
his skill as a "maker of men-statues• (a.vSf''-O...VTo rroLoJ, .534 c 4)
by hie rem1ndltrto Glau eon that he can shape women too, for they
were to share in this cl ty · ( 54 5 c J). · Sacra tes now founds
this guardian city w1 th charming offhandedness - all inhe.b1 tants over ten years are to be driven out . •1nto the wilds•,
which will leave a clean slate for the law-giver (541 a 1,
cf. 501 a).
_
· G1aucon recalls accurately where they had been -when they
digressed: Socrates, like tn~)wrestler he ls - Heracles is
the master of all wrestlers
- is to put himself into his
former position to continue to wrestle with the account of
the-degenerate cities.
1.
Plato's RP-public, ed. B. Jowett and L. Campbell, Oxford
1894, Vol.III, p.4; The Republic of Plato, ed. J. Adams,
2nd Edition, Cambridge, 1963, Vol. I, p.l.
L1ade11 and Scott , see
TTt:. )'°a. L t-C 5, ·p.
13 54 b.
3.
Pauly-Wissowa, Real-Encyclopaedle der klasst_~q_h~. Al tertums-
4.
ibid., III,1, see •Bendis" p. 269.
The torch race mentioned may be accounted for by the fact
that Thracian Hecate had the epithet ~ w er cp~ o5 ..
5.
A.dams, I, p. 5.
6.
Jowett, III, pp. 2, 7, and 7~ on 368 a
7.
Also Gorgias 461 a, 466 c; Phaedo 98 e; Phaedrus 228 b.
The schol1ast to Wasps: s3 · says that Sosias ls imitating
Socrates' oath "by the dogw, Aristophan1s Comoediae ed
Dindorf, III, p. 460; cf. Plato: Gorglas, ed. Dodd~,
•
Oxford 1959, p. 262, also Lucian, Philosophies for Sale,
16, who connects Socrates' dog with Anubis, Sirius, and
Cerberus.
8.
Pauly-wissowa, Suppl. III, see wHerecles", pp. 1007 ff.,
1018 ff., 1077 ff.; also Aristophanes, Frogs , 108.
9.
See Jowett, III, p. 7 on Thrasymachus' notorious wildness.
_lf-1.ss.cn~chaft,
Vol. XIX,i, P. 78.
J.
Eva Brann
Annapolis
March 1966
Aristophanes actually compares Socrates to Odysseus, another
famous visitor to Hades. But in the Republic the comparison
is, if anything, adverse. The Myth of Er is offered as an
improvement over Odysseus' boring •tales of Alcinoue" (614
b 1, see scholia) while his soul, disenchanted with ambition,
chooses the nerfectly private (620 c 3), the most un-Socratic,
life .
11.
Cf., for instance, Apology 41 a, Gorgias 523. Justice,
Dike, is called a companion .of the underworld gods in
Sophocles, Antigone 4?1.
12.
See G. Morrow, Plato's Cretan City, Princeton 1960, pp.
13D
er.
14.
Socrates, by descending with Glaucon into the mythical
setting of the Pe1ra1c underworld, has shown him that he
lives his life caught in a mortal Hades. But this demonstration is itself a release, the first step of the rescue_unlike the poets, who fail to wrestle from Hades the shade
they desire (Sympo§.1um 179 d), Socrates, a new Heracles,
knows the way to bring his Theseus up to the world of light.
Yet Glaucon's later life is almost a blank for us; no
reputation, either good or bad, survived him - certainly he
founded no-new Athens. We may be sure that this is meant
to reflect on the dialogue, for 1t forces us to ask whether
the labour of Socrates has, in sober fact, been altogether
lostrhas, after all; come to mere words. The answer, however, to that question will no longer be found in the d1a- ·
logue but only in ourselves.
10.
Tht old saying is used by Socrates 1n a similar way in the
3-10.
.
Hippolyb1s ' opposite proposal for treating children
as purchasable goods and excluding women froQl generation
(Euripides, Hyppolytos 616).
.
Apology (34 d). He too, he says) quoting Homer, has a
family and is not sprung ''from oak or rockn, that ls, he
�-61-
-60-
t oo ha s a private source. The original meaning of
the phrase, wh ich occurs i n the Odyssey (XIX, 163) ,
was evidently no longer known to the scholiast on
.544
d
22.
Note that in this context Socrates first acknowledges
the natural world as the setting and source of human
nature. The character of peoples is, as in Herodottan
ethnology, dependent on the clime under which they live:
Thracians, Scythians, and northerners in general are
lovers of honor, Phoenicians and Egyptians are lovers
of money and the Hellenes in the middle are lovers of
knowledge (435 e, cf. Timaeus 24 c; Epinomis 987 d).
23.
See Adams I, p. 244, note on 435 b.
24.
See Charmldes 164 c 7 for Critias' version of the
Delphic background of this saying •
25.
See
26.
See Meno 80 c, ed. Thompson, p. 112.
27.
On a much lower level, the reiteration of themes, such
as the •oft-toldw tale of the one and the many, has the
eff~ct of making Glaucon nrecollect• (e.g., 507 . a 7,
522 b 1) the unity of the argument. Cf. the~h~nor in
which this kind of memory and recollection (o..v~v?o-'-J )
was held by the Pythagoreans: •A Pythag orean man does not
arise from his bed before he has recollected what happened yesterday. And he performs the recollections in
this way. He tries to recover bi means of the dl_~nola
what he first said or heard •.• " ~Iamblichus, Life .Q.f.
Pythagoras 16),20) . The passage goes on to describe
the discipline of completely recalling the logoi and
erga of the p~ev1ous day , which was considered part of
the training needed fo r acquiring knowledge. It is
obviously a technique Socrates himself had mastered.
a.
345 ff.
15.
See '*iams I,
16 .
See F.M . Coniford , Plato's Cosmology, London 1937 ,
pp. 4- 5. For a to t ally di ffe r ent point of view and
concomi tantl y di f ferent years for the dramati c dat e
of the Republic see A.E. Taylor , A Commentary .Q!l
Plato's Tima eus , Oxford 1928 , pp. 1 5-16 , 4 5.
1?. . A
similar case is found -i n Xenophon's Cyrapaedia and
is expressed 1n the apparent lack of a match between
the title, which seems to promise an account of Cyrus'
upbringing by the Persians (I.11,2), and the content)
which is .rather the education Cyrus gave th~ Perslc;.ns.
This ls because Cyrus, whose name means the "Lord•,
is at once . the beneficiary and the source of Persian
customs; Cyrapaedia therefore means •The Lord's
Educa tion" both in the objective and the subjective
sense o f the genitiye.
J~
Klein, A Commentarz on Plato's Meno, pp. 112-115.
18.
Crati nus from a lost play, The Thracian Women:
TLf/°fi'?"f.. ~" TL l<a...LvO'v ~ya. O"T~,,D LoV.. The cult of
Bendis e vidently wa s f ood for comedy; tt . seems to.
have been the subject of Aristophanes' lost Lemn1an
Wonien.
19.
See R. Hackforth, Plato's Phaedrus, Library o f Libe ral
Arts, p. 118.
20.
An ·otherwise unlikely ancient story to t he ef t'ec t t hat
the whole Rijublio· was stolen from t he wr it i ngs of
Protagoras I>1e1s, Fragmente der Vors okrat1ker, 1 954,
II, p. 265), seems at least to indicat e t ha t there ·
were certdin points of agreement.
28.
See J. Stenzel, Zahl !WA Gestalt be1 Platen und Aristoteles, 1959, p. 190 for a list of many of the ancient
references to tfc:/l l. -rc:L ya. Gotl and for · quotations in
his own text .
21.
Ade1mantus 1 · Gyges story is a witty transformat ion of
Herodo t us' versi on. In the latter, what is r i ght and
lawful is for every man to keep private things private
or "to look at his own" (er Kw rr f E- Lv re vc:L r o...._
{,wu rou,,, I, 8, 16); this is tacitly compared to the
definition of what is just in the Republic,. namely
•to do one's own• ( T~ o..610C rr/>ci.17""€.-0-'), 1. e., to find
one's public place. F-.;J.~ thermore the main faC't about
Gyges' crime in He rodotus , that he is forced to do
injustice precisely because he is ~ in the act
i mposed on him hy the king> is inverted in Adeimantus'
story , and by reason of hi~ ring Gyges becomes invisibly a nd volunta rily c r i mlDal.
29.
Klein, 1b1d. pp. 115-125, "The Dianoetic Extension !2f.
)
,.
)J
€...L K CA 0-L ().. . •
JO.
Klein, ibid. p. 119.
31.
The Pythagorean enterprise of de.vising numerical ratios
to express the relations of the soul's parts, as well
as to express the progression of the world ' s genetic
elements, becomes extremely important in the Academy in
connection with the understanding of e1de as numbere.
An instance is the double progression 2:4:8, which has
the "one11 as its non-numerical source and stands for the
dimensi~nal unfolding of the world from point to solid
(1.e. 2 ). To the dimensions are correlated the cor-
�-62-
responding powers of the soul: !!Q!!!!, dianola, doxa, and
a1athes1a and to these, again, the numbers 1 through 4
(Ep1n9111a 991 e, cf • .Aristotle On the Soul 404 b 20 and
Philoponus' commentary on th«tpassage). These are the
formulaic results of just the kind of consideration the
D1T1ded Line invites.
J2.
One or the older combatants ls Pythagoras who ls said
to haye seen Homer and Hesiod suffering in Hades for
what they said about the gods (Diogenes Laert1ua III,21).
3J.
The objeota on the D1v1ded Line are only twice ·referred
to 1n terms of mimesis (510 b J and 5J2 · a J, cf. 507
c ~ )•
• · In the Ph1lebu,a, the Good 1• approached as a •third
thing•, other than and aboTe both pleasure and human
•1•dOll (-20 b 8). .As a hUllan go9d it has three char~1
,·:·1·aot••let1c•: 1 t 1• "perfect• ("'TE)\e.o "_ ) , "adequate•
( ltt:..o...vov· ) and ''ohoiceworthy" (o.t,peT05, 20 d); its
_
power, a.gain, cannot be •caught• in one idea but must
be captured 1n three: beauty, ayametry and truth {65
a 1), whoae relation ia not unlike that of the three
effects of the power or the Good, namely world, knowledge and being, in the Republic.
3.S.
Ct.
)6.
7or the hoao1on as the bonding pr1nc1ple making knowledge po•a1ble, and associated terms, like paradelffa
.e.nd an•lqgi•~ 1n the .Aeadem~ see Pauly-Wissowa, II ,
•, 2 under -Speu•1ppos •, pp. 1641-1658.
31.
Cr • .ldama II, pp. 441,4?0 ff.
•)8.
There 18 also .a curious story about an artificial Hades
•h1eh Pythagoras is said to have built - a little chamber under the earth into which he disappeared for a long
tlae and then aaeended, announcing that he had dwelt in
Hades (Diogenes Laert1ue VIII,41).
·
Aristotle, Retaph!sica I, (ed. Ross), p. lv111 ff.
tor further references.
39 • . Iambl1ohua; Life of Pythagoras, 165,12; see Note 27.
40.
See Jowett, III, p. 326.
41.
.Adame I~, p. 16J ff.
42.
'
remarks on Plato's use of the word
q>o..u ~of, po· nting out that he uses 1 t 1n ·the two senses
1
of6.n>.o05, •simple, honest" and t<<i.i.c::o5, •bad• (III,6J).
Actually, of course, Socrates often uses 1t ironically
to mean •the great thing which everyone el!e overlooks!!.
Di~enea · Laertius
-63-
43.
For instance, Plato is said to have generated the cosmos,
1.e., the !1~n1mal itself, out of the idea of the 0ne and
primary lent-~th, breadth and depth• (Aristotle, On the
Soul 404 b 20).. With this passage goes the numerical
generation of the soul describ~d in Note 31.
44.
Pauly-Wissowa, Suppl. III, p. 1007;
���
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Aristotle and St
is
who
a
so.
his very
because
fact that man is considered as
another but
monads arei
dividuals
tion
this rule is God, who acts
all of the
are we to
the
universe is
nature ·
Leibniz calls
must seam to be
into societies.
·what soit is clear that
monads themselves have
ever to do with
into existence or with br
these
all sorts·
about
clear
other
groups of monads
the world.
Each group consists
able
an innumerdominated
one
as
observes
cause
is
lection of
are
a certain
we
some desire or need.
Insofar as
we consider to be
some other time
state meets
consider it better
Because the
constitution of and
may seek
men affect
in it clues as to
of
worse
�2
when a man says:
But what
uwe also see that every substance has
(which becumes
substances , that
a consequence of its ideas
determines it
God
makes all possible
most
Hare Le
what we
is
upon
which God de-
call the divine-creature
tarmines ·the
them in per-
upon this divine
feet
goverernance as any other group of monads.
interest of
the effect of human action and
passion upon the whole
of men is somehow lost
are both the result of the
can
Sines
of the human monad, to
another set of apperce
set
is
the often in-
that
God
at all a
is
of
about
before us a record of the rise and fall of nations
the eternal
of man. What we are to find in his
and
if we are monads, is
that we are to find
the same
the occurences of nature:
the laws that constitute the eternal, Godthat
Ula have no real social
, I suspect that
of the nature of
such a
of the cosmos with its
turn to other
most monads would
are
constitute the
not so
under the var
bur
consideration of the
as a fact is
Its
are in the
of effects as
in human societies.
for a monad, then,
a necessary consequence of divine
and foundation is found in the
ction of God, which neces-
sitates that he choose the best of all possible worlds.
say about the
act as
of monads is that
existed in groups
the
would expect Leibniz to show no interest at all
1
If all we can
made to
are
of God, then we
in
and the
However both
end
, for
of our search for
God which assures us of the
laws ..
ics
and
H
action of God.
as a sort of
be
Thus it seems that the
set up as be
!:::..::~~~::=......:::.!~~~~L.::!.=.::::~
xxxii
over a moral
of
�3
tompos~d
of all .the spiritual monads.
of this kingdom any
influenc~
Still he - does not give the members
upon each
othsr~ :· and
it strikes ma as rather
odd to . speak qf a kingdom in which each subject has -contact only with
the king or a family in -which each member
ha~ : contact · only
. I suppose that one of the greatest advantages -of
disharmon~
that it excludes all possibility of
teeing the reasonableness of the universe.
~uch
a
with the father •
syst~m
would be
or sedition thus guaran-
The quesfion still remains,
however, what sufficient reason -drove Leibniz e0en tb speak of a kingdom
of. monads of a rational or spiritual
natur~
at ·all?
Since (eibniz often calls this kingdom the kingdom of God~ it seems
reasonable to assume that he intended it to have some relation to what is
traditionally
have been redeemed.
' .
of as t _ e ki_gdom of God, the ki_ gdom _ those who
h
n
n
of
thoug~t
A consideration of Leibniz' kingdom in relation to
those set forth by St. Thomas
nominal.
sugg~sts
that any connection is merely
In the Thomistic system men are considered as belonging to
two societies:
naturally to the state and supernaturally to the Church.
The end of the state ·is the good life of its citizens.
~ ~.
Since the good
.
life means the virtuous life, the end of human society is for St. Thomas
virtue.
The Church is of course what the
phr~se
kingdom of God would
i. .
mean to St. Thomas.
The end of the Church is the salvation or eternal
beatitude of men.
This beatitude consists in their participation in the
life of the Trinity.
natur~l
(The
society to which . men belong should
not hamper their belonging to the Church, but the two are not the same.)
We have airea~y seen that for Leibniz the~e is only one kingdom to which
men belong.
We have also seen
tha~
by calling it the kingdom of God he
suggests an anal9gy with the second. of th~ _ -Thomistic kingdoms.
twp
Yet
when Leibniz speaks of the kin~d9rn of God as a moral kingdom within the
physical one, one is
remi~tjed
mqre of _
St. Thomas' natural society of
men which is ordered toward virtue.
But if each monad is dependent solely
·and absolutely upon God, there is no
metap~ysical
because a finite monad
we try to equate
. .'
~:
.
.
no contact with any other finite monad.
ha~
'.
basis for such a society
.
When
~ingdom
of God and that of St. Thomas, we run
in.to rat.her sharp cont.radictions.
.
.
. .
.The very . .existence of the Church de.
Le~bniz'
'
'
'
.
~
pends u~6n the p~~or _ existerfe . of ~wp _ other societiea.
the-~e is h.urnan · society.
The first of
n ' is within this society that the redemptive
�4
act iv
of God, which leads to the establishment of the
takes
Leibniz has the moral world exist
ical
For St. Thomas the redemptive activ
-within the natural human
as a
of God takes
which is quite distinctive in that it
of persons over and
the rest of the
The distinction between s
monads is
in
when he
We mentioned in
its and the rest of the
s
the other
ish-
of the
of God.
necessary to the existence of
of God as St. Thomas understands it, that is the Tr
the
Since Leibniz never mentions the
he would do with it.
, it is a little hard to say what
He may s
consider it so detrimental to the
of God as a monad that it is not worth discuss
make a case for the
However one can
that he would have to re
When St. Thomas is be
such a doctrine
in the
str
first three books of the
, he never
either, but in his meta
the
ical discussion of God
treatment of the
is the second person of the
In short, for St
It
who entered the human society as
man s redeemer thus establish
God.
ical
As we have already noted, human societies are not so dis
able in Leibniz.
he
within the
, the relation between these two is not the same as in the
former case.
world.
of God
ive mission the
Thomas the
of God is the result of a
of human and divine
Leibniz has no human so
his
str
of the function
for him to have any divine
llie can also argue that
the will of God makes it
The intellectual operations of God
form the foundation of the Thomistic unders
are to know and to will.
Al
of the
, as we shall see later, there is some
question about the exact corres
of the
sible
between St. Thomas' understand
of God and Leibniz', it is Leibniz' under
o
the will which makes a Trinitarian God incompatible with his
In St. Thomas the action of the will of God is love.
His will loves what is known.
These two
lect at which St. Thomas arrives
the subsis
relations which
ics.
His intellect knows.
ions of the divine intelbecome in his
the three persons of the Tr
�5
The beatitude . of ·man, whiQh is
t~e
end of the kingdom of God, consists in
shar .ing.· the life of t;hese th+ee persons, which life cons .ists in love . ~ The
·. .
.
reason that I say · that a Trin. tarian G~d is impossible fo Leibniz' system
i
is that for him the
pr~rnary
action nf the will of Cod is not love but the
creation of the best of .a ll possible worlds.
~ir•cted
- ~cit
to an aGtion
outs~de
Thus the . will of God
of himself, and if ·6ne were to
i.~
conside~
God's
of··will as a basis for a _
person, the unity of God will be violated.
If love is not the fundamental
ch~ef
~ttribute
virtue _
cannot consist in a
shari~g
of the action of God, man's
bf this
God.
attrib~te . w~~h
Isolated an_d acted upon oril/by God, inan's only virtue .lies in his know_
ledge of the harmony which .. govern~
there are great difficulties
wit~
· God . 's
actions.
It seems to me that
the isolation of
being_so .completely invoived with the creation and
.
Le~bniz'
By
monads.
mainte~ance
of a world
of harmonious substances upon which _ alone acts, God has lost his
he
personhood~
_ no longer loves .
He
it is that keeps one
unfolding
~it~in
fro~
Furthermore it i s not even cleaF what
positintj a universal principle of harmonious
all monads and thus doing away .with God all
Altho4gh Leibniz seems very much ·interested in
toget~er.
avoiding ~ p~nth~ism ~r
a
syste. m. like that of Spinoza, it does not seem to m that his radical
.
e
abolishment of society helps him tb dcr so.
he likes it or not, Leibniz has
le(~
It seems . rathe~ that
open a very
~eal , possibility
w~ether
.for the
substitution of nature for God even within the framework of a strict
separation between individual .s·u bstances •.
f inal, end of man . i t
b~comes
Once knowledge becomes the
'very diffitult to distinguish God from nature
as the basis of this knowledge.
Earlier we raised the question as to the
sufficient reason for Leibniz' introduction of the moral kingdom.
Per-
haps this reason can be found in the desire tp avoid pantheism by establishing God as a monarch, that. is by. giving him some kind of personality so ·that he cannot be liMked or identified with
natu~~.
But can
Leibniz me~nihgfully introduce .a kingdom without allowing his splritual
. m~nads . to
act upon each other?
Can God be the oniy monad 6apabl~ of
. infl!-JEH'l_,ing another monad and · still be transcendent an9 be_ s_pok~n of as
c
.. .
a person; w o. is the head c:if a kingdom?
.h
A~6ordin~ tS -~L~ibniz truths of fact rest on the principle cif suffic i ent
�6
reason.
Truths of reason are based on the principle of contradiction
because they can be reduced to basic principles which make clear their
necessity by showing that what is predicated is contained in the subject.
We
a~e
not able to show that· the predicate of truths of fact is
contained in the subject although Leibniz asserts that as far as the
infinite mind of God is concerned this is in fact the case.
God is concerned all truths are immediately analytic.
As far as
What the princi-
ple of sufficient reason does is assure us of this fact.
It is clear
then that we cannot call the desire to rescue God from pantheism the
sufficient reason for the introduction of the moral kingdom into one's
metaphysics.
It may indeed have been a reason that motivated Leibniz
to devote as much space as he does to it, but in his terms that is not
a metaphysical justification.
rational.
For Leibniz the universe is completely
Presumably there is some better reason than corrective
rhetoric behind his introduction of the kingdom of God.
Perhaps
'
Leibniz' introduction of the kingdom of God is to be taken as an indication that although he says that we can go on speaking as we ordinarily
do even if we adopt his metaphysics, he does in fact think that one's
metaphysical considerations have a bearing upon one's ordinary life,
and he wishes to show men the great unity of all of the completely individual monads in celebrating the harmony of God.
Perhaps he even had
the often quoted passage of St. Thomas:
"It is therefore evident that the opinion is
false of those who asserted that it makes no
difference to the truth of the faith what
anyone holds about creatures so long as one
thinks rightly about God."2)
in mind, and even intended to show that the assumption of monads is not
contradictory to theology by establishing the kingdom of God, although
we have already seen that he does in fact make grace as St. Thomas sees
it impossible by excluding both human and divine society from his system.
Leibniz says near the end of the monadology that the natural and moral
world are in such harmony that all things proceed naturally toward grace.
This statement would seem to suggest another reason for Leibniz' inclusion
of the kingdom of God:
2) S.C.G. II, 3
he needed to explain progress in his world of
�7
pre-established harmony.
which is . .to
e~plain
He gives to each monad a principle of app·e tite
t.he progression within the monad itse1'f".
he was dissatisfied with this
general~
prin6i~le
hav~ . already
Grace as :we
tional sense . in a world of
as applicable to : the
But perhaps
univers~
noticed is only · p6ssibl~ in the tradi-
person~,
and, as Leibniz must have known, a
· parson in the scholastic sense is an individual but not . a monad.
the scholastic concept of
· p~rson
ln
1t·is
as an individual substance of a rational
nature which is extended to the divine persons.
We have already seen
that by abandoning the ·idea of the personhood of God; Go·d is no longer
love, ·and the end of man becbmes knowledge.
love as the end of man, · then
what~ver
harmonious that there simply is no
wo~l~
must
ha~e
ne~d
for
gra~e
as an extraordinary ·
He could . mean, however, that it is simply a fact of -the world
as we observe it
the
grac~ · it
Leibniz means by
Unless he is simply asserting that his world i~ so
to do with knowledge.
pheno.menon.
If knowledge has replaced
t~at
now men as a whola know m6re about the harmony 6f
Altho~gh ~he
than the cave men did.
w6rld is the best
possi~le,
it is still an unfolding world, ·and · this unfdlding is in the direction
of an· increased knowledge on man's part .of its harmony·.
Leibniz continually insists that the harmony which man is seeking is · th~
result of the action of God.
We have already seen one area in which. this
God differs from the scholastic understanding of God.
that this difference
mak~s
We have also seen
it possiblS· ta · extend Leibniz'
s~stem
pantheistic system .which does away with God all' together.
If
w~
to a
examine
Leibniz' God in his · role as creator we will again find this 'possibility.
When . Leibniz
th~refore
asse~ts
that , all being outside of God
i~
contingent and
demands a creat9r,. he ·is merely following his
However• · his concern with
~hawing
s~hol~stic
that the world is the best
masters.
pos~ible
would sound strange to St. Thomas, . T imagine. · For St·. Thomas theN3 are no
such things as possible esse·nces only needing the attribute of being ·ta ·
begin to exist.
~~nces1
possibl~
Although we
~bstract
essehce per se from existing es-
essence is not considered as prio~ to exist~nce.
I~ oth~r wb~ds,
worlds are sort of ·a fiction of man's abstracticin.
monads,· however are completely separate from what the
stood to be the world.
If
th~y
are to
h~ve
any
Leibniz'
· ~cholastics
assur~nce ~t
under-
all that
there even: .is a world1 they· must · assume ·that God acts according tci the
�8
principle of sufficient reason and creates the best possible world.
Here
we run up against what seems to me to be a great problem in Leibniz.
llie
are assured that God chooses the best.
For him the choice of the best is
equivalent to acting according to the principle of sufficient reason.
If
God chooses the best, and he chooses to create a world, not only must that
world be the best possible, but crBation must also be an activity superior
to not creating.
We are told in the monadology that God knows the good
through his wisdom, chooses it because of his goodness and creates it
because of his power.
If wisdom, goodness and power are all part of the
essence of God and are linked in the way Leibniz says that they are, then
must God not of his own necessity create?
Leibniz never says that God
must create, but it seems to me that his principles quickly lead one to
that conclusion.
It seems to me that if creation ceases to be a completely
free act of God and becomes somehow necessary because of his nature, one
might just as well say that nature itself contains a tendency toward being
as well as
monads.
towards the harmonious action of the individual existing
In other words, we can again identify God with nature.
As we
saw earlier, St. Thomas does not consider God's will as acting to create
on a principle of sufficient reason.
will of God is love.
The primary metaphysical act of the
Thus the ultimate reason that is to be given for the
acts of God is love, not some reason.
As I remember Leibniz only mentions God himself as loving at the end of
the Discourse when he speaks of Jesus Christ as showing God's love, care
and provision for intelligible souls.
In other words, we are still in
the context of the harmony of the world.
God cannot very well contain
love within himself for Leibniz because of the nature of his will, as we
said.
Love and grace are primarily actions that take place between per-
sons and there are no interacting persons in Leibniz.
when God ceases to be a
of the world.
person~
llie see here that
his love becomes tied up with the harmony
The action of God ' s will is tied up with choosing and
thereby creating the greatest good.
His love, which was once the primary
function of that will, becomes an assertion of the harmonious and perfect world chosen by that will.
This assertion is very nice for intel-
ligible souls because it means that they will be able to attain their
end, knowledge of this world.
Now, if the will of God is determined by
�9
the principle of perfection so also is his J.ove.
as God is deter·mined
·by · sonie
'rn other words, as -soon
necessity he is no ·longer love. . Clear lY:..
we cannot ·give the love of God as the reason for the existence of the
moral world and the special place that Leibniz accords · it within the
natural ·world?
Can
w~
only say that it must be the · most perfect expres-
sion of the harmony of ·God, and it has its sufficient reason in this
perfect.i6n?
Leibniz' concern when he starts talking about the
~ingdom
He calls such
special monads which mirror not only being but also God.
rational monads spirits.
are capable of know5.ng
These spirits are the image of God in that they
~he
universe
~nd
models. · It is not clebr exactly what
of imitating parts of it by
Lei~niz ha~
of models, as strictly cpeaking a monad cLnnot
he means some kind of mathematical model.
ea~h
monad is a
~~all
of God are those
divinity.
in mind when he speaks
~uild ~nything~
Perhaps
Leibniz then concludes that
It seems that what this divinity con-
sists in is 1.re J.iOWP.r . to discover by what laws the apperceptions
to me by God ar·e ordered.
thought or
· ha0e
· th~
sim~ly
Sublime
A monad is capahle .of no other. -action than
perception in non-spiritual monads.
plea~ure
pr~s;~nted
of
figu~ing · out
that they are
Spirits,_ in short,
actual~y mon~ds.
Wh~n - Leibnli says th~t spirits can see whereas ..other monads have only
mirrors, I understand him ta ·: be asserting ·· exactly this fact.
Later
~n
the Di~~ou~~e L~ibniz asserts that only monads are capable of free action •
..
'
If the bnly ~cti6n of spirits is thought, then all that . this action con-
sis ts· · in i s -the i ntellectual act of choice which accompanies knowle~ g ~.
·
Such ~he~ are the advantages of spirits.· over other monads.
If we . eq~ate
God . ah~ : nature as - we seemed led to do earlier, then spirits are left with
· the soii tary honor of contemplating the order of the war Id with which
. th.ey°' have a most evasive connection, . ·themse.tves harmonized as mu1=h by .a
h~rmony ~h~t they cann~t understand as thosa things whose laws the
~pirit~
do grasp are govetned by that
If ·this idea occurred
t~
harmony~
Leibniz, he probably
d~d
not like it.
He is
not even content to. leave his spirits alone with God in the natural ~orld
but collects them .into ~ha kingdom of God with God as monarch and law~
'. giver .· . He
calls - ~his
s~ciety
God's noblest work because in it God's
�10
gr~atness
glory.
and goodness are realized.
In that realm God properly has
He even goes so far as to say that all other things only pro-
vide the occasion for the spirits to
glor~fy
God.
It sounds as though
what Leibniz means by this statemeht is that the glory of God is the
sufficient reason for the existence of the universe.
In other words,
the best of all possible worlds is that which gives glory to God by
the multiplicity of effects obtained by a few principles.
How are the
spirits to give glory to God if he is not a person but only an infinite
monad?
It seems to me that the only way for them to give God glory is
to engage in that activity by which they imitate him; to arrive through
the use of their reason at a metaphysical system which demonstrates that
God has created the best
wor~d
possible in which he harmonizes the in-
numerable monads so successfully that it is not at all
~pparent
that
there even are such things as monads.
Wh3n Leibniz speaks of God as law- giver, one immediately thinks
harmonizing
a~ti~ity
o~
his
and considers the moral world as merely a special
one of God's coJ.lections of monads.
special law, that of felicity,
However, the city of God has a
Felicity is the perfection of spirits,
and it is the principle of the moral world to spread the greatest possible
fglicity.
Within Leibniz' system one is led to interpret this state-
ment as meaning that in the best of all possible worlds the unfolding
of all the monads according to their inner principle leads to the
greatest possible perfection.
The perfection of spirits is their felicity,
which, we are told, is the principal aim of God.
God loves to be loved.
We are also told that
It seems to me that this love which God is to be
given is the glory which the spirits are to give God by contemplating
the order of this most perfect of all possible
world~
and realizing that
everything in it acts for the establishment of the good.
having his own glory be the principle aim of God.
We are back to
Perhaps to speak of
the glory of God is just another way of speaking of the principle of perfection, but perhaps it is in fact anterior even to the fact that God
always acts in the most perfect manner.
Perhaps it is the way in which
Leibniz finally avoids being pushed into pantheism because whatever principle nature may act upon, it seems to me very hard to say that nature
would act so as to be glorified by men.
Thus the
s~fficient
reason for
�11
the city of God becomes the harmonious recognition by the monads who
share with God the ability to . know of thg
fa~t
glory and .cannot be equated with natJre·.
It might even be that monads
.
.
,.
.
that God acts for his own
are ·: slightiy social in that the glory of God consists in the harmonious
;
· · .. . . . . .
recognition of it by a number of spirits, a society:
It may even be .
·<. that the felicity of spirits demands this society of God and other
spirits and that complete as the isolation of spirits is, man is still
· ·a "
·Pol'itical animal.
••
1
•
.
·. .
•·
·1 ·:· ' :
~·.
:
r .·.
·.
'
•• 1
•
•
'
' : .···
�12
NOTE TO ST. JOHNS MANUAL:
Edward
I
, Tutor
*
The manual states on page 1, with reference to the precession of the
equinoxes,
Either therefore the stars are fixed and the cross
of the equator and eel
ic moves westward with res
to them, as if coming to meet the sun as the sun moves
eastward; or the stars are not fixed, but move eastward with respect to the equator and the eel
ic taken
as a fixed reference scheme. On page 77
gives hoth mathematical and
ical
for the Jatter hypothesis nnd accord
undertakes
to establish the rate of the motion of th€ fixed star
It is the lntent of this note 1) to
above; 2) to suggest that
the two
suggested
11
did not conceive of two such
es ,
could not, anrl, therefore, neither did nor could argue for one of them
as such; 3) to suggest how Ptolemy did understand crucial elements of the
in question such that the account of the precession of the
equinoxes
II
him is the only one possible for him.
What are the two
the above?
The obvious
, where either
answer is that in this case, as in that of the sun s
the eccentric
is or the
'
thesis will account for the
ic
so here there are two different motions conceivable
astronomer that
the appearances
ill
However, the question does not admit of so s
deed true that,
s
(s
an answer.
at a two-dimensional d
tou ouranou) with
eastward about the
of the
'
drawn on it, one can conceive e
of an
of the eel
It is in-
axis, and eel
ic
of fixed stars rota-
ic while the circles on the
diagram remain stationary or, in the alternative, think of the enve
as stationary while the point of intersection of the equator and eel
moves westward with res
to it.
Further reflection on these two
theses", however, in the light of the
* mr.
ic
11
root of the notions of
teaching at St. Mary's College in California.
�13
1) . "h .~avenly . phere•J and · 2)
s
0
equator" leads to some interesting self-
. contradictions· within·. them~ '.· · furthermore, at temp.ts to· -"save" these "hypotheses" generate some · interesting re.suits.
UJe will take · up the "hypothesis"
of the _rotating fixed stars first and call it the "first hypothes?
is" although it is described in.the second. member of the disjunction in the above
quotation from the manual.
The First question
the next-to-last paragraph on page 2 of the
ask~d · in
manual raises the possibility that the phenomenal root of the notion of
. "equator" is that the · fixed stars maintain the· .same courses in their daily
-revolution.
a great
By "equator", -then, it .is possible that we mean the following:
~ircle
at right
~ngles
to tha axis of a sphere whose pole is 1) a
fixed . point in the heavuns at constant dis+.ances · from ·the fixed stars and
2) ·the center of the ·parollel circles desc4·ibed by the · fixed stars in their
daily revolution.
With such an .i_mplied definition of _"equator", however, a serious selfcontradiction appears , in the
fir~t
"hypothesis''·
For, if the fixed stars
.move wlth reference to the pole as conceived above, .there cannot be one
pole and equator . of the
sp~ere.
Without
~
. quat.or, there
s
crossing of the equator and ecliptic either.
ca~
Hence the fixed
be no
~
r~ference
scheme, with respect to which the . fixed stars are in this hypothesis supposed to move
ea~tward,
collapses. _
With the collapse of the fixed
reference scheme, the very "hypo. hesis" itself loses a_ l . int.el~igibility •
t
l
. Thi s " hy pothesis" of .rotat.ing fixed stars and fixed . r~feren c ~ s cheme ca n
be "saved" in the face c;if the aboli9hing . of . t .he equator, however, . by substituting a fixed reiference scheme of ecl.iptic .and . extension of terrestrial
.
.
. ;
equator into
t~e
circle at ri9ht
heavens.
a~gl~s
(The
'
~erre~trial
equator .would be a
to the . axis of. the earth.
pol~s.
would be a straight line . through its
gr~at
The axis of the .earth
The poles of
the.ea~th wo~ld
be those points .on the earth.:above which the daily circular motion took
.
.
~
.
'
place always, reg~~dl~ss .of what s~~r happened to be North Star.) . But
this salvation . requires placing the fi+st Movement into
.
.
'
. a daily
'
rotatiQn : ~rom
because if
the~e
is no
~
west to east about its own axis.
on~
th~
earth itself,
(This is required
axis and equator of the sphere, there can be
no First Movement of .the sphere abqut swcry an axis.)
�14
Hence the
isH, which
11
require an
is said to argue ·for, must
of the s
of
- and hence
a phenomenal root of both notions - different from that
question on page 2 of the manual,
after that for
to above.
the
We shall show here-
the phenomenal roots of both notions and their
definitions are indeed different.
to understand the second "hypothesis 11 fails,
what definition of
thesis
11
the
11
and
is assumed..
On the second
the.
inoxes are
ic moves westward while the
for the da
stars are,
at rest.
Now, since the
it must be
observod against some star on thel
the
that rotate about the
ward, not the
the
rotate,
for the
west-
of
But now i f the
arid its
s
and pole of
else must share in this rotation.
and exhaustive root of the notion of
is this:
of
sinJe evervth
, including the fixed
moves westward
stars, more or less cir
~
ti
, therefore there is a limited s
heaven (ouranos) carried around
its axis.
ical
To think of
is to think of "fixed stars" as one of its constituent notes ..
He~ce
to think of the
as
to think of the latter do
, on the second
about the
so as well.
is 0
,
e of the
But the fixed stars are
at rest.
is
Hence this
also contradicts itself and
This
of
of fixed stars at rest and westward
is~'
intersection of two determinate circles, one of which is at rest and the
other of which with its
can, like the first, be
rotates westward about the pole of the first,
11
saved 11 in the face of 1) abolis
of the
abolition this
requires, if the
11
11
is defined as the
is, like the first,
on page 2 of the
manual suggests) and 2) having the fixed stars both at rest and not at
rest.
For one can make the axis of the earth and the
the earth
to it, the terrestrial
circle
, constant elements.
Then by placing the First Movement in the earth itself, an eastward rotation of the earth about its axis daily, one of the determinate circles,
the equator, and the
westward rotation of the whole are
�15
preserved~
further, by making the earth's axis itself rotate siowly west-
ward ' ~bou~ i the poles of the ecliptic, the point of intersection of the
two
t1~tleai ~ ~6liptic . and
extension of terrestrial equator, _will itself
rotate ! ·we·stili:at~.· At. the same time, . the fixed _stars will be ·at rest while
thef will appear not to be at
rest~ ·.
The following can thus be said about the two "hypotheses".
1) In . their
"salvaged" form, they do provide .two alternate possible accounts for the
precession of the equinoxes.
rotating
trial
~arth
~xis
But to the extent
o~
their "salvation", a
in the first case, .a rotating earth ·plus a .rotating terres-
in · the other, they contradict the Ptolemaic cosmos and cannot
have been considered as alternatives by Ptolemy, at least not within that
cosmos.
2) In their
un~alvaged
form, the second "hypothesis" is totally
unintelligiti.f~.'; wh.iie for the first, there are two possibilities according
·to 'liow the ·"equator" and "pole of the sphere" are defined.
... "pois
a) . If the
of the sphere" is defined 'primarily as a point in the heaven from
which the fixnd stars remain
~t
constant distances, i.e., if the pole of
. . the sphere _ so _designed and defined ~~sen~ialiy as .. to "maiMt~in ~he
is.
fixed stars in
t~e
same courses in their daily revolution 11 , the· f frst
"hypf.)thes is" . col~apses and contradicts i tsei f.
· s.p'1ere
0
..
is so
design~d
b) If the "pole of ·the
and defined as to do something · else, a consequence
of which could be the approximate maintenance of t~e fixed stars in the
.same courses in their daily revolutions, the first "hypothesis" may be
. able to stand firm.
III
P~olem~
in ·his acbount ~f the ~recession of the equinoxes does not
co~~ei~e of two such "hypotheses" and, indeed, could not.
a)· Nriwhere in the Almagest does Ptolemy mention .two hypotheses with ref· erence to other things, e.g., the sun's
merit ions· .two hypotheses.
irregul~rity,
he specifically
On page 77 he _repeats the "conjecturett of
_
Hipparchus that the sphere of the fixed stars has a very slow movement
in .. the "direction contrary to that of .the pr i~e movement
simply adds ·"l'n we shall show this . is so • • • .,
on page 77 he gives mathematical and
physic~!
~
• • tt and he
In the se.cond paragraph
reasons .for determining
the length of the year as "the time in which the sun proceeds continuously
from some fix~cf point on this circle (the e'Cliptic) back to :the · same point",
�16
not for accounting for the precession of the equinoxes by means of one
instead of another hypothesis.
Although it is true that this method of
determining the length of the ·year does involve the "fixed reference
scheme" of ecliptic and equator, it is equally clear that Ptolemy is not
here considering this reference scheme as an element in one of two hypotheses that would account for the precession of the equinoxes .
On pages 226-232, where the precession of the equinoxes is more amply
discussed, Ptolemy nowhere alludes to two hypotheses of which he is
choosing one.
Rather does the language suggest that the fixed stars are
"observed" to move eastward very slowly and that the problem is to determine the pole of this motion and its rate.
b)
for the reasons given under (II) above, Ptolemy could not, within his
framework, have considered the second "hypothesis" a viable account, and
it is hence not surprising that he does not discuss it in his Almagest.
IV
How then does Ptolemy define the "equator" and "pole of the sphere"
so as to be able to account for the precession of the equinoxes by means
of the rotating sphere of the fixed stars without falling into contradiction?
The answer thet emerges from the Almagest is the following:
for
Ptolemy the phenomenal root of the notion of " heavenly sphere", "pole
of the sphere", and "equator" is the sensibly daily parallel/concentric
circular motions of all the heavenly bodies.
The "sphere of the heavenn
is such a thinkable entity as will furnish a noetic
11
background" for the
intelligibl e uni f i cat i on of the many i ndiv i dual da ily and s e nsibly parallel/concentric circular motions.
The upole of the sphere 11 is the intel-
ligible center of these many daily sensibly parallel/concentric circular
motions.
The "equator" is the greatest of these sensibly daily parallel
circles.
Thus on page 7 Ptolemy makes it quite clear that the notion of
the "pole of the sphere" came to the ancients - and he associates himself
implicitly with their "thought'' (ho sphairiko ennoian) - from seeing the
parallel circles of the rising and setting stars (both wandering (plan~n)
and fixed (aplanon), but especially from the concentric circles of the
"always visible" stars.
Ptolemy does not define the"equator" and "pole of the sphere 0 so as to
"maintain the fixed stars in the same courses in their daily revolution."
�17
(manual, p. 2) . ( 1.) -~.t .is obvious·' from ttie ·above that if a·n ything is main; . :.-~
t
tained in the . s_
arne. c~urS?~es }'! daHy revolution ,by the "pole . of . the sphere.,
it · is all the . heaver:-ly bod~es, not just the fixed. stars. But since this
.
.•
. ·.:
"pole" ,.does not main.t~in , everything , in the same courses in their .daily
'
·•
(
.
.•
revolution (for oi;i p. ~ 12 . h~ ·
~nt~oduces ' 'the·· other movement'' · to .~ccriunt for
0
the lack of maintenance of the ~ams cour~ 'e"s' ori the part: of the sun'·· moon'
and planets) therefore there is no
sphere" that
th~ · fixed
~ecei~ity
~he ·
in
riotion
~f
"pole of the
·&tars either maintain the same courses in their daily
revolution. • (2) Ptolemy on the top of _. page 13 explicitly limits "pole of
the sphere" and hence "Fi~st .Movement" to the motion
bodies in paths "sensibly similar and parallel".
I
•'
'
•
of all
the heavenly
(3) The. fixed stars - are
•
always ~ef{ried in te~ms of thJ~r . constant angular dis~ances froM ori~ another
and never 'in terrris of c.unstant ar:igular di::; ~ance from the '''pole of· the
.
·'
'
·.
sptiere• 1 .' :(4) The sphere : of the heaven_ is always distinguis_ ed from the
,.
h
sphere of the fixed stars.
not be the
~
(5) The "always visible" stars of pagE:l ? · need
stars at all periods of time.
To be "always visib.Le" for
a star means merely ?or it, during the course of a year or so, never to
sink below the horizon.
There are only two places in the text that might lend support to the view
that Ptolemy's notion of "pole of the sphere" requires that the fixed
stars maintain identical courses in their daily revolution.
page 13.
(1) Only the sun, moon, and planets are mentioned as partaking
in the "otheru movement.
do not.
Therefore, the
from the fixed stars.
Therefore, the argument runs, the fixed stars
0
pole of the sphere" is at cons tent distances
Therefore the fixed stars must maintain identical
courses in their daily revolution.
silence:
Both are on
But this is a mere argument from
the fixed stars are not explicitly excluded from the "other"
movement; and in Book III, page 77, they are explicitly included in it.
(2) The other text is more convincing.
Ptolemy says, also on page 13, that
the sun, moon, and planets move "contrary to the general movement, towards
the east opposite to the movement of the fixed stars which preserve their
respective angular distances and are moved as if by one sphere."
The
argument runs that here the motion of the heaven and the motion of the
fixed stars are explictly identified through a common opposition to the
motion of the sun, moon and planets.
Therefore, it is alleged,
�18
since
results in the
·constant
11
of the s
the fixed stars,
tha s
must conceive of
, as
as
at
that will
the fixed stars in the same courses in their
for
even this passage is not
to say that the fixed stars
are
moved
0
)
as if (
Since, therefore,
, and
are moved
is careful not
one s
one s
has notions of
0
of the
that neither in their
roots nor in their
definitions require that the fixed stars maintain the same courses in
their
revolution, he is
and, with
even
is
free to preserve these notions
the fixed reference scheme of the first
the face of the
fixed stars - a rotat
is ,
which for
ion of the precession of the equinoxes.
im
�19
THOMAS HOBBES, THE PASSIONATE POLITICIAN
Alfreda Verratti '66
"The comparison of the life of man to a race, though
it hold not in every part, yet it holdeth so well
for this our purpose, that we may thereby both see
and -remember almost all the passions before mentioned.
But this race we must suppose to have no other goal,
nor other garland, but" being foremost, and in it:
.
To endeavor, is appetite.
To be remiss, is sensuality.
To consider them behind·, is glory •
. To consider them before, is humility.
To lose ground with looking back, . vain glory.
To be holden, hatred.
To turn back, repentance.
To be in breath, hope.
To be weary, despair.
To . endeavor to overtake the next, emulation.
To supplant or overthr9w, envy.
To resolve to break through a stop forseen, courage.
To break th~ough a sudden stop~ anger •
To break through with ease, magnanimity.
To lose ground by little hindrancec, pusillanimity.
To fall on the sudden~ is disposition to weep •
. To see another fall, is disposition to laugh.
To see one out-gone whom we would not, is pity.
To see one out-go whom we would not, is indignation.
To hold fast by another, is to love •
. To carry him on that so hoideth, is charity.
To hurt one's-self for hast•, is shame.
Continually to be out-gone, is misery.
Continually to out-go the next before, is felicity.
And to forsake the course, is to die."
·!
"Human Nature" ,from Body, Man, and
Citizen, p. 225 - Thomas Hobbes
*
*
*
*
*
*
*
*
*
*
In the Introduction to the Leviathan, Hobbes sets up a standard by
which his work is to .be
true or false.
ju~ged,
a standard by whieh it is to be declared
This standard does not have the objective quality of a
measuring stick which all men agree to be
a subjective standard.
~ne
meter or one yard; it is
Hobbes says:
"He that is to ~overn a whole nation must read in himself, not this or that particular man, but mankind;
which, though it be hard to do, harder than to learn any
�20
language or science, yet when I shall have set
down my own reading orderly and perspicuously,
the pains left another will be only to consider
if he also not find the same in himself. For
this kind of doctrine admits no other demonstration."
Leviathan, p. 24 Thomas Hobbes
Hobbes is inviting the reader to reach an agreement with him by simply
considering whether the things which he says about mankind are not true
of himself also.
However, he cautions in this same introduction that we must find in
ourselves only the similitude of the passions, not a similarity in the
objects of the passions.
For these objects, he says, differ in all men.
(Leviathan, p. 24)
From this introduction it would seem that we could expect a political
philosophy which is grounded upon the nature of each particular man and
upon mankind in gen&ral, a philosophy which would consider the basic
elements which a man must have in order to be a man and upon these build
a political system which is consistent with peace and security.
for
Hobbes makes this promise in the beginning of his De Cive or the Citizen:
"For were the nature of human actions as distinctly
known, as the nature of quantity in geometrical
figures, the strength of avarice and ambition, which
.is sustained by the erroneous opinions of the vulgar,
as touching the nature of right and wrong, would
presently faint and languish; and mankind should
enjoy such an immortal peace, that • • • there would
hardly be left any pretence for war."
De Cive or the Citizen, p. 3
Thomas Hobbes
This is exactly the task which Hobbes has set out for himself, that is,
to understand . the nature of human actions as clearly and distinctly as
the nature of quantity in geometrical figures, and to explain this
nature so clearly that any man need only read into himself and find there
the counterpart of Hobbes' description.
Part· L - On Method
The method .which Hobbes ·uses to construct his political system in the
�21
Leviathan is that· of
analy~is
and ·synthesis.
his constituent functions .in order to
th~ · nature
discovered
Ha first divides a man into
det~rmine
6f man, he uses this
as to the origin and · construction of the
his nature.
nat~te
~tate.
Then, having
to develop his theory
Ftom the knowledge which
he now has of the construction of the state, he .deduces the attributes,
accidents (as he calls · them)., which it must have.
It is clea~ ~ow closely this method parallels that of the geometers.
As
they first must · determine the nature of the elements. of their science,
namely lines, points, figure, and quantity, so must Hobbes determine the
elements of his :·polit-ica;l ·philosophy, namely man.
Then, as a geometer
would .give the construction of the figu£e whose properties he was to find,
so Hobbes gives the construction of a Civil Society,
t~at
is, a gr6up of
men who have entered into a contractural agreement witn a sovereign to
give up some of their rughts of nature in order that they might live
peacefully.
Then Hobbes__
proceeds ·in true. gee.metrical fashion to deduce
'
.
the properties of -this artificial creation.
From . its construction he
finds out . the duties and . rights .of the citizens and the rights and duties
of the sovereign as a geometer would find out the properties of a previously
defined
circle~
Two questions arise concerning this method, one concerning its form and
the other its content.
The first is simply:
How is his analysis . o.f the
nature of man performed, or in other words, what is his method of dissection.
The second question, which arises from his several
the same subject is:
treatment~
of
Is ··this analysis whic~ he perform~ on m n's charac t er
a
necessary in order to brin~ ~im · to the point of being able to construct
his state?
In order to answer the first . af these·· questions, I believe that it is
necessary to go to the roots of Hobbes' thought and to make a
crit~cal
examination of his definitions of philosophy, method, and logic.
One of the difficulties in examining Hobbes' method is that he ties off
the avenues for disagreement even before they are opened.
He defines philosophy in these two ways:
�22
is such
of effects or
appearances, as we
true ratiocination from the
we have first of
their causes or
And
, of
such causes or
as may be from
first their effects.
we acquire
appearances
the
we have
ion of
, as has been
we have of the
some
the same; and of such
or may be, from the
effect."
p. 24; p. 72 - Thomas Hobbes
He immed
blocks any
to this definition of
say
there should be any cause
• I here undertake no more than
elements of that science
which
may be found out from the
same, or
, the
from the effects; to the end
who search after other
, may be ad11
monished to seek it from other pr
lest in this
of
p. 31 - Thomas Hobbes
However, even
with his definition, it is pos-
we cannot
it, and on the other
, on the one hand, to
sible to
invss
for
and if, in fact, it does insure as firm and infallible a
civil
as Hobbes
In the
es.
, he says that
true ratiocination
is the
ratiocination he means
with words, that is, the
tions and the
The
of words to
of these definitions into
of true
we acquire
correct
for Hobbes, requires little more than
the proper use of the rules of formal
A
of his
which contains a treatise on method, is taken up with the
�23
enunciation of these rules.
They include the logical fallacies and the
division of words into their proper classes.
It is interesting, how-
ever, to consider his understanding of exactly what constitutes a definition.
A definition of Hobbes is a primary proposition (Body, Man, and Citizen,
p. 83).
As primary it is the foundation for all ratiocination or the
forming of syllogisms, and as a proposition, it is the copulation of
two names by which it is understood that the latter and the former are
both names of the same thing (Body, Man, and Citizen, p. 44).
A proposi-
tion is considered as true when the predicate is the name of everything
of which the subject is the name
(Body, Man, and Citizen, p. 48).
The foregoing discussion of definition effectively closes the door on
any equivocating concerning the meaning of words.
A definition is true
because by common consent both subject and predicate have been applied
to the same thing.
And likewise, if the terms of a definition are under-
stood then it is to be admitted without dispute.
For Hobbes says:
"If the scholar understand all the parts of the
thing defined, which are resolved in the definition, and yet will not admit of the definition,
there needs no further controversy • • • it
being all one as if he refused to be taught."
Body, Man, and Citizen, p. 85 Thomas Hobbes.
Now this understanding of philosophy and with it the understanding of
definition as its foundation brings out at the same time the .faults of
past civil philosophy and the hope for future civil philosophy of Hobbes,
the analyst.
Past philosophy has erred because it did not begin from
firm, clearly understandable definitions.
It is Hobbes hope to make the
nature of human actions as distinctly known as the "nature of geometric
quantity 0 and thus effectively end the disputes of the moral and political
philosophers.
I would like to examine now the material contained in the first eleven
chapters of the Leviathan, material which for the most part reads like
a dictionary, in order to see what are the consequences of his definitions of man and their application to his civil philosophy.
�l
24
Part II - Of Man
The purp~~a ~f the first eleven chapters of the Leviathan
man.
is to
d~fine
As the foundation of philosophy for Hobbes rests in definitions,
he must first clearly outline the particles which are to form his -state.
Th'e true and perspicuous explication of the elements
of laws natural and politic dependeth upon the knowledge of wh~~ is human nature • • • Man's nature is
the sum of his natural faculties and powers, as the
faculties of nutrition, motion, generation, sense,
reason, etc. · These powers we do unanimously call
natural and are contained in the definition of man,
under these words, animal and rational • . • Since
:the minutf' and distinct a11atomy of the powers of the
body is nothing necessary to the present purpose, · t ·
will only sum them up in th3se three heads, power
nutritive, power motive, and powei generative. Of
the powers of the mind there be two sorts, cognitive,
imaginative, ·or conceptive and mi;itive . "
•
· ·
11
·
--Body, man, and Citizen, p. 182
Thomas Hobbes · ,
Althouph this quotation is not take from the Leviathan it serves well to
illustrate the purpose ahd
sco~e
of its first eleven chapters.
the parts of man's physical make-up is
n~~
to Hobbes·' purpose.
To know
Similarly,
his sensual appetites are not of use for they consists in the desires to
eat, sleep, and propagate his· kind. But this leaves still the mind of
man, and this is the task Hobbes has set for himself, to classify it and
def in. it.
e
Perhaps the major difficulty is that all thesa ambiguous, dark, and
mysterious characteristics · of man are dumped together like undersized
char~ies
into one big collecting bin called the mind.
All those many,
per·haps infinitely many~ attributes of man · which do not fit into the
· ··sifting bin of corporeality or sensuality are lumped into that great
ambiguity called the mind.
Hobbes task is to classify these remnants
which constitute the greatest and most important part of the definition
of man, and by defining make as clear a concept of him as we might have
of a circle or a square.
Beginn~ng
with the sixth chapter of the Leviathan, ·Hobbes begins his
dissection of the mind of man.
The passions
~s h~ ~e~cribes
·them can be
�25
diagrammed quite neatly
These
passions are
into
the
(See Chart #1)
what Hobbes calls the simple passions; however, they
acquire different names for four
(1)
following chart.
From the opinion
different reasons:
which men have of the likelihood of attaining
what is desired.
(2)
From the object
(3)
From the consideration of many
(4)
From
which is loved or hated.
of them together.
or succession.
their alternation
Leviathan, p. 55 - Thomas Hobbes
If
we consider
these simple passions, as
seeing if they are
find
nothing to
Hobbes invites us to do, by
not things which are in our own
argue with
quarrelliny with his
use
of
here.
Altho~gh
the words good
experience, I can
there is the possibility of
and evil, it is
necessary
to remember his admonition against quarrelling with definitions if the
matter of them be clear.
So far
he
has made no judgment either on these
passions or the use to which they are put.
of the 3imple
forces
It is simply schematic outline
which he finds in the minds of men.
Any value
judgment which he makes is reserved at the moment for a later date.
How-
ever, just as he makes no value judgment on these passions, neither does
he give us yet any clue to the suitability or unsuitability of man to civil
government, or what form this government must take.
As he has said that these passions take various names from the four reasons
given above, he proceeds to give the different names and the reasons for
which these names are taken.
These also can be made into a chart.
Again
he breaks down Endeavor, ot the first beginnings of voluntary motion into
the three major categories of Desire, Aversion, and Contempt.
All these
categories, however, now refer to the desires, aversions, and contempt of
the mind.
He is speaking now of the Endeavor of the Mind.
(See Chart #2)
Hobbes completes his delineation of the passions by defining more closely
those particular areas of Grief, mental displeasure, and Joy, mental
pleasure.
(See Chart #3)
But something rather unusual has happened here in the delineation of Joy
and Grief.
In the first chart of the simple passions, pleasures of the
�CHART
NO. 1
The Passions
Animal or Voluntary Motion
, PULCR~M -
I
I
(
\
\
(SENSUAL PLEASURE
promises good
sense of object
present
i
i
I
I
(DESIRE
; appetite when
object is
APPETITE - \ absent
.\
endeavor
toward
f
PLEASURE OF
GOOD -
anything which
is desired
) LOVE -
.
ENDEAVOR
l
JACUNDUM
DELIGHT Good in effect' appearance or
sense of good
PLEASURES OF
appetite when
object is
present
MIND expectation of
foresight
of end
UTILE -
good in means
/
I
first begin- c
nings of
) CONTEmPT neither to
voluntary
nor away
motion
l
VILE - Inconsiderablethat for which we
have contempt
promises evil
(AVERSION aversion when
AVERSION _ ) object is absent
endeavor
away
·
HATRED -
EVIL that for which
we have aversion
)!
SENSUAL
DISPLEASURE
in
consequence
at-
.~ tained
[PAIN
DISPLEASURE OF
moLESTATION -
evil in
aversion when
object is present
appearance of
sense of evil
mENTAL
DISPLEASURE {GRIEF
INUTILE -
evil in means
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N
CHART NO. 3
/DETECTION
Grief from opinion
of want of power
~WEEPING
~
-
.
Sudden dejection
PITY Grief from t~e calamity of
another with fear that the
like may befall us.
GRIEF
Mental displeasure
trief from discovery of a
defect.
AMBITION -
Grief for success of another
with desire to equal.
Grief for success _of another
with desire to supplant
Joy from apprehension or
novelty (excites curiosity
and is good for men~.
·JOY -
- GLORY -
mental pleasure
joy from imagination of
.one 1 s own power.
Joy from imagination of power if
based upqn flattery or supposed
for delight i n eonsequence~ •
LAUGHTER
Sudden glory.
�26
mind consisted of the
, and
of fores
was the
of the mind if such a consequence was
We see now that this
of the mind,
two th
of one's own power.
which is the end result of
p
and the
of
57)
It is clear from many passages scattered
that it is
Thus, the
are the desire to know the causes of
men
or pride.
attained
, consists in two
, or the
admiration and
th
of an end which is considered
all of Hobbes
works
to a few to desire to know the causes of
which is the
ition of the
of men find
if
mind.
in the
Thus, for Hobbes
of
iew his delineation of Grief
the
own power
or mentsl dis
it
is found
that all men's grief stems from want of power.
and
are felt because of the fear that man has not the power in
himself to withstand a like circumstance.
of power and all
from the
But the question arises
his own
Thus, all grief stems from want
of power
do men desire
desire power for the sake of achiev
power s
Does the Hobbesian
his ob
, or does he desire
for its own sake, for the sake of
?
able to co
I believe that in the answer to this question lies
the true reason for the attributes of his commonwealth.
power
so that he can be assured of the abil
desires
then the s
Even
fear from
If man desires
to protect his life
iolence
of the commonwealth, as Hobbes at least on the surface
would have us believe
is des
to ensure him the peace and
which he cannot have in the state of nature
desire for power is a
which has no other
If, on the other hand, his
necessary propens
than his own
il
of his nature
ing, then the function of the
state is to subdue this natural desire of man which is destructive to
himself, destructive to his fellows, insatiable
and without his power to
control.
This br
this paper,
us back to the second question mentioned in the
is the
is
's character
necessary.:~
of
�27
in order to bring Hobbes to the point of being able to construct his state,
or· ta · phra~e it differently, is it out of this _analysis, this process of
classifyirig and
~etining,
to his commonwealth?
that he convinces us that man's nature is suited
Or rather,
is
it that the major attribute which he
would give man and the one attribute which is necessary for the foundation
of his commonwealth one.to which we are persuaded by his subtle use and
manipulation of words.
There is perhaps a clue to the answer in the positioning of the Chapters
6, 7, and 8.
Hobbs~
In the sixth chapter as I have diagrammed in Chart #1,
presents us with a
dicti6~ary
of men's pass ions.
He does not com-
ment on the passions, that is, he makes no distinction between those which
are conducive to civil
them.
The seventh
~ociety
chapter~
and
tho~e wh~~h
ars · not! :He simply presents
however, presents us
wi~h
a break from ·his
_
passion dictionary, and it is diff , cult to .see what connection .i t. bears to
i
the former.
It contains oo comment on the passions nor an explication.
Rather, it sits unconnected between the dictionary of the passions and the
dictionary . of the . intellectual virtues.
However·, it does contain some passages which, I believe, are quite useful
in evaluating the connection between the subject matte.r which ha.s gone
I
before, namely the definitions of the passions, and that which will come
·'
later, namely, the construction of the commonwealth.
Hobbes speaks of the ends or resolution of discourse.
In this short
ch~pter
He gives us the
criterion by which a work is to be judged a work of science or a work of
opinion.
(Leviathan, p. 62ff)
from definitions through
If discourse is with speech and proceeds
syllogis~ic r~asoning
sion, then it is to be termed science.
to a formally
so~nd · conclu
.If on the ·other hand, the discourse
does not proceed from definitions, or if the
definit~ons
are not joined
into syllogisms, then the discourse begins at some contemplation of one's
own or w.ith that of another and is not to be called science but opinion.
The question which I am .r.aising no_ is whether his
w
in fact philosophy or opinion • . I shall
att~mpt
c~vil
.Philosophy is .
to . judge it from his own
standards, that is, if it is to be found that he fits his definitions
into syllog.isms and farms his,
conclus~fons,
·then it is ·to be ·termed science.
(It must be remembered that· for Hobbes science
o't~
·philosophy "is · conditional not
�28
.)
, and consists of if - then
f however, he is seen
to make a break from his definitions and to base his work upon "some
his own admission, to be termed
of his own, 11 then it is,
the definitions of the
Hobbes
In the e
can also be
, and like the
instead of leav
Chart #4)
and no comment,
us with a
to make a connection between the
not
he
. (See
d
virtues
and the
to describe the causes for the differences of
powers among men.
wit, which for Hobbes consists in the celer
or the abil
p. 68
a scout, he says, which
the fulfillment
the
of the mind is not to control or
passions but to lead them to their desired end.
He has inverted Plato's
the horses in the drivers seat.
of the chariot and has
However, not
The intellect is like
ahead and leads men
of their desires.
but
the servant of the
is
For
she receives from them her s
s
to another, is
to make a swift succession of one
the handmaid of the passions
p. 68)
of
t passions have the s
for Hobbes, those with the
t natural wit, and a man with weak
offense, cannot possib
des ires, no matter how free he is "from
have either
all
to be remembered
such
pass
, compassion, and
as char
is the handmaid to and receives its
sire for power alone
So far the
p. 68)
He has
Hobbes has drawn of man looks like this
of the mind, but his
honor and power.
is in
of his desire for power
~nd
to lead him to
are useful
We are still left, however, with the unanswered
ion of
end.
man desires
We know now that all the faculties of his mind, will
are directed toward
it,
He
with the
also has intellectual virtues, but these are
this power.
from the de-
and in-
we still do not know whether
�ro
OJ
N
CHART NO. 4
The Intellectual Virtues
,·
(ACQUIRED WlT 1
I
That gotten by
method, culture,
and ins tructfon
INTELLECTUAL VIRTUES Those abilitie~ of the
mind such as men praise,
value, and desire should
be in themselves and are
commonly called good wit.
fcooD FANCY The ability to
observe simi- ·
lerity.
Good fancy with
want of direction.
CELERITY
of
IMAGINATION
NATURAL WIT -
CRAFT -
Not had from birth,
but gotten by us~
and experience, not
by method, culture,
or instruction
GOOD JUDGMENT The ability to
observe differences.
STEADY
DIRECTION
The ability
to judge
what is
conducive
to bhe end.
The ability
to judge
what is conducive to the
end with unjust means
�29
it is harmful to himself and his fellow men, or, whether or not it is
conducive· to the in•titution of the state.
This question cannot be answered yet; however, I
beli~ve - that
in this
chapter we h~ve tound at least the beginnings for answering another.
-
•
•
•
~
1
•
·Manely, is Hobbes' politics sc1enca or. opiri~ion.
I will not quarrel with his definitions, but will let them
can see his
descri~tion
stand~
I
of the passions and the intellect as a means to
cla.r ify and make understood the - subject, but whence comes _this all important step of so connecting the passions with the.intellectual virtues
that the intellect
,-power?
ha~
no other function than to serve the passion for
It is not a· definition, nor is it the conclusion of syllogistic
reasoning based on his definitions.
It is a conclusion which I
only
~an
see as based, as Hobbes Wot.Jld phrase it, upon "some other -contemplation
of his 'own." (Leviathan, p. 63)
The thing which is so sttange about.thasa several conclusion he makes is
that he in nb way attempts to
reasoning.
- ~ac~
them up either by example or by
He slips them in sandwiched
between . · t~o s~ts ~f
definitions
completely bald and unadorned.
H~wever,
it would be hasty to make too harsh a judgmerit upon
the~e
few
G rtplusions and call his entire philosophy opinion i f they are not directly
_
o
related to the arid he
philosophy.
pursues~
or if they are not fundamental to his
Therefore, .it is necessary to show the fundamental nec_ ssity
e
to his philosophy of · so relating the passions to the intellect, and by
showing this fundamental
n~cessity
I hope at the same time to answer the
previously outstanding question of why Hobbes' man
se_ek~
for power.
One thing, howeve.r ,' which, I believe, it is safe to conclude even at this
point is that the suitabiiity or unsuitability of man to civil government
and : the form which that government should take depends
whether or not his passions suit him to_ government.
enti~ely
upon
for if his passions
suit him not, his ' reason will provide him no aid sin- e it functions only
c
to aid and abet the passions.
Aside from the above, there is ample evidence throughout all of Hobbes'
�30
works that this is the case,
The introduction to De Cive or the Citizen,
page 9, clearly lays the blame for contention ·and civil war upon what he
holds to be the common but erroneous belief that political philosophy is
an open subject for discussion and comment to whoever is so inclined.
places no faith at all in the powers of the intellect to
conside~
He
wisely
the questions of justice and equity, for to Hobbes, men dispute these
questions only because they expect to gain power by the acceptance of the
opinions they propound.
The princes of old, he says, "kept their empires
entire, not by arguments, but by punishing the wicked and protecting the
good." (De Cive or the Citizen, p. 9)
And the good and the wicked were
determined not by dialectic but by the will of the sovereign reflected
in the laws.
Similarly, when Hobbes sets up his Leviathan, difference of opinion is
considered as sedition, and private political opinions are to be suppressed
by the state.
It is clear that he places no confidence at all in the
ability of mankind to use their reason in any other way than to gratify
their own passions and that the passionate man is the whole man with
reason his servant, not his guide.
We must see now the state of man as Hobbes leaves him in respect to his
passions and particularly that primary passion, the desire for honor.
In
order to do this I think that it is necessary to carefully consider his
application of the words glorying, honor, power, and pride.
To this end,
I should like to synthesize in part the thoughts which he expresses on the
subject in the Leviathan, the De Cive, and his treatise Human Nature.
Power, for Hobbes, is "present means to obtain some future and apparent
good . • • " (Leviathan, p. 78)
power.
Honor is the high evaluation of a man's
It is the opinion which one man has concerning the power of another.
However, a man is honored greatly or honored little according to the
opinion which he has of himself, not according to any objective standard.
Thus a man considers himself honored if the men around him set the same
value upon his power as he does himself.
Now in Human Nature Hobbes says:
"In the pleasure men have, or the displeasure from the
signs of honor or dishonor done unto them, consisteth
�31
the nature of the. pass ions."
Body, man, and Citizen, p. 215 · Thomas Hobbes
He continues to say:
"Glory, or internal gloriation or triumph of the
is the passion which proceedeth from the
imagination or conception of our own power above
the power of him that contendeth wit~ us, the
signs whereof, besides those in the countenance,
and other gestures of the body which cannot be
described; are, ostentatioM in words, and insolency in actions; and this passion of those
whom it displeaseth is called pride; by them
whom it pleaseth, it is termed a just valuation
of himself."
Body, Man, and Citizen,· p. 215 Thomas Hobbes
~ind,
If we remember now that all the mental pleasure which man has is from
glorying, or from the imagination of his own power, we see that he strives
not 'only for power in order that he might have the means to satisfy his
desires, but for its own sake, that he might have the honor of
~is
fellow
men .
But we must ask now, wherein consists honor and what are those things which
are deemed honorable?
Hobbes gives an outline of these things in the
leviathan in Chapter 10, "Of Power, Worth, Dignity.''
It is not necessary
here to give an account of them all; however, he says in summary:
"Honorable is whatsoever possession , action , or
quality is an argument and sign of power. Ndr
does it alter the case ·of honor whether an action,
so it be great and difficult and consequently a
sign of much power, be just · or unjust, for honor
consists only in the opinion of power."
Leviathan, p. 82-83 Thomas Hobbes
Later he says:
"So that in the first place, I put for a general
inclination of all mankind a perpetual and restless desire of power after power that ceases only
in death."
-~ Leviathan, p. 86 - Thomas Hobbes
But why is it that men desire power?
Not only so that they might have the
�32
means to provide for themselves but because the only pleasure of the mind
of man· ·is .. to
-.receiv~
hono.r, and this insatiable ·quest for honor, begot ten
by the pride of ~an, re~ults in the insatiable quest for power, ruthless,
restless and untempered by reason.
.
.
.
This opinion· of : the
n•tut~l · p~oclivity
of mankind . is strengthened in the
beginning · ~f the De Cive, P·: 22. ; i Here Hobbes says that men seek the
society of others for two things only, honor and ·profit, and that he de lights in the company· of
that he can arouse in them an esteem
othe~~ ~nly ~o
for h-is power and . leave behind him the aura . of his glory.
Man is most
pleased with himself when he -can st+r up laughter by the ridicule of another
man's defects and infirmities · and by ·th.a t means buy himself a higher
estimatiori. ·Thus: .
"All the mind's pleasure is either glory, (or to
have a good opinion of one's self) or refers to
glory in t~e end; the rest are sensual, or conducing
tb sensuality, which may be all ·comprehended under
the word conveniences. ·All .society therefore is
either for gain, or for glory; that is, not so .much
· ·for the love of our fellows as · for love of ourselves."
De Cive or the Citizen, p. 24 Thomas Hobbes
Thus we have the· nature .of
~an
for Hobbes
~
a slave ·to his passions, ready
to use all the powers of ·war to satisfy not ·o nly his desire ._ for profit,
but to satisfy that one all ,powerful and
stemming from
p~ide,
insatiat~
which can end only in death.
urge for .honor and esteem
For kings t hemsel ves,
Hobbes says, who 'exercise the . tjraatest power on earth seek, when their
powsr at .home
i~
secure,
n~w : dominions
to cdnquer in order that they might
have the fa~e and hono~ . of new c~~quests. (Leviathan, p. 87)
This is· the man which Hobbes invites us, his readers, to look into ourselves
and find.
If we
~ould
agree with him we must each one find in ourselves
the same ruthless, untempered, passionate man which is the result of his
analysis.
Thus is Hobbes' Leviathan fitiy f:cfrmed to his understanding of man.
is designed to suppress by fear the
his hature.
~ustice
~iolent
It
and uncontrollable surgings of
in. this state cannot be allowed the equivocations of
�33
intellectual disputation . .· It clamps down with the irresistible force of
the sovereign, this being the· only way to ke.ep peace in the state of men.
Hobbes Commonwealth is fitly named the Leviathan:
''Upon the earth there is not his like, . who is
made without fear. He beholdeth all high thi. gs;
n
he is a king over all the Children of Pride."
-- Job XLI: 33-34
Science or Opinion?
Part III
With this understanding of the Hobbesian man I think that it is possible
to answer the following two questions:
(1) Is Hobbes .foundation of poli-
tical philosophy, namely the passions of · men, science or opinion, according to his own understanding of .the terms, and (2) a corollary to the
first, How much of the careful analysis and defining of the passions is
necessary to bring him to the
po~nt
of being able to construct his state.
If we consider the chart which he gives of philosophy in the Leviathan we
see that ~he" Consequences from the Pass ions of Men" which ,a rises in the
'
..
lower right hand corner and which is necessary to the study of Ethics is
not connected to the "Consequences from the Accidents of Politic Bodies;
whi6h is called Politics, and Civil Philosophy" which arises in the lower
left. (Leviathan, p. 76, 77)
The attributes which are given to the state
arise solely from its "institution," that is, from its construction.
The
laws of nature, which Hobbes draws out of the fundamental precept, to
seek peace, are the elements of the construction of the state.
All the
laws of nature are derived from this basic principle by means of reductio
ad absurdum proofs.
This is the case not only in the Leviathan, but is
perhaps more . clearly shown in the De Cive.
The laws of nature · are the
· laws of nature because their contraries lead to war, which is against the
fundamental law of nature, i.e., to seek peace.
However, in order to know what is necessary for peace it is necessary to
.. ,
·:
know what are the causes of war •
In the De Cive Hobbes omits all the careful elaboration of the passions of
men which is in the Leviathan and giv.es,. what he feels is a necessary understanding of the nature of man in order to derive his laws of nature.
But
�34
what does he give here of the nature of man?
Simply this:
(1) that man
is born unfit for society since he seeks it only for profit or for honor,
(2) that all free congress arises either from ~utual poverty,· or from
vain-glory, and (3) that it is a natural proclivity of men to hurt each
other," which they derive from their pass ions but chiefly from a vain esteem of themselves. (De Cive or the Citizen, p. 21-30)
And if there be
added to these things the right of all men to all things, man finds himself
in a state which is "solitary, poor, nasty, brutish, and short." (Leviathan,
p. 107)
Of course, in the De Cive, he does not pretend that he is giving a scientific analysis. (De Cive or the Citizen,
sufficiently known to all by experience.
p~
15)
He gives these things as
But the question is:
Does his
careful defining and categorizing done in the Leviathan give any firmer
foundation for his opinions.
I don't think that it does.
For the passions,
as he defines have been seen, although perhaps not so aptly defined, by
other poets and philosophers who were students of human nature.
It is not
by defining the passions that he draws men as he does, unfit for civil
society and thirsting without end after glory.
It is by (1) depriving man
of the ability to use his intellect to curb or control his passions or in
any other way than to aid in their fulfillment, and (2) by making the intellect so dependent upon them that it derives its
~trength
and agility
frbm their forcefulness, that the Hobbesian man becomes the monster that
he is.
This way of connecting the passions and the intellect, as I have shown be fore, is in no way grounded upon definition or syllogistic reasoning, but
is based upon "some contemplation of his own."
is founded upon this view of
man~
then it too
And as his state in turn
de~erves
the name of opinion,
not science.
Hobbes wrote in a time of political turmoi.
He saw man as the raging beast
of the mob, bent upon destruction, theft, and murder.
draws for us.
This is the man he
But to consider a man in the midst of a civil war and con-
clude that this is hls entire nature is no more valid than to draw from a
man who is drunk the true elements of humanity, unless we are to consider
all the world as drunkards.
�35
. .:i.
GEOMETRICAL CONSTRUCTIONS or
THE SIX IRRATIONALS CALLED. APOTOME
David Sackton '69
In the number books it is observed that numbers may be said to have ratios
in a manner similar to magnitudes.
In book ten, magnitudes (specifically
lines and areas) are reconsidered in light of the number books, and a
relationship is established in proposition five:
Commensurable magnitudes
have to one another the ratio which a number has to a number.
The notions
of commensurable and incommensurable magnitudes are derived from propositions on commoh measure in book seven.
All numbers are measured by the
unit, but magnitudes have no such universal measure.
Thus when magnitudes
are reconsidered after the number books, there is the class of incommensurables, or specifically irrationals, to be dealt with.
The greatest
part of book ten is spent in organizing the irrationals in an effort to
answer this problem.
Ostensibly, the purpose is to give an orderly and
cl~ssification
systematic
of magnitude in light of the number books; in
passing it may_ also be noted that two of the_ regular solids have irrational
sides.
In an effort to understand Euclid's presentation of the irrationals, the
greatest obstacle has been visualizing the lines geometrically.
promptly abandons a geometrical
cou~se
Heath
in favor of an algebraic approach
which becomes· hopelessly involved, while
Euclid'~
figures
a~e
equally
disappointing at critical moments, consisting only of sets of lines.
With
respect to proposition X, 29 and those following, proposition I, 47 is
useful in dealing with commensurability in square.
obvious:
the proposition -affords a method _of
lation to the squares on them,
the
noti~n
d~finitions
- ~nd
The connection is
spea~ing
about lines in re-
this is precisely what is involved in
of commensurability in square.
This notion is vital to the
of the apotomes, and I have found the
~pplication
of proposi-
tions 29 arid 30 most useful in constructing these six irrationals. -The
proof for · eaGh construction is similar to propositions 85 through 90 in
which Euclid ' finds each apotome •
. .The constructions are as follows:
�36
1) To construct a first apotome showing its relation with the lines from
which it is formed.
Let the rational line R
be set out, and AB commensurable in length with
R; therefore AB is also
rational.
Let two square
numbers KG,GH be set out,
and let their difference
HK be not square; therefore neither has KG to HK
the ratio which a square
number has to a square number.
Let BC be taken on the line AB so that, as
GK is to HK, so is the square on AB to the square on BC; [X, 6: por.] therefore the square on AB is commensurable with the square on BC. (X, 6)
But
the square on AB is rational; therefore the square on BC is rational, and
BC is also rational.
And since GH has not to HK the ratio of a square
number to a square number; therefore neither has the square on AB to the
square on BC the ratio of a square number to a square number; therefore
AB,BC a r e i ncommensurable in length.
And they are also rational, there f ore
AB,BC are rational straight lines commensurable in square only; therefore
AC is an apotome. (X, 73)
I say next that it is also a first apotome.
For let AB be bisected at D
and circle AES be described with center D and radius AD.
Also let BE,
equal to the annex CB, be inserted in the circle, and let AE be drawn.
Now
AES is a right triangle (III, 31), and the square on the whole AB is equal
to the square on the annex together with the square
~n
the line AE (I, 47);
therefore the square on AB exceeds the square on CB by the square on AE.
Now since as GK is to HK so the square on AB is to the square on
C~;
there-
fore also, convertendo, GK is to GH as the square on AB is to the square
on AE (V, 19, par.).
But GK has to GH the ratio of a square number to a
�37
sq~~re
number; · therefore the
squ~r~
on AB has to the
on AE the
s~uars
ratio of a square ·number to a square · number; therefore· AB, AE · are ·commensurable in length. (X, 9) · And therefore 'the 'square · on AB ·is greater
than the square on CB by the s~ua~e .· bn ~ ·· strai~ht · line cdmm~nsurable in
length with AB.
· And~he ~ho!~
rational·
~traight
(x' . def •
.I II ' ·1 )
2)
line· R
~et
AB is commensurable: in length with the
out. · Thetefora · Ac is
~
first apotome.
QE r
To construct a second apotome.
A~~--r-4...._
·
______
...._.~--~~
Let the rational straight line R
\
\
be set out, and CB commensurable
\.
with R; th~refore
\\
CB
is ration?!.
Let two square numbers KG,GH be
set out, and let their difference
HK be not square.
Now take some
line AC added in a straight line
with BC such that, as HK is to GK, so ls the square on BC to the square
por~)
on ·AB. (X, 6,
Therefore the square on BC is .commensurable with
the square on AB. (X, 6)
But the square on BC is rational; therefore
the square on AB is rationai, and AB is rational also.
square on BC has not to the square ~n AB the ratio of
And since the
a squar e
~o a sq~are nu~6er, ~C and AB are incommen~urabie - {n length.
.
num
ber
(x;
9)
'
And both lines are rational; therefore BC,AB are rational straight lines
.
.
.
. commensurable in square only; ther~fore AC is an apotome.
· I say · next "that it is ·also a ·second apotome."
for let AB be bisected at
D' and 'circle . AES described with center D and radius AD.
And let BE,
which is "equal to the annex ·BC, be ·inserted ·in the circle, ·and let AE be
drawn.
Now AEB is a right triangle (III, 31), and the square on the
whole AB is equal to the square on the annex together with the square on
the ll.ne At. (I' 47)
by the square on AE.
Therefore the square on AB exceeds the square on BC
And since the square on AB has to the square on BC
�38
the ratio of the
KG to the number GK
therefore,
square on AB is to the square on AE as KG is to GH. ( V,
There-
9, par )
fore the square on AB has to the square on AE the ratio of a square number
to a square number; therefore AB,AE are
Thus the square on AB
a
line commensurab
commensurable with the
in
• (X, 9)
than the square on BC
in
with AB.
the square on
And BC, the annex
line R set out
s
is
Therefore AC is
a second apotome. (X, def. III, 2)
To construct a third
Let a rational s
8
line R
be set out, and let three numbers
L,GK,KH be set out which have not
to one another the ratio of a
square number to a square number
but let GK have
GH
ratio
of a square number to a square
number
be taken such that
as the square
Then let some line
R is to the square on AB
GK, and let BC be taken on AB such that, as GK is to HK
on AB to the square on BC. (X, 6, par.
so is l to
so is the square
Since then, the square on R is
to the square on AB as L is to GK; therefore the square on R is commensurable with the square on AB. (X
6)
But the square on R is rational;
therefore the square on AB is rational
and the line AB is
rational~
Also since L has not to GK the ratio of a square number to a square number
therefore neither has the square on R to
square on AB the ratio of a
square number to a square number; therefore R is incommensurable in
with AB .. (X, 9)
, since, as KG is to HK so the square on AB is to the square on BC;
therefore the square on AB is commensurable with the square on BC
6
�39
But the square on AB is rational; therefore the square on BC is rational,
and the line BC is also rational.
And since GK has not to HK the ratio
of a square number to a square number; therefore neither does the square
on AB have to the square on BC the ratio of a square number to a square
number; therefore AB and BC are incommensurable in length. (X, 9)
But
both were proved rational also; therefore AB,BC are rational straight
lines commensurable in square only; therefore AC is an apotome. (X, 73)
.I say
that it is also a third a po tome.
ne~t
For since, as L is to GK, so
is the square on R to the square on AB; and as GK is to HK, so is the
square on .AB to . the square on BC:
therefore, ex aeguali, as L is to HK,
. so is the square on R to the square on BC. (V, 22)
But L has not to HK
the .ratio of a $quare number to a square number; therefore neither has the
square on R .to the square on BC the ratio of a square number to a square
.
numb~r;
therefore R is incommensurable in length with BC. (X, 9)
neither of the lines AB, BC is
commens~rable
in
leng~h . with
Therefore
the rational
straight line R set out.
Now let the line AB be bisected ~t D, and let the . c{tcl~ AEB be described
·with center D and radius AD.
·•
·Also let BE which is equal to the annex, BC,
'
be inserted in the ·cir.els, and let AE be drawn. r~ow AEB is a right triangle (III, 31), and the square 6n the whole AB 'is equal to the square on
the annex together with ~he ~q~are on the line AE.
Thus the square on AB
is greater than the square on ·ac by the square on AE. Since then, as GK
is to HK, so is the square on AB to ·the square on BC; therefore, conver-
GK is to GH, so is the square ·an AB to the square on AE (V,
tendo, as
por.)
19,
But GK has .to GH the:t ratio of a square number to a square number;
therefore the
squar~ .
on AB has to the square on AE the ratio of a square
number to a
~quare
number; therefore AB .is commensurable in length with
AE, (X, 9)
And so the square on AB is greater than the square on BC by
the square on a line commensurable in length with AB.
s~~aight
lines AB, BC is
comm~nsurable
And neither of the
jn length with the rational straight
. .J:ine, .R set. out; therefore AC ,is a third _
apotome. ( X, d.ef. I q, . 3)
QE F
�40
4)
a fourth
To
R
Let the rational
line R be set out, and AB
8
commensurable in
with
AB is a rational
it;
line.
Let two numbers GH,
such that the
be set
whole GK has not to either
of the numbers GH,HK the
ratio of a square number to
a square number.
Then also let BC be taken on AB such that, as GK is to
HK, so is the square on AB to the square on BC; (X, 6, par.)
the square on AB is commensurable with the square on BC. (X, 6)
on BC is rational; there-
square on AB is rational; therefore the
line BC is rational.
fore the
But the
Now since GK has not to HK the
ratio of a square number to a square number; therefore neither has the
square on AB to the square on BC the ratio of a square number to a square
number; therefore AB is incommensurable in
with BC .. (
9)
And
rational; therefore AB,BC are rational stra
both lines were
lines commensurable in square
therefore
I next say that AC is also a fourth
73
is an
at
For let AB be
and let the circle AES be described with center D and radius AD
Let BE
to the annex BC, be inserted in the circle, and let the line AE be
drawn.
Now AEB is a r
whole AB is
(III, 31), and the square on the
to the square on the annex
with the square on
the line AE .. (I' 47) Therefore the square on AB is
than the
square on BC
the square on AE. Since then, as GK is to HK, so is the
square on AB to the square on BC; therefore,
so in the square on AB to the square on AE .. (V
to GH the ratio of a square number
as GK is to GH,
19, par.)
GK has not
a square number; therefore neither
�41
has the square on AB to the square ·on AE the ratio of. a s·q uare number to
a sq.uare. m,Jmber .; ; t .h erefore AB is :incomme~surable in le~gth with AE. ( X, .9)
Now _
the ~quare on
Aa is
therefore· greater than t~e square on BC by the
square on a straight line incommeinsur- ble with AB.
a
commen~urable
in length with the. rational
strai~ht
And the · whole AB is
line R set out.
fore the - iine . AC is a fourth apotome. (X, def. III, 4)
5)
To
con.struc~
///;/ ~~
/<
Al
----------R
.
·.
.G.....: _ __ --'IJ.~-- - - - - - -·
~~ · ·
,,
-~I B
·b
E
QEF
.a fifth apotome.
--7'--L
/
There-
J
I
~
.
./
/
J
. Let
th~
str~ight
rational
--
line R
be set out, and let BC be commensurable in length with R;
therefore BC is rational.
Let
two numbers GH,HK be set out such
that the whole GK has ·not to
either of the numbers GH,HK the
'
ratio of a square number to a
---------:----
square number.
And let CA be
added in a straight line to BC such that, as HK is to KG, so is the square
on BC
~o
the
sq~are
on AB.
And .the square on BC is rational; therefore
the square on AB is rational;
therefo~e
the line AB is
also r~ational.
Now since, as GK is to HK, so is the square on AB to the square on
(X,6)
~C ,
while Gk' has "·not ·to HK the ratio . of a square number to a squa'r'f3 riutriber;
.:·
therefore neither . has the· squ.a re on AB to the square on BC . -t _ e ratio- o'f
h
a square number to a square number; therefore AB is incommensurable in
length with BC. (X,
~9)
·. And both lines ·are proved rat{bnai;
th~refore
AB,BC .are rational straight .lines commensurable in square only; therefore
the .line AC is an apoto·me. · ( X, · 7.3)
.I say next , ~h~t it is also a fifth apot~~e. · For let .· AB be bisected at D~
and let the circle AEB be described with
equal to the annex BC,
c~nte~ . o
and radius AD.
Let BE, ·
be inserted in the .. circle, _
.and let AE be joined.
Now AEB · is a right triangle (III, 31), and the square on the whole AB is
K
�42
equal to the square on the annex together with the square on AE. (I, 47)
Therefore, the square on AB is greater than the square on BC by the square
on AE.
And since, as the square on AB is to the square on BC, so is the
number GK to the number HK; therefore, convertendo, as the square on AB
is to the square on AE, so is GK to GH. (V, 19, par.)
But GK has not to
GH the ratio of a square number to a square number; therefore neither
has the square on AB to the square on AE the ratio of a square number to
a square number; therefore AB is incommensurable in length with AE. (X, 9)
And therefore the square on AB is greater than the square on BC by the
square on a line incommensurable in length with AB.
And the annex BC
was made commensurable in length with the rational straight line R set
out.
6)
Therefore AC is a fifth apotome. (X, def. III, 5)
QEF
To construct a sixth apotome.
L
Let the rational straight line
R be set out, and three numbers
L, KG, HK not having to one
another the ratio of a square
number to a square number, and
let KG also have · not to GH the
ratio of a square number to a square number.
And let some line AB be
taken such that, as L is to GK, so is the square on R to the square on AB;
and let some line on AB, BC, be taken such that, as GK is to HK, so is
the square on AB to the square on BC. (X, 6, par.)
Now since, as L is to GK, so is the square on R to the square on AB; therefore the square on R is commensurable with the square on AB. (X, 6)
But
the square on R is rational; therefore the square on AB is rational;
therefore the line AB is rational as well.
And since L has not to GK
the ratio of a square number to a square number; therefore neither has
the square on R to the square on AB the ratio of a square number to a
square number; _
therefore R is incommensurable in length with AB. (X, 9)
�43
Again, since, as
is . to HK, so is
~K
square on AB to the square on BC;
th~
therefore the square on AB is commensurable with the square on BC. (X, 6)
But the square on AB was shown rational; therefore the square on BC is
rational; therefore the line BC is also rational.
the ratio of a square number to a square number;
s~u~re
s~uare
cin ' AB to the
Since GK has not to HK
neither has the
~herefore
on BC the ratio of a square number to a square
number; · therefore AB is incommensurable in length with BC. ( X, 9)
And
both lines are rational; therefore AB, BC are rational straight lines
.
.
comme~surable
in squa~~ only; therefore the line AC is an apotome (X, 73)
I say next that it is also·-a sixth apotome. · For since, as L is to GK,
so the .square on R is to .the square on
square on AB · to the square · OR BC:
~.
..
.
'
and as CK is to ·HK, so is the
AB~
therefore, ax··aaguali, as L is to HK,
so .is · the square ·on R to the sqtiare on BC. · (V, 22)
But L
h~s
not to HK
the ratio of a square number to a square number; therefore neither has
the square on R t6 the square ·bn BC the ratio of a sqtiare ·number to a
· sq~are
number; therefore R is
incommensur~bl~
iM leMgth with BC. (X, 9)
Therefor.a .i t has be- n proved that neither ·of the lines AB, BC is · commene
s~rable
in length with the
r~tion~1 ·
line R.
Now .let the line AB be bisected at D, and let the qircle AEB be described
wi~h
center D and radius AD.
And let .the
~in~
BE, equal to the annex BC,
be inserted in the circle, and let AE be joined.
•
•
'
· angle (III, 31), and
the annex.
i-·
~he
to~ether . wit~
on AB is greater . than
.
Now AEB is a right tri-
.
square on the whole AB is equal to the square on
tt:ie square on AE. (I, 4 7)
t~e
Therefore the square
square on BC by the square on .AE.
And since, as
GK is ta . HK., so is the square on AB to the square on BC; therefore, £Q!lvertendo, as GK is to GH, so is the square on AB to the square on AE.
(V, 19, per.)
sq~are
But GK has not to GH the ratio of a square number to a
number; therefore neither has
the - squ~re
on AB to the square on AE
the ratio of a square number to a square number; ·therefore AB is incommensurable in length with AE.' (X, 9)
And therefo're the square on AB is
greafer than the square on BC by the squaie on a straitjht line incommensurable in length 'with AB.
And it ·was proved that neither of the lines
AB, BC is commensurable in length - ~ith the· r~tional straight line R set
out.
Therefore the-·line ·AC ·· is ·a· ~ixth
~po~bme.
(X, def. III, 6)
QEF
�44
, 1613,
ID ING WESTWARD
An
is
Howard
Donne's poem is in three sections:
68
the first a proposition about the
soul, the second a confession of sin and fear, the third a prayer for
The poem increases in emotional intens
with each section
both because of the nature of a proposition, confession and prayer and
because of the form and
of each of these
used are
none the less effective.
obvious,
tion is
the
In form the devices
The proposi-
words "Let man's soul be a
remind one of the form of a Euclidian proposition and it elicits an inresponse.
The
is in the first person and therefore
draws the reader close to the writer and creates emotion in the reader
The prayer is in both first and second persons and because of
the reader in the
sider.
position of both par
The reader is
has been exper
out-
in the prayer because he, like Donne,
the ris
tension of the poem and now needs the
prayer as the natural expression of such tension.
The reader is also
an outsider to the prayer, for the prayer addresses Christ
rest of the poem seems to address the reader.
as well as the increased emotional intens
out of
hear
This
make the reader feel un-
the prayer section, as
while
words not meant for him.
reader Donne has
while the
such a
in the
this section of the poem the powers of a prayer
as well as the form of one, for it is with such mixed
that we
prayer.
The proposition
in primo.
states
The reader must
for that is
which mus
the
to the poem.
devotion to God is the
of the soul to a
He must also
the
motions.
their courses
These
that
mover of the soul and that the influence of
the souls on each other, which creates business and
souls
be
as the
raise some
move
, cause the
anomal
i.c
which are in some way
considered later in the poem and some which are not considered at all.
�45
The ·idea that . devot.ion is the "natu·r al form" of the soul is unquestioned
in the :.poern; a,s in .the Old Testament, it is not a problem.
of why · the soul is sub ~ect to being
11
The question
by others 'hur.r ied" from . its natural
form is as myste.r ious as why the planets have anoma.listic
movement~.
This question, however, is dealt with, though not at all obviously, through out the
p~em.
The opening lines of the confession are the consequence of the proposition,
for jf one accepts the postulates about the soul then he will understand
Do..nne's position of "being carried towards the West" though his "soul's
. .
.
form b'7nds towards the East. fl
The word
II
carried" implies that it is not
by Donner s will 'that he is travelling .but . rather that he is b Bi.ng acte·d ..
upon.
This implication is important, . and . it concerns the qu ost ion ·of wh y
the soul is hurried by ·others from its natur:al form.
sidered . more fully
It will be · con-
late~.
Line eleven begins the explanation of the first .two lines of the confession and the statement of the paradoxes present in God's
men, especially his becoming man.
dealings . wit~
The four lines eleven through fourteen
themselves_ contain paradoxes and the pun on which the poem is· based: · · ·"The
sun by
ri~ing
set".
crucifixion day,
s~
Th~se
th~ · first
lines make reference to two events.
Goodfriday, the sun darkened early in the day,
that by rising that day it in effect set.
Christ the son of God was
born to die as the Oid Testament prophet, said
By his death . Christ
•
Donne's words).
On the ·
made - ~ossible
the suffering servant.
eternal life for men ("endless day'' in
The early darkening of the
different from all other days.
~f
s~n
made the crucifixion · day
Donne speaks as though the sun's action
begot eternal life; this impiication points out the importance of th~
su~
as a linkihg symbol of man and Christ, for the sun reminds us of
~lanets and hence 6f man'~ soul and it remind~ · us of the ~on and .hence the
salvation of man's soul.
As the sun rises in the east, ·so Christ the
son is sy~b~iized by th~ ea~t.
The riding westward ~herefore i~ - ~ turning
away from Christ.
The · puM is· cdmpoµnded in lines 13-14, the lines . in which
save men from
baing . b~nighted
by ~in.
Chri~t.~s
said to
· As Christ the · son conquereq sin,
that is, moral darkness, so the sun conquer.ad physical · .darkness.. . .Christ's
�46
action was accomplished by rising and falling just as the sun's is by
rising and setting.
These two lines make the first eight lines even more
meaningful, for now we see the full relevance of the analogy of the soul
to a planet.
The two analogies form a proportion:
soul as the sun is to the planets.
Christ is to man's
The fact that Christ has such a close
relationship to men magnifies the paradoxical nature of the salvation of
men by the incarnation of God.
The paradox is brought out in the next
lines in which the sun-son analogy is carried further.
Christ is likened
to the sun's effect on men, for as the sun is so bright that men cannot
look at it directly, so the crucifixion is of so much weight that Donne
cannot look at it.
This is as it was in the Old Testament when men could
not look at the face of God.
If the prophets would die when they looked
on the face of God, how much more inconceivable it is for Donne to behold
God dying.
The spectacle made the earth quake and the sun- grow dark; how
then could Donne behold it?
Yet we are constantly made aware of the fact
that men did watch the sight and that such a paradoxical event as the
death of God did occur.
God'·s action is described most radically in lines 21-28.
These lines
also make clear the development of emotional intensity within the poem.
The four sights which Donne names as too much for him to behold are
effective both because they are so shocking and because they are traditional symbols used by the church since early Christian times.
Each
sight named describes the divine partaking of the earthly in a manner which
is incompr ehens i ble .
How are w t o understand the hands w
e
hich span the
poles and tune the spheres being pierced with hol_ s?
e
Hands coonote acti-
vity, and it is God's activity with men with which the church is concerned .
The pierced hands are the traditional symbol of the church for Christ's
death for man's salvation and therefore convey a great emotional meaning
for the Christian.
The picture of God's hand tuning the spheres reminds
the reader of the opening lines of the poem, in which the soul is likened
to a sphere.
We are reminded that it is God who should rule our souls,
not "pleasure or business".
How are we to understand the second divine
quality, the height which is zenith not only to us but also to those on
the 6ther side of the earth, our antipodes?
The words "endless height"
suggest infinity, an especially difficult concept to think about • . The
�emotional intens
is increas
seems
even within these lines
horrible and
How can the blood which
saved men mix with the dust of the earth?
on the
fall
for the next
was so r
The idea of Christ s blood
to the medieval church that the
to receive the wine at
were not
The use of the
s
because of the
because
of blood is es
mov
of Christ s blood in the New Testament and in
the liturgy of the church.
The fourth
most dramatic of all the four
which Donne names is the
, for how can we behold, even in our
, the flesh in which God took substance for man's sake b
1
d and torn 11
men?
a way is
That God should partake of
but that man should
substance is unthinkable
The
the blood it has
of the church.
life in such
to kill God, and mutilate his
is effective as a
because like
tance in both the New Testament and the
Flesh is also
ic of mans weakness;
it is therefore very str
should be
that the div
with
the human in this way
and
These lines are the center of the poem, both
for
express both Donne s own tensions in his life and the
in God s act of
man to save men
which create tens
Donne s tensions are made evident
Christians
lines sta
his abhorrence of the s
force of the o
lines
turns away from God
UJest 11 now becomes more
11
for all
the str
of these
ts of Christ crucified and the
his des
The line
xes
because his soul cons
Hence is 1 t, that I am carried towards the
than before, for now we see
is carried westward, that is, away from God, as if
he
his control and
his will.
That this
how
some force
away is as
icable as the anomalistic movement of the
is not a
tif i-
cation or excuse for the Christian, for when Paul said in the letter to
the Romans
(Romans 7:1
for I do not do what I want, but I do the very
he was s
his need for salvation, not
his own actions.
rors and
them are not an at
rather a
, the lines
5-28 which name the hor-
of the Incarnation and Donne s inab
to excuse himself for
of the
of his
to
to look at
carried westward but
affected
the
�be
le
in
sion is
, for
s
title of the
Goodfr
that man turned
away
the sun
westward and
it too were go
ich is related to these
its course
darkened as
westward
been in the east.
westward which causes
It is the
man because
he cuts himself off from his prime mover
wounded
Christ and rode
for
because he was
his creatures.
The poem continues
, Chris
Donne s question
possib
These lines are
s
because
would not be as awesome as see
seems that
words "and furnished
I
that sacrifice"
ed loss at
ike
one·
ist's death.
loss
human·
sees a
God
his sake
a soul
for
motions around it.
the poem
The prayer
up all the tensions, within
these lines Donne seems
save
soul
These.
·are
to
is
ines
rest
but
prayer
tens ion
prayer but there the words
lines
am carried towards the west
also says that he turns his
for
because
because
Donne is stated in the First
were
state o
ist
s" as in line 7.
or bus
difficult but the last
as I r
receive corrections ,
These contradictions are
reader
dared .. not
0
,the_ poem uand I 11 turn
dates them somewhat.
face" elucithe lines
5-28
toward God or
It seems then that .his r
as of
are
and
a
of fear as
not conquer sin
actions.
controls the sinner and
conquer fear; therefore
Christ 1 s corrections and
alone will not save
Donne
that
is
restore his
Donne has driven out of himself because of the sin
in him
ich he hates and
�49
does not understand.
Only after Christ's image has been restored in
Donne does Donne think that Christ can know him, and hence enable him
to turn his face toward Christ.
I think Donne is using the act of
knowing in the scriptural sense of know intimately and love.
Donne has
already made references to sc.r ipture 'in the poem so it does not seem
unlikely that he is Llsing this important word in a special sense.
Donne's tension and turning away from God involve more
·t~an :simple
Since
will-
ful sinning, his rede·mption will ·require more than simple punishment .
is Christ's knowing him and love for him which will ultimately enable
Donne to turn his ·face toward the east;
It
�50
THE HORSE AND THE ROSE
Veronica Soul
i
the dusk of winter fell before
Midafternoon. Downcast December clouds
Cast mottled grays on narrow streets where I
Hunt out the secret shops for children's
In search of wooden horses set on wheels
Or rockers - carved
hands of father
men
Whose images are ashen like the
I found a man who
have made a horse
One
gay for its first child; one browned
In age with stiff-haired tail to comb and braid.
A man who
have breathed brown air behind
The window where I s
The graying
Was locked outside while he the wooded floors
The shelves with worn tin
shone - d
lit
that burned in browns
I left
The
frozen in cold air,
in brown. Past the
tols, past
The burnished drums, the flower
box
Of
Beneath
folk art
a horse,
A toothless boar
like the
Both brown and
Horse in hand, I left the drums, the guns,
The man. And I in brawn re-entered gray.
ii
The brown I bore reflowered the gray
(I'd faced a wind that left a rose
before it faded from my touch.
tells
flowers
66
�965-66
" JO
UJall
not the best game
tournament,
either
game
in the St. John s
the
Jacobsen, tutor, and David
rounds between
so much the r
- since
there are miscalculations and blunders on
between two
of a tortoise-hare race.
on two
in November, cons
Most of that
ime.
Jacobsen s
is next move
the board before ventur
moves tend to be
the cautious, develo
and not
Mr
Jacobsen s
pe
based on
appropriate to
s
reveals a des
s
contest to a decision
away.
This is a difficult s
withstand, but if a conservative
has
outlives an all-out attack
better position thereafter.
after
won, but
f
sides - as it is in the
of
the game is
game was
ce
67, may ba:the most interest
The source of interest is
To overs
69
mr.
the finals
In this game
at
blundered away his
tournament the
time
-Jacobsen
He-Jacobsen
3
for the iniative
Black
3
2
considered as
3
as 3. ..
Usual is 3.
, N-KB3
2
sound
and
mov~
even
is
4
ities
4
A· possible alternative is
the
UJhite
The
poss
5 ..
3
has
N-83
which threatens to either
I think,
a pawn
a bit
or.
White a
the iniative
pawn on
�52
White-Jacobsen
B
and open the
for his rook
a pawn down still has a ter-
If 4.
NxN, 5 .. PxN
rific attack and I think, will
3
to be followed
win.
7.
and 8-N2 at the r
Then
castle Queen-side and althou
file
time.
if 5 •••
would
and White wins a pawn at least.
Black's center ..
4.
5.
.
BxN+
0 - 0
I think 4.
'
P-Q3 or
for ..
I think N-83 is called
The next move is advan-
Q-K2 or N-83 was necessary
of a com-
as
here because of the possible
attack e
6. NxBP
'
bination which is, I think,
below.
6. PxB
7
PxP
NxP
8
0-0
8-N5 ?
This move
messes up the
whole combination for Black.
The alternative, pursu
the
combination is 8 ••• NxP
Then
9.
and White
the
KP with an attack, while Black
BxBP+,
2 pawns and
and bis
the other hand, 8 ••
If
be best,
, 6. PxP wins a
5 •••
pawn, as the KN is in no
from the
If
5 ••• BxN, 6. QPxB and Black
has no time for NxP because
of
or
• Thus 6 •••
Q-K2, 7. NxBP QxP+ (if 7 ...
NxP, 8
0-0 and White is
ahead) 8.
On
is still under
a rook, or more for a
, QxNP,
9.N-N5+, K-R, 10. R-8,
QxRP, 11. 8-K3, White will
3
it admits the
uselessness of the combination.
9.
P-KR3 ?
White loses an
with this move.
better of 9
chances of
tant
I thought
Q-K or 8-Q2 with
up Black
the defense of his KP.
more
over the doubled QBP is im-
to the defense of the
other pawns adjacent to it and
should be retained if possible
�53
Wh
9.
NxP
or 83 thr
10.
BxN
or P-K5 to drive the
N-85 or K5
een away
from the BP (e.g., 15 •• N-N3
11. QxN
I prefer 11 .. PxB, followed
16 .• N-85 and White must lose
Ulhite
, giv
12 ..
his valuable bishop all
chances
P-K5 when
Black to
against the KNP and KBP.
cable.
move besides
Thetext
8-N2 because of
16
Black retain a
16.
?
, also lets him de-
The farther the pawns are ad-
an attack
vanced, the harder
the
side.
Ulhite
6. B-N2
3
followed
QxP
• N-83 and Black has
?
7" 8-N2
18
KR-8
QR-B is better since
I think 18.
a safe game.
12
QR-8
-8, 17
16.
Better, I think, is 11. •
8-83, 12
Better, I think, is
defend ..
B
1•
are to
BxB
the KR may be needed on the
12 ••
or Q file.
Then if
like 12.
BxB 13
PxB, Ulhite
, 19
still has some attack on
the QN file and the d
could be a
N-84 ?
?
9
Leads to the
the pawns .. 19
lem to defend,
the
undoub
nal
B. QR-8
8-R.
18.
The doubled pawns
QR1-KR8.
Thus if
ltimate loss of
R-K would s
immediate
move
to collect more forces
are a
12
QxB
for defense
9. BxP leers out
13. QxBP
N-Q2
as a
move, but doesn t
work.
or 13 ••. N-R3 followed
QR-8 and N-N4 at the proper time.
14 ..
5
l\l-R5
19
This move was sealed and the
3
QR-8
Q-Q2
R-82
An alternative is 15 •.. N-N3
game ad
20 .. P-Q5
21 .. Q-Q3
here for a week
i\l-N3
�29
5
s
2
2
22
22 ..
2
3
33. 8-K3
25
34
R
35
K-83
36
is a
and
,.,
still
are many
�5
63
52 .. 8
64
53
65
8-82
I still like 53
If instead
66
N-85+
53
8-83
67 .. 8-R7
53
68
K-85
59
White has no defense for
side pawns ..
his
P-KR4 ?
I think this move will win
introduces a whole
where
go wrong
is
54.
55
.
as before •
55
56
P-84
P-R6
57 .. P-R7
57
2
saved
Black a
headaches
assured
poss
a draw des
is
is
moves
are the
t
for Black
58
58
would
58
59
.
have
e.g. '
K-85 ..
P-RB(Q
60
61 ..
P-84
P-84
B-K5
62. 8-N8
K-K5
P-87, etc
P-R4
59
54 •. K-R2
world of
P-86
Ras
PxP
��
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�BEST WISHES TO THE CLASS Of 1966
from the Staff of
C0 L LE GI AN
T H E
St. John's College
Annapolis, Maryland and Santa fa, New Mexico
June, 1966
TABLE OF CONTENTS
Page
. Larry Silverman,
1
66
Veronica Soul,
Plato's Ion and the Whole of Things.
1
66
Poem •
Apollonius Paper
.
Dean Hannotte, '68
Poem •
• James mensch, '67
Essay on Conics by Blaise Pascal.
*
*
*
*
Susan Roberts, '66
Sally Rutzky, '68
Deborah Schwartz, •59•
Vida Kazemi, '68
Paul Ollswang, '66.
Eva Brann.
Cover by James Mensch, '67
• Translated by
Cynthia Siehler, '66
*
*
*
*
*
*
• Editor
Assa. Editors in Annapolis
• Assa. Editor in Santa Fe
Art Editor
• Faculty Advisor
. 1
. 33
. 34
. 44
. 47
�PLATO'S ION AND THE WHOLE OF THINGS
Larry Silverman '66
Senior Th es is
"Poetry. is indeed something div ins. It is at once the center
·and circumference of knowledge; it is that which comprehends
all science, and that ·to which all science must b~ referred.
It ·is a~ .the same time the root and blossom of all other
·= systsms ~~ thought; it i~ that from which all spring, and
that whid\ adorns all; and · that which, if blighted, denies
the fruit and the seed, and witholds from the barren world
the nouri~hment and the succession of the scions of the
tree of life. It is the perfect and consummate surfa6e and
bloom of all things • • • "
-- Percy Bysshe Shelley
1tot6v
*
*
*
*
I
'tt.
be 1.vov· nav't'oba·n~v you"l
•
ytyve~at.
Aristophanes, Frogs
*
*
*
*
*
*
Introduction
Socrates,
~s
Plato presents him to us, seems to take particular de..
light in attacking the poets and their extravagant enterprise.
tokens of his . enmity are, as he says himself, "countless."
The
He
1
· banishes the poets from his city laid up in heaven, ) he makes them
the authors ·6t the most
verses,
3
)
sophi~tical
d6ctrines, 2 } he mutilates
misrepresents their intention,
he out-drinks them.
4
)
and
in
th~ir
one dialogue,
5
)
Yet for all these tokens, it is often hard to
see t .he differences between the philosopher and the poet.
In this .
essay we will consider one ~mall dialogue; the Ion, where Socrates,
by obscuring the differences makes them delightfully distinct.
Through
a rather careful examination of the words and action of the Ion, we .
hope to begin - and merely to begin - to answer an old and .persistent
question:
What is the quarrel between the philosophers and the poets
about'?
Republic, III, 398a; X~ 595a,
Theatetus·, 152e, 3 - 153a, 1
3.) Ion, 538c, 2-3
4)° R;Di:.iblic, 39Db, 1-2
5) Symposium," 223d, 5-10
1)
2)
7-8
�-2-
Plato in the Ion allows us to witness a conversation between two men:
Ion, the celebrated and successful rhapsode, and Socrates.
We learn
from the first lines of the dialogue that the rhapsode has just come
to Athens from the Epidaurian Asculepiad, where he carried away the
first prize for his art.
The two men, who have evidently met before,
exchange a few words about the Asculepiad and (530a, 1-b, 4) speculate
very briefly on the Panathenaic contests.
Their ensuing conversation
falls easily into two parts of approximately equal length, 530a1 536d7 and 536d8 - 542b 4.
In this essay we will deal primarily with
the first part.
*
*
*
*
*
*
*
*
*
*
Part I - Setting
Socrates initiates the discussion in the first part by launching into
the subject of rhapsody.
"I have often envied ( ~~ ~A.waa
) you
rhapsodes your art ( "t~' "tlXVf1£ ) , Ion," he says. ( 530b5 - c6)
art is a dominant theme throughout the dialogue.
obvious way, is Socrates' envy of that art.
over the word 'envy' •
Ion's
So too, in a less
Let us pause for a moment
What we translate as envy is in Greek
Our English word 'zeal' is derived from it. ZttA.cSw
~ flhOW
is more
accurately translated as 'to rival eagerly' ,'to admire', 'to desire
to emulate or to imitate'. Zf!A.6w
connotes a noble passion,
opposed in general and particularly in the Ion to cp9ovlw
which is
•to envy' in a perjorative sense, in the sense of 'to be grudging'.
A
few lines after Socrates mentions his desire to emulate the rhapsode,
he introduces the word . cp9ovlw
"It is clear, " he says t o I on ,
"that you will not begrudge me ( cp9ov~O'E
L{;
)
an exhibition."
juxtaposition of the two words is not accidental.
For as it turns out,
Socrates' desire to emulate Ion is not left unsatisfied.
though
The
And Ion,
he does it most unwittingly, does indeed begrudge Socrates the
exhibition.
The use of the words
CfJA.&w
and
~9ovlw
thus
anticipates the peculiar ironic coloring of the dialogue.
Socrates proceeds to give a description of Ion's enviable ( t:11A.w"tOV
art.
The rhapsode, he says, is obliged to have his body splendidly
adorned, and also to be familiar with many good poets, and especially
with Homer, "the best and the most divine of poets"; and to
l~arn
out
)
�-3-
( £xµav9&ve
LV
)
6
) his· thought.(
OLtlVGH.aV)
The rhapsode must become the interpreter
poet for the audience.
'f)A.Ou a9a t.
~pµf)vla
) of . the
And he is unable to do this well without
standing what the poet says.
( al: La
and not only his words.
.All these things
~nder
worthy of emulation
ar~
),
We note that Socrates emphasizes the rhapsodes obligation to be an ·
'interpreter' of the poet.
ways.
Ion is an interpreter of the poet in two
first, he recites the poet's verses and interprets them drama-
tically on stage.
This is what Socrates seems to have in mind here and; .
I think, throughout the dialogue • . Second, _1on comments on Homer, that
is, he make• speeches about him.
This, as we shall see, is what Ion
understands . Socrates to mean.
Ion is evidently pleased with Socrates' description of rhapsody, and
replies, "You speak the truth, Socrates.
At any rate, this portion of
my art [interpretationl presents me with the greatest labor (
.,
epyov
in vain.
) •"
'JtA£LC1'tO'V
Ion's great .labor .has, to his mind, not been
He is proud of his interpretive expertness and boasts, uNo
one who has ever existed . could speak as many fine thoughts ( ' 'JlO~A~b
xa\ xaA.a,
ot.avo Ca~
) · about Homer as I can."
lured on by his
companion Ion offers to give an exhibition of his skill.
'!It· is
well worth hearing, Socrates, how well I have ·ornamented (x£x6aµ11xa
Homer.; so that I think I am worthy of being crowned with a golden cbown
by th.a Homer idae."
It is quite. clear from the very beginning of the ·
co nversat i on that modesty is not an Ionic
The golden crown is all important to Ion.
virtue~
At Epidaurus, he had won
fame and riches for his recitation of Homer's poems.
did not satisfy him.
But these things
He came to Athens to compete for yet another
prize - the prize for speaking well about Homer.
Ion hopes to display
his own artfulness through his intarpretation of Homer ~ He, implicitly ~
7
and Socrates, explicitly, ) identify this artfulness with wisdom. Ion's
journey to the Homeridae is interrupted by his encounter with Socratas.
Socrates, as it were, supplants the Homeridae, and becomes the proper
6) The verb ~xµav0c!veLV
is ambiguous. It means both 'to learn
thoroughly' and 'to learn by rote'. Socrates, we suspect, though Ion
does not, is being ironic. cf. 542b5.
7) 532d6
)
�-4-
judge of the contest.
Ion is not unhappy with this 'judge'.
For Socrates,
and perhaps the other Athenians, are in Ion's estimation wise men.
That
is, Socrates and those for whom he speaks are the men most qualified to
award the prize for wisdom.
The golden crown will hover over the two
men throughout their brief conversation.
But how does Ion speak about Homer?
answering this question.
tion directly.
puts him off.
There is a certain difficulty in
We are never allowed to witness Ion's exhibi-
8
Twice )he attempts to make a speech and twice Socrates
Ion's first, thinly veiled, offer meets with a reply
that will prove to be the rhapsode's undoing.
to have you heard.
But now answer me this:
"I will yet make leisure
Are you expert ( 0€ t.
vo, )
about Homer alone or about (530d9-531a4) Hesiod and Archilochus also?"
The putting off of the exhibition will not deprive us - the readers of seeing Ion's true skill.
But we must keep our eyes open.
Socrates' question - whether Ion is expert about Homer alone or about
Hesiod and Archilochus also - is striking in two respects.
introduces the word
bce.vcS,
into the conversation.
occurs eight more times in the dialogue.
is well known.
First i t
This word
The ambiguity of
oeLvcS,
It means: a) fearful, dreadful, awe inspiring, and
b) clever, cunning, expert.
Thus, the word can be applied with equal
appropriateness to a tragic hero and a sophist.
It is not unlikely that
Socrates means us to understand the word in both senses, particularly
in Ion's case.
In seven of the eight times that
it is followed or preceded by the word
be L VO£
occurs
linked to a sub-
stantive, that is, 'about something'. Socrates never openly impeaches
Ion's 'wondrous skill'. But ,the tsomething' about which he is skilled
becomes a great question mark in the dialogue.
Indeed, it is the 'about
which' that is in question here. (530d9-531a4)
Second, Socrates' inquiry into the scope of Ion's expertness is rather
odd in itself.
Why should Socrates ask whether Ion is skilled about
Hesiod and Archilochus?
Ion's accomplishments.
It may be that he has a genuine curiosity about
This explanation, however, seems hardly likely.
Socrates had met and probably conversed with Ion in the past.
8)
530d6-8 and 536d6-7
And even
�-5-
if they had never talked before, Socrates has certainly heard a great
deal about one of -Hallas' most celebrated rhapsodes.
Ion is not a man to conceal his talents.
furthermore,
Had he any expertness in
Hesiod and Archilochus, would he not have mentioned in in his .previous
boasting?
And is it conceivable that .Socrates missed the significance
of Ion's omission?
We must conclude that Socrates knows the range of Ion's ·skill.
then does he raise the question?
of Ion's vanity.
Very ·early in the dialogue we learn
Perhaps, Socrates wishes to ·instruct the rhapsode
in humility, by drawing •ttention to the deficiencies in his
But that would be rather pointless • . After all, Ion never
to any knowledge of Hesiod or Archilochus.
nothing about them.
educ~tion.
profesa~s
He knows ·that he
kno~s
He merely claims to be the greatest interpreter
of Homer that the world has ever seen.
nothing more.
Why
That is the extent of it,
9
He is not like the craftsmen censured in the Apology, )
who being wise in one thing consider themselves qualified to meddle
with all things.
If Socrates had w~nted to e~plode I~n's pretensions
would he not have questioned him about what Ion claims to know?
Socrates' question, however, begins ·t6 make.sense when we c6nsider
Ion's answer - an answer that Socrates may well have ·expected.
no,"
the rhapsode replies, "just about Homer.
"Oh
for I think this ·is ·
sufficient (txav~v y~p µoL boxEt . E{vaL
)." Socrates does not
wish openly to cast doubt on Ion's profe·s sed accomplishments. He will
'iufficien~y'
question in the ensuing dialogue only the
complishments.
Socrates puts off Ion's ' dispi~y then by impliciily
raising the question of the rhapsode's sufficiency.
the irony here.
Rec~ll tha~
Ion's great
suc~ess
unsatisfied. · He seeks yet more weaith and
mer~
to exhibit his art before Socratea in order to
vanity.
ficient•.
of these ac-
We should note
at Epidaurus left him
acclaim.
sati~fy
He is eager
his bottomless
Yet this unsatisfied man thinks that ·he and Homer are 'suf...:
It is not without malice that Socrates fails to satisfy
Ion's wants by beginnin~ an ~tt~ck · o~ Ion's 'sufficiency'.
Socrates, pretending to ignore Ion's reply,
thing about which Homer
9)
Apology, 22d7-9
a~d H~siod _ say
a~ks,
"But is there any-
the same things?"
One odd
�-6-
question followed by another!
What does Socrates mean by 'the same
things'?
Ion does not stop to puzzle over it but quickly answers, "I,
at least (
€ywye
),
think there are many ( xa\
1tOA.A.a
"About these things," Socrates continues, "would you expound
) •"
(531a5-b10)
av
) what Homer says
better ( XOAA.LOV
l~~y~aaLO
or what Hesiod says?" Ion replies that he would expound those things
similarly, and cautiously adds, "about which they say the same things."
The preciseness of his answer, which incidentally makes for a rather
awkward sentence, suggests three things about Ion's state of mind at this
moment.
First, in his 'modesty', he wishes to avoid overstepping his
original claims.
Second, he smells a trap and proceeds with caution.
Third, vaguely unsure of what Socrates means, he tries to conceal his
uneasiness by 'rigorously' following the logic of what is for him an
empty argument.
"But what about those places where they do not say the same ·things?"
Sacra tes asks.
"For example, about divination, Homer says something
( A.lye. ..
"CI.
as well as Hesiod (
agrees.
"Well, then," Socrates asks, "could you or one of the good
't£ .
xa\ 'Hcrlooo<;
) ."
Ion
diviners better expound both what these two poets say similarly and
what they say differently about divination?"
Socrates' question breaks
the orderly sequence of the conversation which Ion and the readers have
been trying so hard to follow.
Its insertion into the conversation
leaves certain things unsaid.
Previously Socrates had asked whether
Ion could bet t er expou nd wha t Homer says or what Hesiod says when t hey
say the same things.
His next question should be, but is not, about
Ion's ability to expound the .two poets when they say different things.
To see the force of Socrates' omission we must do something rather bold.
Let us try to fill in the gap.
the dialogue.
Let us try to re-write this part of
Our revision would I think run something like what
follows:
Socrates: Would you expound better what Homer says or what Hesiod
says when they do not say the same things?
Ion: I would expound Homer better.
Socrates: Then shall we say that · Ion is an expert ( b£ I. v6£
about all of Homer, but only part of Hesiod?
Ion: Yes, all of Homer.
)
�-7Socrates: And also those parts of Hesiod where Hesiod speaks the
same as Homer?
Ion: I suppose so.
Socrates: Then you are an expert ( 0€ L vo~
) about
a part and
not about the whole of Hesiod?
1..2!!= Yes, and all of Homer.
Our Platonic revision brings to light a difficulty.
If we have been
at all true to the arguments we see that Ion claims, however reluctantly,
that his wonderfui' expertness, his bet VO"tfl{;
at least, is fragmentary.
But herein lies a riddle.
be partially
?
and by Homer.
OE
,. with regard to Hesiod
Consider how the
wo~d
~ How
can anyone
is used 'both by Plato
Homer: Achilles about whom there is nothing half-way is
L vo~
Plato: the sophist, who by virtue of one art, makes the
things of all arts is
b€LVOb
of part.ial_ be Lv6"t1')G
Yet the meaning of a different kind
is the very enigma that Socrates will later
(533c5-9) 'see and reveal' quite explicitly.
But why is the probiem which is analogous to an ~xplicit theme of the
dialogue only darkly hinted at here?
Why does Socrates obscure the
point by breaking the 'orderly sequence' of the · arguments?
Why is it
necessary to re-write Plato in order to unearth the question?
Let us
recall Ion's confident, if thoughtless, assertion that Homer and Hesiod
.
.
say t he same t hings : on many subjects. 10) lU ha t does he mean by the
phrase •to say the same things'?
sometimes
e~press
the same thought with differertt
.
imply that he
Does he suggest . that the two poets
.
cl~ims
~ords?
That would
.
to understand Hesiod well enough to judge.
how can Ion, who makes no such claim and who
ferent to Hesiod, how can he mean this?
moreov~r
But
is simply indif-
Does he not mean, if he means
anything, that both poets say literally, or almost literally, the same ·
things?
That is, word for word both Homer and Hesiod call Zeus, for
example, .. father of gods and men."
With.this understand~ng, or lack of
understanding, Ion claims to expound equally well _
Homer and Hesiod when
they say the same things.
What an impossible boast!
Ion, in effect,
professes to expound isolated verses of Hesiod with an utter unconcern
for the context.
He does not take · account
of
poetry, o~, presumably, of any other poetry.
ginning, no middle, no. end.·
10)
See page 6.
the whoJeness of Hesiod's
Foi Ion ther~ is no -be-
�-8-
But the problem remains: why does Socrates not expose Ion's misunderstanding of what a poem is?
it?
Why does he go out of his way to conceal
Let us look again at the question interjected by Socrates, "Could
you or could one of the good diviners better expound what these two
poets say similarly and what they say ·differently about the divination?tt
Socrates by posing the question when he does imitates the rhapsode's
faulty notion of what poetry is.
Just as Ion pays no heed to the in-
tegrity of Hesiod, so Socrates pays no heed to the integrity of his
own argument.
by Socrates.
Ion's opinion about poetry is thus dramatically mirrored
The question itself also echoes Ion's opinion.
Is it so
clear that a diviner - even a good one - could expound any passages in
the Iliad or the Theogony, for example, without some understanding of
the whole?
This failure to consider the formal integrity of poetry runs through
the whole dialogue. In the last half of the Ion Socrates 'picks out'
11
( EX~E~OV
)
) and recites five passages from Homer , each having
to do with some art.
Socrates argues that thepractioners of the re-
spective arts would judge better than a rhapsode whether Homer spoke
well or ill in these passages.
No mention is made of the necessity of
understanding the poetical context in which the lines are written.
As
a result, we are told, for example, that a fisherman would be the best
judge of Homer's verses describing an object's descent into the sea.
12
(538d1-5) ) Socrates neglects to inform us that the object whose descent is described in the verses is the goddess Iris.
Thus, a fisherman,
by Socrates' argument, would judge better than anyone else Homer's
account of the movements of the gods.
·
Louis
m' ·d· 13 ) repor t s
eri ier
th a t G th e dou bt e d th e au th en t· ·t y o f th e
oe
1c1
dialogue because he could not believe that Socrates or Plato would
propose "a theory which took no account of forms, and which granted
the sole power and right of judging certain passages in Homer to coach men, fishermen, and doctors." . If we are to understand the dialogue,
11) 539d5-e1: Socrates' 'picking out' of Homer's verses is perhaps
meant to parallel Ion's 'learning out' of Homer's thought. cf. page 2.
12) Cf. Iliad, XXIV, 80-2
13) Platen, Oeuvres Completes, Tome V, 1rePartie; Bude, page 20.
�-9-
we must answer Goethe's misgivings.
Why then should Socrates by interrupting the argument with his question
about divination conceal Ion's misunderstanding of poetic form?
And
why should Socrates, later in the dialogue, exhibit the same misunderstanding?
Why should the subject of poetic whpleness be so conspicuously
absent from a dialogue which seems to
b~,
at least in part, about poetry?
Only after answering this question can we begin to understand the meaning
of Plato . s Ion .
'
Ille leave it open for now.
Before going on to the· next part, we should note another aspect of
Socrates' question - whether Ion or one of the good diviners could bet-·
ter expound (
l( 11Y~<1a 1.0
)
what was said differently and what was
said similarly about divination by the poets.
The notion of a diviner
'expounding' anything at all is somewhat dubious.
will tell us (534c9-d-1), are for the most
In the Timaeus . (71e-72b) divination (
par~
µav1:tx~
Diviners, as Socrates
out of their minds.
) is called god's
gift to human tf")oughtlessness ( qcppoauvu &.vGpwn Cvu
)•
Timaeus is careful to point out the difference between the mad and inspired diviners and thos~ who interpret divinations, the prophets ( i;~
i:wv npocp1')".tWV ylvo<;,) . . S.ometimes .prophets are named divine.r s. by
those who are wholly ignorant (i;b miv ~YV01')KO'l:EG
) that they
are not diviners but . inter pre.tars ( ~n:oxp c.i:a C
) of the mysterious
voice and apparition.
Ion's ignorance leads him to say that the fre-
netic and thoughtless diviners would 'expound' poetry better than he.
Ion, of course, may be mistaken.
Consider Socrates' next question.
"And i f you ( C1U ) were a diviner," he asks, "and if indeed (
E '['IT E p
)
you were able to expound what was said similarly, would you not also
know how to expound what was said differently?"
Ille note that what is
spoken about similarly and differently and the identity of the speakers
are left unspecified.
Ion is thus hypothically transformed into a
diviner who 'expounds' an unknown god speaking about an indefinite
subject.
The tiansformation is only in speech at this point.
We must
await the deed.
To all the dark and ·oracular implications Ion replies, "It is clear
( b~A.ov O'tl.
)."
�-10-
Part II
Whatever Ion may have acknowledged unwittingly his conscious claim is
to expertness
~bout
to him 'sufficient•.
sufficiency.
Homer, and not about the other poets.
This seems ·
Socrates is now prepared to attack Ion's Homeric
The gist of his argument is that expertness about one
poet is expertness about a part and not about all of poetry.
Ion's skill is necessarily fragmentary.
Thus
It does not fulfill the re-
quirements of that true artfulness and knowledge which presuppose an
understanding of the whole.
By questioning the integrity of Ion's
skill Socrates strikes at the two roots of Ion's self-satisfaction:
14)
vanity and the belief that Homer is just about perfect.
Socrates initiates his attack on Ion by asking why it is that Ion is
expert about Homer but not about the other poets.
The ensuing dis-
cussipn falls into three parts.
First, Socrates maintains that all the
poets write of the same things.
Ion agrees but insists that they do
not write in the same way.
For Homer is a better poet than the others.
This leads to the second part.
Socrates argues, by the examples of
the doctor and the arithmetician, that an artful man will know good and
bad speakers alike.
The third part
s~mmarizes
very clear discussion of poetic wholeness.
the other two in a not
This last part is inter-
rupted by a short exchange, which we will treat separately.
A.
The Content
How is it, Socrates asks, that Ion is expert only about Homer.
Or
does Homer speak about anything else than what all the other poets
speak about?
"Has he not told (CLef...~'Au8ev
) about (rcep\
) war
for the most part ("t~ rcof...f...a .
and about the intercourse
of gods with each other, and the\r inte£course with men,
the way indeed they have it (W~ oµ l.AOUO' L
) , and about
the heavenly occurrences ( rca8riµ&-i;wv
) and about those
in Hades, and the births of gods and heroes. Are those
not the things about which Homer made his poem?"
Socrates' enumeration is his genuine tribute to the vastness of Homer's
horizon.
It can be summed up by a phrase: Homer's theme is the whole
14) Homer is the 'most poetical of poets' and is therefore the paradigm
of all poetry. Cf. Republic x, 607a2-4.
�-11of things.
Yet even a tribute from Socrates has its ironies.
the phrase
In his enumeration
of go~s with men' is given a special pr ominence
~ v otµ . '\o·~ ~
~
'~~ vv
The two words mean literally
by the two Words W
·~ntercourse
L
.
"thE;1 way they have intercourse."
By adding the words
The tone in this context
~b ~µ t.Aoucr L
is _ scept~cal.
, Socrates hints that Homer's
report of the intercourse of gods with men is not altogether reliable.
Socrates' tribute is permeated with a much greater irony.
The verb
he used to characterise Homer's 'telling' about things is
bt.€A~Au9ev
b.t.e:A.~Au9e;v
, translated above as 'told .' , is the active per( b t.c!/ €pxoµa t.
fect indicative of b ilpxoµa t.
mary meaning of
.,
bt.e;pxoµat.
is 'to go through'.
)•
The word comes to
mean naturally enough 'to tell thoroughly', 'to relate in
as we say today •to give a penetrating analysis'.
The pri-
d~tail~,
or
But Hornet, according ··
to Socrates, does not merely 'go through' things; he . '~oes throug~
about (
c t.EA~A.u9e:v
ne:p C
through .and about, b Ld
a..nd 'Jt€ PC
) them.
,
What does it mean to go
at the same t.ime? . Is
speaking about something equivalent to saying
through and through?
wh~t
that something is
Does Homer penetrate the whole of things or does
he circumscribe it? Or both? The .ironic interplay of the_ two prepositions, 01.d a.. 7lJ nep C
, r.aises questions that are to come up again.
Ion agrees that all the poets speak about those things listed by
Socra tes .
"But , " he adds , "they have not done. it in the same way as
Homer (O~X l>µ.oCwb nenot.~xa~l. ·xa\ "Oµripob
)."
"lilhat then,· in
a worse way?" Socrates asks. Ion: "Far worse." Socrates: "And Homer
in a better way?" Ion: "Much better, by Ze~s ! " ( Aµe LVOV µl V't'O L
'
VfJ
!:,. ,
La
)
That last bare exclamation - "Much bettet', by Zeus ! 0
constitutes Ion's mhole praise of Homer in the dialogu e.
is not given another chance to adorn the most divine of
B.
- .
The rhapsode
po~t s.
Speaking Well (531d10-532c4)
Ion's praise of Homer opens the road to a discussion of the poetic
manner of speech.
Socrates argues that an artist will be expert about
all those who speak, whether well or badly, on the same subject.
He
f
�. -12-
t
Co
cites as examples t he arithmetician
and the doctor ( la'tpO£
)•
'
J
'
1
,,
'tflV apt. 8µf}'t t.Xf}V 'tcXVflV e:xwv )
uwhen many are speaking about number, and
I
), be so~eone
one of them speaks best, there will, I suppose (bf}TIOU
who knows
(YV~O'e:'ta L
) the one speaking well?"
same man know those speaking badly?
The same, Ion replies.
Ion agrees.
0
Will the
Or will someone else know them?"
"And this is the arithmetician?"
Yes.
Socrates
goes through a similar argument in the case of the physician. When man~
are speaking about the wholesomeness of foods ( uy l € t. vwv CJ' 1.'t WV ~no
'
•
ta
c
:t
EO'~LV
,
), and one speaks best, the same man, the physician, will
., ,,
know the best speaker, that he speaks best ( O't l apt. O''ta A.eye:)L and the
worse speakers, that they speak worse.
"And so in every case ( &e:£
)'
the same man will know the one speaking well and the one speaking ill.·
For if he does not know the one speaking badly, it is clear ( ~~A.ov
)
that he will not know the one speaking well, about the same thing."
Ion
h
agrees ( 0u'tw£
about both?..
)
"Then the same man becomes expert ( bet. VO£
Ion agrees.
"But you said ( q~ cp1£
) Homer and all the other pets • • • speak
about the same things, but not in the same way, but that Homer speaks
well and the others worse."
A.l.yw
"And I speak the truth ( xa\ &A.118~
Ion:
"Then i f indeed
) •II
,,
e:t.ne:p ) you knew the good
speaker you would also know the worse speakers, that they are worse."
"So it seems ( EOLXEV ye:
~ ~eA.'tL£'t€
),u Ion replies.
), we shall not miss
t~e
"Then, 0 best of men
mark by saying that Ion is
similarly expert (be: t. VO£ ) about Homer and all the other poets, since,
J
'-
t
'\
..
he agrees ( au'to£ oµo/\.OY1J
'
t
1
judge ( xp t.'tflV t. xa Vov
) that the same man will be a competent
) of all those who speak about the same things,
~
and almost all the poets do ( · 1!0 t. E:
LV
)
the same things. 0
Ion succumbs to Socrates' interrogation,
"Whatever then is the cause, Socrates, that whenever someone
converses about another P,Oet my mind becomes inattentive, I
am unable to c1ntribute~ ~fthing worth saying, and I simply
fall asleep ( a't€XVW£ Vva°'"td~w
) ; but when someone
mentions something about Homer, straightway I am awake, my
min9 is ~tt,entiv~, and I have a wealth of things to say
( t:un:opw o-i; t. A.eyw
)?tt
There are three points to be noted here:
··
�-13-
The prelude to this exchange was Ion's declaration that Homer is a
1)
much better poet (by Zeus!), and that the other pets are inferior.
Socrates reminds us of that
•u
\
"But you said (
..
cpTJ
<;;;
prelud~
)
as he draws near to his conclusion.
that Homer and all the other p~~ats • • •
speak about the same things, but not in the same way; but that Homer
seeaks well, and the others worse ('tO\I µ€v e:~ YE' 'tot<;; o~
xe: tpov )?"
Ion · emphatically answers, "And I speak the truth ( xa\ &A118fi Alyw
) !"
The boldness of Ion's ahswer indica~es that he knows, or rather that he
thinks h~ knows, the difference between the g66d poets and the· bad 6nes. ·
In Socrates' two examples, the arithmetician and the doctor-, the ability
to discriminate between the good and the bad speakers was sufficient
rea~on
to
c~ll
a man ·artful and expert.
man, the artist, would be 0€ L v&·b .
he
m~ant
When Socrates said that the same
about both the good and bad speakers
that the same . man would recognize the w6rth 6f both. · Ion thihks
he knows the value of the other poets' but he d'a es not' cci'ns id er himse1 f
expert about them.
He understands the word
to be something
OE L vo~
more than the knowledge that allows a man to give tacit approval or disappro~~l
to the speeches of others.
in order to be called
exhibitions and
gold~n
OEL\10~
crowns.
For Ion, knoweldge
mus~
be conspicuous
·Learning must be accompanied by grand
llie might note that poetic excellence is,
like the rhapsode's skill, conspicuous.
Recall how Ion characterized his exhibitions (530d6-7) "It is well worth
'
hearing," he s·aid, ''how well I have ornamented Homer ( WG
7
EU
,
XEX00'-
µ11xa 't~\I "Gµripo)J... .. Socrates later (532d2) echoes the word xocr· lw µ
to adorn - in a diffe~erit, ahd yet, I think, similar context.
He describes
th. rhapsode as ·being 'adorned' with a many..:colored raiment
e
xocr- 11µ€ VOG
µ
~cr9~t-L 'Jt:OLxCA.·fJ
). · Socrates' use of xocrµlw
(XE
here (and
also ~30b6) su~gests that Ion's expe~tness consists iri his power to embellish and to 'be embellished in turn.'
,
llie must not forget that the word xocrµew
range, to order, to make into a whole or
,
XOCJ'µOG
has another meaning:
x6crµoG
to ar-
The making of
is the task of the poet as well as the costume designer.
It may be that Ionic embellishment is not so terribly different from
Homeric ordering.
�-14The discussion about the doctor and the arithmetician, then, draws our
attention to a fundamental difference between their arts and Ion's.
Doctors and arithmeticians judge; rhapsodes, and perhaps poets also,
adorn.
2)
Socrates' argument points out another difference between Ion's art
and other arts.
Both of Socrates' examples - medicine and arithmetic -
are arts that deal with speech.
Indeed, in the case of arithmetic, •to
speak well about number' is to do what arithmeticians mostly do.
metic,
effect
as Socrates has said in the
,,
' ..
( EXOUO'a "tO xupo~ through
Arith-
Gorgias (451b1-4), has its chief
speech about number.
Thus, the
arithmetician will himself speak well about number and will also be a
competent judge of others who speak about number.
Similarly in the case
of the physician, to speak well about the nutritional value of foods is
to do what physicians who study that subject mostly do.
Here again, the
physician will be a judge of those who speak about food, and a speaker
himself.
We cannot extend this reasoning to Ion.
recalled, speaks about the whole of. things.
an expounder of Homer.
Homer, it will be
Ion fancies himself to be
That does not quite make him a poet.
His know-
ledge is limited to Homer and does not go beyond the poet into the world.
Ion is precisely the man who speaks well about the man who speaks well
about everything.
But Socrates, by making us reflect on the difference between speaking
about and speaking about speaking about, is stalking bigger game than
Ion.
Homer too speaks about physicians, for example, who speak about
food.
Indeed, Homer's relation to men, "good and bad, simple and skilled",
is analogous to Ion's relationship to Homer.
The odd way that poets
have of speaking about things was playfully hinted at before in Socrates'
15
enunciation of the Homeric themes. ) Homer, Socrates said then (531c1d1) "has gone thoroughly through about ( Ol.EA~f..u9ev TIEpL
the whole of things.
)"
The question of poetic circumlocution will be raised
again in the dialogue, not in speech but in deed.
3)
The discussion about doctors and arithmeticians has made us attend to
15) pp. 10-11
�-15-
two great differences between Ion's art and other arts.
third striking aspect to this discussion.
There is a
S0 crates, by citing some
not quite appropriate examples and by exploiting the ambiguity of the
word
, elicited a question from Ion.
be L v&b
, .
7
\..
,,
"Whatever then is the cause ('tt. ouv 1tO'te 'to at.'tl.OV .),
Socrates, that when someone co~verses abqut ant>ther goet,
my mind ·becomes inattentive ( OU'tE 1tpOO'EXW 'tOV vou 'V
),
I am unable to contribute anything worth mentioning ( AOyou
a~ LO'V
) , but I simply fall asleep ( &'te:xvwb V'OO''td~w
); but when someone mentions Homer, straightway
I am awake, my mind is attentive, and I have a wealth of
things to say?"
These words reveal for the first time the practical consequences of Ion's
satisfaction with himself arid with Homer.
We ·n ote that ·1istening at-·
tenti_ ely and silently to the speeches of others - the way the doctor
v
and the arithmetician in Socrates' example listen attentively· and
silently - is precluded by Ion.
For him, 'having a wealth of things to
say is the precondition for discourse.
,,
Ion's great labor ( 1tAe: LO''tO'V
) ·of learning out Homer seemed to him sufficient and
e:pyov
almost satisfying.
His only remaining desire is to give an exhibition
of his wisdom.
That a man like Ion should ask a question about himself is an ironic
tribute to the power of Socrates' rhetoric.
Recall how Ion began his
question: 't { oJ v 1tO'te: 'tb a 'C 't L ov
cause, Socrates •
ft
- "Whatever then is the
Ion, the vain rhapsode who earlier sought only
to give an exhibition, is forced by Socrates to inquire into the cause
of things!
as follows.
Alexandre Kojeve summarizes this aspect of the dialogue
"One sees clearly in the Ion a man
satisfied by what he is and who ceases to be
justify this
satisfac~on
in answering the
~o
~ho
believes himself
only because he cannot
questi~ns
of Socrates."
16
)
Let us summarize the points we have made in this section: 1) For Ion,
judgment that is not displayed or displ~yable is ~f little im~ortance. ·
Rhapsodic excellence, as he knows, demands an
outwa~d
shciw.
Or, as
Socrates put it earlier (530b7-8), .Ion's art compells him ttto shine
forth as the most beautiful.of men(. ~b x_
aAACO''tO .Lb cpaCve:_
cr9a1.
It is possible that the
16)
necess~ty
of exhibiting is felt as much by the
Introduction a la.Lecture de Hegel, Se Edition, p. 273
)."
�l
-16 -
poet as by the rhapsode.
2) Ion and Homer practice the same sort of
poetic 'circumlocution'.
3) Socrates has succeeded in making the rhap-
sode wonder about his self-sufficiency.
C.
On the Whole
Ion wants to know why he falls asleep when other poets are being (532c5-9)
talked of and awakens when the conversation turns to Homer.
'1
answers, "It is not hard to see, my friend (
clear to everyone (
TCaV't' C
Socrates
..
w E:'t"a
LP e:
) , but
it is
) that you are incapable of speaking
about Homer with art and knowledge."
cit thesis of the dialogue:
talking about.
t
Here in so many words is the expli-
namely, that Ion doesn't know what he is
It need hardly be added that these words, whatever the
interpretations or qualifications later appended to them, ar unambiguously
insulting.
"For if you could speak about Homer by art, you could speak about all the
other poe t s. For the whole is poetry (
-i;b oA.ov
),
Or is it not?
'\_
TCOLf}'t"LXf}
yap
,,
TCOU
Ion replies, "Yes (
e:O'"tl.V
va' )"
1.
Socrates'
statement - 1CO Lf}"t LX ~ ydp TCOJ ~ CJ''t' L V 't'b OAOV
- is shocking
in its radical simplicity. What does he mean? He certainly suggests, as
Ion understands, that poetry is one art.
greater meaning than that.
But the words carry a much
"The whole is poetry" means what it says.
The true poet, if he exists, embraces and penetrates everything.
He sees
the world in its wholeness and presents it in its wholeness, with a beginning , a middle,and an end.
the whole of things.
In fact, he does more than just present
He makes it.
art of the whole; it is the
Thus the poet's art is not only the
~hole.
The meaning of all this is far from clear.
Given the obscurity and the
,
extravagance of the claim, Ion's matt~r-of-fact answer - Yes (
takes on a comic aspect .
VaL
) -
Either he is indifferent to the whole of things
or he comprehends it quite easily.
Socrates continues, "illhen one has apprehended ( Ad~TJ
"
ever in its entirety ( OAf}'V a~'t'b£
't'p61CO£
't~£
O'Xe,P£w£)
TCEp\ aTCaO'wv 't'WV 't'e:xvwv
)
) any art whatsot"
will the same way of looking ( o
hold with respect to all the arts (
) ?"
,,
EO''t'a L
The question can be
�·-17understood in two ways.
1) After a man has acquired any art whatsoever
in its entirety, in the case of every art, there is the same method of
17
consideration, [in regard to both the good and ~he bad in that art]. )
This reading is supported by the examples that Socrates later gives.
When a man is capable of 'showing forth his opinion ( A1tocp~vaa8a L
,
yvwµ~v
) 11 about the painter Polygnotus, he is also clever
at expressing his opinion about every painter.
There is a second reading
which is more literal and I think more interesting than the first.
2) When a ma~ has apprehended any art whatsoever in its wholeness, he
.
has
.
.
appr~hended
the way of looking at
~11
the arts. (532d1-533a7)
That
is to say, to apprehend one art in its wholeness is to apprehend all.
It must be remembered that n6t every art can be
wholeness because not every art is a whole.
appr~hended
in
i~s
Thus, for example, bridle
makiMg is not a whole art, but a part of horsemanship, which in turn is
18
a part of war, which is a part of politics. ) ln fact, there are
probably only three arts which can make any serious claim to wholeness:
politics, poet.r y, and whatever art Socrates engages in.
Plato's Ion,
as we hope to show, is concerned with examining the claims of these last
two.
That is, the Ion is concerned with exploring the integrity of poetry
and philosophy.
D.
Wisdom
Socrates' obscure question - when one apprehends an art in its
will the consideration
perplexity.
0
~e
wholenes~,
the same for all the arts - causes Ion some
Do you need to hear what I mean by this?" "By Zeus, I do!"
Ion replies with more truth than he knows' .. for I delight (
in listening to you wise men . ( ~µwv ,;wv aocpwv
xa Cpw
)
) •" Socrates'
answer to this is at once the most ironical and the most profound passage
in the dialogue.
"I wish you spoke the truth, Ion ( ~ouf..o Cµriv av O'e &r..~e~
t..lyE L v
) • But you rhapsodes and actors are mise,
and those whose poems you chant. I d,o~ n~tbif~ .Q~t .. ~peak the
truth, such as befits a simple man ( e 1.xbb lo Lw't~v
av8pw1tOV . ).,,. for . example ·, what I just ,now aske9 you, see .
how mean ( cpau'A.ov
) .and simple ( LO 1.W't LXOV
)
it is, and how it belongs to every man to know what I said,
17) Cf. Plato's Ion with Introduction and Notes by J.
Pitt Press Series, Cambridge, 1956, p. 25.
18) Cf. Republic X, 601d-602b
m.
Macgreggor,
�. -18-
that the consideration is the same when one apprehends an
art as a whole. 11
Let us consider some of the ironies here.
1)
Ion's assertion that he delights in listening to wise men is some-
what doubtful.
Indeed, Socrates' response,
11
! wish you spoke the truth"
(that is, I wish you did delight in listening to wise men), suggests
that Socrates at least doubts Ion's veracity.
Has not Ion just told us
that whenever he is not displaying his talents he falls asleep?
Perhaps
Ion in this situation would be more delighted to listen to Socrates than
to answer his questions.
Perhaps his statement is a polite way of saying,
"Socrates, you give your exhibition, and then I'll give mine. But please
no more questions."
2)
Socrates places the rhapsodes, the actor, and
11
those whose poems you
chant" in the same class.
3)
He contrasts poetical 'wisdom' with his own way of speaking the truth,
"such as befits a simple man."
wise men (
4)
O'ocp LO''t'a C
The implication is that poets and other
?) speak something other than the truth·.
Socrates implies (though he never really says it outright) that he
is not wise; yet he speaks the truth.
being wise?
How can one speak the truth without
Or to put it another way, how can Socrates do what he does
almost all the time?
That is a hard question.
We will not attempt to
answer it here; but we can make a few observations about what the
Socratic way of speaking involves.
poetical way of speaking.
It is contrasted to the 'wise' and
It does not have the perfection of form and
the apparent self-sufficiency of poetry.
leading questions.
Socrates speaks by asking
And questions, no matter how 'leading', are neces-
sarily fragmentary and deficient.
They demand for their completion an
answer, even if that answer is only 'yes' or 'no'.
Furthermore questions,
again no matter how leading, make the deficiency of the speakers apparent.
Socrates' way of speaking is 'mean' ( cpauAob
); that is, if we can
borrow from the Theatetus (196d9-197a6), it is 'impure' ('t'OU µ~
xa9apwb b t.aAlyecr9a t. ) , and it 'shamelessly' (
) uses
words whose meanings are not clear.
Finally, Socrates' mean and simple
questions are about the whole of things.
�-19It will be recalled (pages 3-4) that Ion came to Athens to compete
for the golden crown of wisdom.
Though Ion does not at· first realize
it, Socrates too is competing for the same crown.
In the section of
the dialogue we are about to consider an irohic reversal · of roles
takes place •. Ion becomes the simple and unwise Socrates and Socrates
becomes the wise and artful rhapsode.
Ion thus wins the prize for
Socratic wisdom, that is to say, ignorance, and Socrates wins the
prize for Ionic foolishness, which is somehow transformed by Socrates
into wisdom.
Part III
Ion, as we have said, regards Hrimer and expertness about Homer as
sufficient.
Socrates from the beginning of their conversation calls
Ion's and Homer's sufficiency into question.
tion has a remarkable effect.
The Socratic interroga-
It causes Ion to wonder about his habit
of falling asleep when other poets are being talked about, and of
awakening at the
mere mention of Homer's name.
The rhapsode's wondering
about (533c10-d1) himself is very different from his earlier selfsat is faction.
Pressed by Socrates' questions, he finally says, "I
cannot contradict you, Socrates.
,
But I am conscious in myself ( "
eµaui;cp
auvoLba
) of this: that I excel all men in speaking about Homer,
J
and have plenty to say ( eunopw
) ; and everybody else says so too.
Q
But about the other poets I do · ·not speak well.
The~e
Now, see why th.is : is:"
words reveal a great. deal about the character of Ion's self-
knowl·e dge. ·· "I a·m conscious in myself [that I speak well]. .•
" he
remarks, a·nd soon adds, ". , • • · and everybody else says so too. u
rhapsod~'s self-consciousn~ss
for support.
Earlier
19
The
seems to require the approval of others
)in this essay, we pointed out that Ion, while
imagining himself to be sufficient, felt a great need fqr .acclaim.
We
begin now to see how these two aspects of his character are reconciled.
Whenever Ion senses a deficiency in himself, the approbation of the
many · promptly, if
onl~
temporarily, satisfies him.
Socrates, by
silencing the applause, by refusing to' hear and to praise Ion's exh.ibition, has forced the rhapsode to listen for a moment to the muted sound
of his own emptiness.
19)
p. 5
�-20Ion's question sets the stage for a great Socratic performance.
"See
why it is." he had asked, "[that I speak well about Homer but not about
the other poets. J"
Socrates replies,
11
And I · do see and I am about to
reveal (xa\ ~p~, ~ ~Iwv, xa\ ~pxoµaL yl aoL &no~avoJµevo£ )
what I think it to be.tt This theatrical and prophetic announcement is
followed by a long, intricate speech on the nature of poetic enthusiasm .
When Socrates finishes the speech, he and Ion briefly consider what was
said.
Socrates then offers another short declamation of the same theme .
In these speeches Socrates satisfies his old desire to emulate the
rhapsode.
20)
He does what Ion has been trying to do all along.
delivers a rhapsodic and poetic discourse on poetry.
He
We will have to
consider these two speeches and the intervening conversation at some
length.
A.
First Speech (533c10-535a2)
The avowed purpose of the speech is to give an account of Ion's fragmentary expertness.
Socrates maintains
tha~
Ion speaks well about
Homer not by art but by a "divine power ( 8E{a 01: oJvaµL£
which moves him.
)"
He compares it to the power in the stone which Euripides
called the magnet, but the many call the Heraklean stone.
The magnet
is the dominant image in both of Socrates' speeches, particularly in the
,,
second.
(
This stone not only attracts ( ayEL
~ V't' {8f}a L
)
) iron rings but imparts
its power to the rings so that they in turn (
are able to attract other rings.
And sometimes (lvlo't'E
au )
) a very
great cha i n of i ron rings , hanging from one another , is s uspended
( ,,
flP't'f}'t'a L
) •
upon the stone.
spires men
(
J
'
The power in each of these depends ( aVf]p't'f}'t'a L
The Muse works in the same way as the magnet.
EV e€OU£
J
I
a
TIOLEt.
)
She in-
- literally 'makes
them full of god.), and when through these inspired men, others are inspired, a chain is hung out.
Thus all the good poets, and particularly
the good lyric poets, make their beautiful poems not by art but by being
enthused, possessed ( xa't'ex6µE vo t.
(
)
.
)and out of their right minds
Socrates likens the lyric poets to the
Corybantians, the Bacchae, and finally the bees.
20)
Cf. p. 2
�-21"For the poet is ~ light., winged, and _sacred thingJ nor can
he create ( n:OLet.V ) until he becomes inspired (ev8eO£ )
and out of his senses ( €x~pwv
), or whilst any reason
( VOU£ ) remains in him. For whilst he has this possession
( x-1;~µa
) every man is power !ess to produce poetr.y ( n:o LE Lv )
and to chant oracles ( XP f1C1µ.cpoe Lv
) •"
The poets, Socrates repeats, make their poems not by art, but _by divine
lot (
ee {cp
c
µo p Cf
)•
And each is able to do well (
that alone to which the Muse imp~lled ( ~pµ11aev
XaAW£
)
. ) him: this one
to dithrymbics, this to encomia, a third to choral hymns, another to
epics, and another to iambics.
things.
And it . is not by art that they say these
For, if a man could speak by art
about all.
~bout
one, he could speak well
God steals away the minds of men and uses them as his servants,
-
in order that we, the listeners might know that it is not the poet - in
whom mind ( 'VOU£
a
U
) is not present - who speaks these priceless words
"
( ou.,;w n:OAAOU a( La
) ; but that god himself is the speaker.
Socrates cites as proof ( µ.eyLC1'"COV · l: "t£xµ~p LOV
o
i;cp
A.~yq:>
·) . the word
) of Tynnichus the. Chalcidean, who never composed any-
'
thing worth remembering save for . the poem which everyone ( n:a'V"te £
chants, almost the best of the lyric poems.
are not human and of men, but divine and of
)
For these beautiful poems
go~.
And god, in order to
reveal this to us, intentionally. ( ~(en: Ci'f10E£
) sang the
most beautiful song through the meanest of poets ( "tOU ~aUAO"td"tOU
·
-
'JtO L fl"t0\3
).
Century English critic, Sir Philip ~idney, commenting on thi~
21
passage .s a.id ) "Plato, in his dialogue called Ion, giveth high and
The
16~
rightly divine commendation to Poetrie • • • He attributeth unto Poesie
more than my selfs doe, namely to be a very inspiring of a
farre above mans wit."
comment.
divin~
force,
We cannot but acknowledge the justice of ·Sidney's
Yet we suspect, as Sidney does not, that this 'high and rightly
divine commendation' has another side.
We will come back to this speech
again.
8.
The Central Dialogue (53Sa3-e6)
Ion is pleased and moved by Socrates' adornment of poetry.
"By teus, I
21) An Apology for Poetry, p. 192 in Elizabethan Critical Essays, Vol.. i, .
Oxford, 1904
�-22think you do · [speak the truth]!" he exclaims.
your words touch my soul. ,"
"for somehow Socrates,
He agrees that the good poets interpret
the gods for us by divine lot.
Socrates reminds Ion that the rhapsodes
are interpreters of the poets.
"Therefore, the rhapsodes become the
interpreters of the interpreters."
rca V't"c!rca O' C ye
Ion agrees wholeheartedly
).
This emphatic characterization of the rhapsode as the interpreter of
the interpreter is our clue to understanding everything that follows.
Ion, it will be remembers interprets poetry in two ways:
first he de-
livers regular lectures about Homer; and second he acts as the poet's
22
mouthpiece and mime on stage. ) We are about to witness an interpretation in the second sense of the word.
Ion and Socrates together will
dramatically interpret not only Homer's poetry, but also the 'poetry'
that Socrates has just recited.
"S\op,now a9d tell me, Ion, without hiding anything
( Wll arcoxpu'ljJ1J
) what I chose to ask you. When
you speak the lines well and especially thrill the
spectators with some particularly pitiable or fearful
song • • • are you then in vour right mind, or are you
""'r
-'
)
carried out of yourself ( e~w O'aU"tOU V1.YV1J
and does your soul in a divine enthusiasm suppose herself to be among the things that you are describing,
whether they be in Ithaca or Troy, or wherever the
verses chance to place them?"
Ion, again 'moved' by Socrates, replies, "How vivid, Socrates, you make
your proof for me!(~£ ~vapyl£ µot. ~ou"to •••••
"tb "tEXµ~pt.ov
I will answer without concealing anything ( o~ y&p
) •II
He tells how when reciting some lament
his eyes fill with tears.
When the lines are awful and fearful, his
hair stands on end and his
h~art
pounds.
Two things must be noted about this exchange.
First, Socrates has
affected Ion in the same way that Homer affects Ion.
The 'vivid proof'
offered by Socrates has succeeded in transporting the rhapsode not to
Ithaca or to Troy, but to the theatre.
Is it not likely that Ion is
'·deeply moved' by the recounting of his own past experiences?
To be
sure, Ion would not be the only man whose eyes 'filled with tears' at
22) tf. · p. 3
�-23-
hearing or telling the story of his own former triumphs.
Second, Socrates began the exchange with an ironic request.
"Stop now,"
he said, "and tell me without hiding anything what I choose to ask you."
Ion, carried away by the stirring memories conjured up by Socrates, replies that he will answer without concealing anything... · Ion's words are
prophetic. · He indeed will not conceal a thing.
Socrates has thus cleared the way for a grand finale: to place Ion on
stage without .his mask.
"Well, t .h en," Socrates continues, "shall we say that the man is then in
his right mind who, adorned with
many-colo~ed
raiment and golden crowns,
weeps at festivals and sacrifices, when no one is despoiling
hi~
of these
things, or is afraid before more than twenty thousand friendly people,
none of whom is stripping him or doing him wrong?"
Ion '·s answer is very
bold, "No, by Zeus, not at all, Socrates, to tell the truth!"
the fifth and last time that Ion invokes the name of Zeus.
This is
Now the
lightning falls.
"Are you aware that you rhapsodes work the same effects on most of the
spectators?" Socrates asks •
. "I know it very well," Ion fBP,lies.
"For I look down
upon them at such moments (EXaO''t'O't'e . ) and . s~e them
c.i-y,;~g,and staring wit.h awestruck eye_ ( CELV V
s
.
Eµp E1tOV't'ab), marvelling at my words. For I api
obJige.d to,pay t!J.e closest attention t.o them ( crcpo.bp'
OU't'O H; 't'OV vou v 1tpocrlxE I."
) • for ~f I spt
.
them weeping, I myself will laugh taking ( haµ~avwv )
the money; but if they laugh, I myself will cry losing
the money."
Ion has at last revealed his true art - he is a charlatan - and his true
artlessness - he _ not quite aware .that he is a charlatan.
is
has accomplished what he set out to do.
wronged" a rhapsode.
Ss~ ~~~Y 3
He has "despoiled ,'st r :i.;., µd d, and
And all this on a high stage, while we, the spec-
tators, look on with "awestruck eyes."
Socrates, delighting perhi;ipS in
his victory, breaks in"to song.
c~
Second. Speech (535e7-536d3)
ln his first long speech, Socrates employed the _mage of a magnet and its
i
�-24rings in order to describe the chain effect produced by poetry.
last section we saw a dramatic example of this chain effect.
In the
Socrates,
by playing on Ion's vanity, produced a thoughtless and disastrous enthusiasm in the rhapsode.
Socrates again invokes the magnet - with some further elaboration.
"Are
you aware that this spectator is the last of these rings which I said
take from one another the power [transmitted by] the Heraklean stone?
(~no ~DG tHpaxA.ELQ~LOOG A~Otl &n' &A.A~AWV ouvaµLV A.aµ~avct• ;)
'
You ( cr' ) the rhapsode and actor (UTIOXp t.~~G
u
) are the middle ring
' OE µccrOG
~
,
(o
) ; and the first is the poet himself. Through all
these [rings] the god drags (eAXEL
) the souls of men wherever he
wishes, making the power in each depend on the others ( &vaxpEµavv~ G
"r "A.A.,"\.
'
,
E'-> a
f}r..W'V ~f}V buvaµ LV
) ." We note that the image has undergone some changes.
First, it is made more vivid.
Poet, rhapsode, and
spectators are all 'transformed' into iron rings, hard on the outside,
and, we suppose, empty in the middle.
A few lines later (536b6)
Socrates makes the image even more literal by interpreting the word
'possessed' ( xa~lxe~a L
as 'hela' (exe~a t.
)•
The ponderous
iron ring held in a chain is quite different from that "light, winged,
and sacred thing" spoken about in Socrates' first speech.
The order of inspiration has also changed.
relationship of the rings was
consec~tlve
In the previous speech the
from A to 8.
In this speech
the relationship is reciprocal, from A to B and from 8 to A.
This sug-
gests that Ion is 'inspired' as much by the audience as he is by the
poet.
Socrates is not content with having Homer, Ion, and the spectators hang
down in mid-air by themselves.
He heightens the comedy by adding
choruses, chorus-masters, and under masters, hanging down from the sides
(
~ v '"'"\.ay L'ou
~~ J~r..
) of the rings hanging down from the Muses.
Socrates concludes the speech by reminding us again of Ion's peculiar
problem.
"And you, Ion, are one of these possessed from Homer; ant!
whenever someone sings of another poet, you are asleep ( xa8eube: LG
),
and are at a loss for words; but when some strain of your poet is uttered,
straightway you are awake and your soul dances within you, and you have
�-25a wealth of things to say."
Ion had originally broached the subject of
his sleeping habits by saying, "When someone converses about another
) . " NUO''td~w
poet • • • I fall asleep ( vuo"ta'w
asleep, to drop into a doze, to start nodding.·
'VUO''tc!~w
xae eu~w
xa8 eUbw
, the word
means not to fall asleep, but to be asleep.
the word
It denotes a change
Socrates, in this second speech, sub-
from a waking state to slumber.
stitutes for the word
means to fall
, which
Socrates suggests by using
what we should have surmised before now - that
Ian is almost. always asleep.
D.
The Socratic Poetry
Let us reflect a moment over the drama we have just· witnessed. "All of
Socrates' efforts are aimed at uncovering Ion's true identity.
an inquiry to make!
No man is more conspicuous than Ion.
But what
He travels
throughout Hallas performing at all the great sacrifices ~nd festivals.
At some performances more than twenty thousand people sit gazing at ·him.
His body is ornamented with brilliant and many colored garmets and he
shines . out from above as the most beautiful of men.
celebrity, for all his godlike
Socrates insists on
con~picuousness,
asking, albeit underhandedly, Who is Ion, really?
rates' question is obvious.
He is not
Yet f6r all Ion's
s~tisfied
The reason for Socwith .what he sees.
He
realizes what Ion does not realize, that a rhapsode when he is most
conspicuous is most hidden.
Socrates is intent on lifting the rhapsode's
mask and seeing him in his nakedness.
But can Ion's nakedness reveal what he is?
How is that possible?
Ion
is a rhapsode, and a rhapsode out of costume is no longer a rhapsode.
His nakedness, by itself, would reveal nothing.
the problem and offers an ingenious
solutio~.
garb off the rhapsode and puts it on himself.
Socrates is aware of
He strips the tragic
Thus, though Ion stands
on the stage naked, his image in the person of Socrates is appropriately
garbed.
Let us say that in a
mo~~
sober fashion.
We only learn the
truth about Ion when we see the disparity between what he seems to be
and what he is.
Consider the overall structure of the two speeches and the intervening
dialogue:
Socratic poetry - the stripping of lon - poetry.
Ion is
�-26literally surrounded by a mask of 'high and rightly divine commendation'
provided by Socrates turning poet.
rhapsode's character can be seen.
an imposter.
It is only by that mask that the
He is, as we have said, a fool and
On the other hand, the irony of Socrates' two speeches,
his adornment of Ion, can only be seen by looking at the rhapsode in
23
the middle. Earlier )we noted that at one point in the dialogue Ion
is transformed by the protasis . of an hypothetical question into the
expounder of an unknown god.
accomplished in deed.
Here again the same transformation is
Ion, through his poetical simplicity, becomes a
kind of expounder and interpreter of the two speeches of Socrates.
Socrates, we might add, becomes the unknown god.
And
The stripping of Ion
shows the mask of praise for what it is: a mask which seeks to conceal
the object it adorns.
By eeeing the mask as a mask, we learn the truth.
But we have still not done justice to Socrates' poetry.
speech is, as we have indicated, pure comedy.
The second
The image of poets,
rhapsodes, spectators, choruses, and chorus masters all hanging in the
sky stuck to one another is ludicrous.
The 'dramatic interpretation of
Socrates' first speech presented to us in the intervening dialogue is
likewise comic.
A rhapsode inspired by Socrates' flattery shows him-
self to be a fool.
But the first and longer speech read by itself
seems to have another tone.
Sidney's understanding of it as 'high and
rightly divine commendation' is not entirely unfounded.
Let us look
at that first speech again.
The two primary themes of the speech are 1) that all good poetry is
divinely inspired, and 2) that each poet is able to make well only one
While it de'a ls with all poetry the speech gives
kind of poetry.
special prominence to the lyric poets.
quality.
Indeed, it itself has a lyric
In the first half of the speech Socrates develops an elaborate
µ[A.ob
, song or lyric, and µlA. t
, honey, He
compares the · lyric poets ( µe:°A.O'ITO Lo C ) to the Bacchae who draw milk
pun on the words
and honey ( µ~A. I.
)
from the rivers.
the lyric poets themselves ( O'ITEp a~'to\
A.lyou en.
He attributes this simile to
[ ol µe:°A.O'ITOLoC
)•
23) page · 9 ~ · "If indeed you were a diviner, and if you could expound
what was said similarly, would you not also know how to expound what
was said differently." (531b6-9)
J
�-27for the poets tell us, I suppose, that plucking their
,
songs (
µb. . ri ) frorn the honey-flowing _ (µEA. t.pptS"twV)
fouhtains in certain gardens and valle11s of the muse, they
carry them to us, just as the bees ( a L µ€>... L't"ta i) do; and
like the bees they fly.
.
.
'ta
Lyric poetry is emphasized in the second half of the speech also.
There,
Socrates introduces the strange figure of Tynnichus, the Chalcidean, who
"· •• never wrote anything worth remembering save for the paean which
,
everyone ( TtaV"t£b
XdAA.l.C1't"OV
) chants, almost the best (
) of the lyric
poems~"
"t t
••
o •
Socrates tells us that Tynnichus
) called his song an
r~mainder
crxlcov
'in~ention
of Socrates' speech is an interpretation
~f
of the museJ'
The
this line.
By this example above all, it seems to me, the god
would show us, lest we doubt, ~hat these b~autiful
poems are not 'human and of men, but divine and of
god; and that the poets are nothing but the interpreters of the god, bei~g posse~sed by the god from
whom each· is possessed. ·In order to reveal these . ·
things to us, the god in~entionf(llY ,( l~€1t C"tf'IC~G )·
sang the most beautiful song ("to xaA.A.1.{;'t"O'V µeA.o·g
through t.tie meanest of poets ( c
't"OU cpm.>AO'td't"OU
ta
. 1t: 0 I. V't"OU
),
•
In short Tynnichus has said almost exactly
this speech.
~hat
Socrates is saying in
Not only do the two say the same things, but they also
speak in the same style.
Tynnichus wrote a lyric poem and Socrates de-
livers a lyrical speech.
To add to the
simi~arities,
Soc~ates
pre.v iously called his own way. of speaking 'mean ( t}KIUAO~
had
) '. and simple.
In the last line .of his speech, Socrates seems to designate Tynnichus as
the 'meanest of poets through whom the .god sang the most beautiful song.'
It may be that Socrates is not referring to Tynnichus at all.
Just be-
fore, Socrates had called the celebrated paean not the best, but almost
( <1Xebov "t. the best lyric poem.
Perhaps ·the song spoken of in the
last line of the speech is even mar• beautiful then Tynnichus' song.
Perhaps the most beautiful lyric is the song that Socrates is singing.
That would make Socrates the meanest of poets.
It is · our conjecture .that the .Socratic speech ·is an attempt to imitate
and surpass the paean of Tynnichus.
song?
But what is the character of Socrates'
It understands itself as an interpretation of the deity's word.
And it tells us that no man is the master of all · poetry; no poet has
�-28apprehended the whole.
It is, in effect, the Socratic interpretation
of the oracle that Chaeraphon brought back from Delphi.
It will be
recalled that the Delphic oracle designated Socrates as the wisest of
men.
Socrates interpreted the oracle to mean that he, Socrates, is
the wisest because he alone knows that he does not know.
But if Socrates
emerges from the dialogue as the meanest and the noblest of lyric poets,
in what image do we see Homer?
Part IV
Let us reflect a moment on the general character of the dialogue.
much
of what is said in the !oh is about poetry. Homer is called the best
24
and the most divine of poets, )all the poets are said to speak about
26
25
the same things, )the Homeric themes are enumerated, )poetry is de27)
.
.
28)
scribed as a whole,
a poetical account is given of poetic madness,
29
and Homer is quoted five times ). Most of these discussions are not
trivial.
Poetry is surely a major theme of the dialogue.
not the only theme.
But it is
Indeed, for the most part the conversation seems
to be about Ion the rhapsode and his rather peculiar problem.
Ion can
only speak well about one poet; and in his opinion this is sufficient.
The burden of Socrates' argument is to show that Ion's limited expertness is not sufficient for true artfulness.
He maintains that because
Ion cannot speak about all of poetry he cannot speak with art or knowledge about any part of it.
Art and knowledge according to Socrates
require an expertness about the whole.
mentary.
And Ion's expertness is frag-
The rest of the dialogue is an ironic exposition of this theme.
We are confronted with a grave problem - how to unite the two themes.
What does a rhapsode's artfulness, or lack of it, have to do with
poetry?
Or to put it differently, what is the relationship between Homer
and Ion?
There are several obvious answers to that question.
a literal sense, Homer's mouthpiece.
24) 53Db10
25) 531d1
26) 531c1-d1
27) 532c10
28) 533c10-535a2
29) 537a1D-539d1
First, Ion is, in
Second, Ion is a self-appointed
�-29-
expounder and advocate of Homer.
of Homer.
Third, Ion is shown to be a 'descendant'
That is, he is pictured as 'hanging down' from the poet.
fourth, Socrates maintains that the same. diviner power which moves Homer,
moves Ion.
fifth, the rhapsode and the poet are engaged in analogous
enterprises.
Both are interpreters.
Homer interprets the Muse and _
Ion
interprets Homer (535a9).
This last point that there is . an analogy between Homer and Ion can be
extended much further.
We have already indicated that the conspicuous-
ness of rhapsodic excellence has a counterpart in poetry.
further there
is a hint that Ion's embellishments of Homer are akin to Homer's embellishment of the world.
Again,- both Ion and Homer practice what we called
poetic circumlocution - the speaking about men speaking about other
things.
This sort of 'speaking about• is comically impugned in the second
half of the dialogue (536d10-541b5) where Socrates argues that the various
artisans would judge better than the rhapsode those passages in Homer
relating to their arts.
The arguments used against Ion there could be
used against Homer · as well.
Here again an analogy is clearly implied.
Can we find further analog{es· between the rhapsode and the poet?
Consider the main thrust of Socrates' questions about
Ion~
Throughout
the dialogue Socrates is determined to uncover, exploit, and atta6k Ion's ·
failure to grasp the whole of poetry.
He tries in every way to reveal
the insufficiency of the rhapsode's skill.
is:
The question facing us now
Is Socrates making an analogous attack on Homer?
Socrates' attack
on Ion culminates in the two central speeches of the dialogue.
Those
speeches appear to say as much about poets as they do about rhapsodes.
The burden of the argument is that each poet is 'held' by only one Muse,
just as Ion is 'held' by only one poet.
Ion's, is fragmentary.
Homer and Ion
al~ost
Homer's expertness then, like
Thus the two speeches make the analogy between
complete.
All of the analogies and
we have been drawing point out the irreverent and
Ion.
Ion is not Homer.
Yet Plato,
th~ough
image nor a very fair one.
irony of Platq's
the ambiguous, underhanded,
and ironic queitions and speeches of Socrates
rhapsode into Homer's advocate and image.
dism~l
relationsh~ps
tr~n~forms
a simple-minded
It is not' a very flattering
Why does Plato do this?
If he intended to
talk about poetry, why did he pick Ion of all people to represent the
�-30-
best and the most divine of poets?
We will have to deal with these
questions eventually.
If what we have said is correct, we can characterize the dialogue as
follows:
In the Ion Socrates interrogates a rhapsode in order to cast
doubt on the integrity of the poetic enterprise. We can now begin to
.
.
. 30 .
.
answer a ques t ion raise d ear 1 1er ) in th is essay: Why should the formal
wholeness of poetry be so flagrantly disregarded by Socrates?
Perhaps
Socrates regards the structural wholeness of poetry as a mask which
hides a basic insufficiency of poetic discourse.
poetry deficient.
But in what sense is
What is the real meaning of this accusation?
Recall Socrates' extravagant claim on behalf of the poets.
he said, is poetry.
for poetry.
The whole,
Socrates was not the only man to make this claim
Ion's satisfaction with himself and with Homer is a reflec-
tion of his rather dim belief in the completeness and utter sufficiency
of Homeric wisdom.
We prefaced this essay with a quotation from Shelley
in which the great English poet makes substantially the same claim for
all poetry.
But perhaps the most eloquent argument for the perfection
of poetry was given by Homer.
the Iliad to be convinced.
If one doubts this one has only to read
It is this very claim to god-like perfection
a claim that great poetry by its nature almost always makes - that
Socrates comically defends and attacks in the Ion.
The subject of poetic
integrity is a significant theme in many other dialogues besides the
19!:!.· The Sophist, the Phaedrus, the Symposium, and the Republic come
to mind immediately.
Let us look briefly at the discussion of poetr y
in Book X of the Republic.
In the Republic (X, 596d3-4), Socrates says that the poet is
11
in
1:p6nq:> ) the maker of all things." The 'way' by which
poets make all things is imitation. Book X of the Republic contains a
a way ( 'tL'V\
lengthy discussion of imitation.
discussion here.
Unfortunately we cannot examine that
We might, however, consider one sentence (598b5-8)
in which Socrates gives a summary of the argument.
"The mimetic art
is far removed from truth, and this, it seems, is the reason it can
>
'
>y "
produce everything ( nav't'a anepya1.:,E't'a l.
30) cf. pP. 8 - 9
),
because it touches
�-31or lays hold of ( ~<ptt'J!'t€'ta 1.
tha.t a phantom ( e:iowA.ov
) only a small part of the object and
)."
ironic counterparts in the Ion.
This statement has, I think, two
1) Let us recall Socrates' enumeration
of the poetic themes in the Ion (531c1-d2).
(p. 10) seemed to include
sverythi~g.
ling about things' by the words
told through about.
prepositions b
s.a
His list, as we noted
He characterized the poet's 'tel-
O1.€A~A.u9e: \1 ne:p
C
- he- has
We pointed out the ironic juxtaposition of the
and ne:p C
Was he not suggesting that poetry,
though it appears to penetrate the whole, in truth touches only a small
part, the outside of things, the phantom and the shadow of the world?
The attack on poetry seems to be this: the poets, while laying hold on
a small part, think they have captured the whole.
The poets like the
rhapsodes believe themselves to be sufficient (cf. 531a3-4).
2) Ion,
as we have said before, is presented to us as the image and advocate
of Homer.
But Ion is not the only image of Homer in the dialogue.
Socrates in his speeches presents us with another likeness of poetry.
Thus, Ion, by his own word, is the interpreter, and Socrates, by his
actions, is the imitator of Homer.
We can only arrive
a~
the full
image of poetry in the Ion by considering both the rhapsode and the
philosopher.
Socrates' two speeches and the rhapsode they
..
gather constitute the Platonic image of poetry.
sur~ound
.
to-
That image can be
stated as follows: poetry is like an iron ring (represented by Socrates'
two speeches) which encompasses very little (portrayed by Ion).
we should put that in a less offensive way.
whole of th i ngs .
Perhaps
Poetry speaks about the
It does not penetrate the center.
A proper exposition of Socrates ironic attack on p6etic iMtegrity woGld · ·
require a long discussion of images and imitation.
to go into those problems here.
We are not prepared
Our aim in this essay is to begin to
explore the questions which divide the poets from the philosophers.
If
we can give a clear formulation of some of the disputed quest io ns we
will have done what we set out to do.
We are not seeking to give final
solutions, but only to provide the basis for future inquiry.
The Socratic rhetoric also fails to penetrate the center.
Socrates'
speech, as he tells us again and again, is mean, obscure, and insufficient.
�-32Even his poetry, by pretending to conceal that fact reveals it to us.
us
His rhetoric does not satisfy
Ion).
as Homer satisfies · Ion (and not just
And therein lies the difference.
The Socratic masking of ig-
norance is aimed at comically displaying that ignorance against the
background of wisdom.
The integrity of Socratic rhetoric consists in
its single-minded dedication to the uncovering of its own deficiencies.
Socrates mocks our eagerness to produce images and " • • • to take them
.
31)
seriously as serious things that lay hold on truth."
By continually
asserting the difference between true opinion and knowledge, by seeking
to understand images as images, he attempts always to draw us into the
mad enterprise of seeking wisdom by the study of our own ignorance.
That is, he attempts to make us wise.
*
We said before
32
*
*
*
*
*
*
*
*
*
)that Socrates' primary thesis in the dialogue - that
Ion doesn't know what he is talking about - is unambiguously insulting.
That is not the only insult in Plato's Ion.
offense.
There is a much greater
Ion the silly rhapsode is cast in the role of the best and
most divine of poets.
Why does Plato do that?
I think the answer is
simply this: the Homers of our world are almost always accompanied by
Ions.
Supreme human artistry, with its unutterable beauty, its awe-
inspiring vastness, invariably draws to itself a cloud of praise and
human vanity.
The poet's notion of self-sufficiency and our habit in
these times, and at all times, of spelling the word Art with a capital
" A" attest to the kinship of artfulness and vanity in the human sou l .
While the clouds of vanity remain, serious thought about what they surround is impossible.
Witness the case of Ion.
He is the cloud incarnate .
Plato's mockery taunts the poet in us with the malicious insinuation that
behind the cloud of vanity, played by Ion, there lies only a cloud of
vanity.
If we have listened attentively, we poets - and who is not a
poet - should be shocked and offended.
That is, we should be moved to
engage in a serious and honest conversation about poetry and the whole
of things.
If we have been properly insulted, then Plato's charming
little dialogue will have accomplished what it was intended to do - it
will have become the perfect imitation and praise of Socrates.
31) Book X, Republic, 608a8-10
32) p •. 16
�-33-
A DISTANT HEARING Of GABRIEL fAURE'S
. MESSE DE REQUIEM
Veronica Soul '66
Bequeath remembrance to the past and find
Your giving echoed back in startling sounds
Of
requiems.
, A phrase a child was taught
To chant - a dona eis requiem Breaks from
a windowed balcony to set
Its balm of new-learned sounds on brick-laid walks,
Our modern ruins, 'pockmarked paths, now eased
'
·'
With clots of moss that fill the random gaps.
Unchanted asking - dona sis - Utakes
· fore-sung, forgotten crisp eleisons.
- Christe, Christe, boyish choral cries
To crack the hallowed shell of Coventry
Before it heals arise and fall like chips
Of twice and triply shattered colored glass.
Forget this former requiem.
Bequeath
This raw remembrance to the past and take
Soma other in its place:
once Boulanger
Came to conduct her teacher's Requiem.
She, gaunt and gray in fragile black, sent sounds
Of Christe, Christe, to
the open crowd.
No exits for that concert-requiem,
Confined; no streetward Christes to
surprise •
Keep requiems for youthful cries and let
Them strike unstaged in unexpected sounds
Beyond cathedral doors, conservatoires.
�-34-
THAT THE INTERSECTION OF A CYLINDER AND A PLANE,
PARALLEL NEITHER TO THE AXIS NOR -THE BASES OF THE CYLINDER,
AND CUTTING NEITHER BASE, IS AN ELLIPSE.
Dean Hannotte
Introduction
In Book IX of the Elements, Euclid gives, among others, these generally
accepted definitions:
21. When, one side of those about the right angle in a
rectangular parallelogram remaining fixed, the parallelogram is carried round and restored again to the same
position from which it began to be moveo, the figure so
comprehended is a cylinder.
22. The axis of the cylinder is the straight line which
remains fixed and about which the parallelogram is turned.
23. And the bases are the circles described by the two
sides opposite to one another which are carried round.
This paper will prove by means of an orderly progression of synthetic
theorems that the intersection of a cylinder and a plane, parallel
neither to the axis nor the bases of the cylinder, and cutting neither
base, is an ellipse, as defined and discussed in Apollonius' Conics.
r
l
A
cy~inder,
cut by· said
p~ane,
which intersects said figure.
1
68
�· -35-
Theorem 1
Any plane containing only one of two parallel
straight lines is parallel to the other.
Let AB, CD be parallel, and CO lie in the plane MN.
I say AB will not
meet the plane MN.
N
Now AB, CD determine a plane intersecting MN in the straight line CD.
Thus, if AB meets MN it must meet it at some point in CD.
impossible since AB is parallel to CD.
But this is
Therefore AB will not meet the
plane MN, and is therefore parallel to it.
Theorem 2
If a straight lfne is parallel to a plane, it is
. also parallel to the intersectioh of any
plane through it with the given ·plane.
Let AB in the drawing above now be parallel to the plane MN , and let
any plane through AB intersect MN in CD.
Now AB and CD cannot meet) -
because if they did AB would meet.the plane MN.
plane.
Yet AB, CD are in one
Therefore, AB, CD are parallel, which was to be proven.
Theorem 3
The intersection of a cylinder and a plane, either
containing the axis or parallel to it, is a rectangle.
Case I:
Let AB be the axis of a cylinder, and let MDNC be the inter-
section of a plane containing the axis and the cylinder,
MDNC is a rectangle.
I say that
�-36 -
Now the intersection of two planes is a straight line (Euclid, Book XI,
Proposition 3).
Therefore MAD is a straight line, and similarly CBN.
furthermore, MAD and CBN are parallel (Eu. XI, 16).
Now MASC is one of
the positions of the generating rectangular parallelogram
fore
me
is a straight line, and similarly DN.
They are parallel by
virtue of their each being parallel to the axis.
parallelogram.
and there- ·
Therefore MDNC is a
Angle DMC is right because it is an angle of the
generating rectangle, and so therefore MDNC is also a rectangle.
Case II:
Let AB be the axis of a cylinder, and let MDNC be the inter-
section of a plane parallel to the axis and the cylinder.
MDNC is a rectangle.
D
I
I /,
I I,
I /:
,r
I,
I say that
�-37Now the plane cuts the upper base at
has as a side BC also includes D.
D~
The generating rectangle which
For suppose this is not the case, and
that the generating rectangle were ABCD', and that the intersection of
its plane, the cutting plane, and the base plane were 0' '·
Now AB and CD'' would never meet because the latter is in a plane parallel
to the former.
tangle.
Vet they are both in the plane of the generating rec-
Therefore they must also be parallel in that plane.
Now AB and
CD' are parallel by hypothesis and therefore 0' and 0 1 ' must coincide
(Eu. XI, 13).
But then M, D, and 0' (D' ')would lie both on a circle and
on a straight line, which is absurd. · Therefore CD will be a side of a
generating rectangle, and similarly MN.
By this, then, mN and DC will each be parallel to AB, and by virtue of
that fact they themselves will be parallel.
mo
lel (Eu. XI, 16), and therefore MDCN will be a
and NC will also be paralparallelogram~
Now the axis AB is perpendicular to either base as is seen from the
definitions.
DC is parallel to AB and therefore is also perpendicular
to either base (Eu. XI, 8).
It is said that a straight line is ·perpen-
dicular to a plane when it makes right ahgles with all the straight lines
which meet it and are in the plane (Eu. XI, def. 3).
a right angle with NC.
Therefore DC makes
And therefore MDCN is a rectangle, which was to
be proven.
TheDrem 4
The intersection of a cylinder and a plane parallel to the
bases and between them is a circle whose radius is equal to
the radius of · either base and whose center is on the axis.
Let AB be the axis of a cylinder, and let a plane parallel to the bases
cut the axis at O.
I say that the intersected figure about O is a
circle with center at a .and whose radius= PA.
�, and let the
Let there be chosen a random
which contains R,
ABTP is a
, and 8 be labelled
the
f
and therefore
XI, 16 , and therefore
Now PA is
PAOR is a
PA is the radius of the base.
distance between 0 and any
is
R on the
Thus RO
PA ..
Therefore the
But
to the radius
of the base.
And
the
in radius to the base and
is a circle
its center on the axis, which was to be
hav
The line in the
of the axis and the
intersection of the
lines
AB
the axis of a
the intersection
to the
all
inder, and let a
axis nor either base, nor
MPNR..
HJ.
either base, intersect the
Let the
and the base
From O, the intersection of the axis and the cutt
be drawn
any such
neither
icular to HJ.
I
Let RP be
say
RK
inder in
intersect in line
, let OG
to GN, and let RP
�-39-
Let DBF be the intersection of the base and the plane which contains AB
and GO, henceforth called the axial plane.
taining RP and parallel to AB.
Let RPQS be in a plane con- .
Then RPQS is the lower portion of a rec-
tangle by Theorem No. 3, and RS is parallel to PQ, and angle PQS is right.
Now HJ is perpendicular to GN.
But RP is perpendicular to GN.
Therefore
HJ is parallel to RP, and is parallel to the plane of RPQS by Theorem No.
1.
By TheDrem No. 2 HJ is parallel to SQ.
SQ, and RPQS is a parallelogram.
Therefore RP is parallel to
Since angle PQS is right, RPQS is a
rectangle.
Now KL is parallel to AB by Theorem No. 2, and PQ is parallel to AB by
Theorem No. 3.
Since therefore KL and PQ are parallel, RKLS and KPQL
are rectangles, and therefore KP is perpendicular to KL.
pendicular to GN.
But KP is per-
Therefore KP is perpendicular to the axial triangle
(Eu. XI, 4).
As was said before, KP is parallel to HJ.
Therefore HJ, too, is perpen-
dicular to the axial triangle (Eu. XI, 8), and consequently will be perpendicular to Gf.
Since then HJ is parallel to SQ, as was said before,
SQ is also perpendicular to GF.
Now 8 is the center of the circle DQFS, and therefore DBF is a diameter.
SL and LQ, being perpendicular to DF, are drawn ordinatewise to the
diameter.
Therefore SL equals LQ, and since SL equals RK, and LQ equals
KP, RK must equal KP, which was to be proved.
Since MN bisects all the lines drawn perpendicular to it in the figure,
it will henceforth also be known as the axis of the figure.
the perpendicular lines, such
· figure.
a~
Analogously,
KP, will be called ordinates of the
��-41-
Theorem
·6
In the figure, the square on the ordinate is to the area contained by the
straight lines cut off by it beginning fr6m the ends cif the axis as the
square on the line perpendicular to the axis and intersecting the axis of ·
the cylinder is to the square on the axis of the f i:~ure.
Let WOT be that line drawn perpendicular to MN and passing through AB,
and let WTVX be in the plane containing both WT and AB.
I say that
sq.KP:rect.mK,KN::sq.WT:sq.mN.
WTVX is a parallelogram, as shown in the course of Theorem No. 5, and so
WT equals XV,
But
·xv,
passing through B, is a diameter of the base, and
is therefore equal to DF.
So WT equals DF.
The square on LQ equals the rectangle contained by DL and LF (Eu. II, 14,
lines 28,29; or VI, 8, porism).
Since KP equals LQ, that rectangle also
equals the square on KP.
Now, DL:MK::DF:MN, and LF:KN::DF:MN (Eu. XI, 17).
rect.DL,lf:rect.MK,KN::sq.DF:sq.MN.
sq.Of equals sq.WT.
Therefore
But rect.DL,Lf equals sq.KP, and
Therefore, sq.KP:rect.MK,KN::sq.WT:sq.MN, which was
to be proved.
Theorem 7
The figure is an ellipse.
Let AB be the axis of a cylinder, and MWNT the figure. I say MWNT is
, ...
·- . .. .. ... ..,_
.
an ellipse.
~ --
--~-
·
.~
A
. ·~ .
...
-- ......
~
--- -.....~" .1..
,
... . -
C~-----+----t--~~----T~-?q··.
. , .·:
.. r .
./
.
.
i
f
f.
t
-·· ~
- ....--- -·-··~_
j
-.J
.•.
/
,.l
8
... . . . . ._._..._... __.. .... ,...,.---- ..~-~·- ..
_
/
/
�-42Construct MZ perpendicular to MN in the cutting plane, and let it be contrived that MN:WT::WT:MZ (Eu. VI, 11).
Now it is possible to construct
an ellipse in the cutting plane with MN transverse diameter and MZ upright, with the given angle being right, by Apollonius I, 56.
be done, and let CDE be the cone of the produced ellipse.
Let it
I say the el-
lipse constructed in the cutting plane will coincide with the figure
already there.
For assume that it is not the case and let the closed curve MWNT represent the figure in the cutting plane, and let the closed dots MW'NT'
represent the superimposed ellipse also in the cutting plane.
Since the given angle was right, MN is an axis of the ellipse by construction.
Now every point on MN corresponds to 2 ordinates which in
turn together correspond to two points on the ellipse.
That correspon-
dence is exhaustive both of the points on MN and the points on the
ellipse.
That is to say, there is no point on the ellipse which cannot
be connected ordinatewise to the axis.
dric section having also as an axis MN.
The same is true for the cylinTherefore, for both closed
curves, discussion of all the points on MN in their ordinatewise rela tion to the points on those curves treats exhaustively, and which is
to say rigorously, of those points and leaves
~left
unaccounted for.
Now to actualize the very possibility of such an enquiry, a "variable
point" must be discussed in terms of its specific qualities with respect
to the curves, rather than the generalized qualities which might be
�-43-
extracted from the specific qualities of each point on MN with respect
to the curves.
Let this "variable point" be K, and for the moment let it be fixed.
Since
ordinates to either curve are perpendicular to MN, from K they will coincide.
Let KR be the ordinate to the figure, and KR' the ordinate to the
ellipse.
Let 0 be the intersection of the cylindrical axis, and the cor-
responding ordinates be OW,OW', and OT, OT'.
Now sq.KR' :re6t.mK,KN::MZ:MN (Apollonius I, 21).
By
constr~ction,
MZ:WT::WT:MN, and compounding each side with WT:MN we get mz:mN::sq.WT:sq.MN.
Therefore, sq.KR' :rect.MK,KN::sq.WT:sq.MN.
But
sq.KR:rect.MK,KN::sq.WT:sq.MN (Theorem No. 6), and therefore KR equals
KR'.
This contradicts our earlier assumption that there can be a point or
points on the ellipse which are not on the cylindrical section by saying
in effect that every point that corresponds to a point on MN, that is to
say, every point in the ellipse coincides with a point in the cylindrical
section.
Therefore, what has been set out to be proved has been proved.
�SUN
TO BE
James mans ch
Once a very
67
time ago there was no sun to shine down
and br
There was
Dawn
robed
the
black
And the sea.
There was greyness all
the soft
of the waters
And there was darkness on the land.
Now each
, Dawn, the
rose up from
the bed of N
And walked upon the earth until the sea lifted itself
about her feet ..
was sad
And the Dawn who had lain with the darkness of
for there was no
the sea in greyness moved low and
And the Dawn shed soft tears which fell into the sea
as if to catch them.
with the waves l
Thus Dawn
who was called at that time
the other
"the mother of the unborn,
Was seized with a
sadness.
And she lamented and beat her breasts and cut her
ashes she rubbed her face
hair
soot and
her clothes.
looked at the sea, low,
But still the
it
and was sad
For there was
1
Now one
the Dawn of the rosy
walked wet sandled
from the sea
Onto the earth, covered with darkness,
for the
of the black feathered
And the Dawn had conceived an idea.
still
�-45-
Now it was that the Dawn came upon the great fires
leaping into the darkness from the forge of Hephaestus • .
And the lame god was wise in many crafts.
His work was as the intricately wrought gold upon the tripods of ivory
and the many layered shields of the gods.
The lonely god turned upon his staff and his shoulders
were of the pitiless bronze, his neck as alabaster;
And the great coals of his eyes glowed red against the long
black hair and the soot of his body.
And he walked three legged using his staff.
For one leg was white made of ivory inlaid with laughing silver
And the other was misformed, black, and would not support him,
crippled from that time his mother had hurled him to the earth
of the black winged Darkness
For he was not beautiful.
The lame god listened to the Dawn and smiled
and fashioned a great net wrought of white gold
And limping gave the gift to the goddess of the yellow
gown~ .
And Dawn went to the bed of Night and lay down beneath
the black wings
With the golden net between her breasts
and slept with the god.
The next morning, the goddess of the yellow robe
rose up from the bed of Night
And walked on the dark earth until the sea lifted itself about
her feet.
And the Dawn taking the great net from beneath her breasts
Cast it upon the waters.
The tips of the golden waves lifted towards the net and caught
the golden light and fell splashing.
And the net descended beneath the waters.
�-46-
Now a great thrashing arose and the sea which from the beginning
of time was greyness
Appeared violet and golden and green and red.
For a wonderful fish was caught in the toils of the net
with scales all the colors of the rainbow
glowing violently and lighting the sea.
And there was no greyness.
And the Dawn of the rosy fingers with the golden net
brought the wonderful fish ashore.
And wonderful!
The great fish, coloring the whole world, vomited out the sun
and fled back into the sea.
And the newborn sun rose bringing day and light.
The yellow robed Dawn had no sadness.
Now after twelve of the Hours had died,
the great ball of the sun fell dying into the sea.
But from that day on, the Dawn of the yellow gown rises
at the morning from the bed of Night
And casts her net upon the waters landing the wonderful fish
who vomits out the great ball of the sun.
And there is no darkness nor sadness with the day.
�-47-
ESSAY ON CONICS BY BLAISE PASCAL
Translated by
Cynthia Siehler '66
Translator's Note
In the interests of projective geometry, the study of which is predominant during the last half of the senior mathematics tutorial, the following translation of Blaise Pascal's L'Essay pour les Conigues is
offered.*
This essay is one of two extant works of Pascal's Traits
des Conigues, a much larger treatment of projective geometry, the remainder of whose contents is believed lost.
The other work, which we
study during the sophomore year, is entitled Generatio Conisectionum,
and is available in translation in the bookstore.
The Essay on Conics,
published originally in poster form, presents only the enunciations of
its lemmas and propositions.
Lemma I of the Essay is particularly per-
tinent to all projective geometry systems and is known as Pascal's
Hexagon Theorem, cir the Mystical Hexagram, whose figure (see Figure 1)
is described by the letters PKNOVQ.
* French taxt taken from Pascal, Oeuvres
*
*
*
*
*
*
Compl~tes,
*
*
*
Macmillan, _ 1963.
*
Definition I:
When several straight lines meet in a point, or are all parallel to one
another, all these lines are said to be of the same order or of the same
ordering, and the group of lines is called an order of lines or an
ordering of lines.
Definition II:
By "section of a cone" we mean the circumference of a circle, an ellipse ,
a hyperbola, a parabola, and a rectilineal angle; inasmuch as a cone
cut parallel to its base, through its vertex, or in the three other directions · which produce the ellipse, the hyperbola, and the parabola,
brings about in the
s~rfaca
of the cone either
th~ circumfer~nce
circle, or an angle, or an ellipse, a hyperbola, or a parabola.
of a
�-48-
Definition III:
By the word "straight" placed alone, we understand a straight line.
,--__.,,------·- ·--, -,
E/,,.,..
Lemma I:
/\
H/
i
G!
...J. ---·
Pin
- ---/--·- -----r / i
-·y- i
-------------- {/ '\ I I
~-- ----I
·=-~-:-.:_~-- ,, R \
c\ I /
~_,_,...""' .,., . --~Ii m
""K----_..---,:
'0 .
\~\
\
.
\._
!
I
\i
!
" \ii
_1
/
I
.
I
I
I
/
;h .'
\T\it
/ f.b \
;-----~~-----~.//~ \
\
'
x I
fl~~\\---:¥- ·\- ---- '
----;--r--J__
? \
:
\ \\~\/N//
;'
-----..:::--1-,--~---LYJB
1
/ i
I
'.\\
I
- rr--\--.. .__ \
,I
/
·- - - -
;
----
~-l
II
.
-----../?.. _
.
\] _
__.//
'
\
i
\. ;
!
----+----------~.)
s
U------
Figure 1
If in the plane M,S,Q the two lines MK and MV meet in M, SK and SV in
S, MK and SK in K, MV and SV in V, MA and SA in A, and MV and SK in
µ, and if the circumference of a circle cutting the lines MV, MK, SV,
SK in O, P, Q, N pass through two of the four points A, K, µ, V not
in the same straight line with the points M, S, as for example through
the points K, V, I say that the straight lines MS, NO, PQ are of the
same order.
Lemma II:
If several planes, cut by another plane, pass through the same straight
line, all the lines of the sections of these planes are of the same
order as the straight lines through which the planes pass.
(Figure 1)
Given these two lemmas, and some of their easy corollaries,
we shall demonstrate that, with the same things being given as in the
first lemma, i f through the ·points K, V pass any section whatever of a
cone which cuts the straight lines MK, MV, SK, SV in the points P, O,
N, Q, the straight lines MS, NO, PQ will be of the same order.
This
constitutes a third lemma.
Following these three lemmas and some of their corollaries, we shall
give the complete conic elements, namely, all the properties of the
diameters, the parameters, the tangents, etc., the restoration of a
cone on nearly any given data, the description of conic sections through
points, etc.
�-49-
In the course of which, we enunciate the properties which we find therein,
in a more universal manner than usual • . for example, the following:
If
line$ AK and AV in the plane MSQ meet a conic section PKV in P, K, Q, V;
and if from two of these four points which are not in ,the same straight
line with point A, as for example the points K and V, and through two
points N and O, taken on the section, are drawn four straight lines KN,
KO, NV, VO, cutting the lines AV and AP at the pqints L, M,
s,
T:
I say
that the ratio compounded of the ratios of PM to MA, and of AS to SQ is
the same as the ratio compounded of PL to LA, and of AT to TQ • .
We shall demonstrate that if there are three lines DE, DG, DH, which the
lines AP, AR cut at points F, G, H,
the point E, the
r~tio
c,
y, 8, and if in ·oc be determined .
compounded of the ratios of the rectangle EF,fG
to the rectangle EC,Cy, and of the lines AV to AG, is the same as the
ratio compounded of the ratios of the rectangle EF,FG to the rectangle
EC,CB, and of the line AB to AH.
And is also the same as the ratio of
the rectangle FE,FD to the rectangle EC,CD.
Therefore, if through the
points E,D pass a conic section cutting·AH,AB in points P,K,R,t, the
ratio compounded of the ratios of the rectangle Ef,FG to the .rectangle
EC,Cw, and of YA to AG, will be the same as the compound ratio of the
rectangle FK,FP to the rectangle CR,Cw, and of the rectangle AR,Aw to
the rectangle AK,AP.
L
/--- --;-~
/'
/ I/
A "-:.::.._-------~......_
--
8 I
- - -··--- ·-1· ··
I
" ·'\._H
M
N /
/
..
-
\
-r----.. _,_:_- - -..-.\ c
I
/.
I
I
;-......._
I
/
\ ;~-'
/,, . ,
/
~-..,
\
K \/
/\.
,\
· /
.
,/
.
\
. )!
--........._
.............. .........
~
/~/
E
f
.Y
Figure 3
We shall also demonstrate that if four lines AC,AF,EH,EL intersect in
points N,P,m,o, and if a conic section cut these lines in points C,8,f,
D,H,.G,L,K, the ratio compounded of the ratios of rectangle mc,M_ to the
B
rectangle PF,PD, and of the rectangle AD,Af to the rectangle AB,AC is
�-50-
same as
and of the
EH,EG to the
1
is
EK,EL
whose first inventor
We shall also
m
.
minds of our times
one of the
of
of the most versed in
and one
and, among others, the
'
of conics, whose
have
PG
the
ratio of
small in number
on this
witness to those who would wish to inform themselves;
and let me confess that I owe the little that I have found on this matter
to his wr
and that I have tried to imitate, as much as I could
is method in the sub
which he treated without
axial tr
use of the
all conic sections, the marvelous
If in the
there is a
taken
lines KN
four
KO
, VO be taken in such a way that
two lines pass, and if another line cut the section in
, and the lines
the
to the
any one of the
, KO,
YR,
is to the
say that
, , Z B:
,VO in
is
as the
XR,
2
We shall demonstrate also that i f in the
ell
or a circle AGE, whose
the section at A, and i f ' hav
AB be taken
in square to a
and if CB be drawn, and then
to AB,
of a
or an
is C, there be drawn the line AB
drawn the diameter CA, the line
of the
some other line, for
of the
DE,
the section in E, and the lines AC,CB in points D,F:
If
�-51-
the section AGE is an ellipse or a circle, the sum of the squares on DE
and OF will equal the square on AB; and in the hyperbola, the difference
of the squares on DE,Df will equal the square on AB.
We shall deduce also some problems, for example, from a given point to
draw a line touching a given conic section.
To find two conjugate diameters at a given angle.
To find two diameters at a given angle and in a given ratio.
We have several other problems and theorems and several corcllaries of
preceding propositions; but the mistrust I have of my little experience
and capacity does not permit me to bring forward any more until it has
met the scrutiny of some skilled gentlemen who will oblige us in taking
on that task:
after which if they judge that the matter merits being
continued, we shall attempt to carry it as far as God gives us the
strength to take it.
�
Dublin Core
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Title
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The Collegian
Description
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The Collegian began as a student newspaper; became a college community literary publication in 1952 and continued until 1969; became a student newspaper again in 1969; discontinued publication from 1980 until 1989 when it again became a student literary publication.<br /><br />Click on <a title="The Collegian" href="http://digitalarchives.sjc.edu/items/browse?collection=26">Items in The Collegian Collection</a> to view and sort all items in the collection.
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Annapolis, MD
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St. John's College Greenfield Library
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51 pages
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text
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paper
Dublin Core
The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/.
Creator
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Roberts, Susan (Editor)
Title
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The Collegian, June 1966
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1966-06
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Issue of The Collegian. Published in June 1966.
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Collegian June 1966
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Annapolis, MD
Santa Fe, NM
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St. John's College
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English
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pdf
The Collegian
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