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The St. John's Review
Volume XLVI, number one (2000)
Editor
Pamela Kraus
Editorial Board
Eva T H. Brann
James Carey
Beate Ruhm von Oppen
Joe Sachs
John Van Doren
Robert B. ltllliamson
Elliott Zuckerman
Subscriptions and Editorial Assistant
Blakely Phillips
The St. John's Review is published by the Office of the Dean, St. John's
College, Annapolis: Christopher B. Nelson, President; Harvey Flaurnenhaft,
Dean. For those not on the distribution list, subscriptiOns are $15.00 for
three issues, even though the magazine may sometimes appear semiannually
rather than three times a year. Unsolicited essays, stories, poems, and reasoned
letters are welcome. Address correspondence to the Review, St. John's College,
P.O. Box 2800, Annapolis, MD 21404-2800. Back issues are available, at
$5.00 per issue, from the St. John's College Bookstore.
©2001 St. John's College. All rights reserved; reproduction in whole or in
part without permission is prohibited.
ISSN 0277-4720
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��Contents
Essays and Lectures
Plato and the Measure of the Incommensurable
Part One: The Paradigms of Theaetetus ....................................... S
Amirthanayagam David
We Nietzscheans ............................................................................... 45
John Jfrdi
The Power & Glory of Platonic Dialogue................................. 84
Carl Page
The Discovery of Nature ............................................................ .! IS
James Carey
��Plato and the Measure of the
Incommensurable
Amirthanayagam David
Part One
THE PARADIGMS OF THEAETETUS: A fresh interpretation of the geometry lesson (Theaetetus 147c-148b) and its significance for Plato's development*
I find the grounds for a new reconstruction ofTheodorus's geometry lesson (Theaetetus I47c-148B) in the detail of Plato's prose. I shall
first present this reconstruction, and then discuss the significance of
the mathematics involved, both in itself and for the development of
Plato's later philosophy-nothing less than a revolution in his
thought-which is represented by the sequence of dialogues Theaetetus,
Sophist, and Politicus.
Early in the Theaetetus Socrates has already raised the animating
question of the dialogue: what is knowledge? Theaetetus answers by
pointing to different types and objects of koowledge, such as the
things Theodorus koows (geometry) and the koowledge of craftsmen
(I 46c). We did not want to count its sorts and objects, says Socrates
(I 46E), but to find out what "koowledge" itself is. He adds that if one
does not know what the word "day" refers to, if it is a mere name,
there could be no illumination in defining it as oven-maker's clay and
brick-maker's clay. Besides, the simple answer to "What is clay?" would
be earth mixed with water (147c). Perhaps Socrates is asking for an
account that connects a name to a nature. At any rate, Theaetetus
Amirthanayagam David is a tutor at St. John's Coilege, Annapolis.
* Many thanks to Ian Mueller and the members of the Ancient Philosophy Workshop at the
University of Chicago, 1990-91; to Howard Stein, University of Chicago, for a detailed critique;
to the members of the Theaetetus study group at St. John's College, Annapolis, in the spring of
1999, especially Curtis Wilson, Chaninah Maschler, and Joe Macfarland; to Eva Brann; and to
my late teacher, mentor, and friend, Arthur W. H. Adkins.
�THE ST. JOHN'S REVIEW
6
thinks he has just encountered an example of such a thing in the course
of a lesson given by Theodorus, to him and his young friend also
called Socrates. (Theaetetus looks like the famous Socrates; young
Socrates bears his name; there is a third companion and fellow wresder
mentioned (I 44c), who remains an unknown.) What Theaetetus had
done in response to the lesson ofTheodorus was to come up with new
names-or rather, to apply old names in a new way-so as to demarcate for the first time two different kinds of square roots.
Some heretofore neglected particles occur in Theaetetus's description of Theodorus's lesson; here is John McDowell's translation:
El£.: IlEpi: 6vvafl£WV "tL YJflLV El£o0r.opo£ oO£
ifypmp£ "ttJ£ "t£ ,;pGwoo£ n£pL Kai n£v"tinooo£
ano<paivwv ClLL fl'f]KEL
oVflflE"tpOL "tTI
s:_/
...
(./
JtOuLUL<;t, KUL 0'\J"tW KU"tU flLUV EKUO"trJV
/
'
npompO'UflEVO£ flEXPL "trJ£
EJt"taKmOEKanoOo£.
ov
-
'/C./
Theaetetus: Theodorus here was drawing diagrams to
show us something about powers-namely that a
square of three square feet and one of five square feet
aren't commensurable, in respect of length of side,
with a square of one square foot; and so on, selecting
each case individually, up to seventeen square feet.
Note that "powers'' is misleading here. Wilbur Knorr points out
~/
~
/
that u'\JVUflL£ and u'\JVUflEL mean "square " an d "'m square "throughout Greek mathematical literature, including in Hippocrates of Chios,
who was a contemporary of Theodorus and Theaetetus; he shows that
Plato also uses the terms consistendy in this sense, citing the Republic
587D, Timaeus 54B, and Politicus 266B. 1
�DAVID
7
The use of 'tE-KUL in Greek composition signals a grouping by
the writer; the paired elements in this case are 'tTJs; 'tp Gtol\os; (the
square of three feet ) and JtEV'tEJtolios; (the square of five feet). The
balance and symmetry of the formulation, 't'ils; 'tE 1:pGtolios; JtEPL
KUL JtEV'tEJtolios; with JtEPL accented in postposition, seems to suggest a natural balance in flanking elements. I was led to wonder, could
there be something special about this pair of squares in the context of
Theodorus's investigation? Since he takes up each square individually
( Ka'tC't ~-tLav £Kclo-t'Y}V ), is there a reason why these two are paired?
On reading the linking particles with their natural sense, the connecting phrase Ka'L oV'Loo shades into a non sequitur: after proving something about a pair of squares, Theodorus "in this way" selects each
square individually. But if this pair served as paradigms for the later
squares,
a
better sense
can
.
be giVen
to
'
KUL
</
O'U'tOO ...
npoaLp01Jf.LEVos;: once he had proved something about the two paradigm cases, Theodorus could thereby pick out in advance
(npompEOf.LUL) each succeeding case, reducing them one by one to
either of the paradigm cases, up to the seventeen-foot square. This
reading would be consistent with Plato's phrasing: l(ypatj>E ... aJto<pai:vwv governs only the three- and five-foot squares, about which
(nEpL) Theodorus would have formally demonstrated something, and
npompO'Of.LEVos; covers each of the following cases, which he would
have only needed to "piclt our:'
A simpler reading of Kat OU'tW would suggest that Theodorus
covered only the odd number squares: having started with three and
five, he continues this way in order (the series being three, five, seven,
etc.). Certainly, the sense of npompEO[.LUL only demands that there
be some kind of advance selection involved, whether the cases of three
and five formed a paradigmatic basis for the selection or merely established a pattern of successive odd numbers. It may also be that the criterion of selection preceded and included three and five, not as analytic paradigms but simply as first cases; pe<haps Theodorus was pick-
�8
THE ST. JOHN'S REVIEW
ing out individual numbers because they were already known or intuited to have incommensurable roots, and the object of his lesson was to
offer proofs of the fact. On this reading, one would need to explain
why he omitted the case of two. But on this reading as well, and indeed
on any other, one must still ask why three and five should be paired;
and we observe that only in these two cases is there an explicit reference to the giving of proofs.
The next sentence in the passage has caused a lot of trouble, most
recently in the unfriendly debate between Knorr and Miles Burnyeat in
the pages of Isis. 2
~
St"
,
1
EV uE 'tUU't'l']
'
/
ltW<; EVEO?(E'tO.
At that point he somehow got tied up.
The question comes to this: did Theodorus get "tangled up" in the
case of the seventeen-foot square, or did he merely stop (for some reason or no reason) at that one? Inference from the many examples in the
lexicon under EVEXO~UL suggests the former, but Burnyeat, following
Mansfield, argues that instances of this word which mean "get entangled" furnish in context an explicit cause for the difficulty.' Knorr's
reconstruction of the proofs, by means of Pythagorean triangles and
number triples,
... entails the division of the problem into classes of
numbers, represented by the numbers 3, 5, 6, and I?.
Each class requires a treatment differing from the
others. But the method, successful for the former
classes, fails at I 7.'
Burnyeat rejects this reconstruction, and the reading of nw<;
no evidence for the treat-
£vfcrxno that it implies, because he sees
�DAVID
9
ment by classes in the text. My reading would help to supply that evidence: the cases of three and five could be seen as paradigmatic for the
other cases, representing in Knorr's scheme all numbers of the form
(4N+3) and (8N+5).
There is no evidence, however, for treatment by jour classes. The
class of numbers represented by six in Knorr's solution need not have
been part of Theodorus's lesson as it is described in the text; we hear
only of three, odd-number examples (and this may in itself be evidence that Theodorus only covered the odd numbers). It is perhaps a
weakness of Knorr's reconstruction that the number seventeen does
not fall into either of the classes represented by three and five, but is
made to represent a separate class. It is a strength, however, that it
shares this class (8N+ I) with all the odd square numbers (nine, twenty-five, etc.); Knorr suggests that the failure of the method in this case
is what led Theaetetus to a new approach, precisely via the distinction
between square and non-square numbers. 5
There is a serious objection to Knorr's approach, however. His
proofs of root-incommensurability for the classes ( 4N+3) and
(8N+5) do not themselves depend on the proofs for three and five;
the general cases must be proved independently, with a dose of algebraic manipulation. Indeed, if Knorr wants to avoid the worst kind of
anachronism, involving the use of zero, the cases of three and five
(N=O) must be specifically excluded from the proofs. There is no hint
in the text, however, of this kind of generalization. My reading allows
only that the individual, concrete proofs for three and five may have
been the paradigms for the later cases. The generality would in that
case have to be contained in these very proofs.
...
, ,
Knorr argues cogently that 1tcpL <'lVVU[!EOlV "tL ••• cypmj>E means
that Theodorus "proved something [about squares J by means of diagrams;' rather than that he merely drew the squares or that he only
proved something about them. 6 Where moderns are accustomed to
express the generality of arithmetical solutions through algebraic for~/
�10
THE ST. JOHN'S REVIEW
mulae, those Greek mathematicians whose work culminates in Euclid's
Book VII appear to have used geometrical diagrams in this capacity, as
themselves the immediate means to convey the universality of a proposition in arithmetic or number theory. I therefore sought something in
the structure of the possible diagrams for proving incommensurability of the side in the cases of the three- and five-foot square that made
them each essentially paradigmatic. The reconstruction requires successful proofs which suggest through the generality of their diagrams
an applicability to an infinite number of cases, but which appear to
involve a difficulty in the case of the seventeen-foot square.
The solution was surprisingly forthcoming: it requires but two
simple theorems, one for each paradigm case, which fall out from the
Pythagorean dot-arithmetic (also reconstructed in our time, with considerable elegance, by Knorr); and it satisfies all interpretations of the
activity implied by ypa<jlELv. In fact, each of Knorr's own criteria for
a reconstruction of the lesson' is met most elegantly by this method.
I constructed the roots by using pairs of successive integers, following Malcolm Brown's lead.' When each of these pairs-{I,2},
{2,3 }, {3,4 }, etc.-is taken as leg and hypotenuse of a right triangle,
the desired sequence of squares, equal to the sequence of odd numbers, is produced on the remaining legs:
1
4
9
�DAVID
11
The odd numbers therefore form a kind of natural sequence in
their square representations: they can be understood as the first "offspring" in two dimensions of the natural numbers in one, when these
are successively "mated" by means of right triangles. The objection
that the text seems to say that Theodorus proved something about
squares in general-and hence an assumption in reconstructions that
he covered the case of six and a puzzle as to why he left out two-can
be met by considering that in the context of a Pythagorean geometrical arithmetic, the odds beginning with three form a distinct and natural genetic grouping among the square versions of numbers. The text
bears without strain the sense of a movement &om general to specific.
Theodorus proved something about squares: namely, about that natural
sequence of squares which begins with three and five, that they are each
incommensurable with the unit length. Moreover, the allusive quality
of the description would suit an association with a well-known
Pythagorean construction such as the one drawn above.
The three-foot and five-foot squares are the first two constructed
by means of these pairs of the natural numbers. The form of proof is
reduction to absurdity. Take the first case: the side of the three-foot
square (or the "three-foot side") must be either commensurable or
incommensurable with the side of the unit square (or unit side").
11
Assume it commensurable. Then there exists some ratio of numbers,
A:B, between the three-foot side and the unit side. Take this ratio in its
lowest terms; then either A is odd and B is even, or B is odd and A is
even, or both are odd. But the hypotenuse is even:
B
�12
THE ST. JOHN'S REVIEW
Therefore both A and B must be even (by Knorr's Theorem V.I4
about Pythagorean triples ).9 Hence either A or B or both must be odd
and even simultaneously, which is an impossible situation for a number. The three-foot side and the unit side cannot, therefore, have the
ratio of a number to a number, and they are incommensurable. 10
The generalization immediately follows &om the diagram: all of
the roots constructed by a triangle with an even hypotenuse-i.e., constructed byrhe pairs {I,2}, {3,4}, {5,6}, {7.8}, etc. yieldingv3, v7,
VII, VIS, etc, on the remaining legs--generate the same paradox (that
a number must be simultaneously odd and even) if they are assumed
to be commensurable with the unit side. Each of these triangles has the
following paradigmatic form in the diagram drawn in the course of the
proo£ on the assumption that there is some numerical ratio A:B
between the root and the unit:
A~<B
oddx B
The five-foot square, constructed by means of a triangle with an
odd hypotenuse, presents the only alternative paradigm produced by
these numerical pairs:
2
t~-·
evenx B
�DAVID
13
The right-hand figure represents the numerical relations between
the sides of the triangles in the proofs for all the cases involving an odd
hypotenuse-i.e., those triangles built with the pairs {2,3}, { 4,5},
{ 6,7}, etc., yielding v5, v9, VI3, etc. on the remaining legs. In each
case, assume that the particular root is commensurable with the unit.
Then it has a ratio of a number to a number with the unit side, A: B.
In lowest terms, one or both of these numbers is odd. If B is even, the
hypotenuse is even, and so A would also be even, as before; hence B
must be odd. Then A must also be odd, since it is a given that the other
leg is even; if A were even, the two even squares on the legs would
equal the odd square on the hypotenuse, which is impossible. But if A
is odd, the square on the remaining leg must be equal to a difference
of odd squares. This could only be true if it were a multiple of eigbt. 11 A square
that is a multiple of eight is also a multiple of sixteen. It must therefore have a side that is a multiple of four. Since B is odd, this side is
equal to a rectangular number, (even) x (odd), and the (even) side must
itself be a multiple of four, if the whole number is also to be a multiple of four. We must therefore pick out and examine each of the relevant cases in turn, to see if the even member of the number-pairs is
a multiple of four. If not, the condition is not met, A can be neither
odd nor even, and there can be no ratio of numbers A:B such that the
respective side is commensurable with the unit side. In the case of
{2,3} and the five-foot square, for example, we find the condition
unmet, since two is not a multiple of four: the five-foot side is therefore proved incommensurable with the unit side. In the next case-the
nine-foot square constructed by the pair {4,5}-the condition is in
fact met, and the nine-foot side (i.e., three) happens to be commensurable. Meanwhile, the side of the thirteen-foot square, constructed by
the pair { 6, 7}, is proved incommensurable, for six is not a multiple of
four.
This establishes the paradigmatic nature of the two proofs and
their diagrams. The cases of three and five involve the only two kinds
�14
THE ST. JOHN'S REVIEW
of triangle produced by the constructiog number-pairs: those with an
even hypotenuse and those with an odd. For the former diagram we
must invoke the theorem that if the hypotenuse is even, both legs of a
numerical right triangle are also even; for the latter, that a difference of
squared odd numbers is always a multiple of eight. (These theorems
are easily demonstrated by means of dot-arithmetic.) The assumption
io each case that the constructed side is commensurable with the unit
side-that it has the ratio of a number to a number with the unit
side-leads to the violation of an underlyiog principle: in the threefoot case that a number cannot be both even and odd; io the five-foot
case that a number cannot be neither even nor odd.
But when we come to the case of the seventeen-foot squarewhich in this reconstruction does not constitute a separate paradigm,
but is an example of the construction iovolving a triangle with an odd
hypotenuse-the method appears to fail:
8B
8
Because eight is manifestly a multiple of four, we cannot prove, by
means of the second of our paradigm proofs, that the root of the seventeen-foot square is iocommensurable with the unit. This represents
a distinct entanglement,
Theaetetus next says, in McDowell's translation,
C..vJ_1,..,
,._)I
'I'][!LV O'UV ELO't']A{}i 'tL 'tOLO'tJ'toV, EltELC\'1']
lmetpot
.,
,
,;o nA.ip'Jos; ai C\uvaf!ets;
...
-
,.
C./
EqJULVOV'tO, rtELpa8'1'jVUL 01JAAa~ELV ELs; EV,
�DAVID
15
t.f
1
I
O't<{l naaa<; ,;av'ta<;
,
'
npooayonE'UOO[-IEV 'tU<; 1\'UVU[-IEL<;.
Well, since the powers seemed to be unlimited in
number, it occurred to us to do something on these
lines: to try to collect the powers under one term by
which we could refer to them all.
The o'iJv in the first line, however, is most naturally taken as continuative! and not as some kind of ambiguous disjunctive. Here is my
paraphrase of the above sentence, filled out to show how it follows on
the peculiar problem brought on by the case of the seventeen-foot
square:
Then [in our difficultyJ something of this sort
occurred to us: since the squares [equal to odd numbers which have incommensurable sidesJ were appearing to be unlimited in multitude, to attempt to collect them under one term, by which we shall in future
call all such squares [thereby distinguishing them
from squares equal to odd numbers which do have
commensurable sides].
It must be remembered that the seventeen-foot square foiled our
technique by behaving like the square of an odd number (e.g., nine), a
number with a rational root: the square on the even leg of its proof
diagram was a multiple of eight. It is therefore natural that the idea for
a new start, which occurs to Theaetetus in his perplexity over the
breakdown of Theodorus's method, involves first distinguishing
between those odd numbers with a rational and those with an irrational root (later classified as types, respectively, of square and oblong
number).
�16
THE ST. JOHN'S REVIEW
Several kinds of interpretation of the passage must fall by the wayside. Theodorus's "lesson" is not a pedagogical exercise, where the
answers are already known and the cases selected for display. Nor is the
episode included by Plato merely to make historical concessions (however vague or however specific) to the achievements of Theaetetus and
his instructor. Theodorus's was a genuine investigation, which lighted
on a genuine perplexity; Theaetetus's new definitions, which keyed his
fUture researches, grew out of an attempt to resolve this perplexity.
We may now reconstruct Theaetetus's reasoning in full. Two
aspects of Theodorus's technique break down in the seventeen-foot
case, The first is the principle, which underlies the preceding proofs,
that a number must be either even or odd. In this case the principle
leads to no absurdity; indeed, the proof presents no obstacle to the
idea that the side of the seventeen-foot square is a normal odd number(!). The fUndamental Pythagorean clivision among numbers by even
and odd, which in a sense characterizes the UpL{}[.lbc; concept-the
"even and odd" is sometimes used as a synonym for apL{}[.loc; in
Plato-proves to be of limited utility in the study of incommensurable lengths. Theaetetus must look for a new fundamental characteristic of number in which to ground the investigation of incommensurability. The second breakdown occurs in Theodorus's method of construction. Each of the odd numbers is figured as a square. This is possible because every odd number equals a difference of consecutive
square numbers (in Pythagorean tenus, the odd numbers are the series
of gnomons which produce one square number from another). Our
method for generating the odd squares, by constructing right triangles
with pairs of consecutive integers (producing consecutive square numbers on the hypotenuse and remaining leg), works for this reason, But
when all the odds are figured as squares, one cannot make out the perfect, rational-sided squares among them (like nine, twenty-five, etc.)
from the rest. The method points this up by failing to distinguish
between such perfect squares and cases like seventeen.
�DAVID
17
Theaetetus tackles both problems in one deft move. He makes a
fresh division of all number (,;Clv apLElf!OV nav,;a) which will now
isolate perfect squares from the rest, in place of the distinction by even
and odd. If my interpretation is correct, an entanglement in a demonstration based on a geometrical representation of odd numbers by
Theodorus has led to a geometrical distinction amongst all numbers
by Theaetetus. The new name he was seeking for the odd squares
whose sides are incommensurable is "promecic;' or oblong; which is to
say, they are no longer thought of as squares at all. This category
includes, of course, many even numbers as well, and the new generality is marked by Theaetetus: three and five and na<; o<; al\uva,;o<;
>/
,
/
·""~·
.
LaO<; 'LOUKL<; YEVEOuuL, " every num b er wh'lCh ts una bl e to b e generated as equal-times-equal;' belongs to the new class (I48A). The
even-odd distinction belonged to number as such; the new one arises
from a geometrical interpretation of number. But the whole problem
of incommensurability arises in the interface between number and
magnitude: hence the new definitions might be expected to suggest
new solutions in this difficult domain.
Theaetetus for the first time exploits the breakdown of the geometrical analogy so that it becomes heuristic: whereas in geometry,
every rectangle can be reduced to a square of equal size, whose length
of side is the geometric mean in relation to the sides of the rectangle,
a promecic number cannot be reduced to a square number. The side of
the square which equals a promecic number becomes the new referent,
in Theaetetus's scheme, for the word 1\VVUf!L<;;, it is described by
"
Theaetetus as incommensurable with a f!T]KO<;, his name for the side
of a true square number. The geometrical analogy allows this
1\uvUf!L<; to be conceived of as the irrational geometric mean between
the rational factors of an oblong number.
Theaetetus first describes the promecic number, in relation to the
square number, as 't0v 'toLvuv f!E'ta¥;U 'tOU'toU, "the number which
is in between it:' (I47E) On the level of plane numbers, this makes
�18
THE ST. JOHN'S REVIEW
sense; oblong numbers (2, 3, 5, 6, 7, etc.) are scattered in between the
square numbers (4, 9, 16, etc.). On the level of the associated lines,
however, this description becomes far more interesting. The
llvv6.f.lEL£ lies between the f.l~K'I] as geometric means which bring
them into relation. The unifjring power of the mean proportional is
one of its seminal virtues. Theaetetus's achievement is to conceive of
the irrational roots for the first time as mean proportionals. This
allows them to be seen no longer as perplexing and intractable, but as
types of beings that in fact unite all number-no longer stumbling
blocks to number theory, but the essential intermediaries that relate
I
numbers to each other. To describe both the f.l'I]KO£ and the ll'UVctf.tL£
~
as sides of squares is so emphasize their nature as mean proportionals:
a f.lTJKO£ is the rational geometric mean between the unit and a square
number; the 1\uvctf.tL£ is the irrational geometric mean between two
I
'
f.l'I]K'I], the ratwnal factors of an oblong number.
What was once unutterable and unreckonable can now give an
account of itself: a 6-Dva~-tLI;, lying . . in between," is commensurable
with f.t{]Kos; in square only. So successful was this account that such a
line, commensurable in square, is henceforward called p'l]'tO£ in the
ancient world, 12 though it is still irrational in modern terms.
Theaetetus's new definitions allow these kinds of irrational lines to be
seen not as the opposite of what is rational or utterable ( ct-'Aoyct or
.,
ctp-p'l]'tct), but only as "other;' different in kind. This classification
ofTheaetetus's may well be the specific paradigm for Plato's solution
to the Parmenides problem (see Sophist 257B f£). Not-being is not the
>
I
opposite ( EVctV'tLOV) of being, says the Eleatic stranger, but what is
, oth er, E'tEpov m reratton to b emg; moreover, t h e nature o f t he
·
·
other is proved to exist and "to be chopped up in small bits distributed over all beings in their relations to one another" (Kct'tctKEKEp~
~ \
,
I
ll
II'
f.lGt'tLOf.lEV'I]V £1tL 1tctV'tct 'tct OV'tct 1tp0£ ctAA'I]Act, 258D-E).
Behind the metaphor lies a mathematical paradigm: Theaetetus has
distributed the not-rational amongst all number (1:ov apt{h!ov
c''
)·
�DAVID
19
Jtdvt:a ). as the geometric means which define the relationships
between numbers.
The notion of the heuristic paradigm takes on a central
significance for Plato in the Politicus. It informs a new conception of
philosophical inquiry.~' One is to approach the unfamiliar and
unknown by placing it alongside the known and the familiar, so that
elements (G'tOL)(fLa) and combinations (G'VAAaf:laL) in the latter
become paradigmatic for possible ways of interpreting the former. The
whole analysis of weaving in that dialogue is meant to serve as an
instructive paradigm for the analysis of the statesman. Theaetetus's
classifications demonstrate this method. By bringing alongside something familiar from geometry-the reducibility of rectangles to equal
squares via the geometric mean-he is able to discern a new
classification of all number, one which elegantly circumscribes the irrational. The "paradigmatic method" is to characterize his future
researches as well. The commentator to Euclid's Book X (thought to
be Pappus implies that Theaetetus took the arithmetic, harmonic, and
geometric means, all of them now considered rational, as models for
three new, profoundly irrational lines, the binomial, apotome, and
medial. 14 At the end of Book X (Prop. I I 5), the last of these is then
shown to define a further, infinite class of irrational lines. At each
stage. the unfamiliar is made known by means of the familiar; the
appr]l:OV is analyzed and combined in terms of the elements and syl' '
!abies of the pr]l:Ov. At Theaetetus 202B, Socrates describes a dream
which teaches him that elements are af,oya, while combinations are
pr]1:d'L. It is therefore fitting that Theaetetus's act of combination
(G'VAAaf:ICLV EL<; EV, 147E), based on a geometrical paradigm, renders its object prrc:6v. The Eleatic stranger intends, at Politicus 278E,
that this kind of inquiry by means of paradigms may bring us to a
•
.
'"
t
"
state of wakmg, mstead of a dream (uJtap avt' ovupa·toc:;).
*
*
*
*
*
*
*
�20
THE ST. JOHN'S REVIEW
The peculiar nature of the irrational geometric mean between
rational factors, Theaetetus's 1\vvcqw;, may well have served as the
paradigmatic inspiration for Plato's new solutions to the Parmenidean
and Protagorean paradoxes. This will become clearer as we examine the
peculiar ontological and epistemological characteristics of this
1\uvaf.tL£.
With regard to its ontology, viewed from the geometrical standpoint, the irrational mean offers no intrinsic difficulties; it is a stable
entity, a side of the square equal to a given rectangle, easily and elegantly constructed inside a circle.!' But with regard to the way it comes
to be known-the way it comes to be measured, from the arithmetical
standpoint-it turns into a very shifty thing. To measure a liuVUf.tL£,
we have to make a promecic number more and more square, so that its
rational factors (f.tllK1'J) come to approximate the root. We do this by
interpolating arithmetic and harmonic means between the two factors.16 It can be shown (as by ProclusY' that for any two factors A and
B, the harmonic mean C and the arithmetic mean D stand in this relation:
A:C::D:B
This means that the rectangle AB equals the rectangle CD. Since
AB is our oblong number, CD is an alternative representation of it. If
one then interpolates two new means between C and D, and continues
the process, one generates pairs of factors of the same number that
become more and more equal, which give successively closer rational
approximations to the geometric mean from above and below. Note
that however many means one interpolates, the rational factors remain
unequal, and oblong numbers never actually become squares. As
Theaetetus describes an oblong number, "a greater and a lesser side
always contain it:' (I48A) Brown argues, following Toeplitz, that the
use of "always" (O.c() is significant here in its technical sense (i.e., that
of Euclid's X. I and X.2), and implies the application of a continued
process. 18 (This technical" sense is in any case rooted in the everyday
11
�DAVID
21
usage of this adverb, whose sense is both distributive with respect to
instances of the subject, and frequentative with respect to the verb.)
The text may be seen to allude to the continued process of interpolations described above, and to the fact that it can never yield equal sides
for a rectangular number. The geometric mean stays in between: while
A: X:: X: B, so also is C: X:: X: 0, and C': X:: X: 0'.
The interpolated means "trap" the buvaru~ length within an
arbitrarily small interval. Each successive interpolation divides the previous interval between the rational factors by more than half: the new
arithmetic mean cutes off exactly half from above, and the new harmonic mean some more from below. By Euclid's X.I-a central theorem in applying the method of reciprocal measurement,
&vtlvcpa(pEOL~, which is associated with the mature Theaetetus-it
follows that the interval between the successive pairs of arithmetic and
harmonic means can be made to shrink smaller than any given magnitude. It is not only this interval that evanesces, but also the difference
between the geometric mean and each of the other two means respectively. This means that the difference between the true length of the
geometric mean and each of its under- and over- estimates is evanescent, and there is a strong inducement to see the irrational mean itself
as characterized by the narrowing oscillation of its extremes. This is
not a nai've interpretation of the measuring process: in the case of a
rational geometric mean, or [.lflKO~, there is a number inside the interval which the estimates approach; but in the irrational case, there
appears to be no normal numerical entity involved, and we do not
know how exactly the mean behaves inside the decreasing rational
interval which defines it. We only know that at each stage, it lies in
between the harmonic and the arithmetic estimates, while approaching
each of them in turn to less than any given difference.
There is evidence in the Epinomis that an irrational geometric mean
was thought of as oscillating between the arithmetic and harmonic
ones (see 99 lA-B). In a passage which extols. the ubiquity and power of
�22
THE ST. JOHN'S REVIEW
'tO bLltAdOLOV; "the double," in proportions, the Athenian stranger
turns to the means associated with this interval. He gives standard
definitions of the pair of rational means (amounting to the fact that
the arithmetical is equidistant from its extremes, and the harmonic
differs from its extremes by the same proportional part of eath one);
he then points out that in the interval between six and twelve, they are
'
., /
.
called the 'Y]~WALOV and the EltL'tpL'l:OV. He adds that m between
these same ones (to{rtOJV a{nffiv f.v 'tClJ !J.EOq:>) is a proportion
that has been given to the dance of the Muses, "which turns itself
about to one or the other of these two" (en:' a~cpO'tEpa O'tpE,/
'
cj>O~EV'YJ).
We first observe that the a'pLflWJ<; concept involved not just concrete assemblages, but also urepetition" numbers (i.e. &~£, 'tpL£, etc.). 19
Therefore if we investigate any example of doubleness, or utwice;' we
are just as specifically studying "the two" as when in studying a particular isosceles triangle, we can prove things about all isosceles triangles qua isosceles. The interval I2:6 is an example of 2:I, of 'tO
biJtAdOLOV bLdO't'Y]~U or the "double interval." 20 The practical
advantage of studying higher multiples of a given interval is that the
rational means can be interpolated without fractioning the unit. In the
interval I2:6, the arithmetic and harmonic means are nine and eight
respectively; hence the stranger describes their ratios with the lower
t..
/
)
/'
extreme as the 'Y]~LOALOV (9:6 reduces to 3:2) and the Em'tpL'tOV
(because 8:6 reduces to 4:3). If we then interpret the object which
turns itself about Elt' a~cp6'tEpa as the oscillating geometric mean
between the two rational means, the other phrase describing it
(mv'n.ov atl'tWV EV 'tt\) ~f'mp) becomes explicable; for we recall
that this object is not only the geometric mean in the interval I2:6, but
also in the interval 9:8, defined by the pair of rational means (the referents of 't01J'tWV atm:ov) inside I2:6. Since the division between
nine and eight happens also to represent a division in the seventeen
steps of the epic hexameter, the dance of the Muses, the writer draws
�DAVID
23
a connection between the dynamic geometric mean in the double
interval and the turning point in the dance.
At Parmenides 129B, a young Socrates asserts that "if someone
proved that similar things in themselves ( atna
O[!OLa) became
' /
dissimilar ( UVO[!OLa), or the dissimilar similar, that would, I think,
be a portent:' Theaetetus's lluva[!L~ is the portent made manifest:
insofar as it i~,the length of a square, the one which equals an oblong
number, it is O[!OLOV; but insofar as it is approximated to the point of
identity by unequal rational factors, it is forever UVO[!OLOV.
<
/
O[!OLWOL~ is the principle Theaetetus has applied to number; in the
new arithmetic, one makes unlike" ( &.vO~oLOL) promecic numbers
more and more square, or "like" ( O~OLOL). The upshot is that arithmetic becomes conceived of as a kind of geometry, and indeed, by the
time of the Epinomis, the entire activity of geometry is characterized as
the "making like" of numbers that are by nature unlike. (Epinomis,
990d) The Athenian stranger is led to describe this numerical geometry as a wonder, of divine and not human origin. Perhaps he is think'
ing about the 1\uva[!L~, the portent which it seeks to generate.
I earlier suggested that the relation of the 1\vva[!L~ to all number
stood in direct analogy with the nature of the "other" to all being.
This "other" was the basis for Plato's new conception of not-being; he
was concerned to show both that it exists and that it is distributed over
all being in its inter-relationships (Sophist 258D-E). This second characteristic seems clearly to implicate the &6va[!L~ as a paradigm; but
does Plato ever try to demonstrate its existence) If this object, like and
unlike, at rest and oscillating, is to be the object-paradigm which
recasts all the hoary debates and turns them on their heads, he must
have been at pains to show that it actually exists.
A key passage in the Politicus answers this expectation. The Eleatic
stranger highlights its importance by pointedly referring to the pivotal
argument in the Sophist about not-being: just as there the hunt for the
sophist was saved by the argument that not-being exists,
1:a
11
�THE ST. JOHN'S REVIEW
24
1.1
'
"'
'-
I
""
'
11.
OU'tW KaL VUV 'tO 1ti-.EOV au KaL el-.aTIOV
f.lE'tprJ1:a npooavayKame'ov yL'yveo8m f.l-.1
' ,, ' ' ,
J' ' ' ' ' ' r.
1tp0£ a~~,~~,'Y]~~,a f.lOVOV a~~,~~,a KaL 1tp0£ 't'Y]V 'tOU
I
I
,/
'
s._' S..
I
)/
f.lE'tpLOu yevemv; ou yap u'Y] uuva,;ov ye OU'tE
').
...
:1
)/i ').
...
.....
...
..
1t011,L'tLKOV OU't' a~~,~~,oy 'tLVa 'tWV 1tEpL 'ta£
npasEL£ fmO'ti](.lOVa Uf.l<jlLO~'Y]'trl'tW£ yeyovE/
'
,
VaL 'tOU'tOU f.l'Y] SUVOf.lOI-.Oy'Y]8EV'tO£.
(Politicus, 284B-C)
so also now, are we not compelled to say that the
greater and the less come to be measured not only
against one another, but also toward the generation of
the mean? For it is impossible at any rate, that either
the statesman, or any one else who has knowledge
about practical affairs, should indisputably come to
exist, if this is not agreed on.
Politics, practical undertakings, and works of art direct themselves
to what is fitting ('to f.lE'tpLov). If such a thing cannot be proven to
exist, the possibility of 'tt:XV'Y] itself comes into question. The stranger
proposes a new division of the science of measurement (f.lE'tp'Y]'tLK~
283o ). The first part involves measurement of greater against less; this
would determine relative excess or deficiency, and, presumably, whether
or not there was a common measure (by the technique of
&v8ucpciLpeOL£). The second part involves measurement towards a
.J
'
/
J
I
,...
mean separated from extremes ( EL£ 'tO f.lEOOV a1to;!KL08'Y] 'tWV
ioz6.,;wv, 284E); and it is likely that the geometric mean, the mean
proportional, is especially meant. Since this mean is the one which
squares the greater-by-less, bringing extremes into balance and making
the lxvof.lOLOV O'f.lOLOV, it must be the one whose preservation brings
beauty to works of art (284A-B); the famous "golden" mean is a
species of geometric mean. The method of interpolating pairs of
rational means as greater and lesser approximations of the geometric
mean admirably suits the terms of Plato's description:
�DAVID
25
,. /
..,
')'
""
.
flELl;;ov 'tE ct[lct Km EAct't'tov flE'tPELOfuL l-11']
' ~~'\ ").
,
' '
...
1tp0£ ct11.A1']11.ct [-!OVOV, ctf..f..ct Km
...,.
'
,....
I
I
npo£ 't'I']V 't01J flE'tpwu yEvEmv. (284D)
The greater-and-less are at the same time measured
not only against each other, but also toward the generation of the fitting.
Note that "greater-and-less" are paired off by 'tE-KctL, and that
they are to be measured "toward the generation" (y{vEOL£) of the
mean. At each stage of the interpolations, one is not comparing the
extremes with each other to find their common measure or their relative excess or deficiency, but one is manipulating the pair of extremes
to generate a number in between them. Take the case of B less than A,
for example; one does not subtract B fi:om A to find their difference,
but rather one adds the pair together and halves the result, generating
the arithmetic mean (D). (In the case of the double, 12:6, we get D
(12 + 6)/2 18/2 9.) Then one multiplies the pair together and
divides the result by the arithmetic mean, to produce the harmonic
mean C. (C (12•6 )/D 72/9 8.) C and D then become the
new pair of greater-and-less (D' (C + D)/2 (9 + 8)/2 17/2
8 I/2; C
(C•D)/D' (9•8)/(17/2) 72/(17 /2) 144/17
8 8/17). Notice how the product of eachpair({C,D}, {C',D'})
remains the same (72) and how quickly the interpolations converge
(the difference between C and D' is already only 1/34th part of the
unit). The whole process is continually generating the [-IE'tpwv, the
geometric mean which runs in the middle of them all (flE'tct!;u) and
=
=
=
=
=
=
=
=
=
=
unites the series of pairs into one
=
=
=
=
=
(cruf....A.af3el.v E~~ £~).
But if the mean is never reached, can it be shown to exist? The
proof would appear to depend on the ontological interdependence of
the arts, the [-!E'tp{ov, and the pairs of greater-and-less. The stranger
�THE ST. JOHN'S REVIEW
26
declares that we must suppose both that the arts exist, and that the
greater-and-less are measured toward the generation of the mean:
,,
'
/
,
,
....
/
'tOU'WV 'tE yap OV'tO<; EKELVU EO'tL, KUKELVWV
)/
' ..... 21
OVOWV EO'tL KUL 'tUU'ta, [.1.1']
'
' ,..
'-U
I
I
I/
'""'
liE OV'tO<; JtO'tEpOV 't01J'tWV OVIiE'tEpOV U1J'tWV
,,
'
EO'taL JtO'tE.
(284D).
For if this [the mean J exists, those [the greater-andlessJ exist, and if those arts exist, these [the greaterand-lessJ also exist, but if one of them [the mean or
the arts J does not exist, neither of this pair [the
greater nor the less J ever will.
The passage is admittedly very difficult, in text and translation,
because of a possible ambiguity as to the referents of the correlated
demonstratives; but it seems clear that an existence proof is at issue.
That the greater and the less exist, no one would dispute. But if we
deny the existence of either the [.LE'tpLOV, or the arts, each by means
of which the greater-and-less are made known and defined, we run the
risk of denying existence of this pair of fundamental opposites. Hence
we accept, provisionally at least (284D), the existence of the mean. The
greater-and-less measured against one another discover a common
measure or the unit-Plato's paradigm, perhaps, for that which is.
Measured toward the generation of the mean, they discover a measure
in between the greater and the less, which still is greater-and-less; a
measure that is always coming to be, in the relations between things
that are. In this relational mode of being, Plato has his paradigm for
the "other;' and a beachhead against Parmenidean ontology.
*
*
*
*
*
*
*
�DAVID
27
Plato's answer to the Protagorean conundrums on flux is also based
on this new branch of f,I,E'tPYJ'tLK~, measurement toward the y€vEGL<;
of the mean. At Sophist 24 7D-E, the stranger sets it down as a provisional solution to their paradoxes, that whatever possesses a power
(6-tiva[,!,L<;) to act or be acted upon, even only once, is truly existent,
and then formally defines beings (t:a OVTU) as OUK a'A'Ao 'tL JtA~V
OVVU[,!,L<;, nothing else than OUVU[,!,L<;. It is highly unlikely that such
a word could be both novelly and proximately applied by Plato without some sort of cross-reference.
'
This answer, that being is O'UVU[,!,L<;, comes after the stranger has
cornered these thinkers into admitting that the incorporeal exists in
some way. The "flux theorists" have then to say what being is, in a way
that covers both the corporeal and the incorporeal (247D). I must
therefore show how Theaetetus's OUVU[,!,L<; is a saving answer on both
these levels. Let us turn to the Theaetetus, where a Protagorean theeory
of sensation based on mutual measurement gets a thorough setting out
by Socrates, and where once again the non-corporeal is required to
exist.
Brown has led the way, by showing that Socrates's version of the
Protagorean theory of sensation is modeled on the continued process
of interpolation to approximate the geometric mean.22 The odd
expressions in this passage of text become happily explicable on these
terms. Here are some of Brown's list of correlations: uthe object
sought is ... an 'in-between' (f,I,E"ta1;u n) (I54A), which ... is to be identified by a process of 'measuring and being measured' (n:apaf,I,E'tp01lf,I,E8a ...n:apa[,i,E'tpou[,i,EVOV) (I54B)"; "the object determined 'is nothing in itself, but is becoming for someone always'
Is;.\
'1'
l\
J
'
I
e. /
) '\"'.'
) \
,
8 )
( O'UuEV ELVUL EV av,;o Ka8 av"to, a~~.~~.a 'tLVL UEL YLYVEG aL
(I 57A-B; cf. I53E)"; and "the intermediate stages of the process are
'infinite in number, but paired off' (n:'A~8EL [,i,EV UJtELpa, o[O'U[,i,U
OE) (I56A-B):' In this last passage we can add some very telling details:
it is out of the coming together and rubbing against one another
�28
THE ST. JOHN'S REVIEW
'
,
'
/
'
v
(OfA.LALa<; 't£ Km 'tpLljJEW<; npo<; aA.A.T]A.a) of that which has the
power (lluvaru<;) to act, and that which has the power to undergo,
that the infinite, twinned offspring come; these paired offspring, the
sensed thing and the sensation of it, are "forever falling out together
.
'
'
') .
an db emg generate d"('' 01JVEK1tLJt'tOUOU KUL YEVVW!lEVT]For
UEL
O.eL O'UVEKn'Grcouaa, we could as well pave rendered: heing interpolated together, in a continued process:' The notion that an object of
sense and a sensation are mutually measured, and that they are infinite,
paired-off interpolations, can hardly belong to any "common sense"
11
theory of sensation; Brown can produce a concrete, mathematical anal-
ogy which could have motivated this otherwise bizarre formulation.
The key to this analogy is that Socrates's Protagoreans explain the
phenomenon of sensation as one of mutual measurement of object
and percipient. This way of thinking, by the old version of
!lE'tp'f]'tLKi], leads to their positions on the ultimate relativity of experience; measurement n:pot;
'
'"
af...A.'Y]Aa generates a common measure or
unit, but since each percipient and the entire world of sense are in constant flux, and their interaction with one another changes them both,
this unit is redefined by each sense event. Unity in sense-experience is
therefore dependent on the particular state of a human being at a particular time; man is the measure of all things. Plato's solution is to
apply the new theory of measurement: he accepts the premise of
mutual measurement in sensation, but he can now generate a kind of
unity that is independent of subject and object, at the same time that
it embraces them, To call the opposed poles of measurement
lluva!lEL<; (156A) is to signal their relation, not to each other, but as
first approximations of the mean proportional which defines and
unites them both. One has not done away with flux by any means;
Socrates ill and Socrates healthy each define different intervals with the
same wine, so that the series of interpolated means are also different
(yielding the sensation of sweetness in one case and bitterness in the
other, 159c-E). But one has analyzed sense phenomena in a way that
�DAVID
29
reveals unique classes within them; the geometric means define infinite
series of correlated sense experiences. The point of defining being as
liuvarw;, the capacity to act or be acted upon, even only once, is to
show that even the most random and isolated phenomenon, occurring
once to a single percipient, in and of itself defines an infinite class
through the mean it generates. The upshot is, Brown observes, that
"the flux of phenomena may after all be 'saved' for knowledge." 23 The
ingenuity of the approach is that the very fact which made such experience seem intractable for science, that the
11
tubbing" of perceived
object against percipient observer changes them both, is now made the
essential condition for generating unity in phenomena (represented by
the geometric mean) via a continued process. This is the same ingenu-
ity that Theaetetus displayed when he solved the problem of incommensurability by newly exploiting the relation between geometrical
figures and numbers, which had created the trouble in the first place.
The need to admit the existence of the incorporeal is demonstrated by the need for some faculty within us to account for our ability to
compare data, to recognize what is common to all and to categorize
experience in terms of the philosophical oppositions (i.e., being and
not-being, like and unlike, etc.). 24 Theaetetus is convinced that this is
done by the soul, and cannot be done by any one of the bodily sense
organs; for which he is called "beautiful" (KaAO£) by Socrates (185DE). If this faculty can compare sense data from different organs, then
its work consists in comparing means, which are expressed as ratios in
terms of their respective extremes (like the ~[J-UJAWV and lm:('tpt'tOV
in the Epinomis passage, 991B). Therefore this faculty compares ratios,
and its activity must be the calculation of proportions ( avaA.oy(snv). As strained as this might sound, Socrates' choice of words
\:>ears out the analogy: the word used to describe this faculty's ability is
auA.A.oytO[J-0£ (186D) ; the verb which characterizes its activity is
&vaA.oyfso[J-m (186A) and the products of its work are 'b.va.A.oyLO[J-a'ta (186c) . The theory of sensation had entailed that the
�THE ST. JOHN'S REVIEW
30
objects of sense be commensurable with their proper sense organ
(sU[t[tE'tpov, I56D). But one cannot hear through sight or see
through hearing (I84E-I85A). Therefore the faculty which has to
compare and to
u
square" the data from different sense organs, must
deal with problems of incommensurability. We have already seen how
Theaetetus's lluva[ttt; has helped to facilitate such studies,
The answer that being is llvva[ttt; is therefore shown to resolve
both the corporal and incorporeal aspects of flux theory as Socrates
presents them-in suth a way as to gather them into one account-if
an explicit reference is taken to Theaetetus's lluva[ttt;, and the new
branch of measurement science. Sense phenomena can then be shown
to have a ratio (ii"J(ELV A.oyov). because object and sense organ generate a mean, and the percipient soul becomes a kind of A.oytatLKOt; or
J.lE'tP11'tlK6; (uratio-" or umeasure-calculator") , because the new
techniques allow for the handling of incommensurability.
Clearly, the aims of Plato's application of measurement theory to
sense perception are not the same as those of modern science. No
actual measurements are generated, for example. (The whole thing
turns a bit silly if numbers are plugged in.) Plato's aim might rather
have been, in the spirit of ancient astronomy, to u save the appear11
ances:' As I understand this notion, it does not mean to reduce the
appearances to measurement!' To save the appearances is, in Brown's
phrase, to "save" phenomena for knowledge, by supplying a rational
construct in the form of a mathematical model that could account for,
or at least correspond to, the perceived data, This is the kernel of a
paradigmatic method. There is no necessary entailment of a claim that
the model has a causal relationship to the appearances, or that it represents the physical reality standing "behind" the appearances; it has
rather the free, associative illumination of a paradigm. This was true
even for Ptolemaic astronomy, where the principle of uniform circular
motion did eventually generate accurarely predictive models for the
perceived non-uniform orbits in the heavens. This achievement in
�DAVID
31
astronomy of predictive correspondence between hypotheses and phenomena set a standard thereafter for the saving of appearances. In
Plato's time, however, Eudoxus devised astronomical models which
could not have been accurately predictive; yet they could still have been
seen to u save" the appearances, in that such salvation might have been
seen to come through the ascent itsel£ from the spangled particularity
of sensual observation to the realm of the mathematical. Rather than
recording the movements of the decorations on the celestial ceiling,
which one perceives by sight-see Plato's disparaging remarks on the
current state of astronomy (Republic 529A f£)-Eudoxus was developing models for them, based on the mathematics of uniform circular
motion, which one grasps by argument and reason. To reduce the disorder and particularity of appearances in the sensible world to mathematical generality and principled order would be to save the appearances-for reason, and from chaos. The reduction requires at least a
qualitative correspondence between paradigm and reality; hence
Eudoxus's models had to be able to reproduce retrogressions in the
orbits of the outer planets. It took a considerable refinement in the
models and the observations-and possibly in philosophical outlook
as well-to achieve the quantitative correspondence in Hipparchus
and Ptolemy, where the retrograde motions were given by the models
in magnitude and in time. Even Ptolemy, however, is concerned to distinguish his work and discipline as mathematics, and not physics or theology, although it makes some concessions to these other fields. To the
mathematician, in contrast with the physicist or theologian, the existence of different, equivalent models, such as eccentric circles and
epicycles, or even heliocentricity and geocentricity, is a point of contemplative delight; for those others, a point of anxiety and dispute.
When it comes to the sublunary sphere, Plato accepts the premise
of radical flux. He apparently held this view all his intellectual life (see
Aristotle's biography, Metaphysics 987a30f£). All things are in motion,
and so are their measures (i.e., the individual percipients); hence the
�32
THE ST. JOHN'S REVIEW
measurements they take-i.e., individual perceptual judgements of
things as to their sensible quality or size-are also in flux, (The same
wind can appear hot and cold to different people, I52B.) The premise
of flux apparently entails the premise, "nothing is one in itself"
(I52D); this is the mathematical version of the relativist premise,
uthere is no objective measure:' Different percipients-and the same
percipient at different times-represent different measures, and hence
there exists a problem of radical incommensurability between individual perceptions. There can therefore be no question of a quantitative
application of measurement theory to the phenomena. The very fact
that perceptual events and judgements are judged to be completely
unique and individual (fl\tov-see, eg., I 54A) should suggest that
they are not susceptible to general treatment of any kind, let alone to
mathematical treatment. The world of sense, when approached in
terms of these kinds of premises, ought not to be salvageable for
knowledge.
All the same, for the metaphor of sensation as measurement, a
notion attributed in the Theaetetus ultimately to Protagoras (I52A),
there is life yet, The new branch of measurement science can supply an
intriguing model for at least a qualitative saving of the appearances,
Here, as in the sublunary sphere, we also have things and their measures, extremes and means, continually changing. But this does not prevent them from being related to a single magnitude-to two definite
magnitudes, in fact, for the size of the rectangle contained by each pair
of interpolations, as well as its geometric root, remains the same.
Hence there can be a kind of unity predicated of a continued process
of change; and so perhaps a predication of unity need not be precluded from sense experience, even in a world of unceasing flux, In addition, the measure of the root of this constant magnitude represented
by the rectangles, the geometric mean approximated by the arithmetic
and harmonic means, is a measure that is continually coming to be, but
never is. As such, it is uniquely suited as a qualitative model or paradigm for perception, which seems to share this property in the sensi-
�DAVID
33
ble world. That which is ("ta Ovta.) comes to be, as a perception, through
a continued process of measurement with the percipient. The first step
in applying the new kind of measurement as a theory of perception
would be to say, with the Eleatic stranger, that being (,;a bv,;a.) is
liuva.w~.
*
*
*
*
*
*
*
The vastly different implications of the two kinds of measurement
are brought out by Socrates' example of the dice (IS4c). If one compares six dice with four dice they look greater, but if one compares six
dice with twelve, they look less. This seems to involve a paradox,
because nothing can ever become greater or less in size or number
while it remains equal to itsel£ Two other postulates are said to contend with this one and with each other in our souls, when we think
about the six dice becoming greater and less: anything in respect of
which nothing is added or subtracted is neither increased nor diminished, but is always equal; and that which did not exist before could
not exist afterwards without a process of becoming (I54A-B).
Brown has pointed out that the way Socrates compares six with
four and twelve-that the difference in each case is half of the compared term (I 54c )--is an explicit recognition of six as the harmonic
mean in the interval defined by four and twelve as extremes. 25 He then
takes the reference to the harmonic mean as an allusion to the geometric mean in the interval, to which the three postulates mentioned
above apply in a mathematically interesting way-a way that justifies
Theaetetus's dizziness at such paradoxes (ISSc). This is by way of
defending Plato against the likes of Bertrand Russell, who refers to
Plato's difficulties in these matters as "among the infantile diseases of
philosophy:' 26 The text does not support Brown's defence, however.
Socrates and Theaetetus seem genuinely perplexed by any three-term
comparison, whether among dice or between the size of Socrates and
�34
THE ST. JOHN'S REVIEW
two stages of a growing Theaetetus (I55B-c). This is because the art
of measurement (but not necessarily philosophy) is in its infancy;
measurement n;po<; aA.A.l']A.a can only distinguish the greater and the
less, and the intermediate objects inevitably called up by a three-term
comparison become equivocal in a rather straightforward way. The
concreteness of the cited examples-remember that Plato always talks
about dice-may help to reinforce the odd intuition that an object
changes into its opposite while staying the same.
The new branch of f.tE'tpl']'tLKi), measurement toward the generation of the mean, legitimizes the intermediate. It generates objects that
are definitively ubetween" all rational numbers, as we have seen. Plato's
deft presentation points the way to the mature science of measurement. Comparing six dice to four and twelve is to measure tangible
quantities against one another, so as to cause perplexity about the relativity of six; seeing 6 as the harmonic mean in the interval 12:4 is to
see it as a generating approximation of the only non-relative, or utransrelative:' entity inside the interval: the geometric mean or mean proportional. As one generates it geometrically, it exists unchanged and
remains equal with itself. As one generates it arithmetically, it is now
greater now less, now increased and now diminished, continually com-
ing to be. The geometric mean is therefore an exception to each of the
three Protagorean assumptions about relativity, just as it was to the
Parmenidean ones about sameness and being; and we have already seen
how Plato tries to prove that it exists.
Brown was right, therefore, in recognizing the reference to the harmonic mean and its allusion to the geometric mean, but he was at least
partly wrong about the significance of the allusion, That the same
number or magnitude can be called both greater and less seems to be
regarded as a genuine paradox; the problem can be nullified by rethinking the process of measurement, as a generation of means, rather than
as a direct comparison of quantities. A mean is a mean in relation to
what is greater and to what is less; the greater and the less, in turn, are
�DAVID
35
so in relation, as extremes to a mean. Hence extremes and means can
only exist and be defined in terms of each other. A mean is therefore
a thing which demands to be comprehended on all these terms: it is
one thing remaining the same as itself, and it is greater, and it is less.
The concatenation of these properties is no longer paradoxical, but
rather uniquely definitive, in the case of a mean. The trick is therefore
to define numbers and magnitudes, where the purported paradox of
relativity is observed, as means. This is precisely what Theaetetus has
already done. Not just the incommensurable roots (buVU[.IEL~). but
,
all numbers and commensurable lengths (f.IYJKYJ) are recast as geometric means between the unit and square and oblong numbers (that is, as
sides of the square representations of all numbers). This is once again
to resolve a difficulty by redefining its terms, and to resolve a paradox
by exploiting its own conditions. Theaetetus can cure his dizziness by
turning the problem upside down. To reclassify rational and irrational
lengths as types of means is to make these relativistic creatures, with
their seemingly paradoxical mixture of properties, the very standards
of measurement; the
11
in-between, now takes on the substantive exis-
tence in measurement science which once belonged exclusively to number. By referring to the problematical, "in-between" six in such a way
as to identify it as the harmonic mean in an interval, Plato would seem
to be hinting at this kind of a solution during Socrates' very articulation of the paradox.
I do not mean to suggest, here or elsewhere, that the algorithm of
interpolating means is some kind of cryptic code to Platos meaning.
For one thing, a mathematical model needs to be interpreted before it
can be interpreted; in itself, the means algorithm is about measurement
in the abstract and nothing else. (Even here, however, as I have suggested, the question what is a mean?" and the follow-up does it
11
11
exist?" can have serious philosophical consequences, such as the postu-
lating of a relational mode of being.) What I do see is the persistent
heuristic and often playfUl application of a paradigm. The most seri-
�36
THE ST. JOHN'S REVIEW
ous and striking interpretation of this paradigm is as a theory of sense
perception; but there are other exemplars in the Theaetetus. At I 80E,
Socrates, tells Theodorus that by advancing little by little (Km;a
Gf-UKpov), they have unknowingly fallen into the midway position
between the Parmenideans and the Heracliteans ( Et~ 'tO [.l{aov
JtE1t'tWK6,;E~-recall aE'i. CJ'UVEKJtLJt'tQUGct, I 56B); their plight is
compared to that of the people caught in the middle of a wrestling
school tug-of-war, who are dragged toward opposite sides of the dividing line. On the one hand, this image is amusing and self-explanatory,
and fully realized on its own terms. But one can discern behind it the
notions, entirely neutral in themselves, of incremental interpolation
toward the measurement of a mean, and oscillation around the meas-
uring line. The mathematical model can hardly be said to explain or to
interpret the image. The reverse is in fact the case: it is the tug-of-war
which interprets, and gives content to, the paradigm. But just as in the
case of Socrates's dice, an awareness of the underlying paradigm can
suggest lines of thought that are textually based, and yet not necessarily part of the literal intention of the interlocutors in the dialogue. A
mean is something which brings into relation and, in this sense, unites
its extremes. It is therefore of considerable interest for a student of
Socrates and Plato to wonder what a mean position between the
Parmenideans and the Heracliteans might be like. The means algorithm and the image of the tug-of-war can be seen to do a double duty:
conceiving of opposed positions no longer as opposites but as
extremes is the first step towards our some
day, as we still say, "squar-
ing" them, generating a solution in the mean between them; while at
the same time, the image of being caught in the middle and pulled to
either side captures the present predicament of the participants in the
dialogue.
A significant portion of the Theaetetus is devoted to an exhaustive,
case by case analysis of the possibility of false judgement, depending
on the premise that with regard to each thing one might have an opin-
�DAVID
37
ion about, one either knows it or one doesn't. But Theaetetus is forced
to adopt this premise of polar, or opposite conditions when Socrates
asks him to leave out the states which lie in between knowledge and
ignorance (ftE'tal;u 'tOlJ'tWV, I88A), such as learning and forgetting.
I think few readers would agree with Socrates's daim here that these
intermediate processes have no bearing on the discussion. Does not the
text rather invite the reader to consider, on his own at any rate, the
nature and the implications of such mean states as learning and forgetting? Are they not significant in themselves, and especially crucial as
a basis for the task at hand, an investigation of the cognitive mechanism which might result in false opinion? The midway cases of learning and forgetting exhibit the paradoxes we have come to expect of
means: it would seem that in the midst of these conditions, knowledge
and ignorance are both present in the mind at the same time and about
the same thing.
In the middle of the dialogue (I72c-I77B), Socrates digresses to
paint the portraits of two incompatible human types, the man of the
city and the philosopher. The opposite qualities of these figures take
on a new significance if the figures are interpreted not as opposites, but
as extremes. The reader will notice that the philosopher described is
not in fact like Socrates: he is rather a latter-day Thales (I 73E ff.), an
astronomer, physicist, geometer, and general investigator into the
abstract natures of things; a man more reminiscent of Arist.ophanes's
parody than Plato's Socrates. In the Socrates of the Theaetetus, we see
instead a mean between extremes, between the man of the law courts,
whose time and speech are strictly circumscribed, and the philosopher,
whose time and speech are all his own (I72D-E). Socrates has the
leisure, on the one hand, to pursue an investigation into the definition
of knowledge with Theaetetus, including time for fresh starts and
digressions (I 72D); on the other, we are reminded quite pointedly, by
way of ending the conversation and the text, that Socrates has to break
off until the next day so that he can keep his appointment in court, to
�38
THE ST. JOHN'S REVIEW
meet Meletus's indictment. Socrates' time is not his own; and his life
will depend upon his ability to speak the speech of the law courts.
It is tempting to compare Socrates' two patterns, his "paradigms
set up in the midst of existence" (176E), with the paradigms of
Theaetetus. The divine and the perfectly just would be figured as foursquare and O[J.OLOV, and the. human and the political as inherently heteromecic. A tragic dimension emerges if one interprets Socrates's models as themselves an investiture of the models of the measurement paradigm. We are encouraged to become more and more like the divine
and the just; but it is a structural feature of the interpolation algorithm
that however equal it becomes, the rectangle can never become square.
The flight from our mortal nature toward the divine is described by
Socrates as ~[J.O'i:Wm£ or assimilation to god; ~[J.o(wm£ itself
(Socrates repeats the word, I 7 6B) is then explained as becoming
1\{Kawv and dmov in the com~any of <j>p6vrJOL£. But in the mathematical setting, the process of O[J.o(wOL£ can never be completed;
and the suggestion in this context may be that ultimately the divine is
irreconcilable with the human, that the life of pure philosophy is
finally incommensurable with the life of the city. The demands of the
philosopher, who asks "what is man?" (I74B), can never completely
escape the demands of society, and its conventional expectations of
man. The life and death of Socrates embody a paradigmatic dilemma:
however long and full the measure of his days, and hence however long
the process, through the purgations 'of philosophy, of assimilation to
the divine, of becoming truly just and holy and wise,-there will come
a day of reckoning by a different number, and the city will lay its claim
to him.
A further note about the dice: the interval I 2:4 is a species of the
Tp~.:rtA.amov 1\LaOTrJfJ.U, 3:1. The interpolated means, beginning
with eight and six, are therefore fourth-multiple approximations of the
side of the three-foot square. The full significance of the example is
.now manifest: it illustrates the new way to investigate incommensu-
�DAVID
39
rable lengths, taking up again the first ofTheodorus's cases, and applying the continued process involved in the squaring of Theaetetus's
oblong numbers.
*
*
*
*
*
*
*
In addition to that portentous entity, the o-6va!H~. two methods
associated with my interpretation of the geometry lesson, proof by
reductio ad absurdum and the method of exhaustion, also become paradigmatic for Plato in this trio of dialogues. The former may have long
since been the inspiration for Socrates's familiar technique of reducing
his interlocutor to perplexity. It shows up at various stages of the
argument in the Theaetetus, as for example at I 54C-D, where Theaetetus
is reduced to both affirming and denying one of the Protagorean postulates we have just discussed. Whereas in mathematics, this method
achieves the positive result of refuting a hypothesis, and proving its
contrary, Plato romanticizes the notion somewhat for philosophy; he
is interested in perplexity itself as a heuristic state, and marks the wonderment that it brings on. in Theaetetus as a sign of his being a
philosopher (I SSc-D ). But Plato also relies on the rigorous conception
of the proof: at a crucial point in the Sophist, it is proved that some of
the forms and genera must mix with each other and others not, only
because the other two possibilities-that none of them do or all of
them do-have been reduced to absurdity (252E). The upshot is an
unexpected discovery of the philosopher and his science, while
Theaetetus and the stranger had been looking for the sophist (253c).
Dialectic is the science which divides things by form (?too~) and
genus (yrvo~). and he who is capable of this science is the one who
can best discern the complex interrelationships among the formswhich ones unite others, which are parts, which wholes, and which
stand apart from mixing (253D-E).
�40
THE ST. JOHN'S REVIEW
The method of division, which characterizes the investigations
into the sophist and the statesman and which is identified with dialectic (253D-E), is based on the method of exhaustion. This is the postclassical name for the continued process of measurement we are now
familiar with, One "exhausts" a magnitude by continually cutting off
rational segments of it, each of them more than half of what is left.
If these rational u shavings" are strung together, one can approximate
the length, say of a geometric mean, to an arbitrarily high degree of
accuracy. Once again, as Plato invests the mathematical paradigm with
the dress of the dialectical process, he romanticizes it: at Sophist 261AB, Theaetetus complains that as they get closer to their quarry, the
sophist keeps throwing "problems" in their way, like successive defensive walls (npo~ArJ[!U'ta); the stranger assures him that any attacker
,
r
'
;
, '
who can rnake "contmuous progress rorward"(' 'tO rtpoa8EV act.
EL~
npmtvm) should be confident of success. And to be sure, while the
stranger never fails to string together the divisions which measure" his
subject (e.g., at 268C-D for the sophist), his main concern is at least
equally with the division process itself, and with the training it provides in distinguishing classes (see Politicus 285C-D). But there is still a
concession here to the mathematical: at Politicus 287c, the stranger
advises that in these procedures, one must divide by a number as close
as possible to two, This serves a double purpose; it maximizes the
number of divisions that will need to be made, thereby increasing a
student's experience with the handling of kinds, while also providing
the minimum subtraction required (more than half)," to guarantee the
11
u
exhaustion" of the subject.
The aim of the division process is still to produce a definition, and
in this sense it can be seen as a refinement on the original Socratic
methodology. But definition is here seen, perhaps for the first time
explicitly, as a kind of measurement; this is a return to the root mean-
ing of the term, which involves the setting of limits or boundary
marks (Clp'LsELV). The Forms only enter the picture as the necessary
�DAVID
41
terms of division, and the measures generated, to ''trap" the undefined
object in an exhaustive process. It would seem that a considerable point
of departure for this new vision of dialectic lies in the notion of forms
as measures.
That the philosopher and the philosopher's art can be characterized by these continued processes marks a stunning change in Plato's
thought. Brown draws the following conclusion:
... in Theaetetus, and apparently in response to a lively
sense of the mathematical achievements of this companion and colleague, Plato seems to be yielding
somewhat to an epistemological suggestion derived
from Theaetetus's notion of continued processes.
This would involve thinking that opinion, and perhaps even perception, if they can be processed in just
the right way, ought to be taken seriously. Further, it
would involve his thinking that knowledge is not fully
characterized by the fixed and finished objects (Ideas)
toward which it may proceed, but that it is at least
partly characterized by the approximating process
itsel£ This would mean that at least in one aspect of
it, knowledge is a continued process of learning.28
I would make a stronger claim for Plato's development: the more
usual theory of forms, which involved forms as paradigms in the sense
of ideals, has been reformed or even replaced in these dialogues, on the
inspiration of the new measurement paradigms created by Theaetetus.
That Plato himself recognized a development is evidenced by his curious wording at Sophist 248A: he there refers to certain idealists, who do
not believe in motion and mixing, as
nthe friends of the forms" ('to:U;
'tWV c'L6wv q)LA.ov~). That Plato could use such a phrase, in relation
to what is usually thought of as his singular philosophical achieve-
�42
THE ST. JOHN'S REVIEW
ment, must have staggering implications for those who would chart the
history of his thought. Did these friends of the forms use to be friends
of his? Or were they the older gentlemen described somewhat
unflatteringly at 25Ic, possibly older, rival Socratics? If so, was the
original theory of forms perhaps a Socratic or a Parmenidean invention? However these questions are answered, and whatever is the true
measure of the distance between Plato and the "friends of the forms;'
the sum total of my arguments is that there was a revolution in Plato's
conception of epistemology and ontology, necessitated by the existence of the curious object at the heart of the new measurement science: the irrational geometric mean between rational factors,
Theaetetus's <'iuvarw::;. This object and this science serve as paradigms
for a brave new approach to some very old and perplexing problems.
Perhaps there are grounds for a revolution in our sense of Plato's
development, to match the turn in the man.
Notes
I. Wilbur R. Knorr, Evolution of the Euclidean Elements (Dordrecht and
Boston: D. Reidel Pub. Co., 1975), 65-9.
2. Wilbur R. Knorr and Miles F. Burnyeat, "Methodology,
Philology, and Philosophy, Isis, I979, 70:565-70
3. Miles Burnyeat, "The Philosophical Sense of Theaetetus's
Mathematics:' Isis, I978, 69: 489-5I3, on pg. 5I3.
4. Knorr, Evolution, I 92
5. Ibid., 192
6. Ibid., 69 f£
7. Ibid., 96 (In full: "(a) The proofs are demonstrably valid. (b)The
treatment by special cases and the stopping at I 7 are necessitated
by the methods of proof employed. (c) The proofs will be understood to apply to an inhnite number of cases. (d) No use may be
made of the dichotomy of square and oblong numbers in
Theodorus's studies, either in the demonstrations or in the choice
�DAVID
43
of cases to be treated. (e) Theodorus's proofs utilize the special
relations of the lines in the construction of the dynameis. The geometrical methods of construction are of the type characteristic of
metrical geometry as developed in Elements II and are closely associated with a certain early style of arithmetic theory. (f) But the
arithemetic methods by which Theaetetus could prove the two general theorems , on the incommensurability of lines associated with
non-square and non-cubic integers, were not available to
Theodorus:'
8. Malcolm Brown, "Theaetetus: Knowledge as Continued Learning;'
Journal of the History of Philosophy, I969, 7:359-79, on pgs. 367-8
9. Knorr, Ewlution, I 58
IO. This proof is given by Knorr, Evolution, I84
I I. Ibid., I 59
I2. see Euclid's Elements X De£ 3
I3. see Plato's Politicus, 278b-e
14. see Euclid, The Elements, 3 vols., Vol. 3, ed. Sir Thomas Heath
(Annapolis: St. John's College Press, I947), 3
IS. see Euclid ILI4 andVI.l3
I6. Brown, "Theaetetus:' 371 f£
I7. Proclus, In Platonis Timaeum Commentaria, 3 vols., Vol. 2, ed. Ernst
Diehl (Leipzig: Teubner, I903-6), I73-4
18. Brown, Theaetetus;' 371
I9. see David H. Fowler, The Mathematics of Plato~ Academy (Oxford:
Clarendon Press, I 987), I 4 f£
20. see Plato's Timaeus 36A for this usage
2I. The reading of B and T; editors usually read touto
22. Brown, "Theaetetus," 3 7 6-7
23. Ibid, 377
24. see Theaetetus, I 85c
25. Brown, "Theaetetus:' 3 74
26. quoted in Brown, "Theaetetus:' 373, note 38
11
�44
2 7. Euclid, X. I
28. Brown, "Theaetetus;' 379
THE ST. JOHN'S REVIEW
�-.::f We Nietzscheans
!ft- John Verdi
Friedrich Nietzsche was born in 1844.* He went to good schools,
studied hard and by the time he was 24 had been appointed professor
of philology at the University of Basel. He abandoned the academic
world after about ten years, and began to live here and there in France,
Switzerland, and Italy, never remaining in any one place for more than
a few months. His life was solitary, but not unhappy. In 1889 he suffered a complete mental collapse from which he never recovered. He
died in I 900. While he flourished and was writing the books for which
we remember him, virtually no one paid any attention to his work.
Now it seems that everybody has something to say about Nietzsche.
What Martin Heidegger wrote of him a few decades ago might still
be true today, that Nietzsche is "either celebrated and imitated or
reviled and exploited:' I
Nietzsche has excited and polarized people throughout the twentieth century. Even now he remains as enigmatic as Plato: we are forever uncertain what he believes and what he intends. Consequently
everybody has something to say about Nietzsche, even Nietzsche. He
calls himself a ''godless anti-metaphysician;' a "very free spirit," an
11
irnmoralist;' an uartist," one of the umore spiritual beings of this
•
age, horne1 " II£ 1 " ptous, u•
ess, 1ear ess,
mcomprehenst'ble." An d m Ecce
Homo, his last book, he says: "I am not a man, I am dynamite ....! contradict as has never been contradicted and am nonetheless the oppo11
11
11
'
"
John Verdi is a tutor on the Annapolis Campus. This lecture was delivered on March 26, 1999.
*I would like to thank the National Endowment for the Hwnanities and St. John's for having
given me the opportunity to spend much of the last two academic years (1997-1999) studying
Nietzsche. I'd also like to thank the members of last semester's study group on The G191 Science for
their insight, enthusiasm and good spirits, and for helping me learn how to read Nietzsche more
carefully and more critically.
�46
THE ST. JOHN'S REVIEW
site of a negative spirit. I am a bringer of good tidings such as there
has never been." 2
I have kept in mind while preparing this essay that some of you
may have never read any Nietzsche, others may have been introduced
to him only recently or haphazardly, and still others may know him alltoo-well, What I have to say about Nietzsche shall focus on one of his
books, his most comprehensive, coherent, and accessible book, Beyond
Good and Evil, in particular on the Preface, because I believe that here at
St. John's our best public conversations usually focus on books, not on
people or "issues:' The essay comes in five parts, Each of the first four
parts begins with, and subsequently comments on, some of the
Preface, so that by the time I have finished the last of these, you will
have heard the entire Preface. In the last section of the lecture I shall
suggest that Nietzsche aims in part to re-establish, re-vivify, and
transmogrify an ancient tradition of spiritual exercises, going back at
least to Socrates, exercises which Pierre Hadot says had as their goal "a
transformation of the world;' and "a metamorphosis of our personal•
113
Ity.
Part One
Supposing truth is a woman-what then? Are there
not grounds for the suspicion that all philosophers,
insofar as they were dogmatists, have understood
women badly? That the gruesome seriousness, the
clumsy obtrusiveness with which they have usually
approached truth so far have been inept and improper
methods for winning a female? What is certain is that
she has not allowed herself to be won-and today
every kind of dogmatism stands sad and discouraged.
1j it is left standing at all! For there are scoffers who
assert that it has fallen, that all dogmatism lies on the
�47
VERDI
ground-even more, that all dogmatism is breathing
its last.'
In the first line Nietzsche alludes to Machiavelli's remark in The
Prince about fortune. Machiavelli writes:
Fortune is a woman ... and one sees that she lets herself
be won more by the impetuous than by those who proceed coldly. And so always, like a woman, she is a
friend of the young because they are less cautious,
more ferocious, and command her with more audacity. 5
Machiavelli also says that "fortune shows her power where virtue
(virtU) has not been put in order [so as] to resist her;' and that the
prince is "prosperous who adapts his mode of proceeding to the qualities of the times" ( ch. 25). Later, Nietzsche says that Machiavelli
cannot help presenting the most serious matters in a
boisterous allegrissimo, perhaps not without a malicious
artistic sense of the contrast he risks-long, difficult,
hard, dangerous thoughts and the tempo of the gallop
and the very best, most capricious humor.'
Nietzsche's own style, which is inextricably interwoven with his
thought, can often be described in just such terms. "[T]here is art in
every good sentence-art that must be figured out if the sentence is to
be understood!"' Nietzsche wants us to recognize from the opening of
the book a certain kinship he has with Machiavelli in both content and
style.
Nietzsche continues the questioning by asking if all philosphers,
at least to the extent that they have been dogmatists, have not been
clumsy in courting truth and winning her heart. He implies that truth
�THE ST. JOHN'S REVIEW
48
cannot be discovered by some method, as Descartes had hoped, but
only won by someone able to command her. Nietzsche doesn't tell us
if all philosophers heretofore have been tactless dogmatists. He hints
that they have usually taken a fruitless approach to truth, but the allusion to Machiavelli, and the description of his style, suggests that he
at least was hardly a gruesome and awkwar~ suitor. Most philosophers,
however, have been too grave in their search for truth, not gay and playful enough to have gotten very far with her.
But what does Nietzsche understand by dogmatism anywayl Recall
that Kant had set himself the task of criticizing dogmatism in The
Critique of Pure Reason, where he characterizes it as
the presumption that it is possible to make progress
with pure knowledge, according to principles, from
concepts alone ... and that it is possible to do this
without having first investigated in what way and by
what right reason has come into possession of these
concepts.8
Kant believes that when we employ concepts dogmatically-that
is, to "yield strict proof from some principles a priori"-without first
having made them give an account of their origin and a justification of
their use, they lack the power to yield truth, but create illusion in its
place, Kant and Nietzsche both challenge dogmatism as that mode of
thinking which sets arbitrary limits to the questions philosophy may
ask.
Nietzsche disagrees with Kant in at least two important ways. Kant
believes in a class of truths which are both necessarily so and about the
empirical world of experience, not merely about logic or the relationship of pure concepts to one another. These synthetic a priori truths
constitute the substance of arithmetic and geometry, and also the
foundations of classical mechanics, namely, Newton's three laws of
�VERDI
49
motion. The examples Kant gives are that seven plus five equals twelve,
that a straight line is the shortest distance between two points, and that
in every transfer of motion between bodies, action and reaction must
always be equal. For Nietzsche the central question of Kant's
Critique--how are synthetic judgments a priori possible?-leaves at
least one "truth" unassailable and immune from question, namely, that
there exist synthetic judgments which are true a priori. For Nietzsche
the prior question is, Why is belief in such judgments necessary? Why
must man believe them to be true? In fact, Nietzsche believes that
dogmatism exists whenever a philosopher needs to resort to any kind
11
of given;' any truth he claims is "evident," whether it be Descartes's
11
1 think;' Hume's "impressions and ideas," or Socrates' belief that the
search for truth will make us better people. He says,
There are still harmless self-observers who believe
11
that there are immediate certainties"; for example,
"I think;' ... as though knowledge here got hold of its
object pure and naked, as "the thing in itself;' without any falsification on the part of the subject or the
object. But that u immediate certainty," as well as
"absolute knowledge" and the "thing in itself;'
involve a contradiction in terms; we really ought to
free ourselves from the seduction of words!9
The second way Nietzsche differs from Kant-and perhaps from
all other philosophers before him-lies in the very value each attributes
to the kind of truths dogmatists seek. For "the secret wish and hidden
meaning of all dogmatic aspirations" has been that their truth is supposed to be a truth for everyone. Yet,
11
whatever can be common,"
value:' 10
Nietzsche says, "always has little
And with this Nietzsche
catches all of us up short, for what else can truth be if not something
universal? Of course my truth" and your truth" can differ in trivial
11
11
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THE ST. JOHN'S REVIEW
ways, in the sense that umy experience" can differ from yours. But
Nietzsche is talking about the truths of philosophers, that is, truths
about being and becoming, knowledge and ignorance, good and eviL
In fact, Nietzsche worries deeply about truth, and expresses this at the
beginning of Part One of Beyond Good and Evil, when he raises two
astounding questions: what is the source of our will to truth? And
what is the value of this will? The first question, Nietzsche says,
brought him to a long halt; but it was the second question that
brought him to a complete stop. "Why not rather untruth? and uncertainty? even ignorance?" These are the questions the Sphinx really put
to Oedipus, the questions behind the riddle. For Socrates, the answer
to both questions suggested in the Symposium and elsewhere, is that
truth is intelligible and that everything intelligible is beautifuL
Nietzsche, however, believes that our intellectual conscience demands
that we consider other possibilities. The truth as such about life may
be unintelligible; it may be ugly. He says:
Something might be true while being harmful and
dangerous in the highest degree. Indeed, it might be a
basic characteristic of existence that those who would
know it completely would perish ...The question is to
what extent it is life-promoting, life preserving,
species-preserving, perhaps even species-cultivating. 11
The dogmatists' belief in the value of truth, "truth for its own
sake;' must itself be scrutinized, in order to uncover its origins, which
may lie deep in the cave of human instincts and drives.
[F]or all the value that the true, the truthful, the
selfless may deserve, it would still be possible that a
higher and more fundamental value for life might
have to be ascribed to deception, selfishness and lust,
�VERDI
51
[and that the J good and revered things [might be J
insidiously related, tied to, and involved with these
wicked, seemingly opposite things-maybe even one
with them in essence. 12
Having thus challenged dogmatic philosophers in the first three
sentences of the Preface, Nietzsche then suggests that perhaps dogmatism has already been knocked down, that it may even be dying. So
why the hoopla of the opening sentences? Well, not Nierzsche but certain uscoffers" or tidiculers" claim that the end of dogmatism has
arrived. I suspect that Nietzsche does not believe this himself for one
minute. The myriad forms dogmatism takes can become clear to us
only after we recognize the scope and implications of Nietzsche's
questions about the value of truth. Any activity based on a search for
truth "for its own sake" is dogmatic, because it precludes raising the
question, "Why seek truth?" And where questions are forbidden, dogmatism rules. In The Gay Scienee he puts it this way:
11
[w Jill to truth" does not mean "I will not allow myself
to be deceived" but-[ and] there is no alternative"! will not deceive, not even myself"; and with that we
stand on moral ground....Thus the question "Why science?" leads back to the moral problem: Why have
morality at all when life, nature, history are "not
mora1"? 13
The scoffers who think they see all dogmatism in the throes of
death do not recognize what it really is or the extent of its presence.
These are perhaps the skeptics Nierzsche later criticizes, who believe
that their newly won "objectivity" demands that they refuse to affirm
or deny. "They no longer know independence of decisions and the
intrepid sense of pleasure in willing-they doubt the 'freedom of the
�THE ST. JOHN'S REVJEW
52
will' even in their dreams." 14 Nietzsche is not one of the scoffers, and
skepticism is not an adequate response to dogmatism. "[T]he worst of
harbors is better than to go reeling back into a hopeless infinity of
skepticism." IS
Part Two
Speaking seriously, there are good grounds for the
hope that all dogmatizing in philosophy, however
solemn and definitive its airs used to be, may never-
theless have been no more than a noble childishness
and tyronism; and perhaps the rime is very near when
it will be comprehended in case after case what really
has been sufficient to furnish the cornerstone for
such sublime and unconditional philosophers' edifices
as the dogmatists have built so far: any old popular
superstition from time immemorial (like the soul
superstition which, in the form of the subject and
ego superstition, has not even yet ceased to do mis-
chief); some play on words perhaps, a seduction by
granunar, or an audacious generalization of very narrow, very personal, very human, all too human facts.
(Preface)
Once Nietzsche rejects those cnttcs of philosophy who have
ingested the "gentle, gracious lulling poppy of skepticism;' he suggests
that dogmatism might manifest merely the growing pains of philosophy, the naive attempts of a youthful beginner, full of ardor and noble
ambition. When Nietzsche tells us there are grounds for this hope, he
has in mind such signs as the decline of belief in Christian dogma,
which he announced in The Gay Science with the pronouncement, "God
is dead:' 16 This decline has come about through the ever-increasing
�VERDI
53
severity of the Christian demand for truthfUlness, and along with it
has come a growth in pessimism, that is, in the possibility of raising
the very question of the value of existence. To Nietzsche these are
signs that philosophy is beginning to shed its worn out dogmatic skin,
one which had been needed, and had served a usefUl purpose, but may
have outlived its time.
Nietzsche views these events as full of hope for philosophy's
future. He cares about philosophy, and it means a great deal to him
that the so-called death of dogmatism not signal a death of philosophy itself. but a coming to maturity after the necessary naivete of its
youth. Nietzsche's philosopher is
the man of the most comprehensive responsibility
who has the conscience for the complete development
of manY
Unlike the scholar and the scientist,
a philosopher demands of himself a judgment, a Yes
or a No, ... about life and the value of life. 18
Nietzsche then holds out to us the further hope that soon we shall
be able to see on exactly what kinds of foundations "unconditional
philosophers' edifices" have up to now been built. He first mentions
"any old popular superstition," from which he singles out what he calls
uthe soul superstition;· one form of which is the subject and ego
11
superstition:· For Nietzsche,
11
superstition !I is not necessarily a bad
word. At certain times during the development of a people, superstition is "actually a symptom of enlightenment;' a "delight in individuality;' and a "sign that the intellect is becoming more independent:' 19
At those times superstitions can give rise to
11
individuals" who mark
the "highest and most fruitful stage" of a culture. But once a supersti-
�54
THE ST. JOHN'S REVIEW
tion has outlived its usefulness, its remains, deeply embedded in the
beliefs of a society, can function as a basis for the erection of colossal
fictions, which Nietzsche believes need to be exposed, weakened, and
dismantled.
Nietzsche's criticism of the soul and ego superstition begins with
a characteristically brief critique of "materialistic atomism" in Part
One of Beyond Good and Evil, an argument which rests ostensibly on the
suggestion made in the eighteenth century by Boscovich that atoms
might be understood not as particles or substances, but as centers of
force or fields of influence. Nietzsche compares him favorably with
Copernicus, when he says that
[wJhile Copernicus has persuaded us to believe, contrary to all the senses, that the earth does not stand
fast, Boscovich has taught us to abjure the belief in
the last part of the earth that "stood fast"-the
belief in "substance," in "matter;' in the earth-residuum and particle-atom.
Then he goes on.
One must, however, go still further and also declare
war, a remorseless war to the knife, against the
"atomistic need" which still lives a dangerous afterlife
where no one suspects it.... [O]ne must also, first of
all, give the finishing stroke to that other and more
calamitous atomism which Christianity has taught
best and longest, the soul atomism,
by which Nietzsche means "the belief which regards the soul as something indestructible, eternal, indivisible:' He leaves the way open to a
new version of the soul-hypothesis, such as 'mortal soul; and Soul as
11
1
�VERDI
55
subjective multiplicity; and 'soul as social structure of the drives and
affects' :• Nietzsche then goes on to question the belief that we possess
uimmediate certainti' of the existence of the self" or the 1:'
11
11
When I analyze the process that is expressed in the
sentence, "I think," I find a whole series of daring
assertions that would be difficult, perhaps impossible,
to prove; for example, that it is I who think, that
there must necessarily be something that thinks, that
thinking is an activity and operation on the part of a
being thought of as a cause, that there is an "ego;'
and finally, that it is already determined what is to be
designated by thinking.
It was pretty much according to the same schema that
the older atomism sought, besides the operating
"power;' that lump of matter in which it resides.
Nietzsche even suggests that the soul superstition supports the
false distinction between ufree will" and "unfree will/' or between that
which is a cause of its own motion and that which is not.
When we project and mix this symbol world [of
cause and effect] into things as if it existed in itself;'
we act once more as we have always acted-mythologically. The "unfree will" is mythology; in real life it is
only a matter of strong and weak wills.
11
The second kind of foundation for dogmatism which Nietzsche
uncovers is language. He returns repeatedly throughout Beyond Good and
Evil to the theme of the power of language to falsifY, mislead, and
seduce. In fact the book has begun with a joking bit of grammatical
�56
THE ST. JOHN'S REVIEW
metaphysics, for part of the significance of the opening question"Supposing truth is a woman-what then?"-turns on the fact that in
German, as in the Romance languages and in Greek, the noun for
11
truth" is feminine. Nietzsche seems to be saying, let's see what we can
do with grammar, what we can spin out from an accident of language.
English provides no simple way of capturing this subtlety, an example
11
of Nietzsche's own capricious humor."
But grammatical jokes are deep, as Wittgenstein said. The falsifYing power of language, and the philosopher's responsibility to recognize it and make use of it, lie near the heart of Nietzsche's concerns
in Beyond Good and Evil. In section 20 he writes:
The strange family resemblance of all Indian, Greek,
and German philosophizing is explained easily
enough. Where there is affinity of languages, it cannot fail, owing to the common philosophy of grammar-l mean, owing to the unconscious domination
and guidance by similar grammatical functions-that
everything is prepared at the outset for a similar
development and sequence of philosophical systems.
Later, in section 34, he asks even more trenchantly:
What forces us at all to suppose that there is an
essential opposition of utrue" and ufalse"?...Why
couldn't the world that concerns us-be a fiction? And if
somebody asked, "but to a fiction there surely
belongs an author?"-couldn't one answer simply:
why? Doesn't this "belongs" perhaps belong to the
fiction, too? Is it not permitted to be a bit ironical
about the subject no less than the predicate and
object? Shouldn't philosophers be permitted to rise
above faith in grammar?
�VERDI
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Even what he refers to as the "fundamental faith of the metaphysicians in opposite values" rests on the awkwardness of language
which "will continue to talk of opposites where there are only degrees
and many subtleties of gradation:'
In a short and unfinished early essay, entitled On Truth and Lying in
a Nonmoral Sense, Nietzsche argues that not only does language not adequately represent reality, but also that only through our collective forgetfulness of the origin of truth and falsehood are we led to imagine
that language does have this power. Nietzsche suggests that the concept of truth originated in a social agreement to end the "war of each
against ali;' which established "the first laws of truth:' The fact is that
"the creator of language ... only designates the relations of things to
men, and for expressing these relations he lays hold of the boldest
metaphors:' 20 Language, therefore, is rhetoric, because it
u
conveys an
attitude or opinion, a partial view rather than an essential knowledge
of the thing" ( R, xiii). Concepts are formed through equating what is
essentially unequal. through seeing the individual as a representative of
a kind rather than in its full particularity, which would be closer to our
actual experience. Concepts simplif)r experience and therefore falsify it.
This seems to me to be a complete reversal of what Hegel says in
the section in The Phenomenology on Sense-Certainty, which is
a view of our awareness of the world according to
which it is at its fullest and richest when we simply
open our sense ... to the world and receive whatever
impressions come our way, prior to any... conceptual
activity. 21
Hegel argues that when the subject of sense-certainty is asked to
say what he experiences, he finds his attempts to be empty. If he tries
to speak of the 11 here" and unow" which he is experiencing, not even
.
,
he h unse If can know wh at h e means by "here" an d " now," an d "I"
�58
THE ST. JOHN'S REVIEW
unless he means something universal, beyond the immediate place,
moment, and person, For Hegel the particular is nothing other than
the irrational and the untrue. Nietzsche, however, believes that the initial effort to verbalize experience and thereby bring it to consciousness
constitutes the first falsification of experience, the first lie, the original
sin of language. "Fundamentally, all our actions are altogether incomparably personal, unique, and infinitely individual....But as soon as we
translate them into consciousness they no longer seem to be." 22
Thus, Nietzsche does not mean to say that language "falls short"
of reality, or that it could perhaps be improved to reflect reality better.
No,
even our contrast between individual and species is
something anthropomorphic and does not originate
in the essence of things; although we should not presume to claim that this contrast does not correspond
to the essence of things: that would of course be a
dogmatic assertion and, as such, would be just as
indemonstrable as its opposite.
What then is truth)
A movable host of metaphors, metonymies, and
anthropomorphisms: in short, a sum of human relations which have been poetically and rhetorically
intensified, transferred, and embellished, and which,
after long usage, seem to a people to be fixed, canonical, and binding.2'
Nietzsche does not suggest that truth could be anything but a kind
of agreement about words, and therefore a falsification. He himself
uses every manner of grammatical and rhetorical device in his writing.
But we can become less forgetful of the origin of truth, perhaps to our
�VERDI
59
benefit. What he says in section 24 of Beyond Good and Evil might now
seem less paradoxical than it usually does on first reading. There he
writes that
only on this now solid, granite foundation of ignorance could knowledge rise so far-the will to knowledge on the foundation of a far more powerful will:
the will to ignorance, to the uncertain, to the untrue!
Not as its opposite, but-as its refinement!
This account of language poses serious problems for Nietzsche's
own writing. He knows that he cannot remove himself from the "nets
of language" 24 except by remaining silent, which he might have done
by employing a different medium for his art. But the tradition he
intends to call into question has itself been established and nourished
through language, and so he believes his critique must also be accomplished through words.
The third cornerstone for the grand edifices of the dogmatists has
been laid by bold extensions of narrow, limited, personal human experiences. The naivete of the dogmatist allows him to create facts for all
mankind from a parochialist perspective. Nietzsche writes in a section
srx:
Gradually it has become clear to me what every great
philosophy has been so far: namely the personal confession of its author and a kind of involuntary and
unconscious memoir; also that the moral (or inunoral)
intentions in every philosophy constituted the real
germ of life from which the whole plant had grown.
�THE ST. JOHN'S REVIEW
60
"There are moralities;' he says in section I 87,
which are meant to justify their creator before others.
Other moralities are meant to calm him and lead him
to be satisfied with himself....With others he wants to
Wreak revenge, with others conceal himself....
Of Kant in particular Nietzsche says:
Even apart from the value of such claims as "there is
a categorical imperative in us;' one can still always
ask: what does such a claim tell us about the man
who makes it?
The answer Nietzsche puts in Kant's mouth is, "What deserves
respect in me is that I can obey-and you ought not to be different from
me."
Part Three
The philosophy of the dogmatists was, let us hope,
only a promise across millennia-as astrology was in
still earlier times when perhaps more labor, money,
ingenuity, and patience were lavished in its service
than for any real science hitherto: to astrology and its
"supra-terrestrial" claims we owe the grand style of
architecture in Asia and Egypt. It seems that all great
things first have to bestride the earth in monstrous
and frightening masks in order to inscribe themselves
in the hearts of humanity with eternal demands: dogmatic philosophy was such a mask, for example, the
Vedanta doctrine in Asia and Platonism in Europe.
�VERDI
61
Let us not be ungrateful to it, although it must certainly be conceded that the worst, most lingering, and
most dangerous of all errors so far was a dogmatist's
error-namely, Plato's invention of the pure spirit
and the good in itself. But now that it is overcome,
now that Europe is breathing freely again after this
nightmare and at least can enjoy a healthier-sleep,
we, whose task is wakifulness itself. are the heirs of all that
strength which has been fostered by the fight against
this error. To be sure, to speak of spirit and the good
as Plato did meant standing truth on her head and
denying perspective, the basic condition of all life.
Indeed, as a physician one might ask: "How could
the most beautiful growth of antiquity, Plato, contract such a disease? Did the wicked Socrates corrupt
him after all? Could Socrates have been the corrupter
of youth after all? And did he deserve his hemlock?"
(Preface)
Nietzsche does not deny the greatness of dogmatic philosophy, a
greatness at least as powerful as astrology, to which we owe the
magnificence of the pyramids and other grand edifices throughout
Asia. He implies that astrology is a mask, perhaps a mask which had
to be worn by what he calls "real science;' before it could expect
human beings to be equal to its demands. Dogmatic philosophy, too,
he hopes, has been simply the shocking and terrifYing mask philosophy has been required to wear, to allow it to make its way into the
hearts of men. The teaching of the Veda in Hinduism is an example
from Asia of such a disguise, while Platonism has been the European
version of the mask.
Nietzsche singles Plato out from among the many dogmatic
thinkers of European philosophy, because his error has been the worst
�62
THE ST. JOHN'S REVIEW
and most dangerous, that is, his invention of the pure spirit and the
good in itsel£ One might even be tempted to suggest that the sum and
substance of Nietzsche's negative teaching is that there is no pure spirit and there is no good in itsel£
Is Nietzsche's disagreement with Plato on these two important
matters enough to explain why he calls Plato's error the worst and
most dangerous? Other dogmatists have held similar views: Lucretius
comes to mind as a materialist who seems not to have believed in pure
spirit, and as for not accepting the good in itself, I can suggest HegeL
Nietzsche says that Plato's influence through Christianity has been
enormous; this might be good reason to take aim at him. But even this
seems not to be enough, especially considering with what great respect
Nietzsche always viewed Plato, who possessed, he says, "the greatest
strength any philosopher so far has had at his disposal" (I9I). Besides,
Nietzsche goes on in the Preface to say that the specific form of dogmatism Plato represents has been overcome, and that Europe is once
again breathing freely; But this release from the so-called Platonic
nightmare only allows us a more comfortable sleep. For the heart of
Nietzsche's struggle with Plato is that in order to speak of the spirit
and the good as Plato did, he had to deny perspective, which Nietzsche
calls "the basic condition of all life;' and which he often couples with
its correlative concept, interpretation.
Perspective, as Nietzsche understands it, is not equivalent to
"point of view" in the sense that one might be able to adopt other
points of view, positions from which to look at something-say, a
sculpture-but from which we might shift, to get a new take on things.
All ordinary seeing through the eyes is perspective seeing in this sense,
but is not what Nietzsche means by perspective.
Another more subtle view of perspective could be the experiences
of Leibnizian monads. Leibniz writes in the Monadology that
because of the infinite multitude of simple substances there are, as it were, just as many different
�VERDI
63
universes, which are, nevertheless, only perspectives on
a single one, corresponding to the different points of
of view of each monad. 25
[E]ach simple substance is a perpetual, living mirror
of the universe.
A monad differs from a body in that space and time are both qualities of the monad, and not extrinsic to it. That is, a monad is not in
space in any usual sense.
Nietzsche sometimes sounds like Leibniz, as when he says that
[i]nsofar as the word "knowledge" has any meaning,
the world is knowable; but it is interpretable otherwise,
it has no meaning behind it, but countless meanings ....It is our needs that interpret the world. 26
Just as each monad reflects God from a unique perspective, so, too,
we might think, we interpret the world each from our own unique perspective. Nietzsche's "will to power" might be one such perspective.
Perhaps some perspectives are better than others! just as some monads
reflect God more fully. And maybe Nietzsche believes "will to power"
is one of those better perspectives, perhaps the best one.
On either account-perspectivism as analogous to visual optics or
to the spiritual optics of Leibnizian monads-perspective would itself
be understood from a vantage point outside perspective. In the case of
the eye, one admits the existence of objects to be seen and space in
which both we and the objects co-exist. In monadic perspective, the
reflections are not essentially spatial but spiritual: God is the object
which the monads "view" or "reflect." And so on this account, too,
perspective in the end requires at least a viewer and a viewed. When we
turn to uinterpretation;' there, too, we would require a text, a scene, a
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THE ST. JOHN'S REVIEW
clue to be interpreted by an interpreter, The number of possible perspectives and interpretations need not be limited in either account, and
it is imaginable many will exist alongside one another.
Nietzsche, however, for whom perspective is "the basic condition
of all life;' holds a different understanding of it, one which seems to
teeter on the brink of conceptual incoherence.
It is no more than a moral prejudice that truth is
worth more than mere appearance; it is even the
worst proved assumption there is in the world. Let at
least this much be admitted: there would be no life at
all if not on the basis of perspective evaluations and
appearances."
And in The Gay Science, he says:
How far the perspective character of existence
extends or indeed whether existence has any other
character than this; whether existence without interpre11
tation, without "sense;· does not become nonsense";
whether, on the other hand, all existence is not essentially actively engaged in interpretation-that cannot
be decided even by the most industrious and most
scrupulous conscientious analysis and self-examina-
tion of the intellect; .for in the course of this analysis
the human intellect cannot avoid seeing itself in its
own perspectives, and only in these, 28
The paradox that haunts this account of Nietzsche's perspectivism
can be stated thus: Nietzsche seems to be suggesting that all understanding, all knowledge, is perspectival and interpretive. But if it is,
how could we know this, since the intellect would always possess only
�VERDI
65
a perspectival view of its own working, not the God's-eye or objective
view that it would seem to require? That is, if the intellect creates its
own world, it can never discover this, because any experience it has is
one which it creates. Kant side-steps this problem by accepting as given
the existence of necessary truths about experience, that is, synthetic a
priori truths. These serve to remove him from the total immersion in
perspective Nietzsche proposes. Kant achieves his perspectival success
along the same lines as does Leibniz, that is, by a conceptual dualism
which permits him to entertain the hypothesis that we create experience while not at the same time committing him to the belief that that
hypothesis, too, is a product of perspective. Nietzsche's thoroughgoing monism, if such we may call it, will not permit this because it does
not admit that there is anywhere to stand-or even to imagine-outside
perspectival knowledge. "Facts are precisely what there are not, only
interpretations:' 29 Truth always belongs to a perspective, much as all
language consists of metaphor and anthropomorphism. There can no
more be a final interpretation or ultimate perspective than there can be
a last style of painting or a last school of music. And just as there cannot be a painting done in all styles, or a piece of music written in all
schools, there can be no perspective or interpretation which encom-
passes all perspectives, all interpretations. Nor can one adopt a perspective at will, for perspectives represent forms of life, and it is only
through a new perspective that an old one can be seen as the simplification it was.
This truth-that truth is creative-is essentially life-giving,
according to Nietzsche, because it is itself a manifestation of the will
to power of all things. An interpretation imposes an order on what is
essentially without order. "Interpretation is itself a means of becoming master of something:' 30 This doctrine of perspective as will to
power is neither relativistic nor nihilistic: not relativistic because it
does not claim that every perspective represents merely an incomplete
or inadequate view of the world, as Leibniz attributes to his monads;
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THE ST. JOHN'S REVIEW
not nihilistic because it does not claim that all interpretations are of
equal value, that all are equally life-promoting. Nietzsche's perspectivism has its roots in Heraclitus's aphorism, panta rei, ouden menei, every-
thing changes, nothing remains the same. The world as such possesses
no character to be discovered, but only characters to be created. 31
To return to Plaro: he is not alone among dogmatists in denying
the perspectival nature of truth, but he is the classic case. In fact all
dogmatism denies perspective. All dogmatism reserves at least one
truth as untouchable, one Vlh ich may not be ca!Ied into question and
which must therefore be considered binding on all people. The danger
Nietzsche sees facing modern man is that he shall continue to sleeppeacefully now, but sleep nonetheless. Modern man is characterized
especially by his belief that his freedom from Platonism and
Christianity implies that he is now objective and impartial, or can be
whenever he should so choose. The success of science and scholarship,
and the rise of the historical sense, only serve to encourage modern man's
conviction that he is on the right track to arrive at truths about nature
and man's place in it, even without the support of pure mind, the good
itsel£ and God. Nietzsche considers this "good conscience" of modern man to be merely another period of sleep, because the dogmatic
center of the scientist's and scholar's pursuits has not yet been honestly confronted. Even the anti-Platonism of empirical science has at its
core mathematical physics, and "mathematics has very much to do
with the pure mind of Plato:' 32 In The Gay Science Nietzsche says:
it is still a metaphysical faith upon which our faith in science rests ...that Christian faith which was also the
faith of Plato, that God is the truth, that truth is
divine.-But what if this should become more and
more incredible, if nothing should prove to be divine
any more unless it were error, blindness, the lie?
�VERDI
67
For Nietzsche the belief that truth has been found poses a threatening seduction, threatening because the denial of perspectivism can
hinder the future development and enhancement of mankind, which,
he believes, requires perpetual experimentation of the most radical and
dangerous kinds, including the continual overcoming of old beliefs
and ways of seeing by new ones. In The Gay Science he says that "the
secret of harvesting from existence the greatest fruitfulness and the
greatest enjoyment is-to live dangerously!' His concern is strikingly
similar to Socrates's concern in the Phaedo. There Socrates wants to lure
his friends away from the seductive nihilism of misology, the hatred of
the logos, of discussion, because of its repeated failure to arrive once
and for all at the truth concerning the most important things. For
Nietzsche the belief that one has arrived at the truth, or at a method
for finding the truth, threatens mankind as much as the misologist's
depressing belief that the truth can never be found. Both Socrates and
Nietzsche, while perhaps inhabiting opposite poles with respect to
what they consider the highest values for man, nevertheless stand
remarkably close in their fear that discussion and exploration about the
value of life might eventually die.
Part Four
But the fight against Plato or, to speak more clearly
and for "the people;' the fight against the Christianecclesiastical pressure of millennia-for Christianity
is Platonism for the people;'-has created in
Europe a magnificent tension of the spirit the like of
which had never yet existed on earth: with so tense a
bow we can now shoot for the most distant goals. To
11
be sure, European man experiences this tension as
need and distress; and twice already attempts have
been made in the grand style to relax the bow-once
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THE ST. JOHN'S REVIEW
by means of Jesuitism, the second time by means of
the democratic enlightenment which, with the aid of
freedom of the press and newspaper-reading, might
indeed bring it about that the spirit would no longer
experience itself so easily as a uneed:' (The Germans
invented gunpowder-all due respect for that!-but
then they made up for it: they invented the press.)
But we who are neither Jesuits nor democrats, nor
even German enough, we good Europeans and free, very
free spirits-we still feel it, the whole need of the
spirit and the whole tension of its bow. And perhaps
also the arrow, the task, and, who knows?, the goaL..
(Preface)
With the image of the tense bow in the first sentence Nietzsche
alludes to Heraclitus, one of his heroes, and perhaps his model for
Zarathustra. Heraclitus says:
They do not apprehend how being brought apart it is
brought together with itself: there is a connection
working in both directions, as in the bow and the
lyre. 33
Nietzsche admires Heraclitus for four reasons: Heraclitus does not
distinguish a physical world from a metaphysical one; he denies being
for becoming; he teaches the productive power of strife and rebukes
those who would seek to eliminate it; and he rejects any cardinal distinction between man and animal. 34
From the spiritual tension produced by the struggle between
Christian dogmatism and its opponents has now arisen in Europe the
possibility of shooting for "the most distant goals:' Christianity,
unlike Platonism proper, exists for the masses. For Nietzsche this means
�VERDI
69
that the struggle with it is one of noble men against "men not noble
enough to see the abysmally different order of rank, chasm of rank,
between man and man:' As a religion for sufferers, Christianity has
"preserved too much of what ought to perish." 35
Europeans have for a long time felt this tension as a discomfort,
something they would rather be without, so that they might sleep even
better. Nietzsche pinpoints two attempts to slacken the bow. The first
is the militant reformation of Catholicism by the Jesuits after the
Council of Trent in 1563. It "focused on the priestly magic of the
Eucharist... and the education of an elite loyal to throne and altar:'
Nietzsche calls Jesuitism "the conscious holding on to illusion and
forcibly incorporating that illusion as the basis of culture." 36 The great
opponent of this movement, not mentioned by name in the Preface,
but to whom Nietzsche refers elsewhere as uthe most instructive of all
sacrifices to Christianity" (EH, II, 3), was Pascal.
Jesuitism has been vanquished, but the second attempt to loosen
the bow continues still, and that is the democratic enlightenment,
which Nietzsche calls the heir to the Christian movement. Modern
democracy is
not only a form of the decay of political organization but a form of the decay, namely the diminution,
of man, making him mediocre and lowering his
value. 37
The Germans, who are responsible for the invention of gunpowder (according to Nietzsche) and are to be praised for this, perhaps
because it is a means of enforcing orders of rank, are nonetheless to
be condemned for their invention of the press, which has been perhaps
the single greatest cause of the spread of the democratic movement
through the dissemination of newspapers.
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THE ST. JOHN'S REVIEW
The danger democracy poses for the future of man, the danger of
the mediocritization of man, is, as Zarathustra says, that once the last
man has become dominant, "man will no longer shoot the arrow of
his longing beyond man, and the string of his bow will have forgotten
how to whir!...Everybody wants the same, everybody is the same:' 38
Nietzsche worries about the leveling effect of democracy because he
considers man's nature to be changeable, and that it is only through
culture that man's nature can be enhanced or diminished. The emergence of a higher humanity requires the flourishing of culture, which,
he says,
has so far been the work of an aristocratic society... a
society that believes in the long ladder of an order of
· rank and differences in value between man and man,
and that needs slavery in some sense or other. 39
Democracy seeks to obliterate these distinctions and thereby to
promote weakening of culture and consequently of the human species,
Life simply is will to power, that is, according to 259,
essentially appropriation, injury, overpowering of what
is alien and weaker; suppression, hardness, imposition
of one's own forms ....
Nietzsche is no democrat, but rather a good European and a very
free spirit. As a European he disavows nationalism, But while Europe's
democratic movement is making Europeans more similar to each other,
the conditions it creates "are [also J likely in the highest degree to give
birth to exceptional human beings of the most dangerous and attractive quality;' individuals whom he describes as "an essentially supranational ... type of man ... a type that possesses, physiologically speaking,
a maximum of the art and power of adaptation as its typical distinc-
�VERDI
71
tion:' As a good European it is "the European problem" that he takes
seriously, that is, the cultivation, perhaps from this group of highly
adaptable individuals, "of a new caste that will rule Europe:' 40
Nietzsche also calls himself a free spirit. Not yet a new philosopher, a philosopher of the future, but nonetheless living "beyond good
and evil;' the free spirit recognizes that "everything evil ...serves the
enhancement of the species 'man' as much as its opposite does:' Free
spirits are
[aJt home, or at least hav[ eJ been guests, in many
countries of the spirit; having escaped again and
again from the musty agreeable nooks into which
preference and prejudice, youth, origin, the accidents
of people and books ... have banished us. 41
The free spirit distrusts thought, is free of the prejudices of past
dogmatism, and is left witb only one virtue, honesty. The free spirit,
Nietzsche himself. still feels the whole tension in the bow, and perhaps
more than that. He may also have tbe arrow in his hand, the will for
tbe task, and the vision for tbe goal.
This goal is the philosopher of the future. These new philosophers
Nietzsche calls u attempters:' He goes on:
Are tbese coming philosophers new friends of
"trutb"? That is probable enough, for all philosophers
so far have loved tbeir truths. But they will certainly
not be dogmatists. It must offend their pride, also
their taste, if their truth is supposed to be a truth for
every man.
The task of tbese philosophers is to create values.
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THE ST. JOHN'S REVIEW
With a creative hand they reach for the future, and all
that is and has been becomes a means for them, an
11
instrument, a hammer. Their knowing" is creating,
their creating is a legislation, their will to truth is will
to power.42
These thinkers, writers, preachers apply "the knife vivisectionally
to the very virtues of their time...to know a new greatness of man:' They
will be men of action and the makers of events, but only because "the
greatest thoughts are the greatest events:' 43 Their work will be with the
creation of new interpretations, new perspectives on man, and their
tool will primarily be language. Perhaps there have already been
philosophers of the future, philosophers concerned with the future of
man. Nietzsche seems to imply that Socrates was one, when he says
that Socrates "cut ruthlessly into his own flesh, as he did into the flesh
and heart of the 'noble: " Perhaps Machiavelli was another. I am very
uncertain about both of these. But Nietzsche I think is one, and Beyond
Good and Evil is an example in nuce of the work the new philosophers
will be required to do. The subtitle of Beyond Good and Evil, "Prelude to
a Philosophy of the Future;' means to remind us of Wagner, whose
music was called Zukunftsmusik, future music, and whose preludes contain the motifs of the operas they introduce,
The next philosophy of the future will be post-Platonic and postChristian, since it has been Platonism and Christianity which have provided the tension for the bowshot away from themselves. It will also
be post-modern in that it will have recognized the contradiction inherent in modern man's belief in detached objectivity. Finally, the philosophy of the future will be post-scientific, not in the sense that it will
demand the abandonment of science as a human activity, but rather in
that it will recognize that man cannot be advanced through science as
long as science seeks primarily his ease and comfort.
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In Nietzsche's eyes the responsibility of philosophers for the
future of man is enormous. The possibility exists that they will not
appear, or will fail, or turn out badly. Nietzsche believes that as a
species we are "still unexhausted for the greatest possibilities;' but
there is no guarantee that we shall realize them.
Part Five: Spiritual Exercises
Nietzsche believes that all concepts, types, and species are fluid,
continually subject to shifting and displacement. This radically
Heracleitean stance, that everything changes, nothing remains the
same, leads him to take another step with Heraclitus, that all of nature
lies in its acts, and that there exists a perpetual interconnectedness of
things. "If we affirm one single moment, we ... affirm not only ourselves
but all existence. For nothing is self-sufficient, neither in us ourselves
nor in things:' "To say to an individual, .. .'change yourself' means to
demand that everything should change, even the past:' 44
Nietzsche also believes that all knowledge requires self-knowledge
first of all. In Beyond Good and Evil, 80, he writes:
A thing explained is a thing we have no further concern with.-What was on the mind of that god who
11
counseled: uKnow thyself!" Did he mean: Cease to
concern yourself! Become objective!"
Later, in 23 I, he says:
One sometimes comes upon certain solutions to
problems which inspire strong belief in us; perhaps
11
one thenceforth calls them one's convictions:'
Later-we see them only as steps to self-knowledge,
sign-posts to the problem we are-rather, to the great
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THE ST. JOHN'S REVIEW
stupidity we are, to our spiritual fate, to what is
unteachable very "deep down:'
Nietzsche believes that knowledge is a creative act, and that selfknowledge is the act of becoming who we are,
human beings who are new, unique, incomparable,
who give themselves laws, who create themselves. To
this end we must become the best learners and discoverers of everything that is lawful and necessary in
the world.45
It seems paradoxical that Nietzsche should speak of the self at all
in the light of his criticism of soul-atomism and his sweeping
Heracleiteanism, The resolution lies in his notion of the eternal return
of the same, that is, the belief that all events and things have occurred
countless times before just as they are occurring now, and shall occur
again countless times to come. When he first introduces this uncanny
thought in The Gay Science, in a section entitled The greatest weight, he asks
how we would respond to the proposal that
"[t]his life as you now live it and have lived it, you
will have to live once more and innumerable times
more; and there will be nothing new in it, but every
pain and every joy and every thought and sigh and
everything unutterably small or great in your life will
have to return to you,
all in the same succession
and
sequence:' ... How well-disposed would you have to
become to yourself and to life to crave nothing more
fervently than this ultimate eternal confirmation and
seal?46
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And in Beyond Good and Evil, 56, he represents "the most high-spirited, alive, and world-affirming human being" as one "who wants to
have what was and is repeated into all eternity, shouting insatiably da
capo...to him... who makes it necessary because again and again he needs
himself-and makes himself necessary:'
Nietzsche considers the eternal return his most incisive thought,
but not because it is a novel or startling hypothesis about the universe.
Nietzsche knew that it had been proposed before; he himself attribc
utes it to the Pythagoreans, and a form of it can be found in
Empedocles. As a proposal about the universe, it cannot be proved: by
hypothesis there can be no evidence for it, since any evidence would
require that there be a way to distinguish one occurrence of an event
from an earlier or latet one, which would violate the condition that
every recurrence be exactly like every other. According to Leibniz's
principle of the identity of indiscernables, any purported recurrence
identical in every respect to the initial event could not be a recurrence
at all, but would be the selfsame event.
But Nietzsche asks not simply, could you believe this eternal
return?, but rather, can you want it, desire it, will it? The possibility or
impossibility of the eternal return as a "fact" seems less important to
Nietzsche than the act of will it would take to embrace the very concept that all things might recur endlessly. But if all things are interconnected, then what I am now requires that the world have been just
as it has been, with nothing out of place. For I am a peculiar
confluence of events, an intersection of the activities which make up
nature. To will that all might be just as it is is to affirm myself just as I
11
11
am. To say Yes" to the entire past and future is to say Yes" to I who
am in the present. This act of willing the eternal return is the act. of
willing myself, of becoming who I am. It is not something I achieve
once and for all, but is a continuing process, a self- and world-affirmation that constitutes the continuing creation of myself and incorporation of the world.
�THE ST. JOHN'S REVJEW
76
The self which is thus ever becoming itself is then not the atomic self Nietzsche rejects early in Beyond Good and Evil. It is instead an
ongoing act of will, and specifically of will to power, which in forever
making the self takes into itself the past, present and future. This creation is what Nietzsche means by knowledge.
If this account of the eternal return and its connection with the
self is not entirely wrong, then we now find ourselves in a position to
suggest that Nietzsche is engaged in a new form of spiritual exercise.
According to Pierre Hadot, spiritual exercises constituted part of an
ancient tradition which considered philosophy to be a way of life, an
effort at learning how to live, and not merely a search for truths or
11
construction of systems. These exercises correspond to a transforma-
tion of our vision of the world, and to a metamorphosis of our personalitY:' Stoic exercises involved investigating, reading, listening, paying attention, meditation, self-mastery, and indifference to indifferent
things. Meditation, for example, attempts to control inner discourse by
rendering it coherent. Epicurus, too, emphasized spiritual exercises,
such as the assimilation of brief aphorisms upon which one might
meditate, and the study of physics. Philosophy seen in this light is a
therapeutic activity, the purpose of which is to produce and maintain
health in the soul.
Hadot believes that Socratic dialogues are a kind of communal
spiritual exercise, because at stake in them is not "what is being talked
about, but who is doing the talking." Socrates invites the interlocutor
to uan exal:nination of conscience;' and this requires that at every
moment the interlocutor give his explicit consent. "The subject matter of the dialogue counts less than the method applied in it, and the
solution of a problem has less value than the road traveled in common
in order to resolve it:' For the ancients, according to Hadot, the goal
of spiritual exercises is
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77
a kind of self-formation, or paideia, which is to teach
us to live, not in conformity with human prejudices
and social conventions ... but in conformity with the
nature of man. 47
In Nietzsche's hands spiritual exercises become the ceaseless activity of self-examination in order to create ourselves and thereby become
"he poets o f our 1· "
t
1ves.
One thing is nm!ful.-To "give style" to one's character-a great and rare art! It is practiced by those who
survey all the strengths and weaknesses of their
nature and then fit them into an artistic plan until
every one of them appears as art and reason and even
weaknesses delight the eye. 48
Nietzsche says that
[ t]he Greeks gradually learned to organize the chaos by
following the Delphic teaching and thinking back to
themselves, that is, to their real needs, and letting
their pseudo-needs die out.... This is a parable for
each one of us: he must organize the chaos within
him by thinking back to his real needs.49
This activity of thought and inner discourse can have the effect of
"[imposing] upon becoming the character of being;' which Nietzsche
11
says is the supreme
will to power:'
In Nietzsche's hands spiritual exercises again assume the character
of a way of life. Philosophy, "the most spiritual will to power;' thus
also becomes a way to live, a continual making and re-making of the
self and the world, an imposition of forms and unities on the essen-
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THE ST. JOHN'S REVIEW
tially formless and chaotic. Our intellectual conscience also requires
that we recognize and acknowledge the values that ground our beliefs,
for every belief is determined by some value. Nietzsche believes that
"the only critique of a philosophy that is possible and that proves
something... [is) tryiog to live in accordance with it:'
The aims of philosophy thus conceived parallel those of education.
How can man know himself? ...Let the youthful soul
look back on life with the question: what have you
truly loved up to now, what has drawn your soul
aloft, what has mastered it and at the same time
blessed it? ... [T)hey constitute a stepladder upon
which you have clambered up to yourself as you are
now; for your true nature lies, not concealed deep
within you, but immeasurably high above you.... Your
true educators ... reveal to you what the true basic
material of your being is. 5°
The best educator offers the student no more, but no less, than the
opportunity to acquire iosight into his own nature.
However great the greed of my desire for·knowledge
may be, I still cannot take anything out of things that
did not belong to me before; what belongs to others
remains behiod. 51
We Nietzscheans believe that no educator, not even Nietzsche, is
in -a position to prescribe to us how we are to make our lives unique.
Zarathustra warns his followers:
�VERDI
79
go away from me and resist Zarathustra! And even
better: be ashamed of of him! Perhaps he deceived
you.
In the last section of Beyond Good and Evil Nietzsche once again
recalls Plato, perhaps his greatest teacher and deceiver. Nietzsche says:
Alas, what are you after all, my written and painted
thoughts!...What things do we write and paint ... we
immortalizers of things which let themselves be written-what are the only things we are able to paint?
Alas, always only what is on the verge of withering
and losing its fragrance!...[O]nly birds that grew
weary of flying and flew astray and now can be
caught by hand-by our hand!
This reminds us of Plato's own warning in his Seventh Letter, in
which he says about what he himself has taken most seriously that
I certainly have composed no work in regard to it,
nor shall I ever do so in future, for there is no way of
putting it in words like other studies. Acquaintance
with it must come rather after a long period of attendance on instruction in the subject itself and of dose
companionship, when, suddenly, like a blaze kindled
by a leaping spark, it is generated in the soul and at
once becomes self-sustaining.
The "weakness of the logos;' that is, the inability of language to
capture the philosophical insight, is no more for Nietzsche than it is
for Plato a reason to abandon the activity of philosophizing. Still, profound differences separate Plato and Nietzsche, a separation made
�80
THE ST. JOHN'S REVIEW
forcefully evident by Nietzsche's iotroduction of Dionysos io the
penultimate section of Beyond Good and Evil, for Dionysos is a philosopher. "Gods, too, then philosophize;' contrary to what Diotima tells
Socrates io the Symposium (202C-D).
In closiog I would like to cite a passage from Emerson, whom
Nietzsche discovered while a teenager and continued to read and
admire throughout his life. It comes from his essay "Circles;' and the
description is one I would not hesitate to apply to Nietzsche and
which, I believe, Nietzsche would not refuse Plato, Emerson writes:
The key to every man is his thoughts .... Beware when
the great God lets loose a thioker on this planet.
Then all thiogs are at risk, It is as when a conflagration has broken out in a great city, and no man
knows what is safe or where it will end. There is not a
piece of science but its flank may be turned tomorrow; there is not any literary reputation, not the socalled eternal names of fame, that may not be revised
and condemned. The very hopes of man, the
thoughts of his heart, the religion of nations, the
manners and morals of mankind are all at [hisJ
mercy.52
Notes
I. Martin Heidegger, Nietzsche, trans. D.F. Krell. (San Francisco:
Harper, I979) I-II, 4.
2. Friedrich Nietzsche, Ecce Homo, trans. R. J. Holliogdale. (London:
Penguin Books, I992) I6, I.
3. Pierre Hadot, Philosophy as a Wcty of Lift. (Oxford: Blackwell, I 995)
82.
4. Friedrich Nietzsche, Beyond Good and Evil, trans. R.
(London: Penguio Books, I 990) Preface.
J. Holliogdale
�VERDI
81
5. Niccolo Machiavelli, The Prince, trans. Harvey C. Mansfield, Jr.
(Chicago: University of Chicago Press, I985) ch. IS.
6. Nietzsche, p. 28.
7. Ibid., p. 246.
8. Immanuel Kant, Critique of Pure Reason, trans. Norman Kemp Smith
(New York: St. Martin's Press, I965) B, xxxv.
9. Nietzsche, p. I 6.
IO. Ibid., p. 43.
I L Ibid., p. 39; 4.
I2. Ibid., p. 2.
I3. Friedrich Nietzsche, The Gay Science, trans. Walter Kaufinann
(New York: Vintage Press, I974) 344.
I 4. Ibid., p. 208.
IS. Friedrich Nietzsche, "On the Uses and Disadvantages of History
for Life," Untimely Meditations, trans. R. J. Hollingdale (Cambridge:
Cambridge University Press, I983) IO.
I 6. The Gay Science, p. I 08.
I 7. Beyond Good and Evil, 6 I.
I8. Ibid., 205.
I 9. The Gay Science, 23.
20. "On Truth and Lying in a Nonmoral Sense," Philosophy and Truth:
Selections from Nietzsche's Notebooks of the Early 1870's, trans. Daniel
Breazeale (Atlantic Highlands, N.J.: Humanities Press, I979) 82.
21. Charles Taylor, Hegel (Cambridge: Cambridge University Press,
I975) 140-I.
22. The Gtry Science, p. 354.
23. "Truth and Lie," p. 84.
24. 'The Philosopher;' in Breazeale, p. liS.
25. G.W. Leibniz, Philosophical Essays, trans. Roger Ariew and Daniel
Garber (Indianapolis: Hackett Publishing Company, I989) 57.
26. Friedrich Nietzsche, The JtJll to Power, trans. Walter Kaufmann and
R. J. Hollingdale (New York: Vintage Press, I968) 481.
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THE ST. JOHN'S REVIEW
27. Ibid., 34.
28. The Gay Science, p. 374.
29. The Will to Power, p. 481.
30. Ibid., p. 643.
31. See Alexander Neharnas, Nietzsche: Life as Literature (Cambridge:
Harvard University Press, I 985).
32. Leo Strauss, Unpublished lecture notes for a class on Beyond Good
and Evil.
33. The Presocratic Philosophers rev. ed. G S, Kirk and JE. Raven
(Cambridge: Cambridge University Press, I957) 2I2.
34. Friedrich Nietzsche, Philosophy in the Tragic Age of the Greeks, trans,
Marianne Cowan (Chicago: Henry Regnery Press, I962) 5-8; See
11
also, Uses and Disadvantages," ix.
35. Beyond Good and Evil, 62.
36. See Lawrence Lampert, Leo Strauss and Nietzsche. (Chicago:
University of Chicago Press, I996) 33.
37. Beyond Good and Evil, 203.
38. Friedrich Nietzsche, Thus Spoke Zarathustra, trans. Walter Kaufmann
(New York: Viking Press, I966) Prologue, 5.
39. Beyond Good and Evil, 258.
40. Ibid., 242, 251.
41. Ibid, 44.
42. Ibid., 2I I.
43. Ibid., 285.
44. Will to Power, I032; Twilight of the Idols, trans. R. J. Hollingdale
(New York: Penguin Books, I990.
45. The Gay Science, 335.
46. Ibid., 34 I.
47. Hadot, 93, !02.
48. Gay Science, 290.
49, "Uses and Disadvantages;' 2, IO.
50. Ibid., 3,1.
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83
51. Gay Science, 242.
52. Ralph Waldo Emerson, Selected Essays, eel. Larzer Ziff (New York:
Penguin, 1982), 229-30.
�The Power & Glory of Platonic
Dialogue
Carl Page
In Book One of his Mtmorabilia, Xen'1phon reports Socrates conversing with the sophist Antiphon. Towards the end of their conversation, Socrates speaks of sharing wisdom with one's friends:
... just as someone else takes pleasure in a good horse
or dog or bird, so I take even more pleasure in my
good friends, and should I possess anything good I
teach it, and I recommend my friends to others from
whom I believe they will receive some benefit regarding virtue. And the treasures of the wise men of old
that they have left written down in books, unfolding
the scrolls, I carefully go through them in common
with my friends; and should we see anything good, we
single it out, and we consider it great gain should we
[thusJ become helpful to one another. (1.6.I4)
Xenophon comments: "When I heard these things, he certainly
seemed to me a supremely happy man and someone to conduct those
heeding him into a good and noble life:' Xenophon's testimony to the
value of books in their relation to friends is striking, given his upright
character and worldly competence-a man fully capable of successfully leading others in the grimmest of life and death circumstances. He
must have had rather special books in mind.
What, then, is involved in reading Plato's dialogues together as
friends, carefully turning their pages, seeking out the treasures that
have been written down by a wise man of old? What ought we be after?
Carl Page is a tutor at St. John's College. This lecture was delivered at Annapolis on November
20, !998.
�PAGE
85
What would Plato have us find? What would he have happen, as the
result of our reading? The answer to such questions cannot be straightforward, but the dialogue form of Plato's writings-graciously and
thankfully-makes unavoidable our consciousness of what it means to
read them. Looked at a little more carefully, they also make unavoidable the question of what it means to speak, write, or read in the name
of philosophy, and-from another angle-they encourage meditation
on what it means to speak, read, or write at all. To presume that we
already know what a dialogue is for, what philosophical speech really
aims at, and what we should be getting out of reading Plato, is therefore to ignore, perhaps even to violate what I shall be suggesting to you
are Plato's wise and manifold purposes. In particular, your single greatest practical failing as readers of Platonic dialogue will regularly be the
assumption that you can remain spectators of its dialectical drama,
disinterested onlookers, that you can remain aloof from its proceedings to pick and choose among the thoughts you imagine the drama to
be presenting to you. Your single greatest theoretical failing will regularly be to suppose that you know the nature of the philosophical life. I
do not doubt that Plato both understood and allowed for the fact that
many people would easily make both these sorts of mistake, each in his
own way, but that should not lessen your resolve to be counted among
the readers he most wished for.
Tonight I want to assemble some reminders to help stop you
falling short of Plato's potential friendship. I hope to do that, principally by recalling how thoroughly strange the dialogues are and by
reflecting a little on why that might be. From the very start, therefore,
you can see that my speech will be far more practical and erotic, i.e.,
aimed at nudging your habits and ideals, than it will be doctrinal and
theoretic-which is to say, aimed at informing you of something. In
this respect, my speech about Platonic dialogue reduplicates the central character of the dialogues themselves.
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THE ST. JOHN'S REVIEW
A few procedural observations, First, my main design is to present a
view of Plato and his philosophical activity, rather than to justify my
interpretation of them. I confine myself to presentation, partly
because of time, but mostly because I think justification comes up as
a serious question
only after one is convinced that something is inter-
esting enough to warrant that sort of effort-should circumstances
require, It is the interest I would like to provoke first. My second note
is a confession, Although much of what follows could be called
methodological, I ofi:en find myself impatient and ungenerous with
such reflections, with abstract worries about how one ought to do
things instead of getting on with doing them. Methodology, critique,
and meta-theory tend to be airy and undisciplined, they lend themselves to indecisive, apparently endless bickering, they encourage an
odious sort of intellectual smugness, and their attention to matters of
form is frequently at the cost of return to the concrete content (whose
understanding they were originally supposed to serve). Nevertheless,
any serious well-directed work does need orientation, does need some
understanding of what it's about, and this is especially important for
those who have only just begun, In philosophical matters, the Delphic
injunction to know oneself looms as large over Socrates as
it -docs over
Kant, notwithstanding their disagreements over how best to fulfill the
responsibility. It seems, therefore, one must at some point or other run
the risks of transcendental narcissism for the sake of self-knowledge.
Third, some of the topics I shall explore will sound like variations on
the familiar, perhaps even tired old Straussian themes of esotericism,
noble lies, persecution of philosophy, and the rest. But not everyone
here has heard these important refrains. I intend to repeat my versions
of a few of them eloquently and incisively, along with a couple of riffs
I hope no one has heard before. I deliberately refer to "my versions" of
these refrains because I disagree with an underlying assumption commonly at work in their interpretation: that philosophy is by nature
politically alienated and must therefore exercise a condescending
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87
accommodation, compelled by necessity, to the city and to ordinary
human life. Some of my reasons for this deep disagreement are woven
into what follows, though I do not make them thematic. One last
introductory word. I shall not hesitate-rather shamelessly perhapsto speak on philosophy's behalf. By my acknowledging this presumption in advance, you can at least see that I appreciate what might be
questionable about my immodesty.
The Oddities of Platonic Dialogue
A moment ago I hinted that there is something important in the
very fact of Platonic dialogues, something that goes beyond and maybe
even upsets the conventional meanings typically associated with philosophy books and their academic study. This needs to be made explicit.
PLATONIC ANONYMITY. The dialogues are fully dramatic, i.e., they
portray logoi in action and deeds of speech but never disembodied
assertions. This form is unusual and was noted by Aristotle near the
beginning of the Poetics, where he speaks of "the Socratic conversation;' classing it together with the mimes of Sophron and his son
Xenarchus (I447biO). Sophron was a fifth-century Syracusan writer,
reputedly admired by Plato. His mimes were dramatic renderings in
verse of everyday people, designed to be revelatory of their characters.
Plato's dialogues are either directly performed, simply narrated, or narrated within a performed frame, but in all cases not a word is said in
Plato's own voice, except the titles. The dialogues not directly performed permit external comment by their narrators, but there is
never-unlike the passage from Xenophon with which I began-any
authorial comment from Plato himself.
In this respect, the Platonic corpus is like the body of
Shakespeare's plays. Just as we must wonder exactly how far Prospera,
for example, can be taken to speak for the Tempest's author, or Hamlet
or Lear, so too must we wonder how far Socrates or Parmenides or the
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88
Eleatic Stranger or Timaeus or the Athenian Stranger can be taken to
speak for Plato. This question was known to Diogenes Laertius in the
third century a.d., though many contemporary readers seem to have
forgotten it. Despite the unremitting anonymity, however, it must be
added that the dialogues are known to be Plato's and were circulated
from the start under his authorship. We are therefore meant to notice
that the dialogues contain no direct word of Plato's own. He addresses us, but he does not declare himsel£ Ancient rumours of secret
Academic teachings notwithstanding, in his own time Plato was just as
reticent about his ultimate insights and purposes, providing almost no
other clues but the dialogues themselves. They are like "the lord, whose
oracle is at Delphi," that neither reveals nor conceals, but gives a sign"
(Heraclitus, Frag. 93) and, like the sibyl hersel£ "with raving lips,
uttering things unlaughable, unbeautiful, and unperfumed, they reach
with their voice across a thousand years, because of the god" ( c£
Heraclitus, Frag. 92). So, Plato whispers an intriguing name into our
ears-Phaedrus (whom everyone knows to be very beautiful), Theaetetus
(whom everyone knows to be very clever), Meno (whom everyone knows
11
to be very bad); either such names or sometimes a provocative title-
Socrates' Defense Speech, An Intimate Drinking Party, Civilized Order,
Regulations,-then he draws the curtain back, to disappear, not off-stage
but behind the masks, bringing life to each and every one of his dramatis personae-the personae Platonis.
LOGICAL DERANGEMENT. The god-inspired oracle at Delphi
uttered things "unlaughable, unbeautiful, and unperfumed;' the very
same qualities we meet with in Plato's oracular dialogues. Before fully
realizing that strange fact, an experienced and competent reader might
well approach the dialogues assuming that philosophy is meant to be
or at least ought to include the art of telling, insightful speeches, and
that a philosopher's discourse should be more accurate, more illuminating, more comprehensive, and more self-conscious than any of our
other ways of talking. Plato's dialogues, however, present quite a dif-
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ferent face, despite their being finished works and despite how plainly
philosophy is their centre of gravity. Individually and as a whole they
are, at first sight, if not a conceptual chaos at least a tangle of conflicting and unresolved accounts, often at cross-purposes with one another, and sometimes in ways their speakers seem not even to appreciate,
let alone understand. I list the most obvious features.
Many of the dialogues are aporetic, i.e., they lose their way and
never seem to find it again, no matter how serious the resolve with
which they began. One tends to get used to this, but the failure of
comfortable closure-even in the manifestly great works, such as the
&public-reliably irritates any classroom of first-time readers; as,
indeed, it should. Some of the dialogues that seem more doctrinally
committed, more like "proper" philosophy, e.g., Parmenides, Sophist, are
experienced by many competent readers, at least initially, as rather boring through much of their length, occasionally to the point of unreadability. A good handful of dialogues hardly seem like dialogues at ali,
if "dialogue" be understood as an earnest effort at inquiry in common.
At crucial points in almost all of them, the philosophical argument
relies on images and metaphor, conventionally the tools of poetry.
Worse still, poetry itself seems regularly to be denounced, while
nonetheless used throughout. Even writing itself is declared some sort
of mistake. Also at crucial points, the speech will sometimes turn with
utter logical seriousness to myth, to what are acknowledged within the
conversation as fanciful tales (Republic, Gorgias, Phaedo, Phaedrus). And yet,
ali these myths and images rub cheek by jowl with the most abstruse
forms of technical argumentation and intricately developed analyses,
sometimes lasting for pages and pages-pages that cause painful conceptual squinting, even for the most discursively facile of readers. Yet
again, logical precision can at almost any moment give way to outrageous fallacy, blatant non-sequitur, and shameless ad hominem attack.
Occasionally, the whole show seems a logical farce-as in the Cratylus,
the Euthydemus, and parts of the Protagoras for example-yet everyone in
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the dialogue keeps a completely straight face. There seems to be no
overall plan to the dialogues as a totality; one more or less would not
seem to ruin their effect, and there is no single dialogue that might
count as their culmination or key. Nevertheless, many are linked dramatically with one another, both temporally and topically. Worse still,
some topics seem to be treated inconsistently across different dialogues, and worse again, the topical coherence of individual dialogues
has seemed to many readers to leave much to be desired (Republic and
Phaedrus have given this impression for centuries). Neither can one help
but wonder at the apparent naivete with which the interlocutors so
often proceed, only infrequently stopping to "define their terms"-as
we like to say-often plainly making large and questionable assumptions, sometimes agreeing not to pursue deeper investigations, and so
on, all the while talking about precision and whether we really know
what we think we know, how different knowledge and opinion are
from one another, and what indispensable value there is in self-knowledge.
Finally, as if it were not sufficient that we never hear directly what
Plato himself thinks, the character of Socrates-dearly a protagonist,
though not for that reason equivalent to Plato-is depicted within the
dialogical drama as notorious for his irony. Let me say straightaway,
however, that Socrates' irony does not mean that he isn't serious in
what he does say or that he says the opposite of what he thinks, either
for amusement or social convenience. Socrates' irony is that he know-
ingly never says all that he has in mind, and that he will on occasion
knowingly let his speeches and his deeds contradict one another, both
in the present and across dramatic time. Plato's irony is similar, if not
identical, in spirit. It is an irony that Aristotle described as "graceful
and generous," an avoidance of pretension, especially in matters that
are "unclear and apt to cause no small impediment" (Nicomachean Ethics
II27b22-31).
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In sum, the logical or account-giving, truth-telling face of the dialogues presents a confusing, sprawling, eclectic, thoroughly unsystematic gallimaufry of irritatingly teasing hints at philosophical depth and
meaning. Beware of becoming blind to this obtrusive fact. Everyone
has heard that the whole of Western philosophy is nothing but footnotes to Plato, so the dialogues must be magnificently crafted speeches. Right? Well, they are, but not in the way you might expect. Their
very ugliness, their rebarbative outward appearance is itself a manifestation of the greatest craft. It is great, because we have all-by which
I mean all serious readers since Plato wrote-kept coming back in
amazement and expectation to these astonishingly ugly things. You will
often hear it said that Plato is a master stylist, and indeed he is. He is
a master stylist because he can and regularly does with facility and conviction imitate everyone else perfectly, from Aristophanes' hwnour, to
Gorgias's na'ive urbanity, from Lysias's oratory to Protagoras's logic,
from Hippias's vanity to Alcibiades' disarmingly attractive hubris. Yet
the dialogues themselves remain lopsided, ungainly, "unbeautiful and
unperfumed:'They are nothing that we expect, either as ordinary readers or as readers with more sophisticated views about the nature and
tasks of philosophy. Plato's intensely ironic dialogues, then, are just
like the ironic Socrates, whom Alcibiades describes for us in the
Symposium. Completely ugly on the outside-short, snub-nosed, goggle-eyed-yet nonetheless suffused with a hidden harmony. Like the
Silenus figures Alcibiades goes on to mention, the dialogues are cleverly contrived statuettes, ugly satyrs of undisguised desire on the outside but on the inside filled with images of gods. Alcibiades saw the
gods in Socrates, but on account of his hubristic ambition to command Socrates' eros, he failed to make those gods his own. Likewise,
the reader of Platonic dialogues must abandon the urge to possess.
Blundering, thoughtless lovers, groping after the satisfaction of their
own, preconceived lusts,
will get nowhere.
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THE ABSENCE OF MATURE PHILOSOPHY. Socrates seems to be a
sort of conversational vulture, always hanging around to see if he can
turn the carrion of ordinary conversation into a philosophical feast,
More particularly, he seems to be a sort of psychic vampire as well, circling around all the promising young men, always whispering with
some one or a few of them off in a cor'ler, as Callicles for example
accuses him in the Gorgias. In both cases the hope and promise seem
never fulfilled. There is simply no Platonic dialogue between two
mature philosophers; Zeno and Parmenides happen to be present
together with an inunature Socrates in the Parmenides, while the mature
Socrates is present but does not engage the Eleatic Stranger in the
Sophist and Statesman. As for any dialogue that actively engages truly
potential philosophers, one might look to the Republic but Plato's dialogues furnish no clue as to the later fate of either Glaucon or
Adeimantus, while in the case of the Parmenides, the promising Socrates
is for the most part an onlooker-though he is undoubtedly educated
both by what he sees and by the brief exchange that crushes his fledgling account of Ideas. It is fair to say overall, then, that while Socrates
is forever interested in getting philosophy going and that as a mature
philosopher he is clearly superior to all those he actively questions, we
never really see philosophic conversation underway in full sail, top-gallants flying. Moreover, this omission is explicitly brought to our attention in the Sophist, whose intriguing prologue leads the eager reader to
expect a third dialogue, Philosopher, once Sophist and Statesman are done.
The apparent promise, however, remains unfulfilled. There never was
such a dialogue published, and we are provoked to wonder if it ever
could have been written. We are also invited to think about why
sophist and statesman should be the topics to eclipse so bright a sun
as that.
The common spectacle of the Platonic dialogues is at least the
deferral of fully realized philosophy and more often than not the outright failure of philosophy even to show signs of a healthy beginning.
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On the other hand, Plato himself is standing somewhere beyond that
absence and failure, a position he underlines for us by writing himself
out of a scene in which everyone would most have expected him to
appear-and where he was no doubt present in fact-namely Socrates'
swan-song and death, the scene that Plato dramatized in the Pbaedo.
Whatever else, therefore, that Plato takes his own philosophizing to
be, it cannot be what is represented in the drama of his dialogues. In
particular, philosophy as Plato means it to be understood cannot be a
11
simple equivalent to Socratic conversation:'
I mean that last assertion to be a little shocking. The dialogues are
often thought to be mirrors or representations of real, living communications, or at least of some idealized version of living, philosophic
communication. Moreover, this mirror image is by itself somehow
supposed to draw us too into the same sort of living communication,
as if the imitation became the deed in us by our seeing it. But Plato
did not seek to encode the living communication of philosophy by
imitating it via the drama that is constructed in and as the dialogue.
This is worth stating bluntly: Plato did not write dialogues because he
thought that the proper form of philosophy was the Socratic flim-flam
that takes up so mucb of them. The dialogues are designed to make up
for the fact that Plato cannot be here to talk with us as he would most
desire. They are the monological half of a philosophical communicac
tion that must compensate for the fact that one of the interlocutors,
perhaps the wisest one, is absent. The dialogue is first and foremost a
logos, Plato's logos. That it is dramatic and so on, is all internal to the
fact of its having been written down and published as an artfully contrived speech by one man to the entire world.
This does not sit well with a common contemporary view that
there is nothing else that should emerge from Socratic inquiry except
more Socratic inquiry, that the full, mature form of philosophy-disappointingly but somehow only accidentally missing from the dialogues-would be a conversation between Socrates and his equal in
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logical refutation. To cut a very long and depressing story short, current intellectual orthodoxy claims that the best reasons available to
human beings are always and in principle immanent to the contingent
circumstances of their inquiries, that our deepest thoughts cannot but
be fully conditioned by tradition and circumstance in ways that make
them inevitably finite and parochial, that all insight can never be more
than a single perspective, a point of view taken from within a limited
horizon. This posture has the following peculiar result: to the extent
that there is nothing absolute available in the contingent play of opinions, to that extent it starts to seem absolutely better to be able to
refute an opinion than to assert or maintain it. Human life on the
practical level no doubt calls for provisionally acceptable conclusions,
but on the philosophical or theoretical level all assertions turn out to
depend on the critically complacent failure to have discovered their
refutations, which if not around today surely will be tomorrow-or so
the fallibilist predicts and insists with alarmingly fanatical, not to say
incoherent conviction. It thus also follows that the theoretically open
mind ought to be an empty mind, a mind fortified with a sturdy arsenal
of techniques for preventing any opinion from lodging within it. To have
any opinion at all is to risk the embarrassing accusation of intellectual naivete. Whatever its own merits, this is not the view represented by
Plato's Socrates or his dialogues. Although Socrates claims to lack wisdom-in the teeth of the fact that no one, either inside or outside the
dialogues, believes him when he does so-it is stili wisdom that he
loves, not the lack of it. Contemporary critical thinkers love the lack,
and this tempts them into making a fetish of transcendental detach~
ment and to indulge an infinite, unfalsifiable suspicion for what
Socrates in the Apology calls his "human wisdom" and which elsewhere
turns out to be the science, note that word, the science of erotics.
There is, however, a more substantial point of comparison.
Although both Socrates and the contemporary critical thinker agree
that most people are unhelpfully opinionated (which is by no means
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the same as to say that all their opinions are wrong), the critical thinker
imagines that the fitting response is to work hard on disinterested
mind-skills for keeping all tempting beliefs up in the air, for keeping
the naivete of commitment at arm's length. For Socrates, on the other
hand, the fact that most people are opinionated is a much deeper,
murkier problem, tied up with what souls most deeply want and what
they most deeply fear they can't get. The examination of genuine opinions, i.e., the deep-seated convictions you have about what is true,
good, and beautiful, the convictions whose belief is not a matter of
choice, the examination of those sorts- of opinions is a far more
deli-
cate matter than testing for reasonableness-even if self-styled logicians knew precisely what that really is, which they obviously don't. I
say that so confidendy because I have never yet heard of a logician
helping anyone understand Plato, or Hegel, or Nietzsche, for example-all of whom I take to be entirely reasonable thinkers. They
haven't done much for Aristode either. Plato makes the need for something else especially clear by having his Socrates talk about two unusual and hitherto unrecognized arts: psychic midwifery in the Theaetetus
and philosophical rhetoric in the Phaedrus. The reader is also meant, of
course, to notice how often those same arts are portrayed at work
throughout the dialogues, both by the characters and by Plato himsel£
Philosophical inquiry turns out to be a far more complex activity than
tying people in argumentative knots or never being at a loss for a clever
or merely correct reply. It includes a moral, soul-tending dimension
that pays attention to pedagogical, rhetorical, ethical, and political
matters as well, in addition to the surface dimensions of logic, analytic technique, and epistemic responsibility.
TRANSITION. I have briefly considered Plato's artfully contrived
anonymity, the constant baffling of our logical expectations, and the
dramatic absence of philosophy in a mature form. These observations,
together with the phenomena of irony, both Platonic and Socratic,
plus a glimpse into certain soul-tending arts, all point to the partially
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hidden yet systematically intrusive presence of philosophizing in a
more complex, shadowy form than Socrates' public wrestling matches
or the Eleatic Stranger's diacritical gymnastics. Plato speaks through
indirection and means to indicate that philosophy cannot and ought
not to speak as straight as one might at first suppose, This initially
unsettling conclusion finds several well-known echoes in the Platonic
epistles. "There is no composition by Plato, nor will there ever be one,
but those now said to be his belong to a Socrates grown young and
beautiful" (3I4c). And then in a great and famous passage from the
Seventh Letter:
But this much I can certainly declare concerning all
these writers, or prospective writers, who claim to
know the subjects which I seriously study, whether as
hearers of mine or of other teachers, or from their
own discoveries; it is impossible, in my judgment at
least, that these men should understand anything
about this subject. There does not exist, nor will there
ever exist, any treatise of mine dealing therewith. For
it does not admit of verbal expression like other studies, but, as a result of continued application to the
subject itself and communion therewith, it is brought
to birth. in the soul of a sudden, as light that is kindied by a leaping spark, and thereafter nourishes itself
(34IB)
Nevertheless, Plato wrote dialogues all his life, taking astonishing
pains over their intricate construction. He cannot therefore have
thought them superfluous or trivial, despite his recognition of their
necessary limits. By all normal standards of truth-telling coherence the
dialogues are manifestly deranged; my task now is to address the partly hidden method in their apparent madness,
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Philosophy in the Ironical Mode
According to the reports of antiquity, Aristotle wrote Platonicstyle dialogues in the earlier part of his career. They are, regrettably,
lost-all the more regrettably, seeing that Cicero praised them as golden (though what else should we expect from someone who spent the
greater part of his early years in the Academy teaching rhetoric?).
What we have from Aristotle are documents that may reasonably be
thought of as treatises or at least notes to treatise-like expositions. As
it happens, there is nothing in the Aristotelian corpus as we have it that
can confidently be taken as published writing in the manner of Plato's
dialogues and it is certainly the case that much of what we do have
presents an aporetic, tentative, less than declarative face. Even so, and
with all due allowance for hints at even Aristotelian indirection in what
seem to be far more straightforward texts, the Aristotelian writings
bear witness through much of their bulk to an expository, more recognizably academic style of philosophical speech than the baffling
Platonic form. The comparison shows that Plato perfectly well understood what it would mean to write philosophy in that more straightforward mode-and that Aristotle knew perfectly well what it would
mean to write in the ironic, self-deprecating dialogical mode. In neither case, then, is the form a stylistic quirk or an historically dictated
necessity. Moreover, for both Aristotle and Plato it was a conscious
decision to write at all, since Socrates, just as self-consciously did not.
DIALOGUE VS. TREATISE, What is at stake in this stylistic difference
between dialogue and treatise? At first glance, the Aristotelian style of
telling, philosophical speeches gives one reliably direct ways of talking
about and thinking about the ordered, eidetic structure of things, both
human and non-human. Even if one accepts none of his specific metaphysical results or if one prefers to emphasize the open-ended, aporetic character of certain of his inquiries, Aristotle's noetic tools and cat-
egories have proven themselves of permanent worth. The notions of
substance, essence & accident, form & matter, actuality & potentiality,
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THE ST. JOHN'S REVIEW
together with Aristotle's interpretative specifications of aitia1 arche1 kine-
sis, psyche, phronesis, episteme, and praxis are all ingenious and virtually indispensable devices for anyone interested in the peculiar business of
philosophical articulation, Aristotle's insights constitute a huge fraction of our philosophical patrimony, and amount to a legacy we
should receive with both gratitude and respect, While at least equally
deserving of gratitude and respect, Plato's ironic form of philosophical telling does not emphasize in the same way the ordered structures
that may be seen and understood. Rather, Plato points to what it is like
to be seeing structure, what it is like to be moved by truth, to be astonished by beauty, to aim at and hope for the good. Not only that, Plato
also indicates the manifold ways in which human beings variously fail
and fall short in their attempts to be knowing and wise, Actuality and
achievement rule in Aristotle's philosophic art, eros and lack in Plato's,
The one emphasizes what may be understood, the other the fragile,
unsteady soul that does the understanding. Aristotle is thus the
philosopher of detachment, Plato the philosopher of integrity.
Correspondingly, the danger of Platonic philosophizing is self-obsession and the narcissism of intelligent desire, while the danger of
Aristotelian philosophizing is self-forgetfulness and the indulgence of
theoretical hubris. Strange as it may seem, although Aristotelian exposition puts a premium on truth-telling, in the end it is more guarded.
Aristotle tends to suppress the erotic, the madness of self-transcendence and the nuances of self-knowledge. In particular, he muffles
what is dangerous about philosophy, whereas Plato is comparatively
open about it. Aristotle provides many theoretical insights for which
one can be very thankfUl, yet it is worth recalling that on the death of
Alexander he had to flee Athens, pursued by an indictment for impiety. For help in understanding that disturbing fact, one will find more
extensive guidance in Plato.
In distinguishing an eidetic emphasis from an erotic one, I do not
mean to say that the two modes are rigidly correlated with dialogues
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and treatises, as if Plato never really presented a philosophical idea or
Aristotle never worried about the integrity of thinker and thought,
Platonic dialogues can in places be as expository as Aristotelian treatises can in places be ironic and full of finesse. Both modes have their
relative purposes and merits. Sometimes, one is simply ready to hear
an idea, to be told how it is with things, to be shown where the joints
of the world are. At other times, and for different reasons on different
occasions, one needs to understand the circumstances of such truthtelling. "Aristotelians" and "Platonists" have quarreled over these mat-
ters for centuries and will, doubtless, brawl for centuries more. As a
matter of temperament, different human beings find themselves favoring one emphasis rather than the other, but both dialogue and exposition are equally flexible in the hands of masters. In fact, I am quite sure
that philosophic masters need to be masters of both. Let me just state
then that masterful philosophical articulation, in thought or in speech,
requires equal command of what I shall call eidetics and erotics. As just
suggested, eidetics correspond to the objects of contemplation, the
intelligible nature, structure, and wholeness of things. The dimension
of erotics includes how the soul is disposed to think and to act, and
how responsible it remains to itself and its conditions as it engages
both. As it happens, i.e., just as a matter of historical fact, the artful
irony of Plato's dialogues as we have them communicates far more
about philosophical eros-and its failings-in relation to the truth
than do the Aristotelian writings we have. No doubt Aristotle could
have told us more, and has probably told us more than is usually realized, but I think that the matter of fact rests on a matter of principle,
namely, that Platonic dialogue is truer to the manifold needs and realization of lucid, philosophical existence. In particular, it is Platonic
dialogue that can more reliably save us from ourselves, since it is with
respect to the erotic dimension of human endeavour that we keep getting in our own way. that we are the originating sources of our own
unnecessary wanderings and corruption. Eidetics tend, in comparison
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though by no means mindlessly, to take care of themselves-one sign
of which is that they're more teachable.
ORIGINS OF IRONY. Plato hides, though not with complete invisibility, behind his characters. Chief among them is a character, namely
Socrates, not only notorious among his fellow players for his irony but
plainly to us his spectators coy, manipulative, and far from even-handed. Taking courage from the apparent straightforwardness of
Aristotelian exposition, we can hardly forbear an exasperated cry: Why
all the fuss? Why the teasing, not to say irritating indirection? What
prevents philosophy from speaking forthrightly, from saying all she
means? Must philosophy always play false, or perhaps play games, with
our truth-telling hopes and ambitions? In short: what, if anything,
calls for Platonic irony? If we cannot answer such questions, then Plato
can be left to his idiosyncratic, sibylline whimsies. Unsurprisingly, the
dialogues themselves furnish many clues to a more generous understanding. Given that writing dialogues cannot be all there is to the
philosophical life, it will be helpful to consider such writing in light of
that living whole. As I read the dialogues, actual philosophical life has
four principal domains of responsibility: work, pedagogy, guardianship, and civics. By work I mean master-work, the full, unimpeded realization of philosophical insight. By pedagogy I mean the husbandry of
potential and apprentice philosophers. By guardianship I mean the
preservation of philosophy against both external assault and internal
corruption. By civics I mean philosophy's citizenly life and duty within the larger human community that gives it birth. All four domains
suggest good reasons for philosophical indirection, for less than
unqualified truth-telling, though I shall not here be able to pay full
attention to them all.
The most common initial excuse offered for Platonic irony, for
why the dialogues seem so ugly and manipulative and confusing,
appeals to pedagogy, to the requirements, as it is commonly formulated, of getting readers to think for themselves. Certainly, in any worth-
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while education and a fortiori any philosophical education, mere
instruction is not sufficient for understanding. Instruction alone leaves
us, as Nietzsche put it, with a bellyful of undigested knowledgestones; enough to calm our hunger for a while perhaps, yet ultimately
unable to nourish and satisfy. To the extent, therefore, that the dialogues aim at guiding and training potential philosophers, it can safely be expected that they do more than instruct, that they challenge
when we get lazy, inspire when we are daunted, and that they somehow
aid proper noetic digestion. As usually understood, however, this
encouragement "to think for oneself" is interpreted as the develop-
ment of critical thinking skills, skills that may permit you to grind
down those knowledge-stones but which do nothing to help you assimilate whatever truth they may have contained. One must also be wary of
supposing that such pedagogical aims, even when understood in the
best sense, exhaust the possible reasons for dialogical irony, that teaching determines the boundary of Plato's communicative intent. It does
not.
There is another, deeper difficulty with the idea of thinking for
onesel£ Namely, that everyone already does; it's part of the problem,
not the solution. To quote from Heraclitus once more: "though the
logos is common, the many live supposing themselves to have a special
understanding" (Frag. 2). At the most important level, then, irony or
stimulating indirection is a proper part of philosophical pedagogy not
so much because young learners need tricky help with the hard work
of assimilation-which they certainly do-but because we human
knowers are constantly prone to collapse into that state of conscious-
ness Hegel identified as self-certainty. Once in such a state, we can usually only be levered out again with well-meaning, i.e., noble, lies. Being
in the know, the natural condition of the human soul, is so obviously
our greatest adaptive advantage that we keep getting entranced by partial realizations of our wonderful capacity, we keep generalizing our
local insights into global wisdoms. But how is such self-satisfied con-
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viction to be moved, led out of itself. educated? How does one come
to recognize that one does not know? Hegel's dialectic, to the extent
that it may be thought of as containing a pedagogical response to the
problem, is a logical bludgeoning that has turned out to be all but useless, except in the case of a uniquely motivated not to say perverse few.
Socrates, in contrast, seduces many a complacent soul-though not
every one-out of its proclivity to noetic self-satisfaction with all
manner of charms and deceits, as does Plato in turn at another level
of refinement, The essential psychagogical trick in most cases is to
make the higher truth look somehow attractive within the perspective
of the lower, more confined horizon. Plato's Eleatic Stranger classifies
such tricks as belonging to that species of the image-making art that
works with phantoms (fantastics) rather than with likenesses ( eikastics). The distinction is made in a dialogue entitled Sophist (236c).
Philosophy's strictly educative concerns, however, have definite
limits, since not every soul is capable of fully realizing her promise. We
moderns do not like to hear things like this, partly because we tend to
think that reason ought by and large to be perfectible by methods universally available to all and partly because we hate to think that possibilities are limited or that freedom alone might not suffice for realizing the good. Plato is more hard-headed. Serious attraction to philosophy is no guarantee at all of its fulfilhnent, as may be seen, for example, in Apollodorus of the Symposium, who was at least wise enough to
know this fact about himself. Furthermore, while Socrates will converse with whoever comes his way, he does not undertake to teach
everyone, Some souls he passes on to others, often guided by the
admonitions of his daimonion, his divine sign:' His daimonion, of
course-his little daimonic thing-is an inflection of the daimon eros,
in whose affairs he is expert. So Socrates will sometimes help and
sometimes turn aside those who will never be able to manage all that
philosophy requires. As with most serous matters, it is a risky sort of
.discrimination, easily incurring public odium. In Socrates' case, that
11
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risk is the essential meaning of the historical accident that wrapped his
erotic daimonion up into the civic charge of impiety, of importing new-
fangled gods, an innovation partly responsible for his execution. As a
final point it needs to be noted that infatuations with philosophy are
not always so benign as Apollodorus's. The tyrannical ambitions of
Alcibiades and Critias, for example, both gifted intellectually, were
blamed on their association with Socrates, while Plato's Seventh Letterfrom which I have already quoted-exists principally on account of
the havoc wreaked on philosophy's public, indeed international, reputation by Dionysius the Younger, Tyrant of Syracuse, in his efforts to
make Plato's wisdom his own.
My guiding question is whether or to what extent the irritating
indirection of Platonic dialogue can be understood as exercising philosophical responsibility. The particular demands of teaching provide
some plausible grounds, but there are others. Some of these are rather
easy to overlook, once inside the comforts provided by contemporary
academic freedoms. But not only are those freedoms hard-won and in
need of constant maintenance (a task for which philosophy, in virtue
of its disciplinary competence regarding the relation of theory to practice, is the proper guardian), neither is peace the uniform condition
within our necessarily parasitic Republic of Letters. Academic politics
is notorious for its pettiness and intolerance-itself a hardly accidental fact-but more significant are the manifold theoretical disputes over
demarcation, hierarchy, and methodology across and between the various disciplines. Regarding these foundational and procedural
reRections, philosophy's competence and even presence is held in deep
suspicion by the positive disciplines. Within the so-called university,
faction it would seem is the norm-no matter what ideals one might
prefer or hope to see there.
Not everyone can be fully philosophical, you might think that's a
shame; not everyone wants to be philosophical; well, that's their choice;
but not everyone wants philosophy around. That's dangerous. Hence
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the need for what I called philosophical guardianship. Both philosophy
and what is philosophically best in all of us cannot rely on being left
alone. In either the personal or the political case, there are several
intrusive challenges to philosophy's well-being within its larger community: the psychic community of manifold desires on rhe one hand;
the civic community of individual agents on the other. The fights in
borh cases depend on a hunger for wisdom, The Platonic dialogues
emphasize two main sources of intrusive challenge, and though I shall
discuss them mostly in terms of the civic paradigm, the Republic's own
brilliant likeness of city to soul should keep the psychic paradigm
equally in mind. According to Plato's dialogical imagery, then, the
challenges come (I) from the other men of logoi, of whom the two
main classes are poets and sophists, and (2) from the men of the city,
who share wirh philosophy an ambition for the noble but disagree on
the location of its highest form. The latter challenge also has two arms:
that philosophy subverts decent, conventional politics ( Anytus,
Cleitophon), and rhat philosophy is adolescent, laughable, and unmanly (Callicles, Thrasymachus). Adeimantus, who stands for what is necessary and best within the large yet still limited horizon of the city,
bluntly restates these rwo accusations in the middle of the Republic:
philosophers are eirher useless or depraved. They therefore deserve no
place in human community, let alone to be enthroned as its only competent kings. Perhaps the clearest overall Platonic symbol of the political challenge is the dialogue entitled Socrates' Defense Speech, while an
emblem for rhe challenge from rhe men of logoi may be found in that
gigantomachy mentioned in the Sophist, that never-ending battle
between the hard-headed, aggressive ''motion men"-whose general,
so we learn in the Theaetetus, is Homer-and the gentler, more generous "friends of the forms:'
Plato's implied account of rhe nature and grounds of rhese several challenges, I cannot examine in detail here but it is, I think, tolerably clear rhat the predicaments are, in all cases, serious and abiding
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ones. Astute Protagorean prudence, Hippian technical competence,
and effective Gorgian rhetoric all seem far more beneficial-both in
themselves and certainly to their practitioners-than Socratic elenchus
could ever be. Socrates' wisdom appears only to numb people and
make them angry or unhappy. Horner, Sophocles, and Aristophanes all
seem more inspiring and companionable than philosophy's austere
explanations and deflations, from which the gods are missing and in
which, if the divine be mentioned at all, it seems aloof and indifferent
to .human concerns. Too much talk, and talk for talking's sake, are
indeed shameful and unmanly, while delving too deeply into the origins of things does indeed run risk of undermining civic loyalty, familial respect, and even the self-confidence that is a necessary condition
for any worthwhile deed. All these tensions have a symbolic focus in
that disturbing scenario at the end of the Republic's most memorable
image: the philosopher returning to the Cave would be set upon and
killed by those still shackled there, if they could get hold of him. Their
opinions are not so true as they imagine them to be, formed as they
are by the shadows cast from artifacts and statues of real things carried above and behind them by poets, sophists, and politicians, and
they would react with hostile fear if they knew. Yet the lesson is not
that the Cave-dwellers are all contemptibly ignorant and wicked; it is
that pure wisdom is unbearable to the incompletely enlightened soul.
I say "incompletely enlightened" because too bright a light is unbearable, only to those who can already see. There is both a fire and muted
daylight in Plato's Cave. Athens that prided itself on its freedom of
discourse, its accomplishment in tragedy and its welcome to the
sophists, nonetheless executed Socrates and indicted Aristotle.
Philosophy cannot be an unqualified human good, because it is not
unqualifiedly safe to tell the truth. We all know this already. Frankness
is a gift and honour reserved for close friends, and even there it's
difficult. Nor should we be surprised to learn that the truth is dangerous, if-as we hear so often-that knowledge is power. Socrates let
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himself be executed to vivify these sorts of unsettling facts for all
thoughtful souls to come, knowing that Plato was there to write about
it in a way that would keep the recognition safe within the memory of
subsequent generations.
The several differences between what is philosophical and what is
not are none of them merely qualitative; they are &aught with threat
and anxiety of an order that civility alone cannot control because their
roots lie deeper than the city. Furthermore, Plato's sustained attention
to the various assaults on philosophy suggests that none are to be
regarded as accidental, that there are good if incomplete reasons why
philosophy should suffer from them and it is therefore incumbent
upon those pursuing her to understand the justice within such fates. To
the extent that the assaults are not accidental, the need for irony in
dealing with them is more than politic accommodation, Philosophy
needs to make a peace with politics and poetry, with the healthy decency of civic life and with the consoling charms of comedy and tragedy,
but such peace is at best a very unstable friendship of unequals,
Moreover, the instability is reproduced within the individual soul as
well. Each of us must make his uneasy peace both with the needs of
practical life and with the enchantments of art, if we are to live as
thoughtfully as possible, The ironical Socrates in Plato's ironical dialogues can be seen constantly negotiating these inequalities and their
attendant dangers. Budding philosophers can be thankful for the tips.
Guardianship and pedagogy deal, respectively, with the privations
and the potentials of philosophizing. Actual or fully-fledged philosophizing remains, Insofar as irony entails in some sense a playing false,
it might seem that irony could at best be only conducive to and never
constitutive of philosophy's focal activity-which might for the
moment be characterized as consorting with the truth. Yet irony
belongs here too, I think, at the heart of philosophy's defining concern.
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Philosophical account-giving or truth-telling has to be ironical to
the extent that what philosophy is obliged to mean cannot in principle
be given all at once. Philosophical comprehensiveness entails primacy,
universality, and lucidity, i.e., its truth-telling must be a self-illuminated knowledge of ultimate principles in relation to what is. Among
other things, this implies that any philosophical account aims at simultaneous knowledge of the conditions that make possible and justify its
thematic claims; it must not only tell the truth, but somehow also tell
the truth of its telling as well. These conditions for the possibility of
a speech, however, cannot be given along with the content of the
speech-at least not in the same, linear, thematic way. Hence the logical necessity for a two-faced mode of speaking: one aspect to declare
what one wants to say, the other aspect to show that one knows exactly how and why one can say it. Such a two-faced mode of speech is
properly called ironic because it cannot state all that it means at once,
though it is not thereby prevented from evoking the wholeness of the
understanding it articulates-on the condition~ that is, of a generous
listener with an eye for reading between the lines. Failure to appreciate
that philosophy requires at least this sort of irony easily leads to measuring its discourse by a mathematical standard, since the latter is a reasonable measure for interim, though never for primary, insightfulness.
Similar failures have also been responsible for many a foolish trek
across the transcendental desert in search of presuppositionless beginnings. One further consequence is that philosophical speech, because
both primary and comprehensive, cannot be univocal in principle. This
is the deep ground of philosophy's ancient quarrel with poetry and
why metaphorical speech is so emphatically integral to the texture of
Plato's dialogues.
I have just argued that fundamental speech, and this would be in
whatever situation we
find
ourselves moved to give it, has to be two-
faced. It follows that univocal speech-i.e., the speech that gives the
appearance of managing to say all that it means-is not only second-
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ary but also contingent upon that primary equivocation. Univocal
speech is therefore radically unstable, bounded and made possible in its
qualified way by a tacit agreement not to press inquiry beyond a certain point. Part of our human experience of this fact is the disturbing
discovery that plausible arguments can apparently be made on both
sides for virtually anything-the so-called dissoi logoi of the ancient
sophists-and that almost no one is ever persuaded by rational, i.e.,
purely univocal, words alone. In the absence of philosophy or fundamental speech, any assertoric stand thus depends as much on the will
to maintain it, on agreement to abide by the axioms that make it possible, as it does on the content of those axioms themselves. Perversely,
then, it becomes possible to take a stand in words without the corresponding insight and so too without the corresponding resolve or
choice that deemed the axiom worthy-or, rather, one takes a stand
with an alternative, unspoken resolve. That's why Aristotle said that the
difference between the sophist and philosopher lies in their resolve,
their proairesis, not in the arguments they give, Yet note that even philosophy cannot logically repair the breach caused by any such willful
detachment of speech from the soul's orientation and insight. In other
words, philosophy cannot in words alone compel the sophist to come
out of hiding. This is an important lesson of Plato's Sophist and it is
also the reason Thrasymachus blushed, for he eventually had to betray
his sophistry once he had committed himself to the theoretical probity of "precise speech:' It was a noble and educative blunder, In sum,
therefore, human logoi can never by themselves reveal the soul that
makes them-and so we must pay as much attention as we can to
deeds as well, One of the most important resources of Platonic dialogue is, I suggest, their ability to let us see how speeches are anchored
in a soul's resolve, despite the fact that a soul's true love cannot in principle be deduced from the things it says.
TRANSITION. Philosophical insight depends on a complex of conditions, both extrinsic and intrinsic, to which I have pointed under the
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topics of work, pedagogy, guardianship, and civics. In their light, I
have sketched several ways in which irony is native to how philosophy
must deal with what is non-philosophical, with what is potentially
philosophical, and with the truth itsel£ Unlike Athena, human wisdom does not actually spriog fully formed from the head of Zeusthough what the myth means to say is that wisdom, once she has arisen, cannot be fully explained in terms of genealogy alone. Also unlike
Athena, human wisdom has no nectar and ambrosia with which to fortify itself against the many forms of mortal decay. This means that no
matter how like a goddess, pure theorizing on its own is by definition
irresponsible. It also follows that no part of erotics can be set aside on
the plausible yet mistaken grounds that eidetics are philosophy's only
proper concern. Socrates' erotic science may be shady and ironic, yet it
nevertheless belongs to philosophical life quite as essentially the rest.
With this granted, however, it will always remain to consider when and
to what extent one need or ought to talk out loud about such things.
I accept, therefore, that my entire speech, no matter how correct it may
be, remains vulnerable to being judged either tactless, or trivial-to the
extent that it does not emphasize eidetic content.
Why Plato Wrote Dialogues
Philosophical truth-telliog, the sustaioing activity of philosophical
life, has to be two-faced. Hegel's impressive dialectical logic is a concerted effort to smooth out this acknowledged need for irony, an
attempt to resolve self-illumioatiog iosight into a special sort of discursive linearity, into a proof that manages to demonstrate its axioms
as it deduces its theorems. His experiment in philosophical discourse
is weak, however, on two maio counts. First, the logic of Hegel's proof
\s io the end not as methodical as hoped for, indeed required.
Ingenuity is still needed io order to make the crucial transitions, an
iogenuity that Hegel from time to time facilitates with quite remarkable philosophical poetry. A further sign of this same weakness is his
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embarrassment over giving introductions, which he knows he should
not in all strictness use but which he writes anyway. Moreover, since
the introductions are where Hegel encodes the suppressed erotics of
his philosophic art, i.e., what he means to be doing as a man here and
now in love with philosophy, that's exactly why everyone finds them so
intriguing and often more interesting than what follows. Plato avoids
the dialectical inconsistency of such introductions, remaining truer to
Hegel's own insight that philosophy cannot ever in principle begin to
prove itself, that it cannot put itself on trial before the tribunal over
which it presides as judge. Perhaps Hegelian dialectic comes as close as
philosophical discourse ever can to an exhaustive, rationally systematic, univocal self-explicitation. The question, though, is when or
whether we really need such a thing. Plato wrote a defense speech for
philosophy, but he quite deliberately named it after Socrates, not himsel£ The second major weakness of Hegelian dialectic is it's being so
forbidding and dull. This is an important criticism. It says that Hegel's
philosophy by and large fails, as I noted earlier, to seduce, fails to
enflarne theoretical eros, fails sufficiently to help us make insight our
own. Platonic dialogue, in contrast, is remarkably seductive-the unattractive patches notwithstanding. In fact, part of its seductiveness is to
make itself confusing and exciting by turns, whereas Hegelian dialectic plods along in the same old difficult way page after page. Knowing
that Plato can be wonderfully lucid and inspiring from time to time,
forces the reader to seek a reason and so too a meaning for the times
when the text is experienced differently. There is nothing more inspiring than the suspicion of a hidden life, une vie inconnue, half-hidden
depths in which we might swim if only we can prove strong enough.
Platonic dialogue is a complex three-dimensional speech, rather
than a linear, discursive one. Its axes are drama) argument, and character, all
three of which follow their independent but mutually interpenetrating
logics. Take book one of the Republic. Why does Polemarchus interrupt?
How does his account of justice follow up on the account his father,
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Ill
Cephalus, seemed to give? What is the relationship between
Polemarchus and Cephalus? Who is the better man and why? What
things seems good and best to Polemarchus? What things most noble?
What is there in a man like Polemarchus that inclines him to think of
justice and friendship in the way he does? How exactly did he get
talked into agreeing that justice is trivial and base? Are his mistakes
consistent with the partial goods for which he stands? What do
Socrates' examples tell us about Polemarchus's mistakes? What is
Socrates trying to do for Polemarchus? To what extent, if any, is he
successful? Why does he care about Polemarchus at all? Why does
Socrates argue so fallaciously in proving that justice does no injury?
What did he understand about Polemarchus to know he could get
away with the fallacy? Why is Polemarchus so enthusiastic in his final
agreement to be a "partner in battle" with Socrates? How does all this
relate to Polemarchus's action at the very beginning, when he waylays
Socrates and Glaucon? How does it fit with his later interruption, in
book five, when he objects to women and children in common? What
is Plato showing us about the limits of Polemarchus's understanding of
justice? About its merits? Why is Polemarchus there, between Cephalus
and Thrasymachus? And so on. Not until you have some reasonable
answer to all of these sorts questions, and scores besides, can you have
begun to understand Plato's meaning, his logos, in these four or five
pages. You need to become proficient in a multivariable calculus that
simultaneously integrates along the three dimensions of drama, argument, and character to produce a shimmering hologram of meaning.
This dimensional complexity allows the dialogue to mean more than
what it says in its arguments and to reveal more than its narrative
depicts. It opens up a maximum of triangulation between uncertain
souls and their shifty speeches.
Aporia, then, is superficial. It belongs to only one or two of the relevant dimensions and is therefore only an aspect of the whole. The
characters may be in perplexity, and maybe the reader is too, but Plato
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is not. His pictures of perplexity are too finely drawn to be themselves
expressions of the depicted anxieties; they are too precisely located and
elaborated not to be the subject of a higher-order interpretation. What
foolishness would impel anyone to spell out ignorance and error so
intricately, and with such great pains at so great a cost of time, if he
did not have a view of what they meant? F,or all the reasons examined
above Plato conveys his interpretations obliquely, but that does not
mean the dialogues bear out no logos. On the other hand, Plato's logos
is a delicate and subtle thing, not easily separable from the theatre it
animates. It is a sure sign of having failed to understand Plato fully
when one is forced to leave or dismiss any single part of the dialogue
as incidental, as wrapping, as form rather than content. Plato does not
dress up otherwise independent, philosophically sober propositions in
gaudy, entertaining dramatic garb, as if through some aesthetic quirk
he liked to do it that way. There is indeed the thing that he means to
say, but it is not captured by the naked propositional bodies you might
take to be under the theatrical fancy dress. As I have just indicated, for
example, the philosophical meaning of Polemarchus is more than the
partially correct proposition that justice is doing good to friends and
harm to enemies. Among other things, he casts significant light on how
and why the proper discipline of spiritedness is integral to philosophy,
and why friendship is the soul of justice. Quite in accord with a principle Socrates announces in the Phaedrus, everything in the dialogue is
meaningful and everything serves the overall meaning Plato would
communicate.
This raises yet another matter of philosophical tact. According to
what I have just said, it should be possible to spell out Plato's meaning in non-dramatic terms. To be a correct translation, part of such an
exposition would have to be ironical and it would have to encompass
at least the sense of all the implied erotic elements as well as the eidetic ones. Nothing obvious prevents such a gloss, yet even if correct, it
remains to ask whether such a flattened out account could do all or
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~ven much of the work Plato intended and which the dialogues have, in
fact, done and continue to do. The answer would have to be, I think,
no. In one sense, Ideas-by which I mean the fundamental archai and
intelligible structure of all things-are just not a problem; the predicament is that human souls for the most part fail to be ruled by them.
That's something no amount of theory can fix.
I asked the question: what, if anything, calls for the strangeness of
Plato's dialogues, what could justifY their indirection? A natural
instinct, on first hearing such a question, is to look for reasons that
might force or compel the response, reasons why things could not be
done in any other way. In the present case, however, the instinct is misleading. The serious grounds for Platonic indirection I have considered
do not, I think, necessitate the dialogue form. Without being necessitated, however, Plato's dialogues are a beautifully effective response to the
many things philosophy always finds needing to be done. In my own
view, they are the most beautifully effective response we have yet witnessed.
A beautiful, noble, and effective response to abiding necessities is
certainly grounds for praise, but this is not all there is to admire. By
the ambiguous testimony of his letters and by the seamless consistency of his dialogical irony, Plato could not have been writing as an intellectual to express his thoughts or as a scientist to circulate his results.
Perhaps it is hard to imagine there could be any reason for writing left,
besides vanity or madness. Yet, Plato worked at something, and no one
has ever doubted, despite the derangement and indirection of the texts,
that they' are all somehow for the sake of philosophy. I add: for the
sake of keeping philosophy alive and well. Plato wrote for the love and
care of philosophy, for its realization and well-being in living souls as
well as in real cities. He saw clearly in what senses its husbandry,
preservation, defense, and even its central truth-telling activity called
for-though without necessitating-something like his two-faced
books. Among other things, he aimed at philosophy's survival as a cul-
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tural entity in the tradition we think of as Western civilization. In this
he was successful. Unbelievably successful, as may be seen in the fact
that two-and-a-half thousand years later: here we all are, still vitally
interested in what Plato had to communicate, in what a man like Plato
understood the life of wisdom to be. Moreover, we keep being affected by his enigmatic communication, both directly as we study and
through myriad historical reverberations at work behind the scenes of
our own present educations. Even after all this time, we keep taking
good things away from his amazing gift. The dialogues, then, are the
instruments of Plato's megalopsuchia, the unhurried means of a rare but
great and noble deed, the sort of deed yearned for by all men of the
highest human excellence, Plato's great-souled project was to create the
real, on-going world in which we are all now able to carry on with philosophy; he cleared the space, he gave the laws, he holds up the firmament.
As a great-souled man, all honour and praise are Plato's due but we
cannot expect him to be impressed by such external rewards, His ambition was for a deed large, beautiful, and impressive in itself. The reward
for such deeds is the overwhelming pleasure of actually doing them,
though that too is hardly the central reason for which they are undertaken. No great-souled deed can be great, if it cannot be described in
terms of a single-minded devotion that transcends selfish purpose, Yet
it does not follow from this that devotion to such an end is purely
selfless, The great-souled man is himself fulfilled by his devotion to
what transcends ordinary ambition, Thus, Plato wrote not only for
others. He also wrote for the love and care of philosophy in regard to
himself. in regard to his own glories and satisfactions as a wise, superior, and fortunate man. He also wrote his dialogues as an exhibition
of prowess, and for the sake of joy in the exhilarating exercise of his
own powers and command. In the end, Plato wrote dialogues for the
same reason God created the world: because he could. No one, absolutely no one, has come anywhere near matching him since,
�....:; The Discovery of Nature
fj:-- James Carey
On the orcular seal of St. John's College, enclosed within
the Latin motto, H Facio liberos ex liberis libris libraque;' 1 are seven books and
a balance. The books stand for the quadrivium and trivium of the
seven liberal arts, i.e., arithmetic, geometry, astronomy, and music, on
the one hand, and grammar, rhetoric, and logic, on the other. The balance stands for natural science. The founders of our program initially
tried to find a way of regarding natural science, or as we say today "science;' as contained implicitly within one or more of the seven liberal
arts. This attempt, which apparently involved such ventures of fancy as
interpreting mathematical physics as a subset of the liberal art of
music, was unsuccessful. The founders of our program carne to realize
that natural science needed a symbol of its own, and they settled on
the balance. This was a good decision, for, aside from allowing for the
elegance of the College's motto, it recognized a real distinction
between the seven liberal arts and natural science. As regards the correctness of this distinction it suffices to note that during the Middle
Ages there were many religious believers who understood themselves to
be committed to the seven liberal arts, even to be practitioners of these
arts. They did not see any conflict between being practitioners of the
liberal arts and belief in the Bible. None of the claims made by these
arts, even the claims made
by astronomy as it was practiced then, were
thought to be in essential conflict with those of the Bible. The case is
otherwise with the claims of natural science, not only with those of
modern natural science, which of course had not appeared yet, but
even with the natural science of classical antiquity. It is not for nothing that, as the introductions to physics, chemistry, and biology textbooks never tire of telling us, "science" stagnated in the Middle Ages.
James Carey is a tutor and former Dean at St. John's College, Santa Fe. This essay is an expanded
version of a lecture given at St. John's College in Santa Fe on August 22, 1997.
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Now, the object of natural science is, of course, nature. Natural
science is the knowledge of nature. I am told that there is no Hebrew
'
word that adequately translates <j>'UOL<;, the Greek word for nature, and
that the concept of nature is foreign to the Bible, at least to the
Hebrew scriptures. If this is true, it would suggest that the concept of
nature was unknown to the ancient Hebrews. And if those people,
who were aware of so much, were unaware of the existence of nature,
then the existence of nature could hardly be said to be self-evident. It
is not self-evident, then, that natural science has an object, Or, more
precisely, it is not self-evident that natural science has the object it
thinks it has.
We are often told that it was the Greeks who discovered nature,
and that this discovery is the origin of what is thought to be the
uniquely Western enterprise called philosophy. If something was discovered at some more or less identifiable point in the past, was until
then unknown, and continued to be unknown by those who were not
apprised of this discovery, then the existence of the thing in question
can hardly be called self-evident, since it pertains to the very sense of
what is self-evident that its existence is recognized and uncontested by
all, or at least becomes so once it is pointed out, The very discovery of
nature by the Greeks, if it really was a discovery, implies that the existence of nature is not self-evident,
But no lesser a thinker than Aristotle tells us that the existence of
nature is self-evident. In the Physics, we are told that animals and the
parts of animals, plants, the elementary bodies earth, fire, air and
water, and all such things have a principle of motion and rest within
themselves, and are distinguishable from beds, coats, and the like,
which have no such intrinsic principle of motion and rest, The latter
are caused by art, whereas the former have natural causes and exist by
nature. Having located the basis for the distinction between natural
and unnatural things in the presence or absence of an intrinsic principle of motion and rest, Aristotle proceeds to say,
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As for trying to prove that nature exists, this would
be ridiculous, for it is evident that there are many
such things [i.e. things that exist by nature], and to
try to prove what is evident through what is not evident is characteristic of a man who cannot distinguish between what is known through itself and what
is known not through itsel£2
To try to prove that nature exists is a failure because it is self-evident that nature exists. Any propositions that one might invoke to
serve as premises from which one could deduce the conclusion that
nature exists would be less evident than this very conclusion, and for
Aristotle all so-called proofs that deduce the more evident from the
less evident are not really proofs at all. But, again, this consideration by
itself does not cast doubt on the proposition that nature exists. The
reason the proposition that nature exists cannot be proven is then,
again, not that it is false or even doubtful, but that it is self-evident.
Examples of self-evident propositions include certain propositions
of the broadest generality, such as the so-called principle of noncontradiction, and certain propositions of the most restricted particulari-
ty, such as that I have a headache right now. Neither of these propositions can be proven, but this is not because they are unknowable. The
reason these propositions cannot be proven is rather that they possess
such immediate evidence that they cannot be deduced mediately, so to
speak, from propositions possessing greater evidence. A self-evident
proposition is one that, to use Aristotle's expression, is
11
known
through itself:' It is not known through otherpropositions. According
to the passage from the Physics that we were just considering, that there
:rre things that exist by nature and that nature itself exists are propositions that are known through themselves, propositions that have the
character of being self-evident.
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THE ST. JOHN'S REVIEW
Of course, a proposition's being unprovable is hardly a sufficient
condition for its being self evident, for all false propositions are
unprovable and, to say the least, none of them are self-evident.
Moreover there is a whole class of propositions that cannot be known,
by the ordinary means of knowledge at any event, to be either true or
false, such as "He has a headache:' For if he tells us he has one we cannot prove that he is not lying, although we may have no good reason at
all to suspect that he is lying. There is some evidence that he has a
headache, but this evidence lacks the compelling character of either
demonstrative truth or unqualified self-evidence, We take it on faith,
so to speak, not irrationally and not without some evidence, not just
as a hunch or a blind guess, but still without apodictic certainty, that he is
telling the truth when he says that he has a headache.
So we have grouped unprovable propositions into four classes: I)
self-evident propositions of extreme universality, such as the laws of
logic; 2) self-evident propositions of extreme particularity, concerning
things I know about myself: my feelings, my reactions, and so forth; 3)
false propositions; and 4) matters of faith or, if you like, matters of
opinion solely. When Aristotle says that the proposition that nature
exists is self-evident, he does not say whether its self-evidence is due to
its extreme universality or its extreme particularity, but presumably he
thought it was one or the other, In either case, his contention is that
the existence of nature cannot be proven, And if Aristotle is right
about the unprovability of the existence of nature, but wrong in his
claim that the existence of nature is self-evident, as the alleged discovery of nature would imply, then the proposition that nature exists is
either a falsehood or something like a matter of faith,
Before proceeding further along these lines we need to look a bit
.
c1
oser at what 1s meant
by u nature."In common par1ance nature
II
"
refers typically to the whole order of things that are, as yet, untouched
by human art, things such as plants, animals, the sky above, the earth
below, and so forth. Since no one denies the existence of this order of
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119
things, of thiogs not dependent on human ingenuity, the existence of
nature would indeed seem to be self-evident. And yet Aristotle himself
does not define nature merely as that which is not produced by art.
Rather he defines nature, as
a principle and cause of being moved and being at
rest in the thing to which it belongs, in virtue of that
thing and not accidentally.'
Aristotle presents this definition of nature about fifteen lines prior
to his claim that the existence of nature is self-evident, and indeed
alludes to it in the sentence immediately preceding the one in which he
makes this claim. So he is not saying merely that it is self-evident that
there is a difference between natural beings and artifacts, but more
broadly that it is self-evident that the former differ from the latter precisely by having nature within themselves, where nature is construed
precisely as "a principle and cause of being moved and being at rest;'
a principle that is essential to what these natural things are. It appears
to be Aristotle's teaching, then, that it is the existence of nature, understood as this very principle, that is self-evident.
The first attestation of the Greek word for nature occurs in a wellknown passage from Book I 0 of Homer's Odyssey. Odysseus's companions have been bewitched by the goddess Circe. While treating
them to a feast she gave them an evil drug that caused them to forget
their fatherland, after which she cast a spell on them with her wand
and turned them into swine. When Odysseus hears of this catastrophe
he sets off to rescue his companions. But as he approaches the great
house of Circe, he is met in the sacred glades by Hermes, "of the golden wand and in the likeness of a young man:' Hermes tells Odysseus
that he has a potent herb (<j>ap[taKov e'aEJA.bv) that will keep Circe
from being able to bewitch (El~A.l;m) him. Hermes then draws the
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THE ST. JOHN'S REVJEW
root from the ground and shows Odysseus its nature (qn)mv).
Odysseus says,
The root was black, but its flower was like milk. The
gods call it moly. It is hard for mortal men to dig but
the gods are capable of all things.~
When Odysseus afterward enters Circe's house, she attempts to
bewitch him as she has done to his companions. Her attempt fails, and
she exclaims to him in amazement that no other man has previously
been able to withstand the drug she has just given him. Her understanding of Odysseus's resistance to her witchcraft is that, the intellect
(voo<;) in thy breast is one not to be charmed (aK~A.orp:o<;). 5
We note that Hermes does not create this antidote to Circe's evil
drug. He does not produce it out of thin air with a wave of his wand,
so to speak. And though he knows the name that he and the other gods
call the herb, he is apparently not able to bring it into being or even to
make it emerge out of the earth by simply invoking this name. He has
L
to draw (pvnv) it out of the ground. The herb is not a human artifact. It is not even a divine artifact, i.e., a creature in the Biblical sense.
The herb grows in the earth independently, so far as one can tell, of
any contribution on the part of gods or men. By virtue of growing in
the earth independently of the making capacity of intelligent beings,
it has the nature that distinguishes it fi:om products of art, no matter
who the artisan might be. And, as most of you are aware, the Greek
word for nature, <j>vm<;, and the Greek word for plant, <j>V'tOV, are
cognate. Both words stem from the root <j>v- which means "to grow;'
" to put c th" as m u to put rort h buds" or even u to procreate," .
.
i
J.Ot
,
t.e., to
beget a like offspring out of one's own being. The nature of the herb
is its growing, the thrusting down of its roots into the earth and the
stretching out of its leaves and flower toward the light. It is this activ-
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ity occurring independently of gods and men that Hermes shows to
Odysseus.
When Odysseus asserts that "the gods are capable of all things"
in this episode, we should not forget that this assertion forms one
clause of a compound sentence.
It is hard for mortal men to dig, but the gods are
capable of ail things.
All things are possible for the gods, even the digging up of this
plant, Odysseus seems to say. This, however, is a strange way of
expressing the omnipotence of the gods. 6 Moreover, it is not impossible
for mortal men to dig this plant up as well. It is only hard ( KaA.m6v)
for them to do so. What distinguishes the gods from mortal men, what
is advanced as an instance of the gods' omnipotence, and a support for
the ostensibly pious claim that "the gods are capable of ail things," is
the relative ease with which they can dig up the herb compared to the
greater effort required of mortal men.
So nature makes its appearance in Greek thought as an activity of
immanent producing, of development and growth, organization and
articulation, an activity that owes nothing to gods or men. And he who
knows it possesses a knowledge that renders him immune to certain
divine charms or bewitchments? We note that this whole episode is
not narrated first hand by Homer but by Odysseus. It is by no means
certain that Homer intended us to believe Odysseus's account of this
adventure. But he surely intended us to see Odysseus as a man whose
intelligence is illuminated by a knowledge of the natures of things, and
so to some extent by a knowledge of nature itsel£ Homer appears to
be representing Odysseus as a type, or prototype, of the philosopher.
Now it is a virtual dogma in the history of ideas that the discovery of nature by the Greeks was a unique achievement. But this dogma
is false. At least one other people discovered nature independently o£
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THE ST. JOHN'S REVJEW
and probably before, the Greeks, and yet understood it in essentially
the same way that the Greeks did. In ancient India there emerged a
wide variety of speculative schools of thought. 8 Some of these schools
contented themselves with merely extrapolating the consequences and
presuppositions of the reigning Vedic religion; others attempted to
penetrate to and think through the immanent monism that they discerned or claimed to discern as the implicit teaching of the Vi'das; others depreciated the authority of Vedas without rejecting them altogether, invoking their authority only when it was convenient to do so;
and still others rejected this authority openly and across the board.
Finally, one school of speculative thought subjected the fUndamental
claims of religion to a ridicule more explicit and vehement than anything comparable occurring in the West prior to the last century.
Prakriti is a Sanskrit word that is sometimes translated as "nature."
In general, this term names the material order of things, though construed dynamically rather than as mere extended and inertial stuff. The
prefix pra- could be translated as "forth" and is cognate with the Latin
pro- as in "project"-to throw forth, or "produce"-literally, to lead
forth. The root of the word prakriti is
which means to do or to make.
And the suffix -ti, like the Greek suffix -sis, the Latin suffix -tio, and its
English derivative -tion, with all of which the Sanskrit -ti is cognate,
refers to the process of doing something. Motion is the process of
moving, <j>UOL<; is the process of growing, or as we noted earlier the
process of putting forth, as in putting forth buds. And prakriti is the
process of making forth.
The Sankhya school of speculative thought regarded prakriti as one
of the two fUndamental principles responsible for the articulation of
the world. The other principle they held to be purusha, or pure consciousness, Neither principle is reducible to the other, so the Sankhya
school taught, and both are needed to account for the phenomenal
complexity of the world and the correlative consciousness of it. 9 It
.would be a mistake to regard purusha as a kind of ersatz divinity, as athe-
vkr
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ism is one of the teachings of this sthool. 10 Because purusba is pure
consciousness it cannot act at all. It is just an inert, even impotent, witness. But it is still a co-original principle that does not derive from
prakriti any more than prakriti derives from it. Though there are a plurality of purusbas, there is only one prakriti, albeit internally differentiated and in a process of development, even evolution. This development
is provoked by the presence of the inactive purusba. The chief problem
with this account is making sense of how the unconscious prakriti could
be understood to be provoked to development by the presence of a
mere witness. This problem has an analogue in Greek thought. In the
,
passage from the Odyssey that we were considering, the <j>uaL<;, i.e., the
nature or growing, of the moly plant is an unconscious process that is
nonetheless presumably directed upward toward the light, though, to
be sure, only because it is at the same time directed downward into the
earth. Since nature is not art, this directedness is self- directedness. And
yet it is an unconscious self- directedness that occurs not only in the
presence of the earth but also in the presence of the light to which the
plant reaches out. For Aristotle, nature itself is a duality: it is both
matter and form. Matter is nothing actual in itself but is, rather, a
mere potentiality for assuming different forms, and hence is better
spoken of as "material:' It has no existence independent of form. The
prime formal and immaterial principle is the unmoved mover who is
pure intelligence, having only itself for its object, and moving the natural order as ultimate object of the latter's desire. Desire is all on the
side of the material component of nature, inasmuch as desire expresses
an as yet unactualized potentiality. There is a teleological directedness
not only in unconscious though living plants, but even in the inanimate
elements-earth air, water, and fire-where it is found as an impulse
( OP!!~) toward a proper end ('tEAO<;), this end being the natural place
of the element, the place in the cosmos where it belongs by nature and
to which it will return by nature if removed from it unnaturally, i.e., by
force. Just like the Sankhya conception of prakriti, qr(im<; as Aristotle
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THE ST. JOHN'S REVIEW
presents it is a process animated from within. But it is so animated
only because its material principle is paired with something else, ultimately, as in Sankhya, an intelligence or consciousness not reducible to
matter, and to which matter in turn is not itself reducible.
Whether or not the irreducibility of the form-material distinction, and the separate existence of an unmoved mover that is pure
intelligence ultimately moving the whole natural order as well as the
cosmos itself, though only as object of desire, is Aristotle's last word
on the matter, it is surely his first word on the matter. But his first word
is problematic, for it is that nature is a principle (6.p)(rJ) of motion and
rest intrinsic to things that exist by nature. If nature is a duality of
form and material, with at least one formal principle transcending
nature altogether, it would seem that the two component members of
this duality, form and material, would be the real principles. Nature
would not itself be a principle but rather something derivative and secondary. Aristotle does not press this point, but the claim that nature is
a principle, an absolute origin and source of motion and rest, would
suggest that neither the material nor the formal conditions of motion
exist altogether independently of nature. 11
And it is in the concept of nature as a principle in the full sense
of the word, i.e., as a source immanent within the world, an original
and originating source that does not itself originate from another yet
more original source, that we reach what one might call the properly
philosophical concept of nature. For it is in this concept only that nature
is not reduced to the activity, to the artistic production of a transcendent artisan, whether this artisan be conceived as a separate intelli-
gence, a demiurge, or the Biblical God. 12
On looking back again at the passage from the Odyssey, we note
that nothing is in fact said about a source of light toward which the
moly plant grows. Nothing other than the growing itself is presented
as the cause of the growing. Nothing other rl1an nature is responsible
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·for the directedness of nature. Moreover, right after reporting that
Hermes showed him the nature of the moly plant, Odysseus says that,
The root was black, but its flower was like milk.
The contrast, in this [tEV ... DE clause, between the blackness of the
root concealed in the darkness of the earth and the whiteness of flower
above, suggests that the two aspects of nature are less form and mate~
rial than the manifest and the unmanifest. The white flower, the
accomplished product of <jn)mc;, is visible to anyone who casts a casual glance in its direction. Without seeing the root, however, one might
well think that the plant was just propped up in the ground by a god.
The exposure of the black root at work in the darkness beneath the
surface of the earth, which exposure is accomplished only with a measure of effort, purports to show that the plant is not the product of any
artisan at all, but is the product of an activity of producing that is
immanent within the plant and not distinct from it. And, as we noted
earlier, it is this activity that is nature.
Now nature understood nonphilosophically and simply as the
order of what comes to be independently of human ingenuity, the
order of what comes to be ualways or for the most part," 13 needs no
special discovery. The return of the seasons, the rapid growth of plants
afi:er rain, the way in which animals beget their offspring, and all such
things happen in a manner manifestly different from man's production
of tools, clothing, and the like. The awareness of this difference is not
only prephilosophic, but prehistoric as well. This awareness is surely
not absent from the Bible, where some such conception of the natural
order, even if not named as such, is presupposed as the necessary background against which miracles stand out as signs of supernatural intervention from beyond. And, indeed, once the Greek way of looking at
things was encountered by members of the Jewish community around
the third century B.C., the word qromc; found its way into some of
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THE ST. JOHN'S REVIEW
their writings. 14 The term "nature" also occurs several times in the
New Testament epistles. There it refers precisely to this regular order,
and even takes on a normative sense: the natural use of something as
opposed to an unnatural misuse of it:S Moreover, Aristotle had
already noted that nature, used more generally, can also mean the
essence (or being-----Ouo{a) of anything. 16 It need not have any immediate reference to motion and rest. And this use also appears in the
New Testament, at the culmination of the arresting formulation of the
Christian vocation that is found in the Second Epistle of Peter. The
addressees of this eP.istle are told that they have been called by Christ
to his own glory (&bsa) and virtue:
in order that you might become participants of the
divine nature. 17
Needless to say, this New Testament use of the word unature" has
only the most tenuous connection to the concept of nature that we
find in the Odyssey and in later Greek philosophical thought. The discovery of nature as the sole and immanent origin of the things that are
is, as we noted earlier, typically held to be an achievement of the peculiar genius of the Greek mind. Nothing really comparable to this properly philosophical conception of nature seems to have emerged elsewhere,
except under the influence of Greek speculative thought. After all, in
the Sankhya school in ancient India the starkness of the concept of
prakriti is mitigated by the concept of a complementary presence of a
multiplicity of pure consciousnesses, existing independently of prakriti and not derived from it.
But, in fact, we do encounter the properly philosophical concept
of nature, unmitigated, in another school of speculative thought that
existed in ancient India. This school is called Lokayata, from the
Sanskrit word loka, which means world. 18 The Lokayata teaching is
this worldly,'' with a vengeance. All that is, including consciousness, is
11
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reducible to or derivative exclusively from the four material elements of
earth, water, fire, and air. The expression "my body" is merely a grammatical formula and the self it seems to point to as something distinct
from the body and its owner is a linguistic fiction. 19 There is only this
world, a hereafter does not exist, and death is exactly what it appears
to be:
There is no heaven, no final liberation, nor any soul
in another world.20
There is no world other than this; there is no heaven
and no hell;
the realm of Shiva and like regions were invented by
stupid impostors ... 21
Moreover, there is no immaterial and invisible order of existence:
Only the perceived exists; the unperceivable does not
.
extst...
22
There is no divine artisan:
Who paints the peacocks, or who makes the cuckoos
sing? There exists here no cause excepting nature.23
.
Nature is the sole cause of the manifold things that are, at least of
the things that are not made by man:
The fire is hot, the water cold, refreshing cool the
breeze of morn; By whom came this variety? From
their own nature was it born.24
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THE ST. JOHN'S REVIEW
The Sanskrit word that is translated here as "own nature" is not
prakriti but svabhava. The prefix sva- means one's own. The word bhava to
which it is attached means being, or becoming. Its root is vbhu, which
is cognate with <jru, the latter being the root of the Greek word for
nature. One might think, however, that being and nature should be
kept distinct, and that a more accurate translation of the above clause
would be,
By whom came this variety? from their own being was
it born.
Aside from the cognate relation of bhava and qn.Jm,;, there is the
striking fact that, as we just noted, the concept of nature got so broad11
ened in the West that it came to signify the essence, the what-ness"
of even eternal beings and relationships. One speaks, to repeat, not
only of the nature of plants and animals, but also of the nature of
mathematics, the nature of logic, the nature of ttuth, and even the
nature of eternity. Still, this way of using the word "nature'' takes its
departure, and is claimed to derive its justification, from an earlier conviction that what is fundamentally real is the immanent and temporal
order of existence, that being is nature, nothing more or less.25 This
conception that what is fundamentally real is nature, regarded as a
principle intrinsic to the world that lies before our eyes, a principle not
distinct from this world as its originator, is then a conception that is
not unique to the speculative tradition that originated in ancient
Greece. It is paraded quite nakedly in the Lokayata school of thought
that emerged in India around 600 B.C. If indeed the discovery of
nature, in this strict sense, and the emergence of philosophy are two
sides of the same coin, and i£ furthermore, philosophy is not a peculiar dispensation of a blind and inscrutable fate but a possibility coeval
with man, it would be surprising if nature were discovered within one
intellectual tradition only.
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In any case, the discovery of something of interest leads naturally
to reflection on the thing discovered. And this holds true of nature as
well. The discovery of nature leads to natural science. And there was
natural science in ancient India just as there was in ancient Greece. We
have all heard about how primitive "science" used to be before we
moderns got it straightened out, by making it empirical, objective,
mathematical, precise, useful, and so forth. It is the case, however, that
the emergence of modern natural science, along with all its spectacu"
lar achievements both practical and theoretical, is accomplished in
large measure by ignoring and forgetting the questions that animated
premodern ·natural science. It is accomplished by getting down to brass
tacks, assembling some empirical data, taking some measurements,
crunching some numbers, and so forth, in a word, actually doing science
rather than just talking about it, as it is sometimes put rather irritably.
And one need only browse through a copy of Aristotle's Physics to see
how different both its subject matter and manner of presentation are
&om, say, a contemporary physics textbook. On the one hand, the latter is replete with mathematical formulas, and these are virtually absent
from Aristotle Physics. On the other hand, equally absent from the contemporary textbook, and propelling the argument of the Physics, are
questions as to what certain things are: What is motion? what is time?
what is place) what is the infinite? and the like. And, most fundamental of all, what is nature? Since the word "physics" comes from the
Greek word for nature, one would expect the contemporary physicist
to be more interested in trying to find out what nature is.26
But, the contemporary physicist might respond, we already know
what nature is. It is matter in motion. We have been exceedingly successfUl in determining the laws that govern matter in motion, so suceessful, in fact, that all premodern science reveals itself as useless in
comparison. And the contemporary physicist is right. The premodern
investigation of nature was virtually without utility. Utility, however, is
hardly an adequate criterion of knowledge. One repeatedly hears for-
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THE ST. JOHN'S REVIEW
mulations of the kind, "we now know how to do such and such:' We
now know how to split the atom, we now know how to put men on the
moon, we now know how to cure such and such a disease, etc. This
"know how" that we have acquired is undeniably impressive. But the
knowledge of how to do something is not equivalent to the knowledge
of what something is, to knowledge of the nature of the thing in question. The philosophers who founded modernity were quite explicit
about the technological orientation that would characterize the new
science of nature. The plan was to conquer chance, to put nature on
the rack and torture it for the relief of man's estate-in general, to render ourselves the masters and possessors of nature. The philosophers
who founded modernity were hardly indifferent to the nontechnological, impractical, and intrinsically theoretical question of what nature
is. Were they indifferent to this question of "what-ness" they would
not deserve the name of philosophers at all. It has been argued, convincingly I think, that the unprecedented orientation toward utility
that characterizes modern Western science stems from a deliberate
decision on the part of the philosophers who founded modernity to
enlist the support of ordinary nonphilosophical human beings, i.e., the
overwhehning majority of human beings, for the theoretical enterprise.
Ordinary human beings should support the quest for knowledge
because of the material benefits this quest will bring to them, Prior to
modernity, the quest for knowledge was regarded by the nonphilosophic multitude as at best useless and foolish, at worst prideful and
impious. Today unimpeded theoretical enquiry enjoys almost
unqualified prestige in the eyes of the public, and consequently an
immunity from meddling, censure, and persecution by religious
authorities, whose political influence was incomparably greater prior to
the commodious living made possible by the achievements of modern
sctence.
Beneath the glitter of technology, however, and indifferent to the
public applause it evoked, genuinely philosophical speculation about
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131
nature continued unabated. If nature were the fundamental reality, and
the source of all that is, including the human mind, how could it be
mastered by the human mind? How could the producer be mastered by
the product? The problem of the relation of mind to nature, or rather,
since nature deprived of form got reduced to mere material extendedness, the problem of the relation of mind to matter, became the most
vexing problem of early modern philosophy. Variants of this problem
were certainly entertained earlier, not only in classical antiquity but,
not surprisingly, in India as well. In the Lokayata school consciousness
was asserted to be a product of material interaction.
The consciousness that is found in the modifications
of nonintelligerit elements is produced in the manner
of the red color out of the combination of betel,
areca-nut, and lime. 27
The Lokayata school thus managed to assert a materialistic
monism.
All is
one, and this one is matter. But Lokayata seems never
to have gotten beyond simply asserting this monism. The Sankhya
school was unimpressed with the Lokayata assertion, inasmuch as what
it exhibited in boldness was not paired with an adequate appreciation
of the problem: exactly how does mere material interaction give rise to
something so apparenrly different from matter as consciousness? This
question appears to be unanswerable. The Sankhya school did not wish
to retreat from avowed atheism
by introducing a divine consciousness
as the transcendent creator of the multiplicity of individual consciousnesses that exist, nor to reduce this multiplicity of consciousnesses to different aspects of one immanent consciousness. And so the
adherents of the Sankhya school posited this multiplicity as an original and underivable given. 28 And they successfully offset the charge of
covert theism by making these consciousnesses absolutely impotent,29
attributing all action to prakriti, i.e, to material nature.
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THE ST. JOHN'S REVIEW
Aristotle's express teaching on this matter also is similar to that of
the Sankhya school. The first mover, or thought thinking itself or, better, intellect knowing itself, is indeed described as fully active, beyond
all potency but not thereby impotent. Its activity, however, consists, as
we noted, not in what it does to anything else, but in the autarchic unaffected self-activity of self- knowledge, and i11 what it only thereby, so to
speak, "inspires" other things to do. Where the multiplicity of individual human minds comes from, i.e., what the origin of human consciousness is, is not clear. Still, Aristotle's teaching that nature is a cos-
mos teleologically constituted and replete with forms, though hardly
answering the perplexing question about origins, at least keeps consciousness from appearing to be an anomaly within the natural order.
This teaching was not congenial to the spirit and intention of early
modern philosophy. For the mathematization of nature that was
required in order to reduce it to theoretical clarity and distinctness,
and to make possible the consequent domination of nature by art, i.e.,
to make possible technology, required reducing all apparent formal
causes to material causes, and eliminating final causes altogether. As a
consequence of this reduction, the philosophical investigation of the
relation of mind to nature ran right into the so called "mind-body
problem:' Most of the attempts at solving this problem seemed contrived, and some were so extravagant and unconvincing as to cast rea-
sonable doubts on the sincerity of the thinkers who proffered them,
Contemporaries could not help but wonder whether some of these
thinkers were not materialist monists disguising as mind-body dualists.
One early mbdern philosopher who advanced monism with as
much frankness as circumstances permitted was Spinoza. According to
Spinoza, there is only one substance, or real being, namely God. God
has infinite attributes, of which only two, namely, extension and consciousness, are possible objects of human knowledge and experience.
The bodies we see around us and our own bodies as well are but
modes, or modifications, of these two accidents of God. They are not,
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however, modifications of the attribute of extension merely, for they
exhibit another feature in addition to just being spread out in space.
They resist being penetrated, being moved when they are at rest, being
brought to rest when they are in motion, and having their motion
accelerated, decelerated, or altered as to its direction. In a word they
resist any influence from without. This resistance of a body to influence
from without, to influence from another, can be expressed positively as
an endeavor (conatus), an exertion, a striving even, to preserve itse!f in
whatever state it happens to be in. Aristotle, as we have seen, had also
argued for a kind of striving ( op~t~) as propelling the natural motion
of even inanimate bodies. But Spinoza's conatus is not self-direction
toward an end, a "t[A..o;, that is at some remove from the present state
of the body in motion. It is not self-direction so much as self- preservation. This attribute of a body, its endeavor to preserve itself, which is also
called, misleadingly, uinertia;' does not exist separately from the
extendedness of the body, though it is, again, not reducible to the
attribute of extension. If bodies lacked this attribute of endeavoring
to preserve themselves and possessed instead only the attribute of
extension, they would not be bodies, material bodies, at all. They would
be three-dimensional geometrical figures only. If a body's extendedness
is the outwardness, the exteriority of a material body, the aspect that
can be perceived by an outside observer, then the endeavor to preserve
itself is its inwardness, its interiority. This endeavor to preserve itself
cannot be perceived by an outside observer though it can be more or
less deduced from the "behavior" of a body when subject to the pressures of other bodies from the outside or from the experience of the
observer when he stops merely observing this body and tries to do
something to it. The interiority of a body can be "expressed" when it
is provoked, so to speak, by something exterior to it. The endeavor of
a relatively simple body, such as a billiard ball, to preserve itself in the
state it happens be in, in spite of outside interference, can be rather
easily grasped, for it can be encountered as a felt pressure against one's
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THE ST. JOHN'S REVIEW
own body. But all bodies possess this endeavor, the human body
included. And the much greater complexity of the human body,
including the complexity of the brain and nervous system, allows for
much more variegated expressions of the endeavor to preserve itsel£
But this endeavor to preserve itself is still the inwardness of the human
body, just as in the case of a simple body.
So two things, apparently, are claiming to be the inwardness, the
interiority, of the human body. They are, on the one hand, the mind,
and, on the other, the endeavor of the human body to preserve itself
in whatever state it happens to exist in, the inertia" that the human
body has in common with all bodies. Are these apparently unrelated
things, the mind and the human body's endeavor to preserve itself in
whatever state it happens to be in, in some way related? Spinoza offers
fl
a starding answer to this question.
The mind, both insofar as it has clear and distinct
ideas, and also[!] insofar as it has confused ideas,
endeavors (conatur) to persist in its being for an
indefinite duration, and of this endeavor (conatus) it is
conscious. 30
Since, as Spinoza goes on to say in the sequel to this passage, the
essence of the mind is constituted by both adequate and inadequate
ideas, the essence of the mind consists in its striving to persist in its
state, in its striving not to reach beyond itself but to preserve itself in
its present state. The essence of the mind is this conatus. And though
the mind is something altogether different from extension, it is not
something altogether different fi:om, much less separable from, body.
The mind is, rather, one though not the only instance of the conatus of
the complex human body, the attempt of this body to preserve itsel£
The conatus of a simple inorganic body, such as that of a billiard ball,
is then only the primitive prototype of the human mind." Inertia, it
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11
turns out, is not quite so inert" as it sounds. After all, it consists in
resistance to outside influence and in the endeavor to maintain itself in
whatever state it happens to be in, regardless of how it got there.
Now, whatever one makes of the above account, in particular
whether the striving for self-preservation rather than, say, "will to
power;' best defines the inwardness common to all bodies, this account
does have the considerable merit, from the perspective of philosophy,
of maintaining an absolutely necessary, nonfortuitous connection
between mind and nature. 32 For although Spinoza says that the one
substance is God, and that we thinking human beings are but
modifications of its attributes, he also calls this one substance
"nature:' God is not a transcendent being, but nature itsel£33 Nature,
material nature, is however more complex than meets the eye. In fact, the
only attribute of nature that literally meets the eye is extension in
space. The other attribute, consciousness, has to be directly experienced or deduced. But Spinoza says that nature has many more attributes than just these two, an infinite number in fact. By this claim he
seems to point to a certain inscrutability in the workings of nature.
This comes out in his distinction between natura naturata, literally,
"nature natured;' by which he means the productions of nature, i.e., the
11
natural beings, and natura naturans, literally, nature naturing,, i.e., the
producing of the natural beings, or nature proper. It is this latter sense
that most closely corresponds to the distinction that we encountered
between a plant, a !j>utO'v, and the growing of this plant, its !j>vm~,
its nature proper. Spinoza also argues that this sole existing substance,
nature, is both the necessary being and necessary in all its operations.
Nature, natura naturans, does not freely choose to create its products, the
whole complex of natura naturata, as does the Biblical Creator. Nature,
again, is not transcendent to its products but immanent within them,
and so a sharp distinction cannot be made between natura naturans and
natura naturata, of the kind one must make between the transcendent
God and his freely created creatures. Accordingly, the necessity that
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THE ST. JOHN'S REVIEW
holds for natura naturans-a necessity that Spinoza argues for at the
same time that he maintains it to be in large measure inscrutable-this
necessity has to hold for natura naturata as well. Nothing is contingent
in nature, neither its producing nor its products, Whatever exists has a
necessary connection with what came before, and this system of necessary connection in the world that lies qefore our eyes is inviolable
and eternal.
The indemonstrable and hence no more than hypothetical character of Spinoza's assertion, and similar assertions, of an inviolable
necessity of connection, or strict determinism, in the natural order was
exposed by Hume. Hume reasons as follows. The concept of an event,
of something happening in time, can be imagined without connecting
this event in the imagination to a preceding cause. For example, I can
imagine the sudden appearance of a second essay right next to this one,
though to_ be sure I have no reason at all to expect that such a sudden
appearance will occur. Furthermore, I can imagine this event taking
place without having to imagine a cause of it. 34 And what can be imagined can be regarded as possible, at least until it can be shown to be
impossible, by some kind of argument, one that does not beg the question. To put it another way, the idea of having a cause or, for that matter, producing an effect, has no analytic connection with the idea of an
event, an idea of something that happens. Having a cause is not part
of the meaning of an event, in the way that being a closed figure is part
of the meaning of a circle. And so I can think, without contradiction,
of an event as not having a cause in a way I cannot think of a circle as
not being a closed figure. Of course, from a consideration of the mere
concept of an if.fect I can indeed deduce that it must have a cause. This
is what is meant by an effect. But if.fect and event do not have the same
meaning. More is thought in the former than in the latter. And so from
a consideration of the mere concept of an event I cannot deduce, by
logical principles alone, that it must have a cause.
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137
But even if one cannot demonstrate on logical grounds exclusively
that every event must have a cause, experience, at least, would seem to
teach us this. Does it? The cause of an event is not just something that
happens before the event, or even something that happens, so far as we
can tell, invariably before the event. It is not mere temporal succession
that is meant by the relation of cause and effect, but necessary connection. Now, according to Hume, though one can see temporal succession, i.e., one can see a certain event follow another, once, twice, or an
indefinite number of times, one cannot see necessary connection. If necessary connection exists at all it is invisible, a conceptual matter and
not an appearance. And so it is not directly accessible to experience. Nor
is it indirectly accessible to experience by means of an inference from
experience. For if I see two distinct events occur in a certain temporal
order on one occasion only, it would be a mistake to infer that they are
necessarily connected in that order. For example, if the first time I
observed someone carry an umbrella outside I observed a rainstorm
occur shortly thereafter, it would be a mistake to infer that carrying the
umbrella outside was the cause of the rainstorm. And if I observed
this same order of succession, this sequence, on a second, third, or a
fourth occasion, it would still be a mistake to infer a necessary connection between the two events. But how many times does this succes-
sion have be observed for one to be able to infer, logically, that the
prior event is indeed the cause of the latter? No number of successions,
no matter how large the number, really suffices to justify an inference to
a necessary connection between the two events. If it is a faulty inference to say that just because B followed A on one occasion they are
therefore necessarily connected, as effect and cause respectively, then it
is an equally faulty inference to say that just because B followed A on
many occasions they are therefore necessarily connected. To be sure we
come to expect the same succession to hold in the future that has held
many times in the past, but this expectation has no properly logical basis.
As Hume says, it is more a matter of habit than of reasoning. Reason
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THE ST. JOHN'S REVIEW
finds necessity of connection not in matters of fact but rather in logical relationships only, in determining what belongs to or follows from
the meaning of a given concept, as for example an enclosed figure follows
from the meaning of the concept of a circle. 35
According to Hume, then, there is no way of determining whether
necessity of connection exists in nature at all. Now, to return to
Spinoza, the only evidence of an underlying self-contained necessity
properly called natura naturans, can be found in natura naturata, i.e., in the
productions of natura naturans and their ostensibly necessary intercon-
nections. The inability, then, to know with certainty that there are necessary interconnections in these productions, casts doubt back on the
necessity of the producer, on nature construed as the necessary being,
i.e. as natura naturans, thereby rendering Spinoza's whole system ques-
tionable.36
Finally, even if, contrary to what Hume attempts to show, one
could determine that a given event or even all events that fell within
one's limited sphere of experience had a cause, one could not infer
with certainty that absolutely all events, especially those remote in time
or space from the necessarily limited sphere of one's experience, also
have causes, much less must have them. And if one cannot know that
absolutely every event must have a cause, then one can hardly know
that absolutely every event must have a natural cause, a cause of the
same kind as the event, and that it cannot instead have a supernatural
cause. Hume, to be sure, argues against miracles. But his argument does
not get beyond trying to show that there cannot be a sufficient reason
for believing in miracles, particularly for believing in reports of miracles. This, however, is strictly speaking a theological matter, and one that
is open to dispute. Hnme's argnment about causality by itself pre. clndes a refutation of the possibility of miracles on scientific, i.e., naturalistic, grounds.
Natural science as such, then, lacks the wherewithal to refUte the
possibility of miracles, unless it borrows argnments from other
�CAREY
139
sources. For example, there is simply no way of knowing on the basis
of natural science alone that the world was not created by God only
several thousand years ago. All scientific arguments about fossil records,
geological findings, carbon dating, appeal at bottom to the principle of
cause and effect, to an absolutely exceptionless regularity within the world,
which natural science cannot itself validate but must instead presuppose.37 And to the nonscientific proposition that God surely would
not have created the world so that it would look, on scientific inspection, to be so much older than it in fact is, the nonscientific rejoinder
can be made that this proposition presupposes an understanding of
the particular intentions of God that, according to the Biblical
~"~hypothesis" itsel£ is not accessible to man.
All this is not to say that the endeavors of natural science yield no
knowledge at all. Rather, such knowledge, consisting as it does in large
measure of empirical generalizations, has an irreducibly hypothetical character to it. On the hypothesis of an exceptionless regularity within the
world, on the hypothesis that there are no supernatural causes, i.e., no
miracles, such and such consequences follow. And assuming that the
alternative hypothesis, namely, that there are supernatural as well as
natural causes, is itself not a matter of scientific knowledge but of
faith, there is also no way of knowing, with certainty, that the naturalist account of the world is not the true account. This, however, is a
much more modest and, I think, much more sensible claim than that
we know with certainty that the naturalist account of the world is the
true account.38
The discovery of nature is the event that inaugurates the emergence of philosophy, or the life of rational inquiry. Philosophy and
natural science were not originally separate enterprises. In fact, they
did not become separate enterprises until rather recently.39 Natural science is but the outcome of concentrated reflection on nature regarded
as an original, self-producing, immanent activity that is accessible to
reason and experience. Even if scientific inquiry c;umot penetrate into
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THE ST. JOHN'S REVIEW
the heart of nature, even if it cannot, to use the language of Spinoza,
know more than two of the infinite attributes of nature, what it does
know of these attributes is supposed to be sufficient to determine that
they are not ultimately based on the free sponsorship of the transcendent and mysterious God. And yet, as we have seen, it does not lie
within the resources of natural science to establish a claim of such
broad scope. If philosophy were natural science only, it would not be
able know that the discovery of nature was anything other than the
invention of a fiction stemming from human pride and self-delusion,
and so it would not be able to justify its conviction that its way, the
way of autonomous rational inquiry, is superior to the way of simple
religious piety.
Nor is this problem solved by the bold move of making nature the
product of an artisan, not the divine but the human artisan, i.e., the
human mind in its own transcendental dimension as what constitutes
nature, the human mind as transcendental subjectivity.4 For, apart from
other considerations, the avowal of a necessary ignorance of what
°
exists independently of the constituting activity of the human mind
leaves the door open, once again, to the fundamental claims of revelation. The necessary being is not the human mind, which we know in
our bones is finite, but the human mind's unknown cause. And precisely because this fundamental cause, this underlying though
inscrutable necessity, is unknown, there is no way of knowing that
it is
not intelligent, free, and providential. By making finite human consciousness and its constitutive work the primary "known datum;' there
is no way of knowing that the unknown source of this "given;' that
what gives it, is not the transcendent and mysterious God-unless it
turns out that the claims made about this transcendent and mysterious
God, i.e., the claims of revelation, are discovered to be self-contradictory in their own terms, or in contradiction with something else that
is self-evidently true, and hence are ultimately unbelievable.
�CAREY
141
Now, as most of you already know, and the rest of you are soon to
find out, nature as a term of distinction in Greek philosophy, is
opposed not only to art, but also to convention. This distinction was
known in ancient India as well. According to Lokayata, the school that
insisted on worldly things having no cause external to the world but
instead coming to be through solely their own nature, the Vedas, which
served as the basis for the normative character of dharma, the law or
sole right way of life, are
only the incoherent rhapsodies of knaves.4 1
The Lokayata school refused to regard the ancestral religious tradition as authoritative. The ancestral religion was the invention of
fools or impostors, more or less innocent foolishness or a deliberate
lie, but in either case a falsehood. The Lokayata discovery, if it is
indeed a discovery, that the things of the world come to be and are
governed not through the agency of supernatural causes but rather
"through their own nature" is inseparable from their rejection of the
ancestral religion as having an entirely human and this worldly origin,
and their refusal to place their allegiance in any other religion.
Now, since one and the same Greek word (vo[!b£) is used for
both law and convention, the opposing of nature to convention, as has
been frequently pointed out, renders the very expression "natural law"
problematic. A given law may well approximate the standard of nature
but, if the <j>1JGL£-VO[J.O£ opposition is absolute, it can never attain
this standard. Since, in the opposition nature vs. convention the latter
11
becomes mere convention, law too becomes something mere:' And
this is supposed to hold true even of what is called "divine law;' which
now, from the philosophical perspective attained by the discovery of
nature, assumes the aspect of something that could not hold the
unqualified allegiance of a fully rational human beingY
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THE ST. JOHN'S REVIEW
In the Phaedo, Socrates expresses his disappointment with the
inability of natural philosophy to give a convincing causal account of
the world of our experience, an inability particularly conspicuous in its
paltry account of the human concern with the good and the noble, and
the effect our conception of these things has on our lives. In the face
of the manifest inability of natural philosophy to make any sense of
the human soul and its concern for the good, Socrates did not advert
to religion. Instead he undertook a philosophical inquiry into the
human soul with his point of departure being A.6yoc:;, i.e., human discourse, particularly human discourse about the loftiest matters. This
specific inquiry has been called political philosophy. It distinguishes
itself from natural philosophy because it does not undertake an
inquiry into nature directly but, rather focuses on the realm of
specifically human concerns. It is a philosophical inquiry because it
does not appeal to the claims of revelation, but rather subjects these
claims to a rational critique. And it is political philosophy because, if
the divine origin of our idea of the good has been called into question,
the only to place to look for the origin of this idea, and thereby understand the idea itself, is in the human community, i.e., the political order
in the full sense of the expression. It is the ambition of political philosophy to expose what it takes to be the questionable character of
divine law by examining it in light of the opposition between nature
and law. 43
But this enterprise presupposes the validity of the distinction
between nature and law, where the former does not mean simply what
holds always or for the most part. As we noted earlier, nature construed merely as typical regularity of appearance is not only compatible with the Biblical belief in miracles as divine initiatives that are
exceptions to typical regularity of appearance, but is presupposed by
this belief. It is, rather, the bolder conception of nature as a fully selfcontained causal order, self-grounded and admitting of no exceptions,
that is required for an absolute opposition between nature and law, in
�CAREY
143
light of which absolute opposition the former is seen as the truth of
things and the latter as nothing better than a noble lie. And yet, as we
have also seen, this bolder conception of nature cannot be validated
within natural science, or natural philosophy. It therefore cannot be
uncritically or, strange to say, piously imported into political philosophy, but must receive its validation there, if it is to receive it anywhere.
It is in confronting the claims of revelation on the basis of what
we know first hand about the human soul. and the relationship of
human souls to one another under some sort of law, along with an
inquiry into the meaning of revelation itself as a possible experience
of the human soul, that the question of reason vs. revelation, or, more
accurately, the question of philosophy vs. piety-which is the most
choiceworthy way of life-gets joined in earnest. I have said next to
nothing about this side of things here. Instead, I have limited myself
to thinking through the meaning of natural science as a branch of philosophy emerging out of what is claimed to be the discovery of nature
and attempting to account for the world in worldly terms exclusively,
though prescinding from the specifically human experiences. I have
tried to show that natural science is constitutionally incapable of refuting the claims of Biblical revelation. From this it would follow that, in
the absence of a definitive resolution of the issues concerning the
scope of the specifically human experiences, the ultimate worth and
reliability of the naturalistic account of the world, the account of the
world in worldly terms exclusively, is less a matter of knowledge than
of faith.
Notes
I. "I make free men [or human beingsJ out of children by means of
books and a balance:'
•
c.
~·)I
-=
,
,..
,
2. Physics, I93a4. w<; u EO'l;LV 11 cjlum<;, 1tELpao8UL uELKVUVm
...
..
c,
,..,
....
..,
'
'
yEA.owv. cjlavEpov yap on ,;mau-ta ,;wv ov,;wv EmL
noA.A.a. 1:0 1)£ OELKVVvm ,;a cjlavEpa OLa 'tWV ~cjlavwv ou
�144
THE ST. JOHN'S REVIEW
I
I
~
l'..,
''
(..'
6U';U[.IEVOU KpLVELV EcrtL 'tO i'lL'UU"to KUL [.111 6L'UU't0
yvwp L[.IWV.
.
3. Ibid., I92 b 20. Genitive absolute construction: OU011<; 'ti'j<;
.....
'
.... ,
"""'
.....
...,
,
~
<!>UOEW<; UPX11<; 'tLVO<; KUL UL'tLU<; 'tOU KLVEL09UL KUL 11PE,.,'l't./
/
.c.,,
..
'
[.IE LV EV qJ UJtUPXEL n:pwnu<; Ka9' UU'tO KUL !-111 KU'tU
OU[.l~E11KO<;.
4. Book IO, I. 302-306.
5. Ibid., I. 329.
6. C£ Leo Strauss, "Progress and Return," in The Rebirth of Classical
Political Rationalism ed. by T. Pangle (Chicago: University of Chicago
Press. I989), 252; also Seth Benardete, The Bow and the Lyre: A
Platonic Reading of the Odyssey (Maryland: Rowman and Littlefield,
I997), 85-90.
7. Although Odysseus relates that he was shown, and therefore came
to see the nature of the moly plant, he does not say that he actually
ate the plant.
8. The Sanskrit word that I am translating as "speculative school of
thought" is darshana, which stems from the root vdrsh, which in
turn means "to see:' Darshana could be more literally translated as
uperception" or point of view:~ The word "speculative" captures at
least something of the sense of seeing contained in the Sanskrit.
The expression "school of thought" is appended to "speculative"
to express the historic reality that there were groups of thinkers
adhering to similar views, as in the West with the Stoics,
Epicurean, skeptics, and so forth.
9, Sankhyakarika 3.
IO. G. Larson, Classical Sankhya (Delhi: Motilal Banarsidas,I979),
I 98: "Thus, the classical Sankhya recognized no absolute or creator God. To be sure, the gods may exist, but they too are simply
products of the interaction of unconscious mulaprakriti and the
11
conscious purusha:' For further discussion see the references to
"atheism" in Larson's index, especially fn. I 46. Mulaprakriti is origi-
�CAREY
145
nal or primary nature, as distinct from its derivative products or
states. This distinction is roughly comparable to that which
Spinoza makes between natura naturans and natura naturata. See below.
I I. Thomas Aquinas understandably resists regarding nature as a
principle in this strong sense of the term. (In Octo Libros De Physico
Auditu Sive Physicorum Aristote/is Commentaria), Liber II, Lectio I, 295:
H
Ponitur autem in definitione naturae principium quasi genus; et non aliquid
absolutum ... ": "Now 'principle' is placed in the definition of nature
as its genus, and not as something absolute ... " (English translation: Commentary on Aristotle's Physics, Yale University press, I963,
7I). The Greek allows for, though it does not mandate, this interpretation, inasmuch as Aristotle does not define <jrum<; as &p:xl] ...
etc., but as 'tL<; apxl] ... etc. Thomas acknowledges another tradition of interpreting Aristotle's definition in the immediate sequel
to the observation quoted above.
I2. Aristotle's God, though active in relation to himself as intellect
knowing itself (VO'Y]OL<; vo~crew<;), and as a consequence active on
others as the object of their desire and imitation, is not an artisan
(Metaphysics I 072 b I f£). He takes no interest in the cosmos.
Indeed, he is apparently unaware of its existence, inasmuch as he
thinks only of himself (I074b3I-34, Thomas Aquinas's elaboration to the contrary notwithstanding). And if, thinking only of
himself, he is unaware of moving things, he must be unaware that
he is the first mover. Being the first mover, then, does not pertain
to his essence, for of his essence, at least, he is fully aware. Cf
infra, note 37.
I3. Physics, I98b35.
I4. E.g., Wisdom of Solomon, 7:20 ( c£ I3:I!). The word occurs with
some frequency in IV Maccabees. Both these works were written in
Greek. They can be found in the so-called Apocrypha, which consists
of books that had enjoyed some standing within the Jewish community but did not make it into the canon that was established by
�146
THE ST. JOHN'S REVIEW
the assembly of rabbis at Jarnnia toward the close of the first century A.D.
I5. Romans 2:I4-I5.
I6. Metaphysics, IOI5ai2.
"'
'
/
I
I
I7. II Peter I:4, u ... LVU /\La ''W'U'tWV YEV'Y]00E 0ELU£ KOLVWVOL...
..h. I
'!''UOEW£ ... "
I8. Charvaka is another name for this school.
I 9. Sarvasiddhantasangraha, 6, quoted from A Sourcebook of Indian
Philosophy, ( ed S. Radhakrishnan and C. Moore, Princeton
University Press, I 957), 235.
20. Sarvadarshanasangraha, quoted from A Sourcebook in Indian
Philosophy,.22 9.
21. Sarvasiddhantasangraha, 8. 235.
22. Sarvasiddhantasangraha, 5. 235.
23. Ibid., 235.
24. Sarvadarshanasangraha, 233.
25. C£ M. Heidegger, vom l#sen und Begriff der <j>vm£: Aristoteles' Physik
B, I (l#gmarken, Frankfurt am Main, I 967), 370. (English translation byT. Sheehan in Man and World-Val. 9, No.3, Aug. I976,
268).
26. That the typical scientist is so taken aback on being asked the
most fundamental questions about nature leads one to suspect that
what motivates his research is less a love of truth than an infatuation with method. This suspicion is not much allayed by his few
attempts to answer such questions, e.g., by proclaiming that the
origin of all existence was a "big bang;' which was itself precipitated by a "fluctuation" in the "nothing" that preceded it.
27. Sarvasiddhantasangraha, 235.
28. Sankhyakarika, I 8.
29. Ibid., I9.
30. Ethics, Book 3, Prop. 9.
3 I. C£ Hans Jonas, "Spinoza and the Theory of Organism:'
�CAREY
147
(Philosophical Essays, Prentice Hall) I 97 4, 206 f£ On the relation of
mind to the organic body. Jonas argues that Spinoza is the only
early modern philosopher who can account for why the more biologically complex organism has the more complex inwardness.
32. However otherwise different Spinoza, Nietzsche, and Freud are
from one another, they all agree in regarding the mind as an essentially dynamic field of activity, as do Christians. (e.g., Matthew I2:4345; Ephesians 6:I2).
33. If nature exists of necessity, as Spinoza would like to demonstrate, then it can legitimately be called "necessary being," a formulation that the theologians had previously reserved for the transcendent God. But what exactly Spinoza gains, aside from the appearance of piety, by giving immanent nature, the world, or "the all" the
name uGod" is not easy to determine.
34. Indeed, I must imagine some events without having to imagine
their causes. For otherwise, since these causes would also have to
be events, I would have to imagine their causes as well. And so I
would be forced, in imagining any event, to imagine an indefinitely
extended series of antecedent events. And this I surely do not do.
35. Kant's argument for the synthetic a priori is inseparable from his
claim that we have no knowledge of things in themselves, and
hence no knowledge of an underlying necessity such as Spinoza's
natura naturans. C£ infra, fn. 4 I.
36. There is no intrinsic contradiction in the concept of a necessary
beingjreely producing or, rather, creating other contingent, even
free, beings. But this conception ultimately presupposes, for its
cogency, the distinction between essence and energies that is developed
in the work of the I 4th century Orthodox theologian, St. Gregory
of PaJamas. (C£, e.g., The Triads 3; and One Hundred and Fifty Chapters
on Topics of Natural and Theological Science Intended as a Purgefor the
Barlaamite Corruption, Ch. 68 f£). It should go without saying that
this distinction would hardly have been congenial to Spinoza.
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THE ST. JOHN'S REVlEW
37. C£ Strauss, "Progress and Return;' 266.
38. And, indeed, scientists today are wont to emphasize the provisional character of science itsel£ Like many of their contemporaries they have doubts about whether there is such a thing as "the
truth;' whether there is such a thing as "Truth with a capital T'
Science is an ongoing activity of revision: ~~What is true today
may well prove false tomorrow:' uThe more we find out, the more
we know how little we know:' "No scientific account can claim to
be the final account:' This becoming modesty does, however, know
its limits. For there is at least one scientific account that is the final
account. This scientific account is the theory of evolution. We now
know, so we are told, that human life is necessarily the product of
evolution. This, at least is a Truth with a capital T. Unfortunately,
a satisfactory explanation as to why evolution is the scientific theory
that gets to lay unique claim to apodicticity and finality does not
appear to be forthcoming.
39. This fact is reflected in the somewhat anachronistic tradition of
awarding Ph.D's in the sciences-one can hold a doctorate of philosophy in, say, chemistry.
40. This, of course, is the tack that Kant takes in attempting to
refute Hume and establish, as a general principle, that every event
in nature "presupposes something on which it follows according to
a rule;' i.e., that it presupposes a cause. (Critique of Pure Reason,
AI 89; c£ B 232 f£). Whatever else one might say about Kant's
argument, it necessarily deprives nature, now reinterpreted as u an
aggregate of appearances, so many representation of the mind"
(ibid., A II 4) of any claim to be a first unconditioned principle.
In its stead the unknowable thing-in-itself assumes the character of
such a principle, entailing, according to Kant, an ascendancy of
faith over knowledge (ibid., B xxx.).
4 I. Sarvadarshanasangraha, 230. The distinction between nature and
convention in Greek speculative thought seems to have suggested
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149
itself on the basis of travels and the consequent observation of the
variety of customs and laws under which different peoples live. (It
can hardly be accidental that Odysseus is a traveller. C£ Odyssey 9,
line I 72 f£) In the speculative thought of ancient India, a comparable distinction between nature and convention emerged, so far as
one can tell, without the benefit of travels to other countries and
solely as a consequence of reflecting on the possibility of a merely
human origin of the only known dharma: "The Agnihotra [an
obligatory rite for members of upper castes], the three Vedas, the
ascetic's three staves, and smearing oneself with ashes, - Brihashpati
[the founder of Lokayata, c. 600 B.C.] says that all these are but a
means of livelihood for those who have no manliness or sense"
(ibid.).
42. Though c£ 4 Maccabees, 5: I f£ Also, Romans 2: I 4- I 5.
43. For an illuminating appraisal of some of these issues from a
philosophical perspective, see the provocative study by David
Bolotin, An Approach to Aristotle's Physics (Albany: State University of
New York Press, I998), esp. I52-I53, and I 54, fn. I2.
��
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<em>The St. John's Review</em><span> is published by the Office of the Dean, St. John's College. All manuscripts are subject to blind review. Address correspondence to </span><em>The St. John's Review</em><span>, St. John's College, 60 College Avenue, Annapolis, MD 21401 or via e-mail at </span><a class="obfuscated_link" href="mailto:review@sjc.edu"><span class="obfuscated_link_text">review@sjc.edu</span></a><span>.</span><br /><br /><em>The St. John's Review</em> exemplifies, encourages, and enhances the disciplined reflection that is nurtured by the St. John's Program. It does so both through the character most in common among its contributors — their familiarity with the Program and their respect for it — and through the style and content of their contributions. As it represents the St. John's Program, The St. John's Review espouses no philosophical, religious, or political doctrine beyond a dedication to liberal learning, and its readers may expect to find diversity of thought represented in its pages.<br /><br /><em>The St. John's Review</em> was first published in 1974. It merged with <em>The College </em>beginning with the July 1980 issue. From that date forward, the numbering of <em>The St. John's Review</em> continues that of <em>The College</em>. <br /><br />Click on <a title="The St. John's Review" href="http://digitalarchives.sjc.edu/items/browse?collection=13"><strong>Items in the The St. John's Review Collection</strong></a> to view and sort all items in the collection.
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Kraus, Pamela
Brann, Eva T. H.
Carey, James
Ruhm von Oppen, Beate
Sachs, Joe
Van Doren, John
Williamson, Robert B.
Zuckerman, Elliott
Phillips, Blakely
Sachs, Joe
David, Amirthanayagam
Verdi, John
Page, Carl
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Volume XLVI, number one of The St. John's Review. Published in 2001.
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The St. John’s Review
Volume XLVI, number two (2002)
Acting Editor
George Russell
Editor
Pamela Kraus
Editorial Board
Eva T. H. Brann
James Carey
Beate Ruhm von Oppen
Joe Sachs
John Van Doren
Robert B. Williamson
Elliott Zuckerman
Subscriptions and Editorial Assistant
Blakely Phillips
The St. John’s Review is published by the Office of the Dean, St.
John’s College, Annapolis: Christopher B. Nelson, President;
Harvey Flaumenhaft, Dean. For those not on the distribution
list, subscriptions are $15.00 for three issues, even though the
magazine may sometimes appear semiannually rather than three
times a year. Unsolicited essays, stories, poems, and reasoned letters are welcome. Address correspondence to the Review, St.
John’s College, P Box 2800, Annapolis, MD 21404-2800.
.O.
Back issues are available, at $5.00 per issue, from the St. John’s
College Bookstore.
©2002 St. John’s College. All rights reserved; reproduction in
whole or in part without permission is prohibited.
ISSN 0277-4720
Publishing and Printing
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THE ST. JOHN’S REVIEW
3
Contents
Essays and Lectures
Measure, Moderation and the
Mean............................................ 5
Joe Sachs
Plato and the Measure of the Incommensurable
Part II. The Mathematical Meaning of the Indeterminite
Dyad................................................................................
................... 25
A.P. David
Moral Reform in Measure for
Measure............................................63
Laurence Berns
Book Reviews
Eva Brann’s, The Ways of
Naysaying ................................................79
Chaninah Maschler
Eva Brann’s What, Then, is
Time?.....................................................107
Torrance Kirby
The Feasting of Socrates
Peter Kalkavage’s translation of
Timaeus...................................117
Eva Brann
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5
Measure, Moderation, and the
Mean
Joe Sachs
(with particular reference to the story Odysseus tells in
the Odyssey)
Anyone who comes to love the writings and artworks that have
survived from ancient Greece ought one day to visit Olympia. In
Athens there are wonderful things to see, but also evidence everywhere of the destructive effects on buildings and statues of some of
the most polluted air anywhere in the world. But, in Olympia, in
the Peloponnese, where the most famous of the ancient athletic
games were celebrated, one can still breathe purer air, and see glorious sights. In particular, in the museum there, at the two ends of
the large main room, restored to their complete shapes, are the two
pediments of a temple of Zeus built in the decade of the 460s BC.
(Illustrations are at the end of the text.) The form of a pediment will
be familiar to you as what sits above the appropriate sort of
entrance to a temple. Picture a rectangle, wider than it is long, made
of evenly spaced vertical columns; resting on top of this row of
columns is a triangle, shorter than it is wide, with a series of sculpted figures across it. The statue at the center of the triangular pediment is the tallest figure and the focus of the whole composition.
The eastern pediment at Olympia depicts Zeus at its center, in a
monumental style that makes one think of Egypt. In fantasy, one
might see this pediment as a doorway into ancient Greece, leading in
from the east. But the truer doorway to things that are most characteristic of classical Greece is at the other end of the room. The western pediment depicts the defeat of the Centaurs, who are men in
their heads, arms, and upright chests, but horses in their legs and horizontal lower trunks. They are attempting to carry off human
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women, and one young boy, but the sculptor has captured the
moment of their defeat. They are being fought by human heroes,
including Theseus, but they are defeated by a look and a gesture. At
the center of the pediment is Apollo, ten feet tall, looking to his right
with his right arm outstretched, the hand level, the palm downward.
The look in his eyes is not angry but serious, and his face is not
clenched in threat but calm. The centaurs cannot have their way
when faced with the power radiated by such dignity. This scene, displaying in outward figures an inner topography of the human soul,
holds in it something of the spirit of classical Greece. The fact that
you or I can see these seemingly invisible qualities, just by being
patient and receptive in front of some shaped blocks of stone, is one
of the amazing achievements that has survived from that time and
place.
Zeus was, as you know, the father and ruler of the Olympian
gods, and even the name of the town Olympia was taken from its
temple of Zeus, who was the Olympian, but somehow Apollo came
to be pre-eminent among the gods imagined as living on Olympus.
At Delphi, on Mount Parnassus, above the Gulf of Corinth, there
was an ancient temple of Gaia, Mother Earth, which was considered the center of the earth. But people were kept away from it by
the Python, an inhuman monster, until Apollo killed it. The Pythia,
the priestess of the temple, then became a medium through whom
people could consult Apollo, and learn his word, or oracle. The
story of Pythian Apollo embodies the same meaning as that of the
Apollo sculpted at Olympia, a victory on behalf of humanity, won
over older and subhuman enemies. The dragons and half-humans
are not wiped out, but become subject to something shining and
beautiful. I think you will find some version of this insight present
in almost every work you read from classical Greece, though not
everyone would agree, and it may certainly at times be something
hard won and dimly seen. But even tragedy, a type of poetry discovered by certain Greeks, always displays that, even in the most
horrendous circumstances, there is a human dignity that we can still
SACHS
7
recognize; that when it is recognized it commands respect; and that
this respect allows all things to be seen in their true proportions.
Above the doorway of the sanctuary of Apollo at Delphi, we are
told (Plato, Protagoras 343B) that two sayings were inscribed:
Know thyself, and Nothing to excess. These may seem to be disconnected—an exhortation to self-knowledge and a platitude about
not going overboard with anything—but to think them together is
to find the meaning of each. Know thyself means know your true
limits, the greed and ambition to which no human being should
aspire and the depths to which no human being should sink. And
Nothing to excess is not just practical advice; it means that the
nature of anything, including human life, is revealed only when its
true proportions are found—that the truth of anything is its form.
The positive version of Nothing to excess is another saying—
Measure is best—and the measure of a thing is its form.
To take a simple example, what are the right proportions for
the entrance to a temple? When I described the pediments at
Olympia and asked you to picture them and the columns under
them, I’ll bet you got their proportions just about right. The rectangle formed by the columns is wider than it is high. How much
wider? Enough so that it will not look squashed together, but not so
much that it would become stringy looking. Let your imagination
squeeze and stretch it to see what goes wrong, and then notice that
to get it right again you have to bring it back to a certain very
definite shape. This is the golden rectangle. It has been produced
spontaneously by artists, architects, and carpenters of any and every
time and place. What is the ratio of its width to its height? I can tell
you exactly what it is, but not in numbers. I can also tell it to you
in numbers, but not exactly. It is approximately 61.8 units wide and
38.2 units high. That will get you in the ballpark and your eye will
then adjust it to make the ratio exact, but it can be proven that no
pair of numbers, to any finite precision, can accurately express this
ratio, which is that formed by cutting a line so that the whole has
to its larger part the same ratio that the larger part has to the smaller. If you have a calculator, you can check that 61.8 is to 38.2 in just
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about the same ratio as that of 100 to 61.8, but no matter how
many decimal places you take it to, any ratio of numbers for the
parts will fail to match that of the whole to the larger part. We know
many things by measuring, and our usual way of measuring is with
numbers, but in this case numbers are too crude an instrument by
which to know something our eyes know at a glance.
Taking the measure of something, then, does not necessarily
require quantifying it. We are always going too far in trying to quantify things. The intelligence quotient is a precise number, and no
doubt it means something, but it doesn’t capture anything worth
calling intelligence. An acquaintance of mine, who grew up in
Baltimore, once watched an old, uneducated cook in North
Carolina make biscuits. She was writing down the recipe, and at one
point asked “How much shortening did you use?” The reply was
“Enough to make it short.” This example reveals both the genuine
intelligence of the cook, which would not show up on any test
score, and the fact that she was measuring the shortening not by its
volume or weight but by its feel as she mixed it into the dough. Her
hands were performing a qualitative measurement, just as the eyes
of your imagination were measuring the rectangle by its shape,
rather than by the lengths of its sides. You should not be too quick
to agree with me about this, because if you do, you may have to give
up many other things you believe.
I am claiming, and this is something I learned from certain dead
Greeks, that the world really has qualities in it, that they are not
subjective distortions projected onto it, but the true forms of things.
I know them by my senses, and I know them better that way than
by any theoretical explanations of them. With the golden rectangle,
the discovery of the ratio of its sides reveals something that we can
never name directly—we cannot say how many times bigger one
side is than the other, or than any possible fractional part of the
other—but we can still recognize that ratio in two ways: in its sameness with another ratio, or, even more simply, in the distinctively
shaped rectangle it produces. What is quantitatively incommensurable is qualitatively harmonious. Similarly, the experienced cook
SACHS
9
knows that all batches of flour and shortening are not identical, and
that they may not behave the same way at different times of the
year. If you want the biscuits to turn out right, the only thing to
trust is your hands.
We need not go through all five senses, but one example of
measurement by the ear will be helpful. Clamp a guitar string at
both ends, put a bridge under it about two-fifths of the way from
either end, and pluck the two parts. You will hear something interesting. But what if the string is not of uniform thickness all the way
along? If you have measured the two lengths to make them exactly
as two to three, you might still hear something that sounds wrong,
just a little off. The interval of a fifth is produced by strings with
lengths in a perfectly commensurable ratio, all other things being
equal, but the lack of uniformity in real strings means that one tunes
an instrument best with one’s ear. It is true that musicians nowadays
sometimes use little electronic devices that read out frequencies of
vibration. But if the machine malfunctions, it will do no good for
the musician to tell the audience he got all the numbers right. Only
for the ear is there such a thing as being in tune.
Measure, proportion, and harmony are in the nature of things,
and we have a direct responsiveness to them that orients us in the
world. These are not the ratios of mathematics, but incarnate ratios.
And the words pure and applied do not fit the distinction, because
the purer instances of measure are the ones given to our senses. A
tradition preserved by a twelfth century writer (Johannes Tzetzes)
tells us that the inscription above the doorway of Plato’s school, the
Academy, read “Let no one without geometry enter under my roof.”
Does this mean that skill in mathematics was, as we would say, a
prerequisite for his classes? I don’t think so. It seems to me important that the entrant is not required to have mathematics, but geometry. Much of mathematics develops from the act of counting, a fundamental and natural power without which we could not speak or
think, but geometry starts in a different way, from a sensory recognition of the ordering of simple visible shapes. In Plato’s Gorgias
(508a), Socrates actually tells a young man that he is without geom-
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etry, but he is not criticizing Callicles for his intelligence or learning
or skill, but blaming him for a failure of moral choice. The young
man is greedy and in danger of having no friends, Socrates says,
because he does not recognize the way geometrical equality gives all
things the proportions that let them be part of larger wholes. The
loss of a sense for geometry is equated with losing one’s way in the
human world.
An example that shows both the positive and the negative side
of this is the central scene in Plato’s Meno. Meno’s “boy,” a slave
who has never been taught geometry, begins to discover it in front
of us. Relying at first solely on his ability to count, he twice goes
wrong in trying to measure the side of the double square, but counting also shows him he is wrong. With Socrates leading the way, by
drawing figures and pointing at them, the slave eventually is led to
trust his eyes, and to see the square double itself, out of itself. And
while Socrates asks all the questions, the slave has to do all the seeing himself, out of himself, just as he was led to his mistakes, but
made them himself. This is all very elementary, but the slave has
geometry in him, and he also has a little bit of courage and determination in getting it out—two qualities his master lacked when he
found some unexpected difficulty in answering other questions.
And this finally is the point of the scene, the reason Socrates
arranges it in front of us: Meno cannot see that his “boy” is a better man than he is. We can all recognize that certain people deserve
more respect than others, if we are honest, but Meno has lost that
capacity. He has lost his way. He is without geometry.
This way of understanding geometry may help explain an
apparent inconsistency in Aristotle’s Nicomachean Ethics. Near its
beginning, Aristotle says something that might at first seem to be
opposite to the inscription on Plato’s gates. He warns the reader not
to look for the precision of mathematical demonstration in the
study of ethics (1194b 19-27). Is this not equivalent to writing on
the portals of this sort of philosophy, “let no one try to enter here
with geometry”? If so, it is odd that Aristotle fills his exploration of
ethics from the beginning with references to actions that are in pro-
SACHS
11
portion, or in ratio, or in a right ratio. For instance, someone may
have good fortune and a steady course through life, but be knocked
out of equilibrium by some misfortune. The inability to cope with
disaster is out of proportion (1100a 23, 1101a 17) with the rest of
the life. Since some alteration is inevitable, and some grief would be
appropriate, and no rules prescribe its amount or how it should be
expressed, only a geometrical eye can judge this. The fitness of such
actions might be measured with some precision, but it can never be
demonstrated. All the circumstances and all the history of any
action can never be known, too many considerations have to be balanced, and equally good alternative ways of handling difficulties are
always possible.
Aristotle, then, does believe that human actions can be chosen
and recognized as right or wrong with precision, but he denies that
this is the same as the precision of a mathematical demonstration.
But he not only uses the language of ratio and proportion for the
kind of precision appropriate to ethics, he also speaks of all actions
that come from virtues of character as actions that hit the mean.
This is easy to misunderstand, because readers tend to ignore the
warning he gives almost as soon as he begins talking about the
mean, that this sort of mean is also an extreme (1107a 6-8, 22-3).
In fact, people rarely understand that this sort of mean is not quantitative at all. But taking it in a quantitative sense opens the way to
identifying the mean with the mediocre, the middle of the road, or
even middle-class morality, the sort of timidity that shies away from
anything that might distinguish one from the crowd. But one of the
things that Aristotle says hits the mean is courage, and he says plainly that there is no such thing as too much courage.
Now one way to see how courage both is and is not a mean
condition is to extend the mathematical language to a second
dimension, and this is both accurate and helpful. There is no such
thing as too much courage, but there is such a thing as too much
confidence, just as there can be too little of it. Courage occupies a
mean position on a scale of fearfulness and fearlessness. The sense
in which courage is an extreme is on a different axis, one on which
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THE ST. JOHN’S REVIEW
the person who has just the right amount of fear puts that attitude
into action in the most excellent way. We might even liken this twodimensional scheme to the appearance of the west pediment at
Olympia, on which Apollo occupies the middle position, but also
towers over everyone else. Courage is like that. As I say, this is true
and it helps one keep hold of Aristotle’s claim that the virtues are
extremes of human character, but also stand in and aim at a mean.
But for all that, this talk of measuring along two axes seems to
me to be misleading in the most important respect. I can show how
very simply. Just ask yourself if the power of Apollo over Centaurs
and humans would be greater if he were taller. As it is, he towers
over them, but the design could have been made in such a way that
he dwarfed them, reduced them to puny insignificance. With a little bit of play in the imagination, I think you can see that this would
destroy the sculpture’s effect. The designer of the pediment (who
may have been someone named Alkamenes) wasn’t aiming at making Apollo as big as possible, but at making him extend the human
stature just a little. The Centaurs are sub-human monsters; a gigantic Apollo would also be monstrous. The sculptor has not only
placed Apollo in the middle of the horizontal array; he has also hit
a mean along the vertical axis. All the power of the ensemble
depends on getting the figures in a right relation to one another. As
with the golden rectangle (and recall that the pediment originally
sat on top of one), it is not a matter simply of adjusting Apollo’s
height, but of forming a single design.
Apollo’s height is a precise mean between a ridiculous shortness
and a monstrous tallness, but that mean is also an extreme in the
sense that it is unsurpassably right. But the way in which it is unsurpassably right is not quantitative. It is unsurpassably right in the
design to which it belongs. It fits, and nothing else would. Liddell
and Scott, the authors of the standard dictionary of ancient Greek,
will tell you that aretê, the word for virtue, comes from the name
of Ares, the god of war, but another school of thought derives it
from a humble verb that means to fit together (arariskein), or be
fitting—it may be related to a similar humble verb, from wood-
SACHS
13
working (harmozein), from which we get our word harmony.
Courage too, as Aristotle or any thoughtful person would explain
it, comes not from the bloodthirstiness of the war god, but from
recognizing what one’s circumstances call for and carrying it into
action. Only when the circumstances are extreme, as they are for
Patroclus or Hector, does courage call for the extreme risk, or sacrifice, of life, or perhaps, in the case of Achilles, for the sacrifice of
revenge. At the end of the Iliad, the usual ways of confronting an
enemy are no longer fitting, and Achilles recognizes that.
The recognition that Hector’s body belongs to his father and to
his city has nothing to do with anything quantitative. It is not
arrived at by adjusting any sort of dial up from too little or down
from too much. But it is a measured response to the situation that
Achilles faces. It is geometrical equality that Achilles restores, by letting the dead man be given an appropriate funeral. It is dignity that
he measures. Priam, the miserable wreck of an old man at Achilles’s
feet, dominates his action in exactly the way Apollo dominates the
Centaurs. In both cases, anger takes up a subordinate position in the
design of the human soul. It finds its right proportion to the whole.
On a list of the various meanings of the word logos preserved from
Aristotle’s school by an ancient scholar (Theon of Smyrna), one of
those meanings was the ratio of one who gives respect to the one
who is respected. By looking at Apollo in his glory, or at Priam in
his misery, we can begin to take our own measure.
This kind of qualitative measurement is appropriately represented by ratios, because a ratio is not a quantity. A ratio limits a
quantity. It is a revealing fact that we all have trouble remembering
what Euclid means by greater ratio—that it is not the span of the
interval between two magnitudes but the size of the first in relation
to the second that he is referring to. A length, or an area, or a volume, or for that matter a weight is measured by its size or amount,
but a ratio is something on a different order of things. We measure
length by cutting it up and counting the pieces, but ratios do not
admit that kind of treatment. Fractions do. Fractions are quantities
but ratios are not. The nature of quantity is that of material. There
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can always be more of it or less, arranged this way or that. And this
way of looking at quantity helps one see that ratios belong to the
realm not of material but of form.
In the Odyssey, Odysseus tells a story that goes on for four long
books. About two-thirds of the way through it he tries to stop and
go to bed, but his hosts will not let him. He claims the story is taking too long to tell, and there is too much more of it, but they are
spellbound and persuade him to go on. The king who speaks for
them tells Odysseus that there is a morphê upon his words (XI,
367), meaning a shapeliness or gracefulness. This is one of the
words that comes later to be used for “form” in an important philosophic sense. Odysseus need not measure his words by time or number, the king is telling him, because his hearers measure them by
beauty and depth. A form does not merely surround its content
with a shape. It transforms the material and makes it be what it is,
through and through. And just as Alkinous praises Odysseus for the
form of his story, Aristotle too, in his Poetics (Chap. 8, 1451a),
praises Homer for knowing where to start and end an epic poem to
make it be one story goverened by one action.
What is the form that governs the story Odysseus tells the
Phaiakians? Neither they nor we ever take that story to be a simple
report of the events that Odysseus witnessed and took part in since
the time he left Troy. It is a story formed or transformed by art. But
if all stories that reshape events were lies, fiction would simply mean
falsehood. Alkinous distinguishes Odysseus from the multitude of
liars the dark earth breeds. His criterion is not easy to translate, but
it is understandable to us because we too have heard Odysseus tell
his story, and know exactly what he means. Lattimore makes
Alkinous say that the liars make up stories from which no one could
learn anything (XI, 366). The more usual translation has it that the
lying stories are made up out of things no one could see, and this,
in turn, either in the sense that all the human witnesses are dead, or
in a deeper sense. Both translations are possible, and both capture
something of what Alkinous is talking about. Odysseus is trying to
get something out of the Phaiakians, but he is also letting them learn
SACHS
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from his experience, and they count that a fair exchange. Things
that are literally false, contrary to fact, are redeemed from falsehood if they capture truth that goes beyond the merely factual. No
one can go see if the story was accurate, but no sensible person
would try to check it in that way, because its proper subject is something that cannot be seen. The story puts in front of the eyes of our
imaginations things that are invisible.
What is Odysseus’s story about? It is, first of all, full of fabulous
beings, gods and monsters and people who live in strange ways. A
question that is repeatedly asked, not with formulaic phrasing but
with constant changes in its wording, is whether the characters that
are about to be encountered are human, that is, dwelling on the
earth and eaters of bread (VI, 8; IX, 89, 191). And even among
those who are not immortal gods and monsters, some dwell under
the earth and drink blood, some dwell in mountain caves and are
cannibals, and some eat the lotus fruit and dwell in their own psyches. But these non-humans are not only a background against
which the human form is displayed, they are constant temptations
to the humans themselves.
Some of the companions of Odysseus are seduced by the lotus
into the oblivion of ignorance, but Odysseus himself is later seduced
by the Sirens, toward the oblivion produced by the love of knowledge. On either side there is a loss of connectedness to the human
community. And Odysseus’s story begins among the Kikones, where
his men get drunk and reckless with success, and then, when their
luck turns, lose six of their companions out of each of their twelve
ships; his story ends among the cattle of Helios, where the men who
are left, less than fifty of them on their one remaining ship, get hungry and reckless in misfortune, and lose their lives. In both overconfidence and despair their hungers become unmeasured by judgement. And again Odysseus too experiences the same dangers, in his
different way. His hunger for recognition, when he has saved himself and his men from the Cyclops, results in a foolhardy judgement
which brings him Poseidon’s curse, and turns victory into needless
defeat; and this is followed by another foolhardy judgement, that he
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could stay awake for ten straight days with the bag of winds, and
arrive home the single-handed savior of his men. His hunger for
glory is as deadly to his judgement as his companions’ hungers are
to theirs.
This break-down of judgement is again a loss of the connectedness of human community, since disproportionate hunger of any
kind, whether from extreme self-indulgence or extreme need,
brings isolation. After the fiasco with the bag of winds, Odysseus
twice shows himself to us in isolation on top of mountains (X, 97
and 148), and this image surrounds his explicit comparison of a
monstrous Laistrygonian to a mountain peak (X, 113), and echoes
his earlier description of the Cyclops (IX, 187-92). Here is what
Odysseus says when he narrates his first sight of the cave of
Polyphemus: “Here a monster of a man bedded down, who now
was herding his flocks alone and afar, for he did not mingle with
others, but stayed away by himself, knowing no law, for he was
formed as a wondrous monster, not like a man, an eater of bread,
but like a wooded peak of the high mountains which stands out to
view alone, apart from others.” In his outsmarting of the Cyclops,
Odysseus displays the power that lets a puny human master a gigantic brute, but in his glorying Odysseus outsmarts himself, and ends
up no better than a Cyclops.
Finally, Odysseus is measured against the gods. This is most
apparent in his verbal jousting with Athena when he awakens on
Ithaca in Book XIII. She uses superhuman knowledge and magic to
deceive and test and tease him, while he holds his own with his
merely human skills, to her delight. “That’s my boy,” she says in
effect, and he replies, in effect, “So where have you been for so
long.” But this alliance of man and goddess as friendly rivals is not
the one that is his true test. It is Kalypso who offers him the ultimate choice, to be her lover forever, while neither of them grows
old, on an island that grows everything to delight the senses and
requires no work. He chooses to go back into the sea, to work, to
fight, to take chances, and ultimately to die. He does not talk about
any of this in the story he tells the Phaiakians, though he had told
SACHS
17
the king and queen the bare outline of it the day before. We know
the story of Kalypso’s island from Homer’s telling of it, before we
know how to understand it. It is Odysseus who puts it in context.
From the time, early in Book X, when he comes down from the
mountain on Circe’s island, the rest of Odysseus’s story is about his
losing battle to win back the trust of his companions. “I am in no
way like the gods,” he has said to Alkinous, “but count me equal to
whomever you know among humans who bears the heaviest load of
woe.” (VII, 208-212) But unlike another man who might say that,
Odysseus had a choice, and chose human troubles. What he lost,
with his companions, was more worthy of choice to him, than what
he could gain from Kalypso’s gift.
We make much of Achilles’s choice, to live a short and glorious
life instead of a long and ordinary one, and pay less attention to
Odysseus’s choice, to live not at ease forever but for a long but
bounded time, amid troubles that will eventually come to an end.
You probably know that the first word of the Iliad is wrath; of the
Odyssey the first word is man. The shaping of the Iliad rises from
the flare-up of Achilles’s wrath, to come to completion when that
wrath itself finds its limit, not just in duration but in submission to
a higher good; the wrathful, warlike side of human life finds its
form and proportion within a larger whole. The Odyssey is formed
in a different way. It starts in three places (Olympus, Ogygia, and
Ithaca). It backs up, and proceeds for a while on parallel tracks, as
we hear a story told and watch the interaction of the teller and hearers, and finally begins moving forward in its second half. But
through and through, the form that shapes the Odyssey is the form
of the human being, as it shows us a man travelling up to all the limits of what it is to be human, coming to know them, and choosing
to remain within them. A participle in the fifth line of the poem
(arnumenos), as it is usually translated, credits Odysseus for saving
his life, but it has a richer meaning: he earned or achieved his life,
proved worthy of it by learning that it was worthy of his choice.
The Phaiakians understand his story, and honor his choice by making one in its image: they choose to risk their easy life by taking on
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his troubles as their own, and their journey to Ithaca is their last
carefree voyage. The first thing we hear about the Phaiakians is that
they live far away from men who earn their bread (VI, 8), but the
human form becomes visible to them in Odysseus, and draws them
out of their isolation.
In the west pediment at Olympia, human dignity is made visible in the figure of Apollo. In the toils and troubles of Odysseus at
sea, human worth becomes apparent against a background of goddesses and monsters and bad choices. The beauty of the Phaiakians’
action is set against the perversion of the human image in the young
suitors who have taken over Ithaca. The suitors are worse than the
Centaurs at Olympia, who are simply appetites that have not yet
come under control. The suitors have no respect for any man or
woman (XXII. 414-15), and so they cannot be reformed. What they
cannot recognize, they cannot take as formative. Their image, in
their feasting, reflects that of the human pigs on Circe’s island; in
their obliviousness to someone else’s home, it reflects that of the
lotus eaters; and in their reasoning that Telemachus is about to
become an obstacle to their pleasure and so, of course, should be
killed, they are no different from the cannibal Cyclops. Odysseus
knows what to do when immortality is offered to him, because he
has learned to respect the claims of human need, and wants to
redeem his loss of his companions, for which he bears not all, but
enough, of the blame. And he will have to use the same standard to
decide what to do about the suitors.
But in Ithaca and abroad, in the story that surrounds that of
Odysseus, there is a gallery of portraits of simple human dignity.
They work on us to convey the power we respect in old people
whose experience has brought them understanding. One of them is
Nestor, who responds to strangers first by feeding them and only
afterward asking whether they are pirates. (III. 69-74) Pre-eminent
among these figures is Eumaeus, the swineherd, a victim of pirates;
born the son of a king (XV 412), he was kidnapped and sold into
.
slavery, but came to accept his lot as the lowliest of servants with no
bitterness (XIV 140-147). He balances the picture of life on Ithaca:
.
SACHS
19
as the suitors have turned a palace into a pig-sty, Eumaeus, with his
courtesy and shrewd judgement, has turned a pig-sty into a place of
gracious hospitality. Homer refers to him as the godlike swineherd
(XIV 401, 413), and as the swineherd, first in the ranks of men
.
(XVII. 184). But surrounding and woven through all these portraits
of age and wisdom is the un-regarded figure of Mentor. Odysseus
had left him in charge in Ithaca (II. 225-7), but his power to rule
rested on nothing but respect. With the invasion of the suitors, the
foundation of civilized life on Ithaca collapsed, and in the resulting
chaos we hardly notice Mentor, since he cannot fight, and barely
raises his voice. He is glorified in the last line of the poem, when
Athena, in a poetic equivalent of the sculpted figure of Apollo at
Olympia, has put an end to the violent strife of people who are all
alike (XXIV 543), making herself recognizable in the voice and liv.
ing form of Mentor. These last words of the whole poem confirm
our sense that its first word, man, is what it intends to reveal to us,
and the final embodiment of that revelation is in a radiant presentation of a character so humble the poet had to compel us to notice
him at all, a character whose dignity lives only in the medium of our
respect, while that dignity, in turn, is the only foundation for shared
human life. Homer makes us err, in overlooking Mentor, and come
to ourselves in recognizing him, so that, in a small way, we mimic
Odysseus’s journey.
But if we are to take the human measure from
Mentor, that must mean that he displays human excellence, and that would be a very strange claim to make.
The poet Homer can play in a serious way by putting the
kingly soul of Eumaeus in a position in which he has only
pigs to rule over, and he can leave us with the vision of a
goddess who makes a humble man resplendent, but neither of these figures seems to display any maximum of
human possibility. Instead, what we seem to see in them
is the last shred of dignity that cannot be taken away from
any human being by any sort of mistreatment from others, but can only be lost by one’s own act. When
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THE ST. JOHN’S REVIEW
Odysseus comes out of the sea alone on the island of the
Phaiakians, he burrows under a pile of leaves. Here is the
way Homer describes this action: “As when someone
hides away a glowing ember in a black ash heap at the
end of the earth, with no countrymen anywhere near, no
others at all, saving the seed of fire in a place where there
is no other source from which he could start a fire, so did
Odysseus cover himself up with leaves.” (V 488-91)
,
Odysseus almost lost himself on his journey. And the
thing that nearly smothered the last spark of humanity in
him was his drive to excel.
We are told in the third line of the poem that many were the
people whose cities he saw and whose intellects he knew, and for
Odysseus every new experience was a test. Seeing and knowing
were never for their own sake for him. He was always taking the
measure of any new places and their inhabitants, and that, for him,
came to be for its own sake, continually to prove himself more than
the equal of any kind of skill or strength or strategem, and worthy
of respect from anything that exists that can pay respect. He wanted to go beyond anywhere others had been, to find every limit and
surpass it. This fits a conventional understanding of excellence, but
it makes no sense. It aims at nothing but beyond everything, so that
the task is infinite and formless. To achieve excellence in this way is
to measure oneself against what is measureless. Only a being of
infinite capacity could be genuinely successful. One image of human
finitude in the Odyssey is our need to sleep. The journey from
Aeolia to Ithaca is long and hard, but achievable, but also just barely longer than anyone could stay awake for. With a dangerous cargo
like the bag of winds, a sensible captain will have to admit his own
limits to himself, and take someone else into his confidence, but
Odysseus does not permit himself such weakness. That stubbornness costs him more than nine years of trouble, and eventually costs
every one of his companions his life. When we see Odysseus give
way to sleep again, the meaning is exactly the opposite of the former occasion. His sleep brings to an end his efforts to persuade his
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21
comrades, and they eat forbidden meat and die; they decide that
they are no heroes, and cannot hold out indefinitely against hunger.
Afterward, Odysseus never ceases to defend them. But it is usually not his companions themselves that he refers to, but the common lot of human beings that he discovered by paying attention to
them. No less than six times he lectures people about the cursed
belly, and the things its need can drive people to (VII. 215-21; XV
.
343-5; XVII. 286-9, 473-4; XVIII. 53-4; XIX. 71-4). The man who
once despised weakness in himself is now the fierce defender of
those whose strength fails them. His rejection of the offer of immortality is in part a gesture of solidarity with his companions, and his
disguise as a beggar on Ithaca in some way displays the truth. In
front of the Phaiakians, Odysseus could have told his story to present himself as the hero of Troy, the most important man in the
world, but he chooses instead to make his loss and his need central.
He tells one of the suitors “Nothing feebler than a human being
does the earth sustain, of all the things that breathe and crawl on
the earth” (XVIII, 130-1), using the same adjective he chose when
telling Kalypso “I know very well that thoughtful Penelope is feebler than you in both form and stature” (V 215-17). He has learned
,
to see what is fragile in us and in need of protection as having a
higher claim on his effort than any extraordinary achievements that
might extend human glory.
But the radiant dignity conferred on Mentor at the poem’s end,
and glowing from within Eumaeus in its midst, is not the whole of
the human image either. There is also heroic action that is not ambitious for glory but called forth in defence of what is dignified but
weak. In Aristotle’s ethics the word that names human dignity is
spoudê, seriousness, the quality that is apparent in certain exceptional people who know what to take seriously. But in the Odyssey
the focus is on aidôs, respect, the quality present in all of us that
enables us to recognize dignity. Respect can take the place of force,
and can bind together a community, establishing the conditions of
life under which the things that have seriousness and dignity can be
given their due. The actions that embody respect constitute what
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THE ST. JOHN’S REVIEW
Aristotle calls distributive justice, the paying of what is due not
merely in the quantitative medium of money but by reference
always to the qualitative medium of honor. In a just community,
according to Aristotle, there will never be simple equality, but rather
proportional equality, actions and titles and gestures that make evident what different people deserve. And this is what Socrates called
geometrical equality, since it requires an act of seeing rather than
one of calculating.
In the Odyssey, our seeing is put to work most vividly beyond
the world in which we live and make choices, envisioning the
Cyclops, the passage between Scylla and Charybdis, or Odysseus
lashed to the mast while the Sirens sing, but as in the west pediment
at Olympia, these figures depicted as outwardly visible display the
shape of the invisible human soul. The soul that Homer lets us recognize as unsurpassably right in its ordering is the one that we see
in the hero in rags, in his feeble old father in armor (XXIV 513-25),
.
in the boy who calls an assembly of adults, in the woman who neutralizes the strength of 108 men (XVI. 245-51) and stops time itself
for four years by unweaving every night what she wove by day (II.
94-110). It is the human balance in which strength has reason to
give way to weakness, and weakness has resources to find strength.
It is the human mean that can live only within a community. The
best human life is a topic that demands philosophic reflection, but
such reflection would not be possible if one could not, in the first
place, simply see its form.
NOTE:
The central importance in the Odyssey of the respectful attitude aidôs
that makes human communities possible is something I first learned by reading Mary Hannah Jones’s senior essay, “A First Reading of the Odyssey,”
included in the collection of St. John’s College Prize Papers, 1977-78.
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THE ST. JOHN’S REVIEW
25
Plato and the Measure of the
Incommensurable
Part II. Plato’s New Measure:
The Mathematical Meaning of
the Indeterminate Dyad
Amirthanayagam David
I shall argue that the controversial developments—some
would say the reversals—in Plato’s later metaphysical outlook
were in fact an inspired response to some truly epochal developments in the mathematics of his day; in particular, to certain
seminal advances in the theory of the irrational. Following on
my reading of the geometry lesson at Theaetetus 147, and of its
significance for that dialogue and for the Sophist and the
Politicus, I can now shed light on one of the most obscure
notions associated with Plato, a thing known to Aristotle as the
“indeterminate dyad.” The discovery and description of this
remarkable object—remarkable, all right, yet thoroughly nonmystical and mathematically legitimate—can be seen as the
motive force behind some of the arguments and constructs in the
late dialogue Philebus. In interpreting the ancient testimony, my
reconstruction demonstrates that the mathematical meaning of
the late Platonic metaphysics was either not transmitted to, or
simply lost on, the successors of Plato and their critic Aristotle.
But where the philosophers strayed, the mathematicians found a
fruitful path: the conclusion to the work started by Theaetetus
and Plato finds a home of concision and elegance in the mathematics of Euclid’s Book X. A historian of ancient philosophy
may have to distinguish in future between the academics who
inherited Plato’s arguments, and the mathematicians who understood them.
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THE ST. JOHN’S REVIEW
Perhaps the best evidence for a revision, radical or not, in
Plato’s thought comes from Aristotle’s intellectual biography in
Metaphysics A. He there refers to a kaí flsteron, an “even
afterwards” in Plato’s career (987b1). The passage is explicit
that there was a before and an after in Plato’s thinking which
was not apparently defined by the death of Socrates. What is
more, the change was apparently of some considerable moment;
the whole force of the expression is in the kaí; Plato is said to
have accepted the premise of universal flux espoused by Cratylus
and the Heracliteans, even afterwards. The theory of sensation
we have discussed in the Theaetetus is an example of his new
approach to an old premise, an approach based on a new mathematics of measurement.
At one time during the geometry lesson in the Meno, Socrates
counsels the slave boy, who is trying to find the line from which a
square the double of a given square is generated, “if you do not care
to count it out, just point out what line it comes from (e£ m±
boúlei ¡rivmeîn, ¡llà deîxon ¡pò poía$, 84a).” This is the
vintage Socratic irony, a playful but possibly sinister half-telling:
there is in fact no straightforward way to count out such a line with
the same unit measures that count off the side of the given square.
In a passage that means to inspire confidence in our ability to learn,
Socrates hints at a shadowy impediment that lurks, even as the slave
boy triumphs. This problem of incommensurability was the bane of
measurement science—metrhtik≠, that science which assigns
number to continuous magnitude—perhaps onwards from the time
of Pythagoras. Measurement prò$ ållhla, or mutual measurement, the reciprocal subtraction (¡nvufaíresi$) of two magnitudes, came to an end or limit (péra$) at the common measure of
these magnitudes; but if the magnitudes were incommensurable, the
process of subtracting the less from the greater, and then the
remainder from the less, would continue indefinitely (i.e., it was
unlimited, åpeiron). Such everyday magnitudes as the diagonals of
squares with countable sides were årrhton, inexpressible, or
DAVID
27
ålogon, irrational, in terms of those sides, an embarrassment to
any serious measurement science.
The in-betweenness of irrational lengths with respect to rational (countable) ones—in the Meno, Socrates takes pains to show by
a narrowing process that the required length, the side of an eightfoot square, lies somewhere in between two and three feet (83ce)—may have been the clue to a new approach. Plato’s Stranger
proposes a new branch of measurement science in the Politicus
(283d ff.); alongside measurement prò$ ållhla, there is now to
be measurement prò$ t±n toû metríou génesin, measurement
toward the generation of the mean. I have suggested that
Theaetetus’ seemingly humble classification of roots (Theaetetus
147c ff.) was the ultimate inspiration for this formulation; his novel
use of the mean proportional allows number and magnitude (the
phenomena of arithmetic and geometry) to be subsumed successfully under a revitalised and heuristic measurement science.
“’Squaring’ is the finding of the mean (› tetragwnismò$
mésh$ eflresi$, De Anima 413a20),” and he who defines it this
way, says Aristotle, is showing the cause of the fact in his definition.
To square a given rectangle, one has to find the mean proportional
between the lengths of its sides. Theaetetus distinguishes between
two kinds of length as sides of squares: a mêko$ is the length of a
side of a square number (4, 9, 16, etc.), the mean proportional (or
geometric mean) between the unit and a square number; a dúnami$ is the side of a square equal to a rectangular number (2, 3, 5, 6,
etc.)—i.e., the geometric mean between the unit and a rectangular
number—which is incommensurable with the unit in length
(m≠kei) but commensurable with it in square (dunámei).
Taken by itself, this classification is hardly more than a new
way of naming the phenomena of measurement science. Even at
this stage, however, the roots of non-square numbers, formerly
irrational and intractable, have become more expressible (@htá);
they are at least commensurable in square. A third category can
now be envisioned—incommensurability in length and in square—
so that where we had a polar division of opposites (rational-irra-
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THE ST. JOHN’S REVIEW
tional), now we have an enumeration of the phenomena: rational,
expressible, irrational.
But the true mathematical utility of this re-classification lies in
the lucid quality of the geometric mean. We recall that for any interval, this mean can be approximated in length by interpolating successive pairs of arithmetic and harmonic means within the given
extremes. Since in a rational interval, like that between the unit and
a non-square number, the interpolated means are also rational, and
since they define an evanescent sequence of rational intervals
around the same geometric mean, the incommensurable roots of
non-square numbers can now be systematically approximated with
numbers of their own. Each of these lengths, which we nowadays
call √2, √3, √5, etc., is approximated as a geometric mean by one
or more series, each unique and infinite, of arithmetic and harmonic means, which give better and better rational over- and under-estimates (respectively) of each incommensurable length. Though the
geometric mean is never reached, each successive pair of interpolations reduces the interval containing it by more than half, so that
each of the approximating extremes approaches closer than any
given difference to the mean (by Euclid’s X.1). Hence the process is
unlimited in its degree of accuracy.
The uniqueness of each of these “dyadic series,” corresponding
to each of the incommensurable roots, is the key to their achievement. Numbers may now be introduced, in a mathematically useful
and rigorous way, to describe the lengths of these roots.
Measurement science can thereby fulfil its mission, once paralysed
in these cases, to number the greater and the less. Irrational roots
are no longer vaguely “in between”: each dyad of interpolated
means defines all rational lengths, whole or fractional, than which
a particular incommensurable root is greater, and all than which it
is less. Since the “dyadic interval” can be made to shrink indefinitely, these incommensurable lengths have been uniquely measured in
terms of a given unit, as uniquely as any commensurable length.
A rational length is measured by one number, a “one many,” a
single collection of so- and so-many units (and fractional parts).
DAVID
29
These lengths are therefore measured both absolutely and relatively in terms of the unit length; one can answer the question, “How
many is it?” with respect to them. An irrational but expressible
length, on the other hand, is measured by a series of pairs of numbers, a unique but “unlimited” or “indeterminate” dyad (¡óristo$
dúa$). Such lengths are only relatively measured in terms of the
unit; for them, one cannot answer the question “How many is it?”
with a definite number, but one can always answer the question, “Is
it greater or less than this many?” There are now two ways in
which number can be applied to continuous magnitude—with a
normal ¡rivmó$ measured by the unit, or an indeterminate dyad
of such ¡rivmoí—so that both the diagonal and the side of a
square can be “counted off ” in terms of the same unit length.
The original significance of the unit and the indeterminate
dyad can now be recognised in the context of the new branch of
measurement science: the former, already a principle and product
of the existing branch, measurement prò$ ållhla—for the unit
is the measure of all commensurable magnitudes, and the ultimate
result of the reciprocal subtraction of commensurable quantities—
is a measure of all rational means (including the roots of square
numbers). The latter is a way of measuring all the expressible geometric means (the roots of rectangular numbers); it is a principle
and product unique to the new branch, measurement toward the
generation of the mean, for paired interpolation represents a way
to “generate” an expressible geometric mean numerically, and the
resulting indeterminate dyad of greater and lesser values is a precise
and exhaustive way to locate an expressible length within the scale
of the rational continuum. The unit and the indeterminate dyad,
the respective measures of rational and expressible means, are
therefore rightly conceived as the two proper principles of that science which approaches measurement through the construction of
means.
*
*
*
*
*
*
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THE ST. JOHN’S REVIEW
In the Philebus (23c ff.), Socrates proposes a four-part division
of all beings. The first two segments cover the limited and the
unlimited, the once all-embracing Pythagorean pair of opposites.
The third division encompasses those beings produced by the mixture of the polar principles; this mixed category represents the distinctive late Platonic innovation in ontological thinking, outlined
also in the Sophist (see 252e). A fourth division is enumerated to
cover the cause of the mixing in the category of mixed beings.
At first glance, the mathematical subtext of this classification seems fairly straightforward. The unlimited stands for continuous magnitude, that which admits of being greater or less
(24e); the limited stands for number and measure (25a-b). The
mixed class stands, as could be expected, for continuous phenomena that admit of measurement or a scale: Socrates mentions music, weather, the seasons, and “all beautiful things
(Øsa kalà pánta, 26a-b).” The demiurge of the Timaeus,
who constructs a cosmic musical scale out of elements he has
mixed (35b ff.), could be seen as a mythical archetype of the
fourth kind of being, the cause of mixing. The mixer is also a
measurer.
Certain peculiarities in Plato’s presentation suggest, however,
that it is motivated by the developments in ancient measurement
theory that I have described. First of all, the distinction made
between the limited and the unlimited is virtually analytic. This
would not be necessary for a distinction between number and magnitude, because of the phenomenon of commensurability. But the
class of the more and the less, the pair which characterises the
unlimited, is said to disallow the existence of definite quantity; if it
were to allow quantity (posón) and the mean (tò métrion) to be
generated in the seat of its domain (‰drˆ ™ggenésvai), the moreand-less themselves (a dual subject in Plato’s Greek) would be made
to wander from the place where they properly exist (24c-d). The
class of the unlimited therefore stands for the greater-and-less qua
greater and less, those magnitudes which refuse numerical measurement of any kind, like the radically incommensurable lengths
DAVID
31
(commensurable neither in length nor in square). The class of the
limited, on the other hand, is said to cover only those things which
admit of everything opposite to the more-and-less (toútwn dè tà
™nantía pánta decómena):
prôton mèn tò ªson kaì £sóthta, metà dè tò
ªson tò diplásion kaì pân Øtiper ∂n prò$
¡rivmòn ¡rivmò$ ˚ métron ˜ prò$ métron...
(25a-b)
first the equal and equality, and after the equal the double and everything whatever which is a number in relation to a number or a measure to a measure.
The limited is therefore the class of commensurable magnitude.
Is the distinction between limited and unlimited then a descriptive
one based on that between number and magnitude, or really an analytic one between two kinds of magnitude, the commensurable and
the incommensurable?
The mixed class is also described as the class (£déa) of the equal
and the double (25d); this means it must be meant to include within it the whole class of the limited or commensurable. One could
have expected this if it corresponds to a class of scalable magnitudes. But Socrates goes on to add this curious category to its
domain:
...kaì ›pósh paúei prò$ ållhla t¡nantía
diafórw$ ®conta, súmmetra dè kaì súmfwna
™nveîsa ¡rivmòn ¡pergázetai (25d-e)
also so much of a class as stops things which are opposites, differently disposed to one another, and fashions
them into things commensurable and harmonious by
putting in number.
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THE ST. JOHN’S REVIEW
This function appears to be unique to the mixed kind of being.
Since only incommensurable things can be made commensurable,
the unlimited did indeed signify the incommensurable, as was surmised; and the class mixed from the limited and the unlimited
appears to include a new species not found in either apart, which
makes incommensurable magnitudes commensurable by “putting
in” or “inserting” (™ntívhmi) number. With somewhat uncharacteristic acuity, Protarchus understands Socrates to mean that certain constructions (or “generations,” genései$) follow from the
mixing of the Pythagorean opposites (25e). (This interchange
seems to be a single Platonic exposition split between two speakers. The author better remembers his dramatic premises when,
within less than a Stephanus page, he has Protarchus suddenly
express his unsureness about what Socrates could have meant by
the members of the third class.)
The two ways of measuring magnitude in terms of a single unit
length, by means of a number or an indeterminate dyad of numbers,
correspond to the two classes which make up Socrates’ third category. In particular, the second way of measuring corresponds to that
construction described above which is unique to the mixed category. Both take up magnitudes that were formerly irreconcilable, subsumed by an opposition of greater to less—i.e., incommensurables
belonging to the category of the unlimited—and make them concordant and commensurable by “inserting number.” But neither of
them does this in such a way as thereby to reduce these magnitudes
to the class of the limited. Rather, certain lengths turn up in the
measurement of magnitude, incommensurable as such but commensurable in square, that call forth a peculiar application of number, one which inserts greater and lesser values in such a way that
they become more and more equal. This use of numbers comes to
light only in measurement science, and hence only in the mixed category of beings; it does not suggest itself in the operations of pure
arithmetic, the science of the class of the limited (governing numerable, discrete quanta and their formal equivalents, like commensurable lengths). An indeterminate dyad is a numerical description of
DAVID
33
a peculiar kind of length, neither irrational nor rational, but belonging to a third analytic class called “expressible.”
The mathematical subtext of Socrates’ proposal therefore runs
as follows: the distinction between unlimited, limited, and mixed
is, after all, a descriptive one based on that between magnitude,
number, and measured magnitude. But when Socrates attempts to
bring unity to each category, drawing together into one (e£$ ‰n,
25a, 25d, etc.) the beings subsumed by each, he employs a threepart analytic distinction that applies properly to magnitude alone.
That is to say, he brings unity to each of the three realms—number, magnitude, and measured magnitude—by describing each of
them in terms of the particular kind of length, the particular kind
of one-dimensional magnitude, which uniquely characterises it.
Hence the class of the unlimited is not just the class of the greaterand-less, but the class which positively rejects numerical description, like that of the radically incommensurable lengths. (The analogy is strict, for recall that this class is said to reject from its own
rightful seat both definite quantity (posón) and the mean (tò
métrion); on my reconstruction, this means it rejects the only two
ways of counting lengths, either with a single number, or with an
indeterminate dyad of numbers that approximate a geometric
mean.) The class of the limited, likewise, is not just the class of
numerable things, things which can be expressed as ratios of a
number to a number, but also the class of certain kinds of magnitude, those which can be expressed as ratios of a measure to a
measure, for commensurable lengths share all the properties of
numbers. Hence the distinction between magnitude and number
(unlimited and limited) can be reduced to a distinction between
two kinds of line. And finally, the mixed class, or the class of the
scale, though it includes within it the class of the limited, comes to
be characterised by a use of numbers and a kind of magnitude
which are each unique to it. These are the indeterminate dyad and
the lengths which it measures, once incommensurable but now
made “expressible” by the insertion of number. The expressible
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roots form a third analytic possibility within the field of onedimensional extension, alongside rational and irrational lines.
The reductionist spirit of Socrates’ analysis is in the best traditions of ancient mathematics. To reduce one problem to another is
of course heuristic of a solution, but the process can also be useful
in definitions and classifications. An example has been given in
Aristotle’s reduction of the problem of squaring to that of finding
a mean proportional line. One effect of Euclid’s proposition II.14,
which contains a solution to Aristotle’s reduced problem, is in turn
to reduce a comparison in magnitude between any rectilinear
figures to a comparison between squares, and hence to a comparison in one dimension, between square roots. A later and particularly virtuosic example is to be found in Apollonius’ use of the
three kinds of application of area upon lines, the parabolic, hyperbolic, and elliptic, to both name and define the three kinds of conic
section. In Plato’s case, the distinctions between his ontological
realms of the unlimited, limited, and mixed—two of which, as
opposites, had had a long-standing currency in metaphysical thinking—have been reduced to the distinctions between the three kinds
of line studied in the new measurement science: irrational lines
that are incommensurable both in length and in square; rational
lines that are commensurable both in length and in square; and the
expressible lines that are incommensurable in length, but commensurable in square.
This analysis is also in the spirit of the “enumerative” method
Socrates had earlier set out (16c-17a). One is to seek out the form
(£déa) which lends unity to a field of phenomena, and then seek out
those things measured by this hypothetical unit-form (i.e., those
phenomena which are “numbers” if the original form is taken as a
unit). The method intends to be self-correcting, for one is enjoined
in turn to analyse the original unit (tò kat ¡rcà$ ‰n, 16d) in
the same way that one has analysed the enumerated phenomena, to
see “how many” it might actually be. A converse procedure is equally espoused in the case of a science like grammar (18a-d): when the
datum seems unlimited or continuous, as does the phenomenon of
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human vocalisation, one is first to discover the numbers into which
it naturally divides, which govern pluralities such as those marked
out by the distinction between vowels and consonants, before one
proceeds to analyse these further into their units. There may be an
analogy here with modern analyses in terms of “sets,” which also
presume that things need to be sorted before they can be counted
or related. Euclid’s definition of ratio (V requires a relation of
.3)
kind between the compared terms. Even the infinite field of number
itself is nowadays divided in such a way that unitary types may be
distinguished (“Reals” over “Rationals” and “Irrationals”) while
individual members remain both infinite and infinitely instantiatable. An “enumerative theory of forms” would seem to reflect the
ontological and epistemological implications of the interdependence of sorting, on the one hand, and counting or measuring on the
other. The new Socratic method is developed as an explicit reaction
to the Parmenidean or Pythagorean type of thinker—but also, perhaps, to the early Plato—who analyses everything in terms of
opposed principles like the one and the many or the limited and the
unlimited, and fails to articulate the crucial phenomena that are
ordered, like numbers, in between such opposites. Hasty and simplistic analysis in terms of opposites is said to characterise arguments that are made eristically, while the enumerative method, the
method that discovers the numbers of things and their ordered relations, characterises the truly dialectical approach (17a).
Socrates had earlier made it clear (14d-15c) that the familiar
paradoxes of the one and the many were no longer his concern.
Any lazy riddler could prove that an individual like Protarchus, or
a thing made up of parts, was at the same time one and many. It
was the possibility of formal unity, in the face of the sensible births
and deaths of numberless individuals, the unity that is asserted of
things in discourse—whether of “man” or of “ox” or of the beautiful or the good—that was of vital philosophical interest. Did any
such units exist? How might they persist as individuals? And how
is it that they partake of the infinite multiplicity of things that
come into being? The genuineness of these perplexities calls forth
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his enumerative approach, a philosophical pathway that Socrates
says he had ever loved, but which had often deserted him in the
past (16b). The method is hard, but the results can apparently be
astonishing; all the achievements of the arts (técnai) are said to
have been discovered on this road (16c).
The implications of this method, shot through as it is with the
influence of the burgeoning measurement science, are staggering for
the “classical” Plato. Consider that we are here hypothesizing the
existence of forms as measures, enumerating phenomena in terms
of a posited unit-form, and then examining the posited unit, presumably against the phenomena themselves, to check for its possible plurality. The method itself is therefore mixed, in such a way as
to cancel Plato’s earlier formulations. Neither is this the unhypothetical reasoning from forms to forms, whatever that may have
meant in The Republic, nor is it a reasoning from unquestioned
hypotheses, in the manner of synthetic geometry. The once eternal
forms, the objects and immutable guarantors of knowledge, have
become provisional and heuristic.
God is said to have made all beings out of the one and the many
with the limited and the unlimited as innate possessions (16c). This
would tend to insure that all phenomena will be inherently numerable, and hence to guarantee their susceptibility to an enumerative
method; we shall find the unifying form, for it is in there (eflr≠sein
gàr ™noûsan, 16d). It is as though the pairs of opposed ontological elements, once the principles of the eristic disputations, have
now been “re-packaged” in the premises, made the condition for
the possibility of an enumerable reality. Inasmuch as it was
Aristotle’s understanding (Metaphysics M.4, 1078b12) that the theory of forms was invented in the first place to account for our sense
of dependable knowledge in the face of a Heraclitean flux—and
note that the premise of a reality in flux is still accepted at Philebus
43a—it seems that this theory has now been modified to make sense
not so much of our ability to know as of our ability to count. And
this change of purpose is sparked in turn by a renewed confidence
in this sovereign ability, in light of Theaetetus’ successful attack on
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the irrational. Number had at last been restored to some of her
Pythagorean glory, as a measure of the things that are, that they are,
and the things that are not, that they are not, and what is more, of
the things in between. The victory here was sweet indeed, for the
irrational square roots were recovered from the domain of flux and
incommensurability on the very terms by which this domain is distinguished. The indeterminate dyad is both a measurement and a
process of measurement: interpolating means between means
involves a measurer and a thing measured which are continually
changing, just as in the Heraclitean or Protagorean contentions; yet
this process of itself yields a unique measure of the fixed mean proportional between the interpolated means, and makes expressible
and commensurable the once irrational root of a rectangular number.
Indeed, this process of measuring or counting in an indeterminate dyad has proved to be revelatory of form, in the sense that it
creates the class of the expressible and defines the mixed category
of being. On the one hand, things need to be sorted before they can
be counted, and hence the knowledge of form has primacy over
measurement, and the ability to count depends upon the ability to
know. But it would seem in this case that the act of measurement
can itself be disclosive of form, and hence that knowing can depend
on counting. There appears therefore to be a dialectical relationship
between sorting and counting, which is reflected in a self-correcting,
enumerative theory of forms. This methodology of the Philebus can
be seen as reincorporating certain aspects of the Pythagorean, in the
sense that once again, knowledge has become coordinated with
measurement, and to know something is in some sense to comprehend its number.
Confidence in the grounds of an enumerative approach to the
sensible world—a confidence that may once have deserted Socrates
in the face of an irrational diameter, leading him, with Meno’s
honest slave, to the abyss of irony—can allow that significant guarantees of veracity will come from the method itself. There are, for
example, different ways to “count” or measure a phenomenon,
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each of them legitimate, based on the premises and aims of the
investigator, as the several alternate divisions of the sophist and the
statesman make clear. One measure of the truth of a hypothesis,
that such-and-such a form is a genuine unit, must, under this
method, be the economy and scope of the enumeration it affords,
as a unit in fact. A criterion for a successful articulation, a guarantor that a dialectical enumeration corresponds to a real one in the
world, must therefore be the elegance of that articulation, in terms
of the economy of means and breadth of cover which problemsolving mathematicians have always striven for in the concrete
practice of their art.
Indeed, it is an informed sense of respect for developments and
concrete formulations in the arts that seems to move the older
Plato. In the spheres of grammar and music, for example, although
it appears that an abstract analysis in terms of opposites, in the manner of the sofoí, may to some extent be applied in the interpretation of phenomena, by itself such abstract analysis simply does not
make you much of a useful theorist (17b-c). An investigation into
the numbers and kinds of sounds, on the other hand, or an enumeration of the different scales and modes and the vagaries of
rhythm—these, it seems, can truly render you wiser than the common run, in music and in grammar.
Behind this sensitivity of Plato’s to the enumerative and the
concrete aspects of the arts, as against the approach through dogmatic first principles, may rest his experience of the dramatic
changes in the mathematics of his day. A distinction like that
between the rational and the irrational, which must have seemed as
basic to the science as that between odd and even numbers—an
eternal, immutable opposition, seemingly a part and principle of the
order of things—was made obsolete by the emergence into history
of a new formulation through the mind of a single, brilliant practitioner. Recall that Theaetetus’ reforms began very humbly on the
level of classification and definition: he makes the distinction
between square and non-square the basic one for number, beyond
the distinctions between, say, odd and even or prime and compos-
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ite. But of itself this suggests a new way to approach the measurement of lengths, as geometric means, and this further yields, or
reveals, a third, formally distinct category of magnitude called
expressible. Experiencing this revolutionary development, as witness or participant, must lead a thinker away from a view of tà
mavhmatiká as eternal, innate verities that can be investigated and
learned as though by recollection, towards a view of mathematics
that must acknowledge the importance and ingenuity of the problem-solver in situ, together with the power of classifications, definitions and measurements to reveal, or to obscure, the fundamental
nature of their objects. As the traditional theory of forms and the
doctrine of mávhsi$ ¡námnhsi$ can be seen as responding to the
ontology and epistemology of the earlier geometry, so can a selfcorrecting, enumerative theory of forms be seen as a response to the
ontological and epistemological implications of the new mathematics and a dynamic measurement science.
Insofar as other arts aspire to the mathematical, the new philosophical outlook must also apply to them; although, to be fair, the
provisional, enumerative approach would have long since guided
the formulations of practitioners in music and grammar, without a
felt need for a mathematical paradigm or a philosopher’s blessing.
Perhaps one should credit Plato only with waking up to the new
realities of science and art around him, much in the spirit of later
revolutions in philosophy. One need not qualify, however, one’s
estimate of the implications of this change of view for Plato’s political thought; they are as great as the differences between the
Republic and the Laws. In this vein, while Plato’s guardians had
learnt their lessons and then interpreted the world, so that nature
and politics alike would have been for them a kind of applied mathematics, Plato’s statesman is of an altogether different mould of
mathematician. He is a problem solver, in amongst it like a navigator or a physician, who must be able to adapt his laws to suit changing conditions, or improve upon his formulations to serve the present (see Politicus 295c ff., 300c). It is of course notorious that the
guardians’ inability to solve a problem—the numbering of love, and
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40
its irrational quantities—leads inexorably to the degeneration of
their regime.
*
*
*
*
*
*
In Metaphysics N, Aristotle introduces his redaction and criticism of the Platonist (or Academic) metaphysics with this statement:
“All thinkers make the principles opposites (pánte$ dè poioûsi
tà$ ¡rcà$ ™nantía$, 1087a30).” There appear to have been
various schools of thought among Academic ontologists, all of
whom posited the unit as a first principle or “element,” but each of
whom disagreed as to the nature of the opposite principle, whether
it was the “greater-and-less” or the “unequal” or “plurality”.
Aristotle makes short shrift of all these formulations, as they treat
affections and attributes and relative terms as substances (1088a16).
In N.2, he mentions a group who posit the indeterminate dyad as
the opposed element, as a way of getting around some difficulties in
the other versions; but it is still a relative principle, and in addition,
all these formulations fall to Aristotle’s argument that eternal things
simply cannot be composed of elements (1088b28-35).
Aristotle then feels, before he adumbrates his own approach to
ontology, that he must explain why these thinkers ever came up
with formulations so narrow and forced, constrained as they are by
the dogma of opposed principles (1088b35 ff.). His answer is that
they had framed the problem of ontological multiplicity in an oldfashioned way (¡rcaikô$, 1089a1-2), for they were still arguing
in response to certain paradoxes of Parmenides. The implications of
this reconstruction of recent intellectual history are decisive both
for our sense of Aristotle’s access to Plato, and for our knowledge
of Academic thought and its relation to Plato. All the Academics,
and thus Plato as well, are said to reason about existence in terms
of an opposed pair of first principles—always the unit and something else; they do this under the direct influence of Parmenides,
perhaps as part of a tradition of arguing against certain eristic dogmas of his, such as the one which Aristotle quotes:
DAVID
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o∞ gàr m≠pote toûto dam˜, e–nai m± ™ónta
For this may never be enforced, that things which are
not, are.
These thinkers are said to have felt that the possibility of multiplicity in the world would be threatened unless Parmenides were
refuted, and some other thing than unity or being were allowed to
exist. This was the origin of the “relative” principles that stood
opposite the unit. The unit and the indeterminate dyad, on this
scheme of Aristotle’s, are but one alternative among several pairs of
first principles proposed by different Academic philosophers.
The first thing to note is that the Philebus itself is Plato’s direct
and unambiguous criticism of the ontological reasoning based on
two opposed principles, in favour of a technical, empirical, enumerative approach. From the perspective of philosophical method, the
dialogue can hardly be said to have any other point. Plato conceived
of his enumerative method as a more illuminating and more useful
way of articulating phenomena, which comes to yield significant
new categories in the analysis of being (e.g., the mixed one and the
cause of mixing). No further clue seems to be necessary for the conclusion: Aristotle, somehow or another, has entirely missed the
point of Plato’s late formulations, by classing them with the type
that Plato himself characterises as eristic rather than dialectical, and
from which he most particularly wants to distinguish his own.
The next point, however, is that there must actually have been
a vigorous tradition of thought which both preceded Plato and
outlasted him in his own Academy, characterised by the use of
opposites as first principles. To believe so much is the only way to
attach any seriousness to Aristotle’s redaction. This tradition originates with Parmenides, and must once have included Plato in its
ranks, again if one is to pay any respect to Aristotle’s judgement.
But Plato came to argue against such thinkers not only in the
Philebus, but also in the Sophist, where they are called “the friends
of the forms (o‹ tôn e£dôn fíloi, 248a).” These were the lat-
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ter-day champions of eternal, immutable, unmixing forms, the
kind of weary theoretical construct that is often now taught as
Platonism. When the differences seem so clear, the question must
become: How could Plato’s new “mixed” ontology have come to
be confused with the old-fashioned approach through polar principles?
Recall that on my reading of the Philebus, there are for Plato
three ontological realms apart from the agent of cause. The first is
the realm of the limit, the realm of arithmetic, whose principle is
the unit. The second is the realm of the unlimited; its principle,
analytically opposed to the unit, is the dual greater-and-less, the
principle of irrational flux. The third realm is that of the mixed
beings, which I have interpreted as the realm of measurable things.
Its principles are two, and reflect the two ways that magnitudes
may be numbered or made commensurable, absolutely in terms of
the unit or relatively (but uniquely) by an indeterminate dyad. The
thing to note is that the unit appears as a principle twice in this
scheme, opposed in two different ways to two different things. The
distinction between the unit and the greater-and-less is strictly analytic, and belongs squarely in the Parmenidean tradition; whereas
the distinction between the unit and the indeterminate dyad is
merely descriptive, serving to recognise ways of applying numbers
inside the sphere of measurement that happen not to arise in arithmetic. The unit and the dyad are therefore not opposites; they are
simply different.
If a thinker in the Parmenidean tradition, or a historian of the
Parmenidean tradition, were to interpret Plato’s scheme in light of
their own practices, or to force it into a Parmenidean mould to flatter a historical premise, the conflation of the two distinctions would
be an inevitable result. If the Philebus could not be consulted—if it
were ågrafo$ in the sense “unpublished”—no recourse could be
had to the original reasoning; but even if there were such recourse,
Plato’s three realms of number, magnitude, and measure, and the
important differences between the distinctions unit/greater-and-less
and unit/indeterminate dyad, could only be understood in light of
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an underlying mathematical paradigm, as I have argued. Such a
thinker or such a historian would not be likely to know or to care
about the analytic possibilities in one dimension. (This is as much as
to say, he would not know what was meant by the indeterminate
dyad.) He will look for the polar principles in any ontological
scheme; at best he will see that the indeterminate dyad must connote something different from the greater-and-less, as the principle
chosen to stand opposite the unit. But he will never envision a
scheme that encompasses both oppositions.
The question next to ask is whether it was his Academic
sources, or whether it was Aristotle himself who did not understand
the mathematical meaning of the indeterminate dyad. There is
intriguing evidence in Metaphysics M and N for the latter interpretation. It would seem that his sources were in the dark about this
too; but whatever one concludes about the Academy, there is evidence that Aristotle had Plato’s accounts at hand either to quote or
to paraphrase, and that he could not make sense of them.
In N.1 (1087b7 ff.), Aristotle mentions a group of thinkers who
attempt to generate the numbers, o‹ ¡rivmoí, from the “unequal
dyad of the great and small,” taken as a material principle in relation to the formal “one,” and someone else who would generate
them from the principle of plurality. (He probably intends, respectively, the followers of Plato and Speusippus.) The generation of
numbers does not seem to have been a concern of Plato’s, however; the “problem” of multiplicity, or of how things can be both one
and many, which when posed by Parmenides might have led his successors to theorise in the abstract about the generating of numbers,
seems to be regarded in the Philebus (14c-15a, 16c-17a) as merely
a staple of the eristic paradoxes, now subsumed within the premises of Socrates’ concrete enumerative approach. Which is to say, it
appears that Plato is no longer so interested in number theory as he
is in simply counting. I am therefore inclined to think that neither
the above-mentioned group nor the ‘someone else’ represents
Plato’s line of argument, or Plato’s understanding of the unequal
dyad. Aristotle bears this out by going on immediately to mention
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an individual who speaks of the one and the unequal dyad as ontological elements (1087b9), thereby distinguishing him from the
group who had used them (afterwards, I presume) as formal and
material elements in the generation of numbers. Aristotle’s complaint about this individual is that he does not make the distinction
that the unequal dyad of great and small is one thing in formula
(lóg¨), but not in number (¡rivmõ).
Why would not Plato have made this distinction? The unequal
dyad is not one thing in formula alone: the successive pairs of interpolated numbers relate uniquely to one object as well, the side of
the square that is their single geometric mean. Further, since it consists of successively more equal sides of a single rectangular number,
the dyad can quite emphatically and strikingly be said to be of one
number, with a rationale that Aristotle might have appreciated if he
had been more familiar with the construction.
On this model of progressively “equalised” rectangular numbers, we have a transparent motivation for the original formulation
of terms like “unequal,” “indeterminate dyad,” “greater-and-lesser,” and “exceeding and exceeded,” which find their way into the
theories of Plato’s followers. In addition—and this point would
seem to be decisive for the interpretation—we should expect to
find them opposed in this context to a concept of the unit which is
associated with the square or “equal”. On no other grounds but
those of the new measurement science, as I have described them
here, would such an association be expected. Sure enough, the unit
in these theories is described as the equal (1087b5, 1092b1), in
such a way as to mystify not only Aristotle but also modern interpreters of these passages.
Neither Aristotle nor his Academic sources seem to connect
these various expressions with geometrical representations of number; the theories on the generation of numbers betray no influence
of Theaetetus’ square/oblong distinction, nor of the geometrical
interpretation of number that is settled convention by the time of
Euclid. The Academics seem to have posited “ideal” numbers which
were generated individually in succession (two, three, four, as
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Aristotle says in M.7 1081a23, and so without distinction as to
square or oblong) from the unit and the indeterminate dyad.
Aristotle takes some pains to make sense of this theory: if the units
(monads) of ideal numbers are all the same and addible, then they
are not ideal at all, but normal mathematical numbers (cf.
1081a19); but if the monads of each ideal number are distinct and
inaddible, they must be generated before each of their respective
numbers can be generated, as a point of logic (1081a26 ff.). This is
true no matter how these monads are generated; but Aristotle once
more quotes “he who first said it” (› prôto$ e£pµn, 1081a24)—
again distinguishing him from those who later used such phrases as
the “unequal dyad”—to allude to a possible mechanism for this generation of inaddible monads (¡súmblhtoi monáde$): they arise
out of unequals, once these are equalised (™x ¡níswn (£sasvéntwn gàr ™génonto)).
To begin with, Aristotle cannot rightly make attribution to
anyone of a theory on the generation of inaddible monads. As he
says, no one actually spoke that way (1081a36). Aristotle, perhaps
himself in reaction against the eristic movement, constructs these
arguments to save his opponents from the obvious fallacy of ideal
numbers composed of normal, identical, addible monads; yet the
alternative, unstated by them, but which he says follows reasonably from their own premises, turns out to be impossible as well,
if truth be told (1081b1). There is therefore no reason to suppose
that Plato thought or said that the generation of inaddible monads, or any monads, was connected with his notion of the unequal.
On the contrary; Plato seems to have anticipated Aristotle’s notion
of the unit as a measure, both in the intuitions of the enumerative
method and in the specifically mathematical context. At 57d-e, the
distinction is made in the Philebus between the units of the arithmetic of the many, which change as different things are counted,
and those of the arithmetic of the philosophisers, which are always
identical. It would of course have been an easy (but pointless) solution to the problem of the irrational to say that incommensurables
are simply measured by different unit lengths than commensurables.
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The enumeration of Theaetetus and Plato, on the other hand, is
predicated on the assumption of identical units. While some lengths
still remain incommensurable on these terms, all the formerly irrational square roots become expressible through an indeterminate
dyad, and the achievement of this articulation would be lost without the assumption.
What can be attributed to Plato, however, is that his notion of
the unequal involved a process of equalizing it. In neither place in
M where Aristotle mentions this idea (as above, and at 1083b24)
can he make anything of it, nor does it seem to have any intuitive
connection to the Academic number-generation theories he covers
there. The only conclusion, I suggest, is that Aristotle refers to this
conception of the unequal merely because he knows it to have been
true of Plato’s thought. The “Platonists” speak of the unequal as a
generative principle, Aristotle might have reasoned, and who knows
what they mean, as to how it generates; Plato himself also spoke of
the unequal, and the only action he attributed to it was “being
equalized”; perhaps this was somehow the “generating action,” as
obscure as that seems; one ought therefore to mention what the old
man said, in fairness to them. In N, Aristotle for the first time mentions a number-generation theory which did, perhaps, try to interpret the process; it first declares that there is no generation of odd
numbers at all, and that the even numbers are generated out of the
great and small when these are equalised. Aristotle’s criticism of the
logic of this account verges on the sarcastic: faneròn Øti o∞ toû
vewrêsai ‰neken poioûsi t±n génesin tôn ¡rivmôn.
(“Clearly, it is not on account of philosophical theorizing that they
produce their generation of the numbers.” 1091a29) Neither
Aristotle, for whom the notion seemed fatuously self-contradictory,
nor these latter theorists, for whom it was received dogma, could
have known the original mathematical context, for neither could
interpret or properly apply the notion that the unequal as an elemental principle involved a process of being equalized. We can now
restore the context, in the process of “equalizing” an unequal,
oblong number with an indeterminate dyad of more and more
DAVID
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equal rational factors. (It is particularly striking that these latter
Academics seemed to know that the notion “unequal-when-it-isequalized” served in such a way as to divide all numbers, but they
tried, with dismal consequence, to apply it to the familiar, venerable distinction between odd and even; they must have been unaware
of the division of numbers by square and oblong, which supplanted
the earlier distinction in the course of Theaetetus’ study of irrational roots, and where alone the notion of the “equalized unequal”
has any use or coherence.)
“Those who say the unequal is some one thing, making the
indeterminate dyad from great and small, say things that are far
indeed from being likely or possible,” in Aristotle’s view (M.1,
1088a15). He complains that to adopt such ideas is really to adopt
his lowly Category of the “relative” as a substantial, unitary first
principle. Something is great or small only in relation to something
else. Unlike the superior Categories of quality and quantity, which
have more substance because they involve absolute change, whether
by alteration or increase, there is no such change proper to the
Category of the relative. While a compared term may remain substantially the same, it becomes greater or less merely by quantitative
change in the other term. Aristotle is therefore at a loss as to why
such metaphysical honour should be paid to concepts that are
inherently relative.
Plato could have replied: “Consider the nature of measurement
toward the generation of the mean.” In this process, the relative
terms do not depend simply on each other, but both are related to
an unchanging third thing, a single geometric mean. Furthermore,
the pairs of relative terms are uniquely related to their proper mean,
the root of a particular oblong number. And because the greater and
lesser lengths approach closer than any given difference to the
unchanging length of the root, their status in relation to this length,
qua members of an infinite succession of approximating pairs, poses
a heady puzzle for any common-sense idea of their ontological difference from, or identity with, this single length. There is therefore
every reason to see the indeterminate dyad of great and small, a self-
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correcting binary approximation of a single geometric mean, as a
unitary and substantial thing in its proper mathematical context.
But if the context was lost, and one had access only to the words in
its name, then Aristotle’s objections might seem judicious.
That Aristotle knew about the geometry of means is clear
enough, but he must not have been familiar with the interpolation
of means in the peculiar configuration of the indeterminate dyad,
where means become extremes, which in turn beget means, which
then in turn become extremes, while each pair of harmonic and
arithmetic means serves as the extremes to the geometric mean in
the middle. The notion of relativity embodied in this configuration,
involving a process of equalising, and motion towards a fixed
object, is more subtle and peculiar than that involved in a simple
comparison, or even a static analysis expressed in terms of a mean
and extremes. I claim it is this peculiar conception of the relative
that Plato raised to the level of a principle, to stand in tandem with
the absolute measure connoted by the unit.
While the Academic metaphysicians may appear to have used
these very same principles, right down to the letter of their formulation, it is clear that neither they nor Aristotle grasped their proper function. They have nothing to do with accounting for multiplicity in the universe, or with the generation of numbers. They
have everything to do with the measurement of numbers. After
Theaetetus, numbers are figured as square or rectangular; they can
be compared not only in quantity, but in size, by the length of their
square roots, just as after Euclid’s II.14, any rectilinear figures can
be compared by the sides of their equivalent squares. While all
numbers have either absolutely or relatively measurable rootlengths, not all lengths have countable squares. This is one of the
odd new ways that arithmetic and geometry, number and magnitude, become interlinked after Theaetetus’ happy reformulation.
It is therefore in this context, the context of measurement, that
Plato is likely to have distinguished the absolute from the relative,
being-in-itself from relative being. Aristotle alludes to just such a
distinction, in a passage which once again exemplifies his peculiar
DAVID
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mire: he wants to review the Academic theories on the generation
of multiplicity based on certain contrary principles, including principles first conceived by Plato, but conceived in a context where in
some cases they weren’t even contraries, and where they had had
nothing to do with generating either multiplicity or numbers; he
knows the language of Plato’s own articulation of these principles,
but doesn’t have the mathematics to interpret the words. In this
case, he may even foist his own innovations in usage back on to
Plato’s original phrases, just to make sense of them.
At 1089b16, Aristotle once again invokes “he who says these
things,” claiming this time that this person had also proved for himself (prosapef≠nato) that that which was potentially a “this” and
substance (tò dunámei tóde kaì o∞sía) was not “existent in
itself ” (πn kav afltó); it was the “relative” (tò pró$ ti). What
the expression “potentially a ’this’ and substance” may have meant
for Plato is a difficult thing to determine. In particular, Aristotle
seems to take dunámei, with obvious anachronism, in his own characteristic sense of “potentially”; he had just now used the word this
way when introducing part of his own familiar solution to ontological analysis, that we must hypothesize in each case what a thing is
potentially (¡nágkh mèn oun...flpoveînai tò dunámei πn
flkást¨, 1089b15-16). Perhaps Aristotle is here weaving his own
terminology into the Platonic materials? But his next comment is a
scholium, on Plato’s appropriation of the term “relative,” that it is
just as if he had said “quality” (¸sper e£ eªpe tò poión); and
there was never a scholium without a text.
So what could the Greek text “tò dunámei tóde kaì
o∞sía” have meant to Plato? Recall Knorr’s observation that
dúnami$ and dunámei mean “square” and “in square” throughout
Greek mathematical literature. (The only exception is the very passage in the Theaetetus [148a] where the eponymous hero applies
the term dúnami$, for the first time, to a square root.) Thus in
Plato’s context, the same words may well have signified “that which
has particularity and existence in square”—i.e., that which is countable (because it is commensurable) only in square (dunámei), like
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the expressible as against the rational lines. It is these very magnitudes which one could expect to find distinguished as relative in
their being, insofar as their being depends on their measure; the
rational lengths, on the other hand, have the self-subsistent being of
definite quantity, in length and in square, while the irrational lines,
which cannot be made commensurable in either length or square,
are captive to the realm of flux and non-being. If Plato equated
“that which has being” with “that which can be counted”—and his
enumerative method suggests a move in this direction—then it is
entirely and specifically appropriate that that which has being in
square be allowed only a relative existence. It has no autonomous
number, but only a relative count. Even the phrase pró$ ti may
have had a specific connotation for Plato, which is lost in the
anachronistic aura of the Categories; for such beings are measured
by a process that is inherently pró$ ti, “towards something,” measurement toward the generation of the mean. Plato’s distinction
would have been between that which exists or is measured on its
own terms (tò πn kav afltó)—the equal, the square, and rational lengths—and that which exists or is measured toward something
else (tò πn pró$ ti), the unequal being equalized, the rectangle
approaching the square, and the indeterminate dyad approximating
the mean.
It seems clear that any such significance in these phrases could
never have been allowed to emerge through the schemata of
Aristotle’s redaction. He explains (1089b4 ff.) that in response to
the diversion caused by Parmenides, the philosophers posited the
relative and the unequal as the types of opposed principle which,
when mated with being and the unit, generated a manifold reality.
He points out, however, that neither of these posited principles is in
fact the contrary (™nantíon) or the negation (¡pófasi$) of being
and unity; each is rather another single nature among the things that
exist (mía fusi$ tôn øntwn). This is also the point of his critical scholium on Plato’s use of the phrase pró$ ti: the Category
“relative” is no more a legitimate candidate than the Category
“quality” for that contrary and negation of being and the unit which
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the Academics were supposed to be seeking; each is simply “some
one” of the beings (‰n ti tôn øntwn, 1089b20). He goes on to
complain that if Plato had meant to explain how things in general
are many, he shouldn’t have confined his investigation to things that
lie in the same Category (whether this be “substance” or “quality”
or “quantity,” let alone the insubstantial “relative”).
The sense of this reading ranges from the misguided to the wilfully obtuse. In the first instance, we cannot fault Plato for failing
either to prophesy or to apply the revolutionary insights into
ontology expressed in Aristotle’s theory of the Categories. Nor can
we fault him for not being interested any longer, as indeed he wasn’t, in the problem of how things are many. Still less can we fault
him for giving up the reasoning by opposites. He would of course
have agreed that his conception of the relative, in the configuration
of the indeterminate dyad, is in no sense the opposite of the unit
and its measure, but simply a different way of measuring, based
also on the unit, that applies to certain types of being (i.e., certain
two-dimensional numbers and one-dimensional magnitudes—
oblongs and their roots). But the full picture of Aristotle’s plight as
a redactor emerges when one throws in the fact that Plato’s complete formulation did in fact include a genuine opposition as well,
between the unit and the greater-and-less qua greater and less. One
then has a recipe for the peculiar quandary of Metaphysics M and
N towards Platonic thought, based in part on unwitting conflations, but in part also on flagrant, self-serving anachronisms, and
characterised by a haplessness in the face of Plato’s own expressions, when read in light of their borrowed use in the irrelevant
theories of the Academy.
A question remains: where did Aristotle get those “texts” of
Plato, which he seems to treat as quoted material? Although the distinction between absolute and relative being may be consistent with
the Philebus and with other ontological discussions in the later
Plato, the specific phrases which Aristotle comments on, such as tò
dunámei tóde kaì o∞sía, do not seem to occur in the dialogues.
Where, then, did Plato draw this mathematical distinction, and to
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52
what did he apply it? Was it perhaps in a Lecture on The Good—a
lecture which seemed to promise moral philosophy, but delivered
mathematics—a lecture which nobody understood?
*
*
*
*
*
*
The mathematical development of ancient measurement science will prove much easier to trace than its philosophical obfuscation at the hands of Academics and Peripatetics. As forbidding
as the structure of Euclid’s Elements X seems to be, I believe its
logic is profoundly simple, following directly in the spirit of
Plato’s enumerative method, and upon Theaetetus’ geometrical
interpretation of number.
After Theaetetus’ first efforts had rendered all the square roots
countable, he next sought to extend his classificatory net even further into the uncharted regions of the irrational. He could use his
already successful methods as a paradigm: since exploring numbers
in terms of the means between them had yielded the class of
expressible lines, he was led to explore the possibility of means
between the expressible lengths themselves, and the possibility of
irrational means. While in general such means could not be “counted off,” since the expressible lengths, treated as extremes, had not
the fixed values necessary for a computation of means, the mean
lengths could still be constructed and named with respect to rational lengths; just as at the time of the Meno, the root length of the
double square could not as yet be counted, but it could be constructed within the unit square and was named “diameter” (or the
“through-measure”) by the professors (Meno 85b). Orders of irrationals could thus be defined in terms of means, though they could
not be made commensurable.
Just such an assignment of orders is credited to Theaetetus by
Pappus, in his commentary on Elements X, on the authority of
Eudemus’ history of mathematics (now lost):
...it was...Theaetetus...who divided the more generally
known irrational lines according to the different means,
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assigning the medial line to geometry, the binomial to
arithmetic, and the apotome to harmony, as is stated by
Eudemus, the Peripatetic.32
The passage does not suggest that Theaetetus invented the three
lines and their names, but only that he first saw the essential parallelism between the structure of their relations and those of the
familiar means. The medial simply is the geometric mean between
two expressible lengths. That is why it is called méso$, the mean
proportional; the name “medial” serves only to distinguish it in
English. The binomial is a sum of two expressible lengths, and so
can be associated with the arithmetic mean, which is half the sum
of two rational lengths; but the apotome is merely a difference of
expressible lengths, and the connection with the harmonic mean is
less obvious. This also comes clear, however, as one recalls the fundamental feature of pairs of arithmetic and harmonic means which
makes possible the measurement by an indeterminate dyad: if one
applies a rectangle contained by rational extremes to the length of
their arithmetic mean, the height of the new rectangle turns out to
be the length of their harmonic mean. Euclid’s X.112-14 illustrate
a significantly parallel property of binomials and apotomes: if one
were to apply the same rational rectangle to a length that was
known to be a binomial, the height would turn out to be an apotome; further, and curiously enough, the expressible terms of such
a binomial and an apotome would be commensurable with each
other, and in the same ratio. If Theaetetus was responsible for these
propositions, he might well have been led to view the binomial and
apotome as “irrational means” between rational extremes, or as
irrational factors of an oblong number, counterparts to the rational
arithmetic and harmonic means.
It is clear, however, that Euclid’s presentation is not designed as
a theory of means. The bulk of his 115 propositions in Book X are
concerned with enumerating and constructing twelve different
kinds of binomial and apotome, making with the medial thirteen
types of irrational line; the full list is given by Euclid after Prop.
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111, before the proofs that establish the analogy between the binomials and apotomes, and the arithmetic and harmonic means. The
rationale for this enumeration becomes more apparent if one considers David Fowler’s handy grouping of the propositions:
X1-18: general properties of expressible lines and rectangles,
X19-26: medial lines and rectangles,
X27-35: constructions underlying binomials and apotomes,
X36-41, 42-7, 48-53, 54-9, 60-5, 66-70, & 71-2:
blocks of propositions dealing with each of the six types
of additive irrational lines. They are described in X3641 and also, in a different geometrical configuration, in
the Second Definitions following X47,
X73-8, 79-84, 85-90, 91-6, 97-102, 103-7, & 108-10:
blocks of propositions, parallel to the previous, dealing
with each of the six types of subtractive irrational lines.
They are described in X73-8 and also, in a different
geometrical configuration, in the Third Definitions following X84,
X111-14: the relations between binomials and
apotomes,
X115: medials of medials...
As Fowler himself observes, the propositions seem to represent an
exploration of the “simplest operations of adding, subtracting, and
squaring pairs of expressibles.” Before Theaetetus classified them in
relation to the different rational means, the binomial and apotome
may have first been distinguished and defined as part of an investigation of the “arithmetic” of expressible lengths. An investigator
might have said, if we are to understand the expressibles the way we
understand numbers—and indeed, numbers are the very paradigms
of our understanding—then we must comprehend their arithmetic;
what might the manipulations of arithmetic look like when applied
DAVID
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to expressible lines?
Whereas the prospect of such an investigation might have
daunted the most optimistic of researchers, with its seeming openendedness and unlimited number of possible cases, Euclid was
able, by manipulating squares and rectangles, to organize the
infinite additions and subtractions of expressible lengths into six
types each. Thus Euclid accomplished the first ever rigorous ordering of radically incommensurable lengths, as the sums and differences of expressible ones. One cannot measure these sums and differences as such, and so one cannot “count off ” the irrational lines
that are produced; but one can number their types, and enumerate
their orders.
While the fundamental early propositions of Book X are generally credited to Theaetetus, and the propositions about mean proportionals (“medials”) seem to suit his historical and mathematical
character, the enumeration of the binomials and apotomes must
belong to Euclid. Pappus says that Euclid, following Theaetetus,
“determined...many orders of the irrationals; and brought to light,
finally, whatever of finitude (or definiteness) is to be found in
them.” This should naturally refer to his ordering of possible binomials and apotomes, and the enumeration of six corresponding
types. Though they do not depend on the proofs involved in
Euclid’s enumeration, Theaetetus’ propositions, about the relations
between binomials and apotomes, are then placed by Euclid at the
end of Book X, so that they can be expressed in terms of that enumeration, and take on a new authority: each pair belongs to one of
six sets of ordered pairs of binomials and apotomes whose terms
turn out to be commensurable and in the same ratio; each pair consists of corresponding members of one of a finite number of possible combinations of additive and subtractive expressible lengths.
It is possible, then, to trace the genesis of Book X in this way:
Theaetetus first extended the insights of measurement toward the
generation of the mean by using the three means involved in that
science as heuristic paradigms with which to interpret irrational
magnitudes. Just as an expressible length is a geometric mean
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between rational extremes, a medial length is a mean proportional
between expressible extremes; and just as arithmetic and harmonic
means are pairs of commensurable rational factors of the rectangle
contained by the extremes of their interval, binomials and apotomes
are pairs of irrational factors of the same rectangle. In his investigation of binomials and apotomes, Euclid discovered their classification, and thereby produced an ordering of irrationals in terms of
possible types of sum and difference—an arithmetic of expressible
lines. This in turn advanced the classificatory scope of Theaetetus’
propositions on the relations between binomials and apotomes,
when they were placed after Euclid’s work, at the end of Book X.
While Theaetetus could likely have proved that a rational area
applied to a binomial produces an apotome as breadth, and that the
terms of these irrational factors are commensurable and in the same
ratio, Euclid could now add, as he does in the enunciations of
Propositions 112 and 113, that such a binomial and an apotome
belong to the same order.
David Fowler approaches the book from a very different angle,
as part of his reconstruction of the ancient mathematics of ¡nvufaíresi$. He proposes an anthyphairetic theory of ratio, where
ratios between quantities are described by counting the number of
mutual subtractions which can occur between them: one counts the
number of times the lesser subtracts from the greater, then the number of times the remainder can be taken away from the lesser, then
the remainder of that transaction from the former remainder, and
so on; the list of numbers thus produced gives a unique description
of the particular ratio. He finds evidence for the historical existence
of this approach in several quarters, including a direct allusion in
Aristotle’s Topics to a definition of same ratio as same antanairesis
; and he sees the peculiar implications of this ratio theory as providing the most economical of many proposed rationales for the
total sequence and layout of Euclid’s Book II. The most surprising
fact he uncovers is a remarkable periodicity that arises in the anthyphairetic description of ratios of the form √m:√n—that is, ratios of
expressible lines.
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The achievement of Fowler’s work is to have rediscovered, and
in some measure to have resurrected in our day, the other branch of
measurement science, measurement prò$ ållhla. The periodic
repetition of the terms in the otherwise infinite mutual subtraction
of expressible quantities would have been the great discovery of this
science; as Fowler observes:
Those ratios that can be now completely understood
and described in finite terms by the arithmoi include the
ratios of the sides of commensurable squares, that is the
ratios of expressible lines √m:√n...
Note how fitly this parallels the development I have
described in the science of measurement toward the generation
of the mean: those lengths which can now be uniquely measured
in terms of the ¡rivmoí include these same expressible lines,
the sides of commensurable squares.
As far as the rationale for Euclid’s Book X is concerned,
however, Fowler’s reconstruction of the mathematics of anthyphairesis shows only why the relations between expressible lines
would have seemed a thing worth investigating. We gain no
insight into the specific form of the book as we have it, into its
method and structure in the classification of the irrationals;
these are better explained as an integral outgrowth of the new
science proposed in Plato’s Politicus, the science of measurement
toward the generation of the mean. This is not just because
Theaetetus is said to have classified the irrationals in terms of the
different means. Consider that the entire investigative strategy
of Book X, including the work I have ascribed to Euclid, is to
manipulate squares and rectangles, a manipulation in two
dimensions, in such a way as to distinguish and to enumerate the
forms of the associated lines. This approach was born with the
science of measurement toward the mean, on one fateful day. As
he lies dying off-stage, the story is told of how the young
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Theaetetus, Theodorus’ student, on the day of Socrates’ appearance in court, divided all numbers between the square and the
oblong, and distinguished two kinds of line as the sides of
squares equal to each kind of number. The “square side” of an
oblong number is the geometric mean between the sides of the
oblong. The names Theaetetus chose for these two lengths,
mêko$ and dúnami$, did not survive, for the implications of a
classification by sides of squares made the distinction itself obsolete: both kinds of length would now be called @htá, expressible. But the technique applied in his classification was to direct
the exploration of lines to its crowning achievement, in the enumerations of Euclid’s Book X.
We ought, however late, to acknowledge the dramatist who
saw the significance of such a day for history, saw it in a way that
must combine the personal and the universal, the historical and
the mathematical. Innovations in mathematics must have moved
that man in a way that made even innovation in religion seem a
distant charge, a memory of youthful import. We must come to
recognise the changes in this chronicler of the human argument,
as he took his bearings anew, and found new patterns, enumerative structures, emerging in a discourse that strains to keep
pace—paradigms of order no longer laid up in heaven, yet resonant, perhaps, with a piece of divinity. His myth of the globe’s
reversal (Politicus 268d-274e) encompasses a deteriorating
world, but also a return, through the numbering of its classes
and kinds, to the elegance of god’s tenure. Let him stand
absolved at last of the mystifications of his followers: Plato’s
own measures, his own mysteries, must finally furnish our count.
DAVID
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2. Wilbur R. Knorr and Miles F. Burnyeat, “Methodology, Philology, and
Philosophy,” Isis, 1979, 70:565-70
3. Miles Burnyeat, “The Philosophical Sense of Theaetetus’ Mathematics,”
Isis, 1978, 69:489-513, on pg. 513, pg. 513
4. Knorr, Evolution, pg. 192
5. Ibid., pg. 192
6. Ibid., pg. 69 ff.
7. Ibid., pg. 96 (In full: “(a) The proofs are demonstrably valid. (b) The
treatment by special cases and the stopping at 17 are necessitated by the
methods of proof employed. (c) The proofs will be understood to apply to
an infinite number of cases. (d) No use may be made of the dichotomy of
square and oblong numbers in Theodorus’ studies, either in the demonstrations or in the choice of cases to be treated. (e) Theodorus’ proofs utilize the
special relations of the lines in the construction of the dynameis. The geometrical methods of construction are of the type characteristic of metrical
geometry as developed in Elements II and are closely associated with a certain early style of arithmetic theory. (f) But the arithmetic methods by which
Theaetetus could prove the two general theorems, on the incommensurability of lines associated with non-square and non-cubic integers, were not
available to Theodorus.”
8. Malcolm Brown, “Theaetetus: Knowledge as Continued Learning,”
Journal of the History of Philosophy, 1969, 7:359-79, on pgs. 3678
9. Knorr, Evolution, pg. 158
10. This proof is given by Knorr, Evolution, pg. 184
11. Ibid., pg. 159
12. see Euclid’s Elements X Def. 3
NOTES:
1. Wilbur R. Knorr, Evolution of the Euclidean Elements
(Dordrecht and Boston: D. Reidel Pub. Co., 1975), pgs. 65-9
13. see Plato’s Politicus, 278b-e
14. see Euclid, The Elements, 3 vols., Vol. 3, ed. Sir Thomas Heath
(Annapolis: St. John’s College Press, 1947), pg. 3
15. see Euclid II.14 and VI.13
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16. Brown, “Theaetetus,” pg. 371 ff.
17. Proclus, In Platonis Timaeum Commentaria, 3 vols., Vol. 2, ed.
Ernst Diehl (Leipzig: Teubner, 1903-6), pgs. 173-4
18. Brown, “Theaetetus,” pg. 371
19. see David H. Fowler, The Mathematics of Plato’s Academy
(Oxford: Clarendon Press, 1987), pg. 14 ff.
20. see Plato’s Timaeus 36a for this usage
21. The reading of B and T; editors usually read to )to
22. Brown, “Theaetetus,” pgs. 376-7
23. Ibid., pg. 377
24. see Theaetetus, 185c
25. Brown, “Theaetetus,” pg. 374
26. quoted in Brown, “Theaetetus,” pg. 373, note 38
27. Euclid, X.1
28. Brown, “Theaetetus,” pg. 379
29. Julia Annas, Aristotle’s Metaphysics Books M and N, Oxford:
Oxford University Press, 1976, pg. 195
30. Ibid.
31. Knorr, Evolution, pgs. 65-9
32. tr. W.Thomson and G.Junge, in Fowler, Mathematics, pg. 301
33. Fowler, Mathematics, pgs. 169-70
34. Ibid., pg. 192
35. tr. Thomson and Junge, in Fowler, Mathematics, pg. 301
36. Fowler, Mathematics, pg. 17 ff., and see Aristotle, Topics 158b
37. Ibid., pg. 192
38. see Ibid., pgs. 190-1
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63
Moral Reform in Measure for
Measure
Laurence Berns
(St. John’s College, Annapolis)
To what extent are the principles of classical political philosophy and the American polity reconcilable? The Declaration of
Independence did not mean, Lincoln tells us, that all men are equal
in all respects. The Declaration, however, presupposes that the difference between man and man is never as great as the difference
between man and beast, on the one hand, and man and God, on the
other. This “equality” by superiority to beasts and inferiority to the
divine sets limits both to human servitude and to human sovereignty.1 These principles issue in the rule of prudence that just government derives its authority from the consent of the governed. This
equality, as Locke put it, “in respect of Jurisdiction or Dominion
one over another” is not incompatible with the classical principle of
fundamental inequalities in capacities to govern. As a matter of fact
the institution of free elections (the Declaration’s “Right to
Representation”) introducing a principle of merit into the system is
predicated on the existence of such inequalities of ability, and the
capacities of electors roughly to discern them. (This does not, of
course, mean that the judgment of the electors is always correct, but
that it is sufficiently deliberate and well-informed to avoid disasters
that would unhinge the very frame of government.)
The classical position on democracy has been put, I believe,
with great clarity by Thomas Aquinas quoting St. Augustine:
If the people have a sense of moderation and responsibility and are most careful guardians of the common
weal, it is their right to enact a law allowing such a people to choose their own magistrates for the government
Delivered at the Convention of the American Political Science Association,
September 1993, The Washington Hilton Hotel, Washington, D.C.
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of the commonwealth. But if, as time goes on, the same
people become so corrupt as to sell their votes and
entrust the government to scoundrels and criminals,
then the right of appointing their public officials is
rightly forfeit to such a people, and the choice devolves
to a few good men. [S.T., I-II, Q. 97, A. 1.]
I have no problem with this statement in principle, despite the
questionable practicality of its remedy for corruption. As Benjamin
Franklin put it, “If any form of government is capable of making a
nation happy, ours I think bids fair now for producing that effect.
But, after all, much depends on the people to be governed. We have
been guarding against an evil that old States are most liable to,
excess of power in the rulers; but our present danger seems to be
defect of obedience in the subjects. There is hope, however, from
the enlightened state of this age and country, we may guard effectually against that evil as well as the rest.” [Lett. to Ch. Carroll,
5/29/1789] What most threatens the required state of enlightenment today, it seems to me is not any paucity of economic resources
devoted to education, but rather the reigning generally accepted
opinions about what constitutes enlightenment. The AugustineThomas statement suggests, at the very least, that there is a natural
connection between the will to preserve free institutions and the
sense that those living in accordance with them are worthy of them.
How can a corrupt people be reformed? This, of course, is the
problem set for its protagonists by Shakespeare’s Measure for
Measure. Some distinctions between Duke Vincentio’s situation and
ours must be made. He has a single city and its environs to reform,
we have a huge and highly diversified nation. Our laws derive their
constitutional authority from the very people needing reform, his
do not. His polity is monarchical, ours is not. Our polity contains a
diversity of religious sects, his does not. Religious authority and
moral authority, if not united, form a well-functioning team in his
regime, in ours ... they do and they don’t. Obviously we are not
likely to find immediately applicable recipes from a study of
BERNS
65
Measure for Measure. We are obliged to put things in constitutional terms: “the abuse of the first Amendment”; the tendency of
lawyers and judges to ape intellectual fashions, sanctioning licentiousness with shallow-pate notions like freedom of expression, bargain-basement moral autonomy.2 We can, as teachers, try to change
the intellectual fashions. The only way I know how to do that is to
try to rise beyond the realm of intellectual fashion altogether, by
trying to understand the Duke’s problem as much as possible, as my
better, William Shakespeare, understood it.
Vienna, the seat of the Holy Roman Empire, is ruled by a
Duke, who “above all other strifes contended especially to know
himself,... a gentleman of all temperance.” Like those two political defectives, Prospero and Socrates, he has no taste whatsoever
for the theatrical pomposity endemic to political life. His apolitical temperament has caused him wrongly (“t’was my fault”) to
allow Vienna’s strict and biting laws to become toothless and contemptible; licentiousness thrives, and “Liberty plucks Justice by
the nose.”
His keen sense of justice prevents him from punishing in his
own name evil deeds bred by his own permissiveness. But purification there must be. He appoints a Lord Angelo (soon to prove a
Fallen Angelo), a man of “stricture and firm abstinence”, who
“scarce confesses that his blood flows” to stand in for himself, that
is (unlike American executives) to “enforce or qualify the laws.” But
first something should be said about why someone like puritanical
Angelo was needed.
The Vienna presented at first in the play seems to consist primarily of nunneries, monasteries and whorehouses, with almost
nothing in between: the only family man presented is the absurd
comic figure Elbow; austere celibacy, on the one hand, and saucy
profligacy, on the other, again almost nothing in between. As sexuality is debased, celibacy, for some, gains in attractiveness.
Something seems to be radically wrong with the way most Viennese
think, feel and behave in regard to their sexuality. Immediately fol-
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lowing Angelo’s appointment the Duke pretends that affairs of state
require his hasty removal to foreign parts; Angelo is on his own.
Political scientists (Bloom and Jaffa) quite properly refer to
Machiavelli’s The Prince, chapter VII, as the locus classicus for the
Duke’s mode of procedure with Angelo.3 Cesare Borgia on taking
over Romagna found that because it had been very badly governed
it was full of robberies, quarrels and insolence. To reduce it to peace
and obedience he appointed a very cruel man, Remirro de Orco, as
his deputy with full powers. Remirro soon reduced it to peace and
unity. The reform being accomplished, in order to deflect the hatred
it had generated from himself Cesare had the cruel Remirro placed
one morning in the piazza at Cesena in two pieces, a piece of wood
and a bloody knife beside him. The ferocity of the spectacle left the
people both satisfied and stupified. Bacon speaks of this way of proceeding both in his Wisdom of the Ancients [III], and his Essays
[XIII], but both seem to have been published after this play was first
presented. One is tempted to go along with our scientific fashions
and play at being “more hard-nosed than Thou,” but the differences
between Shakespeare and Machiavelli at least deserve listing. The
Duke does not kill Angelo, though he had full warrant to do so;
unlike Cesare with Remirro, the Duke is not interested merely in
using Angelo, but also as with everyone else, including himself,
making him better, reforming him; above all, since he is not omniscient, he is interested in understanding Angelo: “Hence shall we see,
/If power change purpose, what our seemers be.” It is not simply
because he courts popularity, that he doesn’t institute the reform
himself, it is rather because he is not the right man for the job, and
it would not be, or at least not seem, just for him to do so. There is
another work of Machiavelli’s that bears close comparison with
Measure for Measure, that is Mandragola4; the Duke seems to combine characteristics of both Ligurio and Frate Timoteo, but here
again the differences should prove instructive.
The Duke does not leave Vienna, he goes underground in the
guise of a “holy friar” both to observe and invisibly to correct the
course of his reform. Angelo evidently goes to work immediately:
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the houses of prostitution are put down, and a young gentleman
named Claudio is sentenced to death for fornication; for the
woman he is engaged to marry (the marriage delayed by dowry
problems), Juliet, is big with child. Angelo rejects the urgings of his
second in command and his Provost that here the punishment is
way out of proportion to the crime. Claudio has a high-spirited sister, Isabella, who has entered the austere order of St. Clare -“When
you have vow’d, you must not speak with men /But in the presence
of the prioress; /Then, if you speak, you must not show your face;
/Or if you show your face, you must not speak”- as a novice. She
wishes for an even “more strict restraint.” We are, I suppose, to
imagine her quite beautiful; her moral beauty at least engages the
affections of the play’s two main protagonists. She is urged by the
dissolute gentleman Lucio to plead with Angelo for her brother’s
life. Despite her choosing to renounce family life, her’s is the only
powerful display of family feeling in the play. While hearing her
plea the transforming event of the play takes place, Angelo finds
himself possessed by an overwhelming passion, which, both to himself and to her, he calls love for Isabella. He, on second interview,
proposes that she yield her body to him for one night in exchange
for her brother’s life.
The critique of Angelo would seem to be a critique of
Puritanism in general. Licentious Lucio thinks Angelo “a man
whose blood /Is very snow-broth; one who never feels /The wanton
stings and motions of the sense...” This is surely wrong. The Duke
had made a similar, but more penetrating, observation: “Lord
Angelo is precise; /Stands at a guard with Envy; scarce confesses
/That his blood flows...” If he must guard against envy, he feels the
desires whose indulgences he must not be envious of. With old
Escalus, before he has fallen, Angelo admits that he too has had the
desires that lead to the actions he is punishing with death, acting
upon them makes the difference. He is too good, at least too strict
and too proud to consort with the dissolute; he proves to be not
good enough to be celibate. He wants to be associated with the
highly virtuous, is attracted by Isabella’s purity; he wants to pre-
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serve the image of his gravity; and he wants the joys of what he calls
love: your brother shall not die “Isabel, if you give me love.”
He seems to be altogether confused about the difference
between “yielding up thy body” and “give me love.”5 It was
Isabella’s moving persuasiveness that led him to give more attention
to the erotic side of his soul than he could handle: “Go to your
bosom, /Knock there, and ask your heart what it doth know /That’s
like my brother’s fault. If it confess /A natural guiltiness, such as
his....” He replies to himself: “She speaks, and ’tis such sense /That
my sense breeds with it.” [2.2.137 ff.] He did warn the Duke: “Let
there be some more test made of my metal, /Before so noble and so
great a figure /Be stamp’d upon it.” The Duke knows that: “He doth
with holy abstinence subdue /That in himself which he spurs on his
power /To qualify in others.” [4.2.79] The immoderate Puritan
allows the bitterness from his own frustrated desires with perhaps a
touch of envy to spur him on to punish those who will not abstain.
The fear of falling into temptation increases the severity. The intensity of purifying zeal seems to be directly proportional to the
difficulty one has in keeping one’s own illicit desires under control.
The judgment is warped in the direction of severity by what one
feels is required to frighten oneself into abstinence. Isabella’s loveliness and what he sees when he follows her advice and looks into
his own soul push him over the edge.
And now I give my sensual race the rein:
Fit thy consent to my sharp appetite;
Lay by all nicety and prolixious blushes
That banish what they sue for. [2.4.159 ff.]
On reflection it might not seem so strange that modesty should
provoke desire.
Any competent political scientist can figure out why Angelo
never intends to fulfill his side of the bargain. Isabella can find no
“charity in sin.” “More than our brother is our chastity.” The Duke
disguised as Friar Lodowick prepares Claudio for death with a ser-
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mon crammed with Stoic commonplaces on the worthlessness of
life. From here on the Duke uses the holy privileges associated with
his disguise to inform himself of everyone else’s secrets. He overhears Isabella’s account to Claudio of Angelo’s proposal. In another remarkable scene Claudio begins by sharing Isabella’s righteous,
honorable and Christian indignation at the impossibility of Angelo’s
plan. But he has been brought to face the fear of death in a very feeling way.
Death is a fearful thing.
...to die, and go we know not where;
To lie in cold obstruction, and to rot;
This sensible warm motion to become
A kneaded clod; and the delighted spirit
To bath in fiery floods, or to reside
In thrilling region of thick-ribbed ice;
To be imprison’d in the viewless winds
And blown with restless violence round about
The pendent world: or to be worse than worst
Of those that lawless and incertain thought
Imagine howling, -’tis too horrible.
The weariest and most loathed worldly life
That age, ache, penury and imprisonment
Can lay on nature, is a paradise
To what we fear of death. [3.1.115 ff.]
Claudio’s speech is a beautiful illustration of that “very illusion
of the imagination” beautifully described by Adam Smith: the way
a man or woman’s sympathetic imagination attributes to the dead
what he or she would feel being alive, if he or she were housed in
the dead person’s body. And thus “the foresight of our own dissolution is so terrible to us, and ... the idea of those circumstances,
which undoubtedly can give us no pain when we are dead, makes
us miserable while we are alive.” The Duke certainly does not
explain anything like this to Claudio or to anyone else in this play,
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but I don’t think he would disagree with the way Smith closes this
chapter. “And from thence arises one of the most important principles in human nature, the dread of death, the great poison to the
happiness, but the great restraint upon the injustice of mankind,
which, while it afflicts and mortifies the individual, guards and protects the society.” [The Theory of Moral Sentiments, I.i.1.13] Bloom
quite properly refers to Lucretius [III. 417 ff.] in his discussion of
this passage, but Smith, it seems to me, is more balanced, even more
“classical”.
Claudio goes on to plead:
Sweet sister, let me live.
What sin you do to save a brother’s life,
Nature dispenses with the deed so far
That it becomes a virtue. [3.1.132 ff.]
This is not the first time Nature has been invoked to oppose
chastity law. The licentious but eloquent Lucio puts it in a way that
comes close to generally accepted opinion among our intellectuals.
Your brother and his lover have embrac’d;
As those that feed grow full, as blossoming time
That from the seedness the bare fallow brings
To teeming foison, even so her plenteous womb
Expresseth his full tilth and husbandry. [1.4.40 ff.]
The licentious have their say in this play. But Shakespeare has quite
naturally, but not altogether explicitly, built Nature’s answer to
promiscuity into their very speech: it is full of the imagery and fear
of venereal disease. The Duke seems to have come to the realization
that Nature in human society requires law for its fulfillment.6
Isabella is moved by Claudio’s speech, but in exactly the opposite direction. “O, you beast. . . faithless coward...dishonest wretch,”
she replies.
Wilt thou be made a man out of my vice?
Is’t not a kind of incest, to take life [i.e., to be born
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again]
From thine own sister’s shame?
...Take my defiance,
Die, perish! [3.1.135 ff.]
This is not the first time sexual imagery enters Isabella’s speech
in moments of great passion. Answering Angelo she is primarily
thinking of stripping herself for whipping:
Th’impression of keen whips I’d wear as rubies,
And strip myself to death as to a bed
That longing have been sick for, ere I’d yield
My body up to shame. [2.4.101 ff.]
The Duke’s first task is to avert the great impending injustice
brought on by his scheme, but he does it in a way that also seems to
be perfectly calculated to bring Isabella to face her sexuality, and
human sexuality in general, more temperately. His reform will turn
out to be a comprehensive reform; all the representative characters,
Pompey, Lucio, Claudio, Angelo and Isabella are in different ways
reformed. The Duke uses the religious authority he has assumed to
engage Isabella in a plot that will right all wrongs. Angelo, it turns
out, had been engaged to marry a lady, Mariana. When her brother carrying her dowry was wrecked at sea, Angelo “pretending in
her disoveries of dishonour” called off the marriage. This wronged
lady, the “forenamed maid” has unreasonably been driven by his
unkindnesses to a more violent and unruly love for Angelo. She still
regards him as her “husband.” Isabella is to agree to Angelo’s terms,
arrange for a short meeting in a very dark place; Mariana is to be
substituted for Isabella. If the encounter is acknowledged afterwards, it may compel him “to her recompense.” By this, the Duke
argues, “is your brother saved, your honour untainted, the poor
Mariana advantaged, and the corrupt deputy scaled.” The Duke as
friar will frame and make Mariana fit for the attempt. The fact that
this seems to pose no special difficulty suggests that Mariana may
indeed be as right as one can be to mate with Angelo. But it is too
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easy these days to berate Puritanism, Mariana may just see some
nobility in Angelo’s austerity, a nobility that manifests itself to us as
well even in his guilty self-condemnations. It can hardly escape
Isabella’s later reflection that what takes place between Angelo and
Mariana is in many respects parallel to what took place between
Claudio and Juliet. But this conjunction is sanctioned by a holy
man, who declares that “the doubleness of the benefit defends the
deceit from reproof.” Isabella is happy to go along. Even the pleasure of revenge on Angelo seems to be sanctioned by this holy man.
Isabella’s imagination is invited with no impiety to receive scenes of
her enemy coupled with his affianced lover, thinking he is violating
herself. If her soul is puritanical, it will have to become Puritanism
with a certain sense of humor.7
The Duke’s plan for deceiving Angelo succeeds, but Angelo
sends no reprieve for Claudio. On the contrary, he advances the
time for his beheading. He has no interest in preserving the life of
a man privy to his crime, and who, if he has the least grain of honor,
would be bound to think of little else than revenge. The Duke, again
using his assumed religious authority, attempts to get the Provost of
the prison to substitute the head of a convicted murderer,
Barnardine, for Claudio’s, to fool the wicked Angelo again. The
Duke had invoked “the vow of my order.” The “gentle Provost” is
the only one who refuses to bow to religious authority, “Pardon me,
good father, it is against my oath.” When the Duke, without fully
revealing himself, is forced to prove he is acting not only by religious authority but by the authority of the Duke himself, the
Provost goes along. He who refused to subordinate political authority to religious authority for his “care and secrecy” will be rewarded by the Duke with “worthier place.” But Barnardine has been
drinking and is not prepared for death today. He simply will not
consent to die today. This is an amazing prison. They all agree that
to take him in this condition is damnable. Luckily, the captive
pirate, Ragozine, who resembles Claudio, has died that morning:
the perfect head to substitute for Claudio’s. Besides provision of
some fine comedy, the prison scenes are essential for understanding
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the Duke’s basic strategy of reform. Pompey the procurer now put
out of work becomes the prison’s executioner’s assistant. The servant of false love, venereal disease and the unlawful begetting of life
quite easily becomes the true servant of its lawful taking. Pompey’s
coarseness is re-formed to serve the rule of law. The taking and the
begetting of life have been connected before. Angelo declares:
Ha? Fie, these filthy vices! It were as good
To pardon him that hath from nature stolen
A man already made [a murderer], as to remit
Their saucy sweetness that do coin heaven’s image
In stamps that are forbid. ’Tis all as easy
Falsely to take away a life true made,
As to put mettle [metal] in restrained means
To make a false one. [2.4.42 ff.]
As Jaffa put it, “Fornication, as a kind of false coinage of citizens, becomes more than a private action.”8 The regulation of
coinage, society’s circulating medium, is usually a rather unquestioned prerogative of sovereignty. The penalties for counterfeiting
have never been light. To “coin heaven’s image” joins biblical sanctity of begetting to the need for sovereign political regulation of that
private behavior which is the source of life for society as a whole.9
(The coining image occurs at least three more times in the play, in
speeches by the Duke [1.1.35-36], Isabella [2.4.128-29] and Angelo
[1.1.48-50].)
Threats of death color the whole atmosphere of the play. Fear
of death in potential malefactors seems to be indispensable for the
restoration and maintenance of law-abidingness. But absolutely no
one ever gets killed in this prison. It is the genius of this Duke to be
able to employ the fear without ever having to follow through with
the act. The ploy would never work, if it became generally known.
The great final act and scene of the play pulls all strands together, the return of the Duke and resumption of his authority in a
grand public ceremony, where the Duke “like power divine” reveals
all hidden iniquities and resolves all difficulties with perfect justice.
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This justice, both legal and natural justice, is primarily justice in
marriage. For the chaste sexuality of marriage, the raising and nourishing of families under the law, is the solution for the sexual corruption of Vienna.10 The dissolute gentleman, Lucio, is forced to
marry the prostitute who is the mother of his child. Angelo, who
sought Isabella, who was too good for him, is ordered to marry and
love the less scrupulous Mariana. But the Duke knows that the institution of marriage, upon which the health of his polity depends,
will not be on a firm foundation unless it shines forth at the paradigmatic center of society. He too must marry, and marry well. The
high-minded Duke asks the high-minded Isabella to be his wife.
How that works out, we never learn. As part of the apocalypse the
Duke staged for his triumphal return, Isabella was made to believe
that her brother had indeed been executed. It may be that the Duke
wanted her to weigh the events leading to that result more carefully, or merely, as he said, “to keep her ignorant of her good,/To make
her heavenly comforts of despair/When it is least expected.” He
might be made to pay for those hours of despair. These reservations
aside, it seems to be a near perfect marriage. If it should be that the
Duke comes short of perfection by contemplative leniency and
Isabella by spirited severity, it would be by the blending of their
virtues and the mitigating of their defects in their shared lives or in
their offspring that Vienna could hope to receive its perfect Lord.
NOTES:
1. Cf. H.V. Jaffa, The Conditions of Freedom: Essays in Political
Philosophy (Baltimore: The Johns Hopkins University Press, 1975), pp.
152-53; G. Anastaplo, St. Louis University Law Journal (Spring, 1965), 390.
2. G. Anastaplo, “Censorship”, The Encyclopedia Britannica, 15th
Edition, 1986 printing, Volume 15, pp. 634-641; The Amendments to
the Constitution: a Commentary, (Baltimore: Johns Hopkins
University Press, 1995), pp. 52-56: R.A. Licht, “Respect is not a Right”,
Crisis, Vol. 11, No. 7, July-August, 1993, pp. 41-47; “Communal
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Democracy, Modernity, and the Jewish Political Tradition”,
Jewish
Political Studies Review, 5:1-2 (Spring, 1993).
3. A. Bloom, Love and Friendship (New York: Simon and Schuster,
1993), p. 330; H.V Jaffa, “Chastity as a Political Principle: Measure for
.
Measure”, Shakespeare as Political Thinker, eds. J. Alvis and T.G.
West (Wilmington, DE: ISI Books, 2000), pp. 211-12.
4. The most reliable and literal translation known to me is by M.
Flaumenhaft (Prospect Heights, Ill.: Waveland Press, 1981).
5. Cf. W. Shakespeare, Sonnets, Nos. 129 and 116.
6. L. Berns, “Gratitude, Nature and Piety in King Lear”, Interpretation,
Vol. 3/1 (Autumn, 1972), Sections V and IX; “Rational Animal-Political
Animal: Nature and Convention in Human Speech and Politics”, Essays in
Honor of Jacob Klein (Annapolis: St. John’s College Press, 1976), pp.
29-35, esp. section III; [uncorrected version in The Review of Politics,
Vol. 40, No. 2 (April, 1978), pp. 231-54.]
7. L. Berns, “Transcendence and Equivocation: Some Political, Theological
and Philosophic Themes in Shakespeare”,
Shakespeare as Political
Thinker, cited n. 3, pp. 402-4.
8. “Chastity as a Political Principle: Measure for Measure”, citation
n. 3, p. 221.
9. The locus classicus for the relation between private and public, polity and family is Aeschylus’s trilogy Oresteia. The trilogy begins with a
world where family feeling, the spirit of revenge and cycles of blood feuding dominate and characterize political and social life. Agamemnon, the triumphant leader of the Trojan expedition, is killed on his return to Argos
from Troy by his wife Clytaemestra for the sake of “my child’s Justice”, that
is , to avenge the death of their daughter sacrificed to propitiate the gods
holding up the expedition to Troy. The ruling deities are the Old
Goddesses, the Daughters of Night, the “ingrown, vengeful Furies.” In the
second play, Orestes, Agamemnon’s and Clytaemestra’s son, following the
charge of Apollo’s oracle, avenges his father’s death by killing his mother.
The Furies, “the bloodhounds of my mother’s hate,” pursue him. The third
play, The Eumenides, the well-meaning ones, celebrates the founding of the
Court of the Areiopagus at Athens. Orestes seeks sanctuary at Delphi. The
Pythian oracle is overwhelmed by the pursuing Furies. Apollo himself inter-
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venes and stills the Furies long enough for Hermes to guide Orestes to
Athens for a final resolution of his case. At Athens Pallas Athene takes
charge. She who was not born of woman (born from the head of Zeus), a
most man-like female, almost a mean between male and female, turns the
trial over to an open court of Athenian citizens. The Furies argue against,
Apollo argues for Orestes; gods as advocates, before human beings as
judges and jury. The jury of twelve human beings is given the authority to
decide. The sovereignty of hitherto untamable family feeling is brought
under the supervening authority of the polis, the political community.
Although they have the authority, the human beings by themselves are incapable of deciding between conflicting rights of mother and father. The jury
splits evenly. The deciding vote is given to the goddess Athene. Divine help
is required for settling such questions. She decides for Orestes. It seems that
reasonable procedures for settling and dispensing with problems may
sometimes be more important than assurance that the solutions are correct.
These questions are no longer to be dealt with violently behind closed
doors but deliberately before public and open spectacles of law court,
assembly and theater. The Furies are unwilling to accept these dispensations of the younger gods. By a combination of threats and persuasion
Athene cajoles the Furies to integrate their authority over family feeling and
the household into the service of the greater good of the political community. They shall “win first fruits in offerings for children and the marriage
rite.” The Furies finally agree and are transformed into Eumenides. The
feelings they preside over which are capable of tearing the political community apart cannot be extinguished: they are to be redirected against the
despotically minded consumed by “a terrible love of high renown” and
external enemies; they will bolster the mutual love of fellow citizens. “This
is a cure for much that is wrong among mortals.” Cf. M. Flaumenhaft,
“Seeing Justice Done: Aeschylus’ Oresteia”, Interpretation, Vol. 17/1,
(Fall, 1989), pp. 69-109, reprinted in The Civic Spectacle: Essays on
Drama and Community, (Lanham: Rowman and Littlefield, 1994),
Chapter 1; and David K. Nichols, “Aeschylus’ Oresteia and the Origins of
Political Life”, Interpretation, Vol. 9/1, (August, 1980), pp. 83-91.
10. L. Berns, “Gratitude, Nature and Piety in King Lear”, citation n. 6, p.
50: “... love and passion ... need to be controlled by law and authority. Being
conceived outside the ’order of law’, Edmund was banished from the family circle. He is not altogether ’unnaturally’ devoid of family feeling.”
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79
A Review of Eva Brann’s
The Ways of Naysaying
Chaninah Maschler
“The first impetus” for this study,1 Eva Brann tells us in her
Preface, was the desire to deepen her understanding of the two
“capacities of our inwardness” that had been the themes of two of
her previous books, The World of the Imagination and What, Then,
is Time? “As the imagination ...makes present what is not before us
by reason of nonexistence or withdrawal, so memory ...holds what
is not with us by reason of having gone by....Therefore... to understand something of imagination, memory, and time, we must mount
an inquiry into what it means to say that something is not what it
claims to be or is not there or is nonexistent or is affected by
Nonbeing. And that is what I am after in Ways of Naysaying” (pp.
xiif, my italics).2
Addressing, I presume, readers of the first two volumes of her
trilogy, Brann explains that and why there will be less reliance on
introspection and more reliance on logic and language in the present volume: ”We could, it is thinkable, be aware of our internal
images...without having language for them....But whether we
could know about negation—that we are capable of it and how—
without speech is doubtful to me. Hence within my scheme, no,
not, non- are deeper than imagination and time, in the sense that
the former underlie the latter and are revealed in their analysis” (p.
xiii). Earlier in this paragraph, and in more detail later, when summarizing Freud’s essay “On denial” in her Chapter One, she allows
that there is a pre-linguistic “nay-saying of instinct and gesture.”
Since this paragraph is rather condensed, and much hangs by it,
let me try to say in my own words what I believe it to hold: Doing
no, for instance, spitting out or pushing away or averting the gaze,
occurs (ontogenetically and, according to Freud, also phylogenetically) before speech. And a sort of prereflective reacting to heard
Eva Brann’s The Ways of Naysaying: No, Not, Nothing, and Nonbeing. Lanham, Md: Rowman
and Littlefield, 2001. Chaninah Maschler is tutor emeritus at St. John’s College.
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“no,” or even the uttering of the syllable “no” (as mere substitute
for the gesture of rejection) may well be a phase of children’s intellectual history. Further, having images and reacting to them, or to
having had them, can occur without the one who reacts being aware
that what he or she is reacting to is an image. But to peg an image
as an image, which means, to take it as a likeness of its original, that
requires, according to Brann, the thought “This is and is not that.”
Therefore there can be no sizing up of a mirror image, memory
image, dream image, perceptual presentation as “merely” an image
until after negation has entered upon the mental scene. Now knowing about negativity, which is different from prereflectively reacting in a rejecting or separating manner, that could not occur sans
speech. While images are, therefore, existentially “prior to” (earlier
than) speech, in involving recognized negativity they show themselves conceptually “posterior to” speech.3
Brann seems to be employing some version of the
Aristotelian contrast between “first to us” and “first in nature.”
This is how I construe her claims that, while imagining and recollecting are more manifest, negativity lies “deeper” than do
these “capacities of our inwardness”; and that, furthermore,
whatever is condition for the possibility of negativity lies more
deeply still. Her book as a whole will argue that the Platonic discovery that Being “holds” Nonbeing may well be the ultimate
answer to the question “was die Welt im Innersten zusammen
halt” (“what it is that most intimately holds the world together,”
Goethe, Faust Pt. 1, li 383).
The Introduction of Brann’s book is given over to etymology. It draws attention to the fact that in English, German,
French, Latin, and Greek (the languages in which the Western
philosophic tradition is expressed), most of the basic words for
naysaying—no, not,non-,nothing, and negativity—start with a
nasal sound. Jesperson, and before him Darwin, remarked on
this fact and entertained the thought that, conceivably, our signs
for negation are transitional between naturally expressive gesture and conventionally learned word. The n-word would then
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81
have originated as a substitute for the snort of aversion or refusal
and in the course of linguistic and cultural history have proliferated into a multiplicity, the last but not least of which would be
the abstract general negation word “not” we use for contradiction.
In Chapter One, Brann, like many of us today, seems to
share Darwin’s impulse to give direction to speculation about
human archai by studying child development. Accordingly, the
title of her book’s first official chapter—“Chapter One,
Aboriginal Naysaying: Willfull No”—refers initially to “the primordial ‘no’ to everything” of the toddler (p. 9), but eventually
to other respondings (Goethe’s Mephistopheles serving, seriocomically, as paradigm) that reject, disobey, or spit out what is
given. Thus some of the discussion of nihilism in Chapter Six
looks as though it were continuous with Chapter One’s analysis
of childish “no.” The toddler rejects the breast, the command or
prohibition, the saying “so it is” of the grown-up; the nihilist
turns down shared traditions, institutions, and even intersubjectively acknowledged matter of fact.
I loved the affectionate and knowing description of “the terrible twos” in this chapter. I share Brann’s admiration for Freud’s
astonishingly potent brief essay on negation, which she summarizes,
pretty much in Freud’s own words, on pp. 10-12. But it looks to me
as though Freud’s quasi-Nietzschean “genealogy” of the intellectual function of judgment out of the interplay of biologically “primary impulses” has, when Brann is through with it, become tinted with
Augustinian surmises of original sin. In evidence I cite the fact that
it is rather late in the chapter (footnote 28, p. 22) that the “healthy
naysaying” of resistance to temptation and of rebellion against
tyranny are mentioned; also, that the emphasis on self-awareness’
emerging from deeds and words of “arbitrary willfullness” (cf. p.
18) does not seem to be balanced by reflections on the child’s need
to exercise, so as to perfect, skill at matching expectation with outcome, and vice versa. What I have in mind is well-explained by
Jerome Kagan. In brief, Kagan holds that much of what we
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observe in the not quite two-year-old is made intelligible if we
view it as due to the emergence of “three related competencies”:
ability to notice that some happening or action is at odds with
what is right and regular; absorption by the idea of standards as
standards, both those set by others and those set by oneself; awareness of one’s own and the world’s ability or inability to meet standards. I am confident that Brann would agree that these competencies involve the child’s increasingly better memory: Isn’t much
of the toddler’s “testing” of the world, commandeering of adults,
and “first Adam”-like rage at the world’s or the grown-ups’ not
coming through connected with practicing the ability to match
outcome with forecast and plan, remembrance with presentation?
It is my impression that Brann writes more nearly in this spirit in
What, Then, is Time? (See p. 165).
The chief questions asked and answered in Chapter Two, where
the not of logic is taken up, are as follows: 1.What is negation?
2.Where is the sentence negated? 3.Is the positive prior to the negative? 4. How is negation related to falsity?7
Following Aristotle, Brann assigns negating (the act) and negation (the act’s sentential consequence) to the genus of opposition.
An admirable overview of types of opposition, as described and
classified by Aristotle, is provided, while opposition in general is
recognized to be indefinable.8 Plainly, the idea of not is clarified
when, through insertion into its genus, it is made evident that not
must be discriminated from fellow-contenders for naysaying primacy, for example, speaking linguistically, the particles non- or un- or
a- and, speaking semantically (?), the polar relations of contrariety
and privation. The not of contradiction is declared the winner, on
Aristotle’s authority (p. 27). But, Brann hastens to add, contradiction, which is “sheer, unintermediated opposition” (studied as such
under the heading of question 4), belongs to thinking and speaking,
not to things.
We seem, perhaps contrary to expectation, to have ferreted out
something like an answer to the question of what negation consists
in. A summing up of the interim upshot of the inquiry into the
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nature of not is provided on p. 29f. and concludes with the sentence: “Negation arises from the human desire and ability to make
distinctions; it is (most likely) grounded in the oppositions and
polarities that belong to beings....”
Where in the declarative negative sentence is the particle that
accomplishes negation located? is the second question. What
motivates the question? One could imagine a linguist who is trying to learn an exotic language asking it. He would, I suppose,
have tried to obtain a corpus of utterances sufficiently rich to
hold instances of all the elementary affirmative sentence patterns
of that language (supposing this possible); next, he’d have consulted with a native informant as to how one would, in his language, “say the opposite(s)” of these. Assume the native informant is a speaker of English and the linguist’s native tongue is some
non-Indo-European language, say Chinese or Hebrew. If I understand Brann correctly, she believes that the Chinese linguist
would somehow find out that all the elementary affirmative sentence patterns of spoken English are reducible to the triadic pattern S is P How could he have found this out? The best I can
.
come up with is that, in learning English, he relies on the same
logical truth on which he relied when he acquired his mother
tongue—that whatever is said is interpretable as making some
comment on a declared or otherwise manifest topic: The topic is
named by one part of the sentence; the sentence attaches the
comment to the name; and in so doing comments on, that is,
predicates the sentence’s predicate of, the thing or things in the
world that is or are the sentence’s topic.12 The question now
becomes how and why this insight into the logically dyadic T-C
structure of simple 13 affirmative sentences issues in the triadic S
is P structure. The reason for my selecting a Chinese-speaking linguist was, of course, that (as Brann reports in the long and important footnote 22 on p. 64), Chinese sentences do not require a
copula to accomplish the job of commenting. Hebrew doesn’t
either: Joseph holech “merely juxtaposes” what is, strictly speaking,
a participial (thus adjectival) form of the verb to the proper name
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“Joseph” to say what in English would be said by the sentence
Joseph is walking. But nothing stands in the way of a Hebrewspeaking linguist’s learning that in English sentences an “is” must be
inserted between “Joseph” and “walking” for the predicating job to
be accomplished.
What all this fussing is about is the issue how logical and grammatical distinctions differ and mesh. Brann’s fourfold answer to the
question where the negation particle is located in a sentence proceeds, not on the linguist’s basis of studying a corpus of English negative sentences, nor on the logician’s basis of reflecting on the negating jobs that would have to be accomplishable if the tasks of describing and reasoning rightly are to be carried out. Rather, she works
with the S is P pattern of “traditional” logic and negates, first the
“is” or copula, next the “P” or predicate, third the sentence “S is P”
as a whole, and finally, although not whole-heartedly, even the “S”
or subject. Having done this, she points out the jobs done by the
patterns which thus emerge.14
Why does she proceed in this manner? She is, usually, not at all
friendly to mere algebraic patterning. More important, she knows
that Frege, whose “deep critique of the classical view [of negation]”
was taken up appreciatively in the concluding section of the treatment of question 1 (pp. 30-32), endorses something like what I
tried to say through my fable of the Chinese or Hebrew-speaking
linguist, that what chiefly matters is the irreducible logical contrast
between naming and predicating and their complementarity,15
whereas the presence or absence of some form of the verb “to be”
is a linguistic accident.
On first reading I thought that her manner of proceeding in
Chapter Two is due to her not being as convinced as was Frege of
the need for a principled distinction between logic, as a normative
science, and psychology and linguistics as empirical sciences which
acknowledge logical norms in practice (as we all do when we think),
but which do not study them.16 Brann reports and up to a point
explains that Frege distinguishes T-C structures qua what he calls
Gedanken (“thoughts”) from “assertions” (what Kant called “judg-
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ments”). And she appreciates that “thoughts,” including negations,
are for Frege objective and atemporal whereas he regards “assertions” as acts of a speaker or thinker who at some time or other
asserts an assertable or its contradictry. She even quotes a sentence
of Frege’s which brings this contrast to bear on the issue of negation.17 But she refuses to let go of inquiry into what it is in human
beings and the world that leads to nay-saying.18
On second reading I found an outright answer to my question,
why Brann distances herself not only from Frege but also from Plato
and the Aristotle of On Interpretation, in footnote 22 (p. 64). She
writes: “I accept...[‘S is P’] as the fundamental sentence form
because people whose thought is congenial to me19 have built on it
structures that are of great interest, and because I have corroborated by introspection that it is my most basic declarative mode of
internal speech, closer to thinking than the bipartite sentence consisting of a subject and a predicative verb.”20
Postponing till her penultimate chapter, Chapter Six, inquiry
into what she calls the “greatest question,” namely, whether
Something or Nothing is ultimate, the issue in section 3 of the present chapter is whether “in human speaking denial is always derivative and in human speech negation is always secondary” (p. 36).
Boethius, ancient authors in the Aristotelian tradition, and modern
cognitive science are reported to endorse the opinion that the affirmative is prior to the negative, as at first blush it would seem to be,
since any negating particle is an “addendum.” Bosanquet and
Bradley are described as having answered the question in a more
nuanced way: “Negation is not as such a denial of affirmative judgment; it does not presuppose a particular affirmative judgment to be
denied. But it does presuppose some general affirmation, namely,
that of a world having a positive content judged to be real....The
positive judgment itself cannot take place before the distinction
between a mere idea and a fact of reality is recognized. ‘And with
this distinction the idea of negation is given’ ” (p. 40).21 Still, the
over-all conclusion of the inquiry in section 3 is that negation is
“secondary.”
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More minute examination of Bosanquet’s and Bradley’s
remarks on negation might have yielded a scheme for differentiating the diverse senses of the prior/posterior relation; causal priority
might have become differentiated from conceptual priority; priority in dignity or rank from temporal priority.22 But as it stands, section 3 seems to favor a temporal sense of prior/posterior. This bothers me because I am inclined to believe that logicians qua logicians
have no business asking about temporal priority and that conceptually the positive comes or rather is on the scene along with the negative. Thus neither is prior to either.23 As an illustration, consider
the following: At the beginning of the Prior Analytics, Aristotle
defines argument or deduction (syllogismos) as follows: “A deduction is a discourse in which, certain things being stated, something
other than what is stated follows of necessity from their being so.”
I believe that anyone who grasps the type of necessity here spoken
of grasps along with it the impossibility of the contradictory. Upon
reflection I recognize that I base this apparently psychological
observation on the conceptual (i.e. logical) truth that must-bes are
the contradictories of cannot bes and cannot be apart from them.
Indeed, it dawns on me that my seemingly psychological claim may
be nothing but the conceptual truth itelf in another form of words.
The treatment of question 4 (how negation is related to falsity)
shows a respect for Wittgenstein that was, I believe, absent from
Brann’s previous writings.24 His Tractatus is praised both for asking
and for answering the following questions: (1)“How do Truth and
Falsity come to be obverses” (i.e. opposites)? (2)“How is negation
related to them and to truth-values?” (3)“Why are propositions
bipolar?” (4)Can we justify the logic textbooks’ assumption “that
each proposition has only one negative?”(p. 47).25 The two paragraphs immediately preceding the enunciation of these questions
seem to report the answers that Brann found in Wittgenstein. I
quote them in full:
“It all begins with a discrimination exercised by us over a logical space wherein things are seated within their place in their proper relation configurations, a discrimination of the otherness of what
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is false. So prototruth26 is in the world of fact. Now comes a proposition. In its negative and positive sense it is like a solid body that
restricts all movement into a certain place; in its positive sense it has
an empty place where the object can fit in (Tractatus 4.463). These
[comparisons ]are pictures of the ... inherent bipolarity of every
proposition. It shows negation from the beginning related to the
negated proposition, for it is that hole which the negating proposition is blocking (Tractatus 4.0641). So to understand a proposition
is to see the logical space (Tractatus 3.4) and to discriminate what
the facts would have to be like to make a proposition...[i.e. a logical picture] true or false.”
“Truth, then, or falsity, is the consonance or correlation of a
propositional picture with reality (Tractatus 2.21), where reality
(Wirklichkeit) is the existence or non-existence of facts (Tractatus 2;
2.06)—a non-existent fact being one that is pushed out of the world
picture by the fact that exists. In this correspondence is truth in the
primary sense, and it comes in the duality true-false because of the
way logical space divides and we discriminate the facts. In the sense
of propositions lies the polarity positive-negative, the latter of
which is expressed in the sign not- when the facts fail to correspond
to p. Truth values, T and F, are secondary to and derived from negation: ’The sense of a truth function of p is a function of the sense of
p’ (Tractatus 5.2341). Thus T and F are not properties of propositions (Tractatus 6.111) any more than are positive and negative.
The truth values of the truth tables capture the relations of T and F
to p and not-p more than they define the latter.”
Section 4 concludes with the following remarkable observations:
(1)The examination of the Tractatus has revealed that for
Wittgenstein and other moderns “truth comes from the world, and
negation is in propositions. For traditional philosophers it is just the
other way around: Negation is in the world of appearances and in
the beings of the intellect, and truth is in the propositions” (p. 48).
(2)What Aristotle says about the true and the false in
Metaphysics Bk. IV 1011b25 and Bk VI, 1027b19ff tends to show
,
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that Heidegger was quite right when, in his Logic, he denied that
the Aristotelian texts hold a “correspondence theory of truth” (p.
48).
(3)Aristotle speaks “for a world very different from the one in
which the propositional calculus of Russell and Wittgenstein is at
home. For Aristotle negation (I mean negation in an objective form,
contrariety interpreted as Nonbeing and its effects) is in the world
and falsity (I mean the not always unintentional failure of speech to
reveal being is in statements....Whether negation is in the world or
in speech is one of the numerous but interrelated marks by which a
classical world...is distinguished from a modern world. For a world
that has negation built in responds to receptive thought since it
reveals its own distinctions, while a solidly positive one demands
constructive reason since oppositions need to be made” (p. 49).
As the just-reported grand conclusions of section 4 of Chapter
2 tend to confirm, negation became thematic for Brann by virtue of
her interest in the psychological and ontological topics that were
mentioned in the opening paragraph of this review; whereas logicians—from Aristotle through the Stoic logicians and Frege, Peirce,
Russell, Quine—attend to negation chiefly because of how it affects
what is and what is not a valid pattern of argument. Patterns of reasoning or deduction rather than patterns of judgment or of propositions may well be their primary concern.27 This difference
between herself and the logicians might also explain the otherwise
rather puzzling remark, on p. 25, that “by and large the negations
of logic28 take place in symbols and are found in books. They are
not so much naysayings as naywritings.” For the purposes of reasoning the idea of contradiction, that is, of an opposition which is
not only exclusive but also exhaustive, is indispensable: Illiterate
Athenians have no trouble grasping the sense of arguments by contraposition such as, “If virtue were teachable, there’d be teachers of
virtue, yet there are none. Therefore, virtue is not teacheable.” And
I surmise that the pattern of Euclid’s reductios (which likewise
involve the stark negativity of contradiction) was first discovered as
a debating gambit and passed on by teachers of rhetoric. I say this
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partly because it seems to me that even Euclid’s Elements still retain
a viva voce dialogic rhetorical mode.
“When we refer to a nonexistent object, what are we thinking
of and what are we talking about?” (p. 76). Chapter Three begins
by pointing out that this is a distinctively modern question,29 different from the ancient one taken up in Plato’s Sophist, how nonbeing can be, to which Chapter Four will be devoted. Four types of
non-existents are mentioned for purposes of illustration—“members of extinct species [dodos, for instance]...deceased human
beings [for example, Socrates]...artifacts no longer extant,30 but
also all the entities that never did exist in the ordinary sensible
sense, such as unicorns” (p. 79).
Roughly speaking, four types of answers are sketched in
Chapter Three: Bertrand Russell’s “theory of definite description,”
Alexius Meinong’s “theory of objects [and objectives],” the recent
version of Meinong worked out by Terence Parsons in his 1980
book Nonexistent Objects (New Haven: Yale University Press), and
any one of a number of theories according to which “pretense and
make-believe are the chief explanatory principles,...[not of the
behavior of nonexistent objects], but [of] how they manage to
come on the scene to begin with, [and] what we cognitively do to
cooperate in fiction making” (p. 99). From the way these theories
are elaborated it becomes apparent that, although —as the two earlier volumes of Brann’s trilogy argued—our ability to think and
speak truly or falsely of bygone things is testimony to the powers
of the human imagination, in that the feat of “re-calling” depends
on or consists in the imagination’s having succeeded at making
temporally absent things present, it is the “saving” of fictional entities that chiefly matters for the purposes of the present book’s
Chapter Three.
Before she turns to a fairly detailed examination of Russell’s
treatment of proper names and definite descriptions, Brann lets us
know that “the theory that is the winner in the world of logic
[namely, Russell’s], will turn out to be something of loser in the
world of fiction” (p. 76). Russell’s theory, as she tells us Parson too
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observed, pays too high a price for its clarity: “The theory commits
us to treating the sentences of fiction as false, while most of us think
they have at least a sort of truth, and some of us even believe that
they often have more truth than mere fact does” (p. 86). Meinong,
contrarywise, “comes near to saving the phenomena of that intentional experience of central interest to this trilogy...the experience
of imagining (p. 91). Russell’s excision of nonexistents from reality31 is false to the power that some non-existent beings and places
have, moving us “as models and attractors,” and “outliving us by
millennia, and in a word impinging on us as if existence were home
to them as well [as to ourselves?]” (p. 102).
Instead of recapitulating what Brann says about the technical
aspects of Russell’s theory of description and Meinongian rival theories, I want to dwell a little on Brann’s question how we are to
account for the fact that the Natasha, Pierre, and Andrey of
Tolstoy’s War and Peace or the Hari Kumar and Ronald Merrick of
Scott’s Raj Quintet32 have become our companions.
A familiar answer begins by reminding us of our unabating
curiosity about our fellow human beings, whether met in the flesh
or encountered vicariously through what our friends, our children,
our journalists report and our television news programs show. “But
the characters who people novels are immensely more memorable
than the Tom or Dick or Harry that our neighbors tell us about.”
Well, that does somewhat depend on what a particular neighbor is
capable of telling us about a particular Tom (or Jane for that matter), not to mention the particular Tom or Jane spoken about. But
to the extent that it is true, may it not in large part be the result of
novelistic characters’ (at least those that dwell in novels of substance) becoming so much better known to us than any persons not
our “real life” intimates?33 Novelists are much better at noticing
things than most of us are, and better at imparting what they’ve
noticed too. Also, our acquaintance with novelistic characters is a
shared acquaintance, shared with other make-believe characters in
the novel, with the novel’s author, and with fellow-readers of the
novel. It is hardly news that sharing (comparing notes and impress-
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sions) is immensely pleasurable, greatly contributes to a feeling of
solidarity, and is constitutive of our sense of reality.
Add to what’s been said our relish for just about all human skills
or powers, our own as readers and the novel-making skills of the
author. Most important, count in the special joys of play and makebelieve: Aren’t we well launched on the beginnings of some sort of
answer to the question “Why and how do fictional characters
become real to us?”
Brann does not think so. At least, she rejects the idea that what
we relish, in ourselves and novelists, is the exercise of the human
power of make-believe: “Being absorbed into a fiction, living in its
landscapes and with its people, is not well described as a form of
pretense—not on the reader’s or viewer’s part and so much less on
the poet’s or painter’s part....Children, to be sure, play ’Let’s pretend,’ but that is usually when the game requires that roles be
assigned , and I’d bet that the mover of the pretense doen’t often
assign, say, the submissive role to herself; in participating in a novel,
on the other hand, we may well surrender ourselves to the experiences of the underdog ”(p. 99f).34
I wonder whether childish “dramatic play” (as the child psychologists call it) and make-believe of every sort is here conceived
of in all its richness. Think of the infinite variety of solitary and collaborative pretending and letting be we catch our children at! Sure,
sometimes there is one kid in charge (“I’ll be mommy and you’ll be
baby”) but by no means always. Two games of make-believe I
remember watching were: spreading out newspapers on the floor to
be islands and going island-finding, island-hopping, and islandworking; arranging marbles in rows and letting them be children at
school. Neither of these games called for leadership. Older children
would sometimes join the younger ones at play, humbly grateful and
gratified to be allowed “in” on the game. Improvisational theatre
has some of these qualities, I believe, though I cannot be sure since
I have never participated, either as actor or as audience.35 I went on
like this because I want to make concrete that there might be ways
of “taking fiction seriously” and trying to understand why and how
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make-believe matters that don’t proceed by way of ontology but by
way of psychology. The British pediatrician and child psychologist
D.W Winnicott may have something to teach us here.36 And as for
.
grown-ups making believe, I have begun to read Kendall L.
Walton’s Mimesis as Make-Believe, On the Foundations of the
Representational Arts (Cambridge: Harvard University Press, 1990.
Part Four of this book tries to show why it is all right to do without
fictional entities. I should, however, also mention that in Austria, at
the University of Graz, much is currently being written about the
logic and ontology of fictional objects.
A reader of an earlier version of this review advised me that I
need to report where I stand on the issue of the being and non-being
of fictional characters. I am undecided, because I have insufficiently considered (to give just one example) whether my belief that one
can be as mistaken in one’s “reading” of a fictional character as one
can in one’s “reading” of a violin sonata does or does not have
ontological implications. My laziness about ontology may have
something to do with the fact that I lean toward believing that it is
more illuminating to ask questions about how imagined persons
and places are and are not like historical individuals and geographic regions, or how what one learns about good and evil from living
hooks on to what one learns about them from literature, than it is
to delve into ontology.
The rest of Chapter Three is devoted to reflections on lies and
lying37 and to Anselm’s so-called ontological proof of the impossibility of God’s non-existence.38 The setting out of Anselm’s argument is very pretty!
Chapter Four: When we begin to read Chapter Four’s first
paragraph, we are already in possession of the guidepost furnished
in the Preface (p. xiv): “Here [in section 2] comes on the scene the
Non of philosophy (my italics), a prefix signifying not the brusquely rejecting denial of fact in words but the more forgiving opposition of two elements in the same world. The thought of Nonbeing
comes among us as the unbidden effect of Parmenides’ injunction
against it, and Plato will domesticate that same Nonbeing, bringing
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it into philosophy as the relational principle of diversity, the Other.”
But to reach section 2 we must traverse section 1. It begins:
“Parmenides learned from the goddess who dwells in the house of
truth that ’Being is’ and that he must not embark on the way of
Nonbeing. As far as I know, Nonbeing had not established itself in
anyone’s thought—at least in the West—before Parmenides’ deity
warned him off this path of inquiry; nor has it ever vacated its place
in thought since. Her [i.e. the goddess’s] repeated prohibitions and
injunctions against this Unthinkable and Unsayable seem to have
done for this philosophical offense what inveighings against sin
have so often accomplished in the moral sphere—they have
launched it on its career as a well-formulated and ever attractive
presence” (p. 123).
Among the titillating suggestions of Brann’s commentary on
Parmenides’ poem there is this, that this “heroic epic” (in dactylic
hexameter) is “unmistakably [intended as?] a rival to Homer’s
Odyssey,” so that “the ancient difference between philosophy and
poetry” of which the Republic speaks (607b)39 first comes on the
world scene when the journeying of young Parmenides displaces
that of middle-aged Odysseus.
I find myself incapable of paraphrasing what Brann says about
Parmenides. Here are some more quotations: “We often use phrases like ‘sing a song,’ where the object is the action of the verb made
into a thing accomplished. Parmenides sometimes does something
symmetrical with the verb ‘to be’ at the front end of a sentence. He
turns the verbal sense into a subject. But I don’t think that Being or
its negation is thereby established as a thing....On the contrary,
mere verbal ‘Is’ remains the truest kind of showing forth, and the
nounlike forms merely display the inability, or rather unwillingness,
of the goddess’s speech to get outside the meaning of that little
word which courses through human speech surrounded by subject
and predicate. Parmenides’ poem is a rebuff before the fact to those
who will claim that Indo-European languages are indefeasibly subject-and-predicate-ridden. For this is what Parmenides is bidden [by
his goddess] to convey: the sheer Isness of which we always get hold
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when we think beyond multiplicity....The common declarative tripartite sentence...is an implicit expression of three distinctions:
between the thinker and the thought (since some thinking person is
having and uttering a thought); between the thought and what it is
about (since the sentence states a thought-proposition about an
object); and between the object and its properties (since the sentence predicates a property of its subject). At the very beginning,
before these elements have ever been formally established, the goddess wants to prevent them from being distinguished....My main
purpose in this section has been to enter just enough intothe meaning of ‘Is’ to make sense of the ’Is not’ that trails it as its unwelcome
but unshakable doppelganger” (p. 130ff.).
“The next step in the ancient story of Nonbeing is...the reversal of its outlaw status and its integration into the community of
Beings. It is taken in Athens, the city of reconciliations” (p. 138).
What follows the exquisite paragraph whose two opening sentences were just quoted40 is a fresh setting out of reflections on
Plato’s dialogue the Sophist.41
I describe a few of these.
Seasoned readers of Platonic dialogues agree in noticing that
the conversation in the Sophist begins with the question whether
corresponding to the three names or titles “sophist”, “statesman”,
“philosopher” there are three beings or three types of being. Given
the fact that there is a dialogue called Sophist and also one called
Statesman, the non-being of a dialogue called Philosopher is a glaring fact. Some Plato commentators have argued that the Philebus is
the “missing” dialogue. But Brann believes that there are indications
in the Sophist that Plato means us to understand that “sophists and
philosophers are identical,” though differing in three respects: First,
the dialectical skill which is shared by sophists and philosophers is,
in the philosopher, accompanied by a kind of professional ethics.
Dialectic is, for him, a sacred trust. For the sophist it is a moneymaking techne, for sale to the highest bidder. Second, unlike the
traveling sophist, who is detached from civic loyalties, “the philosopher never forgets his human circumstances” (p. 139). Third, the
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philosopher is “that rare sophist who acknowledges Nonbeing
without taking cover in it” (p. 139).
To catch the “vulgar” sophist, the philosopher-sophist—in this
dialogue represented by an unnamed stranger-guest from
Parmenides’ city, Elea—must somehow show that contrary to what
Parmenides’ goddess taught him, Nonbeing is.
But it is not only to catch the sophist; nor just to defend the
possibility of false speech, negative speech, and error. Rather, to
save philosophy itself (to save speech itself?), Nonbeing must be
allowed to be! (Sophist 260A). The stranger therefore, Theseus-like,
or again, Athena-like, bestows citizenship on Nonbeing by declaring
it a form among the koinonia of forms (p.141). It is the diversifying
relational principle or form Otherness, not to medamoos on,
absolute nothing. “It is its ...[being identified] as the Other that
saves it from the utter inability—which Parmenides does indeed
assert—to become sayable....Nonbeing both bonds and negates
among beings, but its negation is not annihilation” (p. 142).
The chapter’s last paragraph makes the transition to Hegel: “In
Nonbeing naysaying has found its enabling principle in the realm of
Being. Now comes a view of speech and thought [namely, Hegel’s]
as themselves having inherent negativity. As Nonbeing was a source
of ontic diversity, so this [Hegelian] negativity will be the source of
mental motion” (p. 144, my italics).
Concerning Chapter Five I merely report that it employs the
trinity Spirit, Understanding, Reason to display and classify the
kinds of negativity encountered in Hegel’s Phenomenology, Kant’s
First Critique, and Hegel’s Logic. Devotees of Hegel will find much
to admire here. The chapter concludes with a paragraph announcing that, though the earlier chapter concerning Parmenides and
Plato and the present one concerning Hegel conspire to reaffirm
that Being is prior to Nothing, this is not as yet fully established:
Therefore Chapter Six42 jousts with the “greatest question”—which
is ultimate, Something or Nothing?
Most winning, witty, and sometimes even wise of all the sections of Ways of Naysaying are the concluding pages of this chap-
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ter, Chapter Six, about Nothing, offered under the seemingly bleak
heading, “Nothing as Inescapable End: Death” (pp. 188-198)!
However much of the time I was rather lost in this chapter. The
reason, I imagine, is that Brann’s question, whether Something or
Nothing is ultimate, never jelled into being a question for me. Yet as
best I understand the chapter, the various items it gathers together—“modern nominalism” (p. 170), Epicureanism and the void (p.
171ff), the “blithe nihilism” of some of the Buddhist schools (p.
173), the political “nihilism” of the mid-nineteenth century Russian
revolutionaries portrayed in Turgeniev’s novel Fathers and Sons (p.
179), and Heidegger’s teachings concerning the nihilating nihil (das
nichtende Nichts, p. 184ff) —are thought to deserve to stand side
by side because they all affirm, albeit in different ways, that Nothing
is more C primordial, more really real, than Something. This is the
sense in which they are all of them “nihilisms.”43 Another thing that
they may have in common is an ontology in which will is prior to
understanding.
It is possible that my failure to understand the chapter and its
leading question is due to incomprehension of Heidegger: I tend to
become so overwhelmed with irritation at his preachy incantational tone, his haughtiness, his tricks of inverting grounds and their
consequents, his abuse of the scholarly riches deposited in etymological dictionaries, that I become incapable of paying attention to
what he says.
Conclusion: (1)Is all human “opposing” (in will, word, or deed)
reactive to, thus parasitic on, a “posing”? (2)Might negating
responses constitute evidence for the being of Nonbeing,
Nonexistents, or even of Nothing? (3)Supposing there are
Nonexistents and Nonbeings, by what powers of the soul do we
encounter them?
In her final chapter, Brann recapitulates the affirmative answers
she earlier gave to questions (1) and (2). But she now expands on
what was said about Nonbeing in her pivotal Chapter Four:
“Besides the nonexistents that respond to our sense of what is missing...there are also declines and falls from existence, right in the
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world around us, that we experience as a sort of nonexistence.
Take, for example, the reflection of a willow tree that appears in a
pond. Take the numerous things and people in the world without
that are not what they appear to be....This last group, fallen existences [my italics], particularly raises the question whether it is our
way of experience or the nature of things that provides the not or
non here” (p. 215). As the past participle “fallen” which I underlined just now goes to show, Brann is introducing a principle of hierarchy into the realm of being. “Nonbeing as otherness is the universal relativity....But there is also ...a vertical Nonbeing....This
Nonbeing...has in it something of absolute inferiority, of defective
or deficient Being” (p. 216). Brann has brought us back to the central books of Plato’s Republic, I mean, books VI and VII, with their
image of the sun, diagram of the unequally divided line, and story
of the prisoners confined to life in a cave.44 It is in this context that
she reaffirms the answer to question (3) that’s been with us since her
book’s opening sentence: It’s neither sensing nor thinking that give
us access to nonbeings and nonexistents but imagination and memory.45
Obviously, then, this review cannot have done justice to the
book it tried to summarize and (in some measure) appraise, since
that book is one third of a three thirds whole. I hope, however, to
have conveyed something of its extraordinary scope, writing style,
intellectual daring and imagination.
NOTES:
1. The Ways of Naysaying: No, Not, Nothing, and Nonbeing (
New York: Rowman & Littlefield, 2001)
2. Cf. What, Then, Is Time?, p. 165:“...we are able to have and interpret
images, to live consciously in the phases of time, and to think and speak negatively. My guess is that these three capacities are really triune, three-in-one.
They may be the root of our humanity, and perhaps the subject of another
book.”
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3. See also World of the Imagination, pp. 405 and 783, where Brann
expresses her agreement with Freud and Wittgenstein that one can “speak of
what is not, but not depict it.”
4. His self-identification, from Faust pt. 1, lines 1336-8, is quoted on p. 14:
“I am a part of the force that constantly wills evil and constantly effects
good....I am the spirit that constantly denies.” Omitted from the quotation,
though surely Nietzscheans would hold that they are, if not the, an arche of
“nihilism,” are the lines: “und das mit Recht; denn alles, was entste-
ht/ Ist wert das es zugrunde geht;/Drum besser ware es dass
nichts enstunde...” (“and rightly so, because everything that originates
deserves to perish. Wherefore it would have been better if nothing had originated.”)
5. Brann’s use of the Freud essay is filtered through Rene Spitz’s The First
Year of Life and No and Yes. I have not read these books. Therefore I
cannot tell whether her complaint that Freud’s speculations— about what it
was that first prompted the human race’s invention of a “symbol” for negation— fail to include reflection on not as accomplishing “denial of truth or
untruth” is also Spitz’s. “Psychoanalytic theory does not tell whence comes
mature negation and possible truth telling; these may not have a naturalistic
genesis” is the concluding sentence of her account of Freud. What a non-naturalistic account of origins might consist in is not explained.
6. The Second Year: The Emergence of Selfawareness (Cambridge:
Harvard University Press, 1981).
7. This list slights her treatment of double negation, of the logical paradoxes that are generated when negation and self-reference are allowed to combine, of the stretching of the concept of number through the introduction of
negative numbers and zero, and of Kant’s discovery or invention of “directed quantities” (vectors) in the pre-critical essay “An Attempt to Introduce the
Concept of Negative Numbers into Philosophy.” Since these topics are listed
in the well-prepared index, I omit page references.
8. Cf. Metaphysics ix, 1048b1-10
9. The quoted sentence ends with the bracketed remark “...of which the first,
the opposition of oppositions, is surely that of thinking itself to its object.”
This claim makes me uneasy, given the remark, on p. xiii of the Preface, that
“the mysteries and conuncrums of intention—denotation and reference,
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sense and meaning...are happily not within the task of this book.” In my estimation, Frege’s insistence on the need for a Sinn/Bedeutung contrast and late
Russell’s attempt to dispense with it must be discussed by anyone who investigates thinking and speaking and their “objects.” Observe also that conversational exchange is given no role in the account. A quick way of making this
manifest is that, throughout the book, saying “no” is classified or explained
in terms of exercising the will, although it surely figures when answering
what linguists indeed peg as “yes/no questions.”
10. My hunch is that Anscombe’s remarks about “internal” and “external”
negation in her Introduction to Wittgenstein’s Tractatus (see in Anscombe
pp. 31, 34, 35, 46, 47, 51), and her question (p. 53) “...Is the property of
being true or false, which belongs to the truth-functions, the very sam property as the property of being true or false that belongs to the propositions
whose internal structure does not interest us?” is what first prompted Brann
to make the question about the “location” of the negation particle thematic.
11. If we are both looking at the ocean and you say “Majestic!” my guess
that it is the ocean that is said to be majestic is pretty safe. That’s how I mean
“otherwise manifest.”
12. For the somewhat ampler statement of this Fregean type of analysis of
“simple” sentences which is the source of my remarks, see pp.132f,
Anscombe and Geach, Three Philosophers: Aristotle, Aquinas, Frege. Please
observe that although English, which has pretty nearly dropped the use of
case endings, tends to place the name of the topic early in the sentence,classical Greek and other languages that use case endings to express syntactic
structure may, for rhetorical purposes, place it late in the sentence. Note also
that nothing prevents a simple sentence’s having a “complex” topic, for
instance the ordered triple {Athena, Athens, this olive tree}, which is, on one
analysis, the topic of the sentence “Athena gave Athens this olive tree.” When
the topic is so identified, the predicate is “—gave—to—” When the item that
would, in Greek, be in the nominative case is singled out as the name of the
sentence’s topic, the predicate would be “—gave Athens this olive tree.”
What chiefly matters, from a Fregean logical point of view, is the contrast
between proper names (e.g. “Theaetetus”) and concept words (e.g “flies” or
“sits”) as in the sentences “Theaetetus flies” and “Theaetetus sits.” A person
who is unaware that the word “give” is trivalent and the word “fly” or “sit”
is monovalent hasn’t got the hang of the semantics of these concept words.
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Cf footnote 11 below. See further Anthony Kenny’s Penguin volume about
Wittgenstein, pp. 121f.
question (p. 63) “Is Being at the true center of every sentence even if it is
obscured by a predicative verb?”
13. How “simple” is to be understood in this context is, of course, much in
14. In the spirit of Kantian “architectonic,” these ways of negating a sentence
are later (p. 95) brought to bear on lying, so as to yield a classificatory scheme
for lies.
21. I note that there’s a large dose of such “idealist” thinking in Freud’s essay
on negation: “the performance of the function of judgement is not made possible until the creation of the symbol of negation has endowed thinking with
a first measure of freedom from the consequences of repression and, with it,
from the compulsion of the pleasure principle.”
15. In the “dream theory” of Theaetetus 202 the mistake is to suppose that
22. Cf. Aristotle, Metaphysics Bk V, Ch.ll.
sentences consist of nothing but names; earlier, at 190, it looks as though sentences are being spoken of as consisting of nothing but predicate words. For
explicit correction of such “homogenizing” treatment of the constituents of
sentences, see Sophist 262.
23. Peter Geach’s essay “The Law of Exclude Middle” (p. 79, Logic
need of saying.
16. Does “doing logic”/“doing empirical science” exhaust the genus “investigation”? Brann would certainly question this bipartition.
17. “Perhaps the act of negating, which maintains a questionable existence
as the polar opposite of [affirmative] judging, is a chimerical construction,
formed by a fusing of the act of judging with the negation.” (p. 128 of Geach
and Black’s Translations from the Philosophical Writings of Gottlob
Frege, Oxford: Blackwell, 1952).
18. In footnote 54, on p. 69, Brann calls on Anscombe to testify that, as
Brann puts it, the Wittgenstein of the Tractatus, in “rejecting inquiry into
the way world, pictured fact, language, and thought are related” and “pretending that epistemology has nothing to do with the foundations of logic
and the theory of meaning,” made claims that are “fantastically untrue”
(Anscombe, Introduction to Wittgenstein’s Tractatus, (London: Hutchinson
University Library, p. 28).
19. For example, and especially, Kant and Hegel.
20. This sentence continues, after a colon, as follows:”The briefest way to
put the reason why is that thinking speech brings its objects to a standstill
even as it goes about discerning them through their properties. The declarative is expresses at once that transfixing done by thought and the expansion
with which the object of thought responds.” The just cited explication of
Brann’s “introspective” report is tantamount to an affirmative answer to the
Matters, Oxford: Blackwell, 1972) contains a nice exposition of this thesis.
Geach, like Brann herself (e.g., p. 28), exploits Wittgenstein’s metaphor of
“logical space” and the notion of boundary for this purpose. Note, by the
way, that it would be a mistake to assimilate Wittgenstein’s logical space to
Brann’s psychic space, as she describes it on the opening pages of her Preface.
Studying Brann’s, Wittgenstein’s, and the cognitive scientist Gilles
Fauconnier’s uses of metaphors of space would be a delicate but worthwhile
undertaking.
24. See, e.g., What, Then Is Time?, p. 112ff. In other sections of Ways of
Naysaying Wittgenstein continues to be treated as the or a bad guy: He
would, as Brann reads him,want to prevent her and fellow philosophers from
investigating whether there is “some one truth behind [the] many appearances” of, in this instance, negativity (p. xiv and note 11 on p. xvii). In the
chapter on nihilism, Brann approvingly reports that Stanley Rosen has
“shown” that “‘Wittgenstein and his progeny are nihilists because they cannot distinguish speech from silence.’” After the brief quote from Rosen, she
goes on to say: “For [according to Wittgenstein] it makes no difference what
we say. It makes no difference because if, as the later Wittgenstein
says...speech becomes meaningful only in a context of gamelike rules and
conventions and as a ‘form of life,’ then we can never get beyond these and
never receive a sensible answer when we query a conventional usage or conventionalism itself ” (p. 183).
25. I was helped by Anscombe’s version of this last question, which runs as
follows: What right do logicians have to define “not” by telling us that “not
p” is “the proposition that is true when p is false and false when p is true”?
The phrase “the so- and- so” is, after all, legitimate only when there is a soand-so and there is only one such.
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26. Does this word (or its German equivalent), occur in Wittgenstein’s text?
27. It is a striking fact that only Aristotle’s treatment of “immediate inference” is taken up (footnote 7, p. 61) and “syllogizing” omitted. Note also that
in Chapter Three, when dealing with Russell’s account of Definite
Description, nothing is said about the need, in mathematical reasoning, for
the principle of “substitutivity of identicals” or the “principle of existential
generalization.” See Ausonio Marras’ Introduction to his anthology,
Intentionaliy, Mind, and Language (Urbana: University of Illinois
Press, 1972) for some brief remarks about the latter two. When all is said and
done, Brann does not seem to be really interested in formal logic. This is how
I account for her not catching the slip in claiming that “In symbolic logic we
do not enter the propositions as we did in section 2, but take them as primitive, symbolized by p or q, etc.” (p. 43; cf p. 212). She certainly knows that
Frege’s treatment of quantification (analysis of the sense and use of such little words as “all”, “some”, “one,” which is needed for doing predicate calculus) is what is usually singled out as the true “advance” beyond premodern
logic; Stoic logic, though “pre-modern,” had already dealt with the definitions of the logical constants of propositional logic and with its basic argument patterns.
I look as though I’m being a pedant about the history of logic. But that’s really not what I care about. Rather, ever since the days that I heard the World
War II German soldiers who were entering Amsterdam, Holland, sing
“Denn wir alle lieben nur ein Madelein, Annemarie” I have wondered, “Should I feel sorry for that girl, Annemarie, burdened with being
loved by this whole troop of men? Or are there as many Annemarie’s as there
are men in this troop, and each of the girls gets one of the singing men? For
a fine essay on this topic, see Peter Geach’s “History of a Fallacy” in Logic
Matters (Oxford: Blackwell, 1972).
28. I believe this means the not of contradiction.
29. I am not sure how “modern” is meant here: post-Occamist, that is postrealist (in the scholastic sense of that word)? I ask for clarification of the
adjective because I am not certain what, exactly, the systemic import of the
observation is. See footnote 23 on pp. 111ff. See also the remark about the
“inherent nihilism of an absolute nominalism” in her commentary on Wallace
Stevens’ poem “The Snow Man” and the continuation of this thought in her
interpretation of “The Course of a Particular,” p. 170. FootnoteA 3 on p. 199
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claims that “nominalism is one of the philosophical positions adopted by
those for whom disillusionment is a warrant of truth” and concludes with a
remark about the “fanatically honest.” These are, says Brann, the folk who
“take pride in shivering in the metaphysical cold.” The quoted passages
sound—what shall I call it?— dismissive to me. I wish there had been something more nearly like an explanation of what the nominalism/realism issue
is and why Brann favors the realists. Cf pp. 4-6 of W Stace, The
.T.
Philosophy of Hegel (New York: Dover, 1955)?
30. Artifacts no longer in use, like sliderules, or tools for living about which
we learn through literary remains but examplars of which have not been
encountered by archaeologists? I try more nearly to specify the question
because I am confused whether the general question of how we can speak or
think truly or falsely of kinds that are“bygones” is being raised or rather the
question how bygone individuals can be referred to? Cf Wittgenstein’s
Philosophical Investigations ¶79 about the many senses of “Moses did not
exist.” See also G.E.M. Anscombe and P Geach, Three Philosophers
.T.
(Oxford: Blackwell, 1973) pp. 135f about the importance of Frege’s reviving
the scholastic contrast between singular and universal propositions.
“Traditional” logic rides roughshod over the distinction. Geach’s essay “Perils
of Pauline” in Logic Matters is refreshingly lucid and unstuffy on the subject of names and descriptioons (and much else besides).
31. Cf. p. 100: ”What Russell says he means, flatly and irremediably, and
therefore he must be flatly and irremediably wrong: It cannot be the case that
what is said about and within fictions is false—unless one maintains that logically accurate speech has no correspondence with humanly normal speech.
For we say both that it is true and that it is true to life that Natasha Rostov
marries Pierre Bezuhov, and we want to keep on saying just that.”
32. See the splendid appreciation of the Raj Quintet in Brann’s contribution
to the anthology Poets, Princes, and Private Citizens edited by Joseph M.
Knippenberg and Peter Augustine Lawler (Lanham: Rowman and Littlefield,
1996).
33. The special pleasure we take in our own children is not solely due to
their being ours; it has much to do with our knowing them better than most
other people’s children.
34. I worry a little about the rhetorical effects of using the words “pretend”
and “pretense” in lieu of “make believe.” But let that pass.
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35. The novelist Jorge Luis Borges writes somewhere, “[The actor] on stage
plays at being another before a gathering of people who play at taking him
for that other person.” I acknowledge, however, that novels differ from stage
plays, involve (in addition to the things mentioned) some special a deux intimacy between the reader and the book.
36. See for example Playing and Reality, London: Tavistock Publications,
1971 and perhaps also some of the essays about Winnicottt included in the
collection edited by Grolnick and Barkin, Between Reality and Fantasy
(New York: Jason Arons, 1978). I particularly recommend Rosemary
Dinnage’s “A Bit of Light.”
37. As best I recall, Brann does not, when treating of “the lie in the soul” (p.
94), worry about what Freud called repression.
38. I was puzzled that Brann did not reserve space in her book to discuss the
important topic of children’s and grown-ups’ often being uncertain whether
this or that “really happened” and whether this or that named individual
(Satan, Cerberus) or species of entities (witches) “really exists” or not.
Helping children sort out the dreamt from what’s in the public world of the
awake is among our parental responsibilities. Thus “...does not exist” seems
to me to hold as important a story as is that about the being of non-beings.
39. Cf Epinomis 990 on that mere farmer’s almanac, Hesiod’s Works and
Days?. Parmenides reputedly was the first to propose that the moon shines
by the sun’s reflected light and that the earth is a sphere; also, that the
evening and morning stars are one and the same. I therefore keep hoping for
a reading of his poem that will show that its episteme/doxa contrast has
astronomical meaning. But no such reading is endorsed by Brann.
40. These sentences allude, of course, to Aeschylus’ Oresteia and Sophocles’
Oedipus at Colonus. This well illustrates the dramatizing vividness of Brann’s
ontological discourse.
41. Cf The World of the Imagination p. 389ff. and Jacob Klein, Greek
Mathematical Thought and the Origin of Algebra (English version,
Cambridge: MIT Press, 1966), p. 82 and A Commentary on Plato’s Meno
(Chapel Hill: University of North Carolina Press, 1965), p. 114f.
42. Corresponding to the afternoon of the day on which Man was created,
male and female, in God’s image? Yes, of course I am joking in playing with
the numbers. But I am not just joking: The chapters in Genesis that tell in
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detail how man became man (chapters 2, 3, 4) hold a plethora of negation
words, whereas the opening chapter lacks all negativity.
43. If there is an explicitly stated definition of the word “nihilism” in
Chapter Six, I need to have it pointed out to me.
44. Cf. Eva Brann, “The Music of the Republic,” St. John’s Review, volume xxxix, numbers 1 and 2. Se especially pp. 75,6.
45. Cf. the discussion of “opinion” on pp. 38ff of “The Music of the
Republic.”
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107
The Potent Nonentity: A
review of Eva Brann’s What,
Then, is Time?
Torrance Kirby
Time, Augustine claims, is so ordinary as to be impossibly
difficult (Conf. XI.14). This is the paradoxical theme to which Eva
Brann returns often (one is tempted to say “time and again”) in her
remarkable, recently published volume What, Then, is Time? Time,
the “potent nonentity,” proves to be as elusive a quarry as the
Sophist himself. The inquiry begins with a high sense of wonder
peculiarly fitting in this of all philosophical quests. The inner experience of time and its foundation or ultimate ground, constitute the
heart of this investigation. Brann employs an extended, highly elaborated aporetic approach to the search for a definition. So numerous and complex are the poriai encountered that this Protean
beast is not pinned down with a definition until well into the closing chapter of the book. The investigation as a whole is composed
in the form of a diptych with one larger panel devoted to the study
of various selected texts or “presentations” by philosophers who, in
Brann’s estimation, “have written most deeply and most engagingly about time.” A second smaller panel contains the author’s own
“reflections” on the matter. She is careful to point out, “study and
thought, though not of necessity incompatible, are by no means the
same” (159). This book is worthy of the most careful reading with
both ends in view.
The predominance of the prolegomena in this investigation is
consistent with the spirit of much contemporary, postmodern
inquiry. Brann’s approach is underscored by the splendidly postrevolutionary claim that her purpose is “not to change the world
but to interpret it!” Viewed in another light, however, the methodology of this book is resonant with the very best ancient authors,
Eva Brann. What, Then, is Time? Lanham, MD. Rowman and Littlefield, 1999.
Torrance Kirby is an assistant professor at McGill University.
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and its hermeneutical approach reminiscent of Aristotelian science.
The first part of the book, a study of earlier philosophical “presentations” of time, constitutes a “history” such as one finds at the
outset of many of Aristotle’s treatises. Brann’s study of the
attempts of her predecessors to define time is thus by no means any
ordinary history. Her extensive review of the preeminent contributions to the hermeneutics of time clarifies wonderfully the question concerning time and enables the reader to make the great
ascent from mere study to thought. In the “reflections” of the second part, Brann proceeds intrepidly to face the question “what,
then, is time?” head on.
Discussion of the “lisping” efforts of predecessors (Metaph.
A.1) in this chase turns out to be a daunting task. The relevant texts
range “from the hard to the hellishly hard,” as Brann puts it. As in
an Aristotelian “history,” the texts are selected with a view to clarification of certain key facets of the problem of definition. Four crucial theories about the nature of time are addressed through the
study of four pairs of philosophers. The originality of Brann’s
approach is striking. The unexpected pairings - Plato and Einstein,
Aristotle and Kant, Plotinus and Heidegger, Augustine and Husserl
- prove to be both inspired and illuminating. An important element
of Brann’s purpose in this approach is to demonstrate that the larger questions about the nature of time are themselves by no means
“time-bound.” By pairing the authors in this way Brann ensures that
the problem of definition predominates over less important considerations. The first approach to the theory of time, as exemplified by
the arguments of Plato’s Timaeus and Einstein’s Special Theory of
Relativity, proposes that time is “external,” namely that time refers
to external motions of which it is the measure, as in the case of a
clock’s measurement of the diurnal rotation of the sun. (The consideration of time as the “externality” of history and its movements
is mercifully ruled outside of the present inquiry.) In the cosmos of
Timaeus, time is the very intelligibility or “numbering” of the external motion of the visible heaven. As Brann puts it, this identification
of time with phenomenal motion continues to “bedevil” the dis-
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course of physics. Einstein displays little interest in the essential
nature of time, but is absorbed rather by the question of quantifying time owing to complications arising from the implication of
temporality in locomotion. After the fashion of the hunt for the
wily Sophist in the Platonic dialogue of that name, the consequence
of this initial “presentation” of a definition of time is to introduce a
dichotomous division - namely between time in the world and time
in the soul - which is of considerable use to Brann in advancing her
own quest for an acceptable formulation. The boundaries have been
narrowed considerably by the exclusion of merely “external” time
as a fallacy.
Before proceeding to the presentations of internal time, Brann
examines a pair who propose highly speculative accounts of the
generation of time out of space. Hegel’s dialectical exposition of the
genesis of time out of space is put forward by Brann as possibly the
most profound of all treatments of “external” time. For Hegel, time
from its first genesis as a pure Becoming, behaves like incipient spirit (Geist): “Time is the Concept itself that is there and which presents itself to consciousness as empty intuition. For this reason Spirit
necessarily appears in time, and it appears in time just as long as it
has not grasped its pure Concept, that is, has not annulled Time”
(Phenomenology ¶ 801). Through a discussion of Bergson’s mission
to suppress “extensive space” in favour of “intensive time” Brann
effects a transition to the second principal stem, viz. internal time
or “time in the soul,” which is the general focus of the remaining
three pairs of texts in the series of presentations.
With her examination of the theories of Aristotle and Kant,
Brann arrives at the second crucial stem of the dichotomous division of time into the categories “external” and “internal.” Although
for Aristotle motion is properly the “substrate” of time, while conversely for Kant time is itself the ground of motion, both philosophers are “driven” to relate the notion of time to a “psychic counting.” As Aristotle says, “time is the number of motion” where
motion is understood as disclosing continuous magnitude. The
“truth” of time resides in the numbering or counting soul that meas-
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ures the before and after of this magnitude. Time, according to this
presentation, is no longer viewed as an independent, “substantive”
reality or but is rather reduced to the status of an accident or predicate which exists “for thought.” For Brann, Kant’s treatment of
time displays a deep affinity with Aristotle’s on this more general
level. The internal sense of time, however, represents much more in
the Kantian metaphysics than ever dreamed of by Aristotle. For
Kant this psychic counting is perhaps the most intimate characteristic of humanity. Indeed Brann shows that Kant’s treatment of time
is most accessible when the Critique of Pure Reason is viewed as “a
new founding of human nature whose centre is time” (55).
Appearances may be removed from time but not the reverse, which
reveals that time, for Kant, is prior in the order of knowing; the
apprehension of change is understood to depend upon the a priori
intuition of time. In one of numerous penetrating aperçus scattered
throughout the discussion, Brann draws attention to Kant’s
nonetheless restricted view of our ability to know ourselves as temporal beings by reminding us of his low opinion of music. This, in
turn, is contrasted with Leibniz’s opposing exaltation of the unconscious counting of the soul in music as “a pleasure given to us by
God so that we may know of him; in music soul is revealed to itself
and God to it” (Principles of Nature and Grace ¶ 14).
In the subsequent paired “presentations” of Plotinus and
Heidegger, the inquiry proceeds to consider the “ground” of temporality—that is, of some higher, possibly transcendent source of
this inner sense of time. Thus the dichotomous division of the
“hunt” advances to a new level of precision. For both Plotinus and
Heidegger, as Brann shows, time constitutes the “deepest condition” for humanity. Plotinus identifies time with specifically
“human” being in its manifestations of a peculiarly ecstatic nature,
by the human’s attempt to escape the element of its temporal fallenness. The Soul’s very “appetite for things to come” (Enneads III.
7.4, 34) keeps her in her fallen state. Temporal being strives for salvation, viz. the overcoming of temporal “dispersion,” through
union with the eternal hypostasis above. Happiness, understood as
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“the flight of the alone to the Alone,” is thus altogether outside
time, for it is no mere mood or emotion, but rather a fundamental
possibility for the soul, that of an undispersed present even beyond
being (Enneads I. 5.7, 15). Time is made explicable through eternity, its original ground. Although radically distinct from Plotinus
with respect to virtually the entire substantive content of his
thought, Martin Heidegger at least shares with Plotinus the supposition that temporality is the key to understanding human existence.
As a being whose essence is its existence, this ultimate ground is for
Heidegger not the transcendent eternity of the Plotinian Primal
Hypostasis, but rather the temporality of human being itself,
Dasein. The discussion stemming from this remarkable dialectical
pairing of Heidegger and Plotinus is particularly illuminating.
In chapter four Brann arrives at her final pairing of Augustine
and Husserl with the observation that no two philosophers are both
further apart and closer together. Through an examination of their
discourse on time as a temporal “stretching” of the soul (distensio,
as Augustine puts it), the argument—for it is indeed an argument—
acquires a distinctly sharper dialectical edge. The coincidence of
identity and difference in their thinking about time is uncannily
appropriate to their strongly dialectical approaches to the quest to
define time. According to Brann, while Augustine sifts through the
phenomena in search of existence and while Husserl neutralizes
existence in order to find the phenomena, both look within themselves for the phases of time, that is to say, for past, present, and
future. For both philosophers, Brann argues, the problem of “internal” time is not to be referred to a higher ontological ground for
resolution, as is the case with Plotinus, for example, but rather time
is to be understood as arising out of and discerned within the soul
or consciousness. Brann’s argument on this point is open to some
dispute, at least with reference to Augustine if not to Husserl.
Perhaps the device of pairing the presentations has led to a downplaying of Augustine’s affinity with Plotinus. It is common among
contemporary existential readings of Augustine to de-emphasise his
dependence upon Neoplatonic metaphysics. He begins his presen-
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tation on time with the “in principio” of Genesis 1, the revelation
of the divine creative activity understood as totally beyond the temporal, narrative realm of human existence. In making his transition
in Confessions from Book X on memory to Book XI on time,
Augustine shifts gears as it were from looking within at the phenomena of consciousness to looking above at the higher ground of
the life of the soul, ab interiora ad superiora. The Creator, who is
altogether above the flux of becoming, is understood nevertheless
by Augustine to be present, knowing, and active within the temporal realm.
While temporal human existence, dispersed or “distended” as
it is through phases of past, present, and future, is to be contrasted absolutely with the undivided existence of “the One,” Augustine
finds nonetheless within the soul as imago dei a positive image of
the activity of God in creation. The enigma of the human experience of time is thus referred by Augustine to the exemplar of the
Trinity for resolution. In the psychological image of the Trinity—
memoria, intellectus, et voluntas—Augustine finds a model for his
reflection upon the experience of time as at once continuous and
without extension. He points to the chanting of a psalm as a potent
revelation concerning time. He reflects upon the recitation of a
song that he knows, Ambrose’s hymn Deus Creator Omnium. The
song is stored in memory, an already completed whole which the
soul intends to sing. Before singing, the soul’s expectation possesses the complete song. As the soul sings, the relation of expectation
to memory shifts syllable by syllable until the entirety of expectation has finally become a memory of the song as completed, as having been sung. Memory, presence, and expectation are united in
the song. Through the singing of praise, itself a mode of confession, Augustine begins to see how the timeless and the temporal
become one. Through song the soul is enabled to think the divine
object in the image, and this, Plotinus certainly would regard as the
most extreme absurdity. Thus, by “collecting” ourselves, we can
escape from our temporal constitution into God’s “standing Now,”
as Brann puts it, into eternity.
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113
Brann concludes the part devoted to presentations of time with
an extensive and complex analysis of Edmund Husserl’s phenomenological treatment of internal time-consciousness. The text of
Husserl’s Zur Phänomenologie des inneren Zeitbewußtseins we
owe, Brann tells us, to Edith Stein’s supererogatory editing of various manuscripts and notations. By way of a background sketch,
Brann offers a helpful introduction to Phenomenology itself and
looks at the influence of Augustine, William James, and Franz
Brentano on Husserl’s reflections upon time. Husserl is particularly
engaged with the problem of integrating the phases of time. Brann
claims that he in fact “solves the problem of relating the present, the
moment of primary perception to its immediate retentional past
and protentional future by giving a model for the orderly sinking
away of perceptions and their intertwining with present consciousness” (160). With Husserl, the presentations have in a certain sense
come around full circle. Husserl brings his account of time to completion by reconstituting “external” time in the form of an absolute
temporal flux which transcends the temporal phenomena of internal time-consciousness and which is, moreover, the underlying principle which sustains human subjectivity. As Brann concludes,
Husserl’s ultimate temporal flux is “a very nearly inarticulable final
fact” (156).
In the Second Part of the book, titled “Reflections,” Brann purports to finally face the question “What, then, is time?” (The claim
that the “Presentations” are a mere exercise in “study” and that
only now, in the final pages is she going to roll up her sleeves and
get down to the serious business of “thought” seems not entirely
ingenuous. Already a good deal of hard thinking has gone into
both the pairing itself and the ordering of the pairs, all of which
serves to advance the quest for a definition.) The reflections proceed with a consideration of certain formal similarities between
time and the faculty of imagination - here, once again, is the
Sophist and the wedding of Being and Nonbeing. Brann shows that
images present a relatively constant picture, viz. Being and
Nonbeing in fusion, while time, on the other hand, is a flux of
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THE ST. JOHN’S REVIEW
“Being as passing over into Nothing and Nothing as passing over
into Being” (Hegel, Phil. of Nature ¶ 259). Time and imagination
are thus connected with one another through the way Being is
related to Nonbeing in both temporal process of becoming and in
images. As might well be expected, Brann offers a fascinating comparison of these concepts by building upon her previous exploration of the faculty of imagination.2
There follows Brann’s own interpretation of the phases of time
together with their appropriate faculties: past and memory, future
and expectation, present and perception. Throughout, she draws
upon the foregoing presentations of time by the philosophers which
provide both the categories and a vocabulary which enable Brann to
penetrate the question deeply and swiftly. This section of the book
is a wonderful demonstration of the dictum of Bernard of Chartres
who claimed to be able to see things far off by virtue of “standing
on the shoulders of giants.” In an interesting and frequently amusing section Brann proceeds to analyse various “time pathologies” as
forms of “phase-fixation.” Here we have an opportunity to reflect
on aspects of time’s “brutal tyranny,” e.g. the contemporary idolatry of novelty, a fixation on the “just now,” the trivialising of the
past in nostalgia or the future obsession of the IT phenomenon.
Brann even reviews cures for these time-induced pathologies such
as that offered by Nietzsche in his teaching on the Eternal
Recurrence of the Identical. Brann counters this frantic cycle of
reincarnation with another, much more attractive option, namely
the concept of Aevum, as manifest in the sempiternity of the angels
in heaven or, alternatively, in the fictional temporality of the novel.
All of this is delightful. Brann recommends the cultivation of “aeveternity” as at least “a partial relief for our temporal ills.”
In the last chapter of the book Brann moves closer to the final
struggle with the definition of time by way of a via negativa. Here
time is finally unveiled as the potent, indeed tyrannical, non-entity.
The revealing is apophatic. Time is not external motion, nor is it an
abstraction from process. It is not a power or force, nor a “fungible
substance” (i.e. time is not even money!). Time is certainly not a
KIRBY
115
mere linguistic usage. As Brann succinctly puts this point,
“Language can guide thought but it cannot constrain it.” (Brann
notes in passing how neatly the distinctions of philosophical inquiry
concerning time seem to turn up in the problems of linguistics.)
Time is not Dasein. Whereas Heidegger regards human finitude as
ultimately expressed in the fact our mortality, that our existence is
“destined” to end, Brann counters optimistically that human finitude is better sought in the fact that we begin, “we do not temporalize ourselves; we are born temporal.” Time is no determinate
being; it is not perceived by the senses, it is without external effects,
and elusive to insight. Time is therefore a non-entity. Though
apparently nothing, time’s “not-being” is nonetheless very powerful
(although, be it noted, not “a power”). “What, then, is time?” Here
the argument finally shifts from marked apophasis to a more kataphatic note. The affirmative definition comes in nine-fold form (a
touch which no doubt would have pleased Pythagoras). It is not this
reviewer’s intent, however, to spill the beans. In order to reap the
full benefit of Brann’s final, dramatic unmasking of Time—to be
altogether “present” as it were at the capture of this elusive beast—
readers are well advised to follow the leader of the hunt herself
along the trail through all its intricate twists and turns. And who
indeed are the intended participants in this quest? Brann recommends her book to anyone who longs to learn about time by pursuing the quest described above, to aficionados, to students who
seek to come to grips with some of the primary texts on time, and
finally to teachers who might be on the look-out for some tips on
selections for a syllabus on the interpretation of time. This is an
unusually difficult book whose author challenges the reader to “take
note” and whose rewards are proportionate to the investment of
careful, punctuated attention.
NOTE:
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1. See Eva Brann, The World of the Imagination: Sum and Substance
(Lanham, MD: Rowman and Littlefield, 1991).
117
The Feasting of Socrates
Eva Brann
Before reviewing Peter Kalkavage’s Focus Press translation of
the Timaeus for the St. John’s community, I must, in all fairness,
confess my partiality. He, Eric Salem, and myself were the cotranslators of Plato’s Phaedo and his Sophist for the same publisher.
Together, over several years, we worked out some principles of
translation which are discernible in this Timaeus version. In fact, I
think the three of us would welcome with some glee the notion of
a St. John’s school of translation. For we wanted to be working very
much with the spirit of the Program and a possible use by our students in mind. We thought that translations of Plato should render
word for word, even particle for particle, with the greatest exactitude, what the Greek said, avoiding all interpretative paraphrase,
craven omissions, and latter-day terminology. But we also stipulated that they should catch the idiomatic expressiveness and the
changing moods of the original. These principles are clearly at work
in this rendering of the Timaeus.
We learned as well, however, that each dialogue is a unique universe of discourse, the artful representation of an inquiry with its
own approaches, terms, settings, and above all its own participants,
each of whom is in a mood specific to this never-to-be-repeated, yet
ever-to-be-continued conversation. Thus it follows that the Timaeus
made its own particular demands on the translator. It is, after all,
less a dialogue than a short tale of antiquity by Critias followed by
an account of the cosmos by Timaeus—a long one. The familiar
voice of Socrates falls almost silent as these speeches are made to be
a feast for his enjoyment—or, perhaps, amusement. Timaeus’s cosmology is full of the sort of technical matter Socrates does not scruple to spoof in the Republic—the very dialogue which establishes
the sort of ideal city that his companions agree to bring to moving
life for him by giving it its historical and cosmological setting.
Peter Kalkavage, Plato’s Timaeus. Newburyport, MA: The Focus Philosophical Library (2001).
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THE ST. JOHN’S REVIEW
Timaean cosmology involves not only the moving spheres and circles that bear the astronomical bodies and the geometric elements
from which they are constituted, but also the musical “harmonies”
(scales) that ensoul the heavens. Three beautifully clear appendices
provide the reader—and this edition is meant for the “adventuresome beginner”—with the fairly elementary knowledge needed to
enjoy this heavenly entertainment. It should be said, though, that
the cosmological astronomy of the Timaeus together with its sober
mathematical exposition in Ptolemy’s Almagest was the serious science that stood behind the New Astronomy of the dawn of modernity. (There is a story—I cannot vouch for its truth—that in the
early days of the St. John’s Program books of astronomy and
physics were to be found in the library ranged under “Music,” courtesy of the Timaeus.) The dialogue is so full of Greek science that
there is a danger of regarding it as a source of antiquarian problems.
But, the translator observes in his Preface, that is the very danger,
the one of reducing the cosmos to a collection of mummified facts
and recondite puzzles, to which the Egyptian priests are said to fall
prey. So less is more by way of learned exegesis, and the well-illustrated appendices give just enough to make the dialogue intelligible
to an amateur.
Since I’ve started at the back, let me say that here too you will
find an English to Greek glossary. The entries tell not only how a
Greek word is translated and, if more than one translation has to be
used, why that is necessary, it also gives the root or central meaning
and others that flow from it. In sum, the entries are a pretty interesting lesson in philosophic Greek.
To go to the front end of the book, there is, besides the Preface,
the Introductory Essay. The Timaeus, the only Platonic dialogue
known in medieval times and in all epochs the most influential one
among those philosophers to whom the constitution of the cosmos
was of central interest, is also, in Peter Kalkavage’s words, “the
strangest of Plato’s dialogues. It is so strange that one wonders
whether anything can be taken seriously . . . . [It] is strange not only
to us but also in itself.” The Introduction is intended to illuminate
BRANN
119
that strangeness without dispelling it. The odd but necessary question is pursued: What is the Timaeus about? Socrates is all dressed
up (kekosmenos) and in a strange mood. He gives a truncated, philosophy-free version of his Republic and asks to be told about this
stripped-down political blueprint mobilized to go to war. The
resulting verbal feast prepared for him among the three eminent
men who are present (one mysterious fourth is absent) has an oddly
skewed relation to the truth and the love of wisdom that are
Socrates’ normal preoccupation, for it is presented as a “likely
story,” and a story of likenesses, the way of being that is so dubious
for Socrates.
The festivity begins with Critias’s retelling of an antiquarian
tale about archaic Athens as told by the Egyptian priests to the visiting lawgiver of Athens, Solon. We hear that this old Athens,
ancient even to the ancients, once defeated a huge and sinister
island empire called Atlantis.* Critias thus presents a pseudo-historical Athens as the embodiment of a “pale image” of the Republic.
There is plenty to puzzle about in this beginning.
For this city Timaeus supplies the cosmic setting; we are invited to wonder how fitting it is. A divine craftsman appears out of
nowhere and makes the cosmos, the well-ordered beautiful world,
in the image of an original model. Hence the cosmos has two wonderful features. It is a copy and thus, while imperfect in its being,
capable of being in turn a model, as it indeed is in the dialogue. And
second, it is intelligible, interpretable, not only as an intentionally
made work of art, but as en-, or rather, circum-souled. For whereas the human animal has its soul within, the cosmos is encompassed
by bands of soul matter. All these wonderful and significant doings
can be read in the dialogue, but the Introduction brings out their
thought-provoking strangeness and their relevance to our humanity.
Thus after the cosmic construction there is a harsher “Second
Founding.” It has an elusive “wandering cause,” the “source of
power as opposed to goodness”—an intra-cosmic, semi-intractable
cause called “necessity” acting in a scarcely intelligible theater of
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THE ST. JOHN’S REVIEW
operation, space. Within it arise body and the human animal: “The
making of man for Timaeus is a pious desecration,” says the
Introduction. It is delegated by the Craftsman-father to his starsons.
This part of the Timaeus, the coming-to-be of organic life within the cosmos, is so weird that our undergraduates aren’t even asked
to read it, yet Peter Kalkavage shows how to begin to make humanly applicable sense of it.
Finally he returns to the question: “Why is the greatest philosophical work on the cosmos framed by politics?” An answer is suggested: The frame signals Plato’s reflection on what happens when
the Socratic search for truth is replaced by a Timaean will to order.
But this shift to the constructive will might well stand for the revolution that initiated our modernity. The means to this new age are
also adumbrated in this miraculous dialogue; in his final assessment
of the Timaeus Peter Kalkavage says that “the likely story presents
the paradigm of what it would mean to use mathematical structures
to make flux intelligible—at least as intelligible as possible.”
Twenty-one centuries later the calculus will perfect these structures,
and so the science by which we live and which Plato has prefigured
will really take off. Read this introduction to get a sense of what it
means for a work to be great, to see deep into things and far into
time.
But better yet, read the splendid translation framed by the valuable apparatus. It is trustworthy; it sticks close to the text, word for
word. But it is also readable—not translaterese but good, lively, and
flexibly intoned English, since faithfulness in translation includes
preserving something of the literary quality of the original. This dialogue in particular is, for all the wild exuberance of its philosophical imagination, written in fresh, plain Greek, though plain terms
are often put to novel uses.—Would you expect to find Being,
Becoming, Same, Other, ordinary words with a gloss of high philosophy, in a cosmological context? Perhaps the best example is the
divine Craftsman. As the translator points out in the glossary, the
Greek word, which has passed into English as “demiurge,” merely
BRANN
121
means a skilled worker available for orders from the public, so it
was just right to preserve that sense with the plain English word. To
help with background knowledge, there are lots of footnotes right
on the page.
Here’s my recommendation, then: We have all these wonderful
alumni seminars around the country. Why not devote one here and
there to a reading of the Timaeus?—And perhaps some participants
might take advantage of Peter Kalkavage’s translation (which is,
incidentally, purposely inexpensive). I’d love to come and help, and
so, I imagine, would he.
*I can’t resist a footnote.
In our own last century, there have been droves of people,
many of them now active, who have fallen into Plato’s antiquarian
trap and gone in search of this lost continent. The description of the
island, which enormous geometrically planned public works have
transformed into something formidably awful, is set out in the dialogue Critias. Its Speer-like architecture (Speer was Hitler’s architect) appealed to the Nazis, whose mythmakers represented Atlantis
as an early Nordic utopia, to be rediscovered by state-sponsored
archaeologists. These people had at least got it right with respect to
the scariness of the drawn-and-quartered, brass-walled locale. Most
modern representations, be they in books, songs, or movies (of
which Disney’s “Atlantis” is the latest) are governed by the mistaken notion that Atlantis was meant to be a lost place of marvels and
beauties, a sort of mid-ocean Shangri-la. It’s actually a totalitarian
topography, the triumph of the will over nature.
�
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<em>The St. John's Review</em><span> is published by the Office of the Dean, St. John's College. All manuscripts are subject to blind review. Address correspondence to </span><em>The St. John's Review</em><span>, St. John's College, 60 College Avenue, Annapolis, MD 21401 or via e-mail at </span><a class="obfuscated_link" href="mailto:review@sjc.edu"><span class="obfuscated_link_text">review@sjc.edu</span></a><span>.</span><br /><br /><em>The St. John's Review</em> exemplifies, encourages, and enhances the disciplined reflection that is nurtured by the St. John's Program. It does so both through the character most in common among its contributors — their familiarity with the Program and their respect for it — and through the style and content of their contributions. As it represents the St. John's Program, The St. John's Review espouses no philosophical, religious, or political doctrine beyond a dedication to liberal learning, and its readers may expect to find diversity of thought represented in its pages.<br /><br /><em>The St. John's Review</em> was first published in 1974. It merged with <em>The College </em>beginning with the July 1980 issue. From that date forward, the numbering of <em>The St. John's Review</em> continues that of <em>The College</em>. <br /><br />Click on <a title="The St. John's Review" href="http://digitalarchives.sjc.edu/items/browse?collection=13"><strong>Items in the The St. John's Review Collection</strong></a> to view and sort all items in the collection.
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Russell, George
Kraus, Pamela
Brann, Eva T. H.
Carey, James
Ruhm von Oppen, Beate
Sachs, Joe
Van Doren, John
Williamson, Robert B.
Zuckerman, Elliott
Phillips, Blakely
Sachs, Joe
David, Amirthanayagam
Berns, Lawrence
Maschler, Chaninah
Kirby, Torrance
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Volume XLVI, number two of The St. John's Review. Published in 2002.
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