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                    <text>Blumenthal 1

The Role of Mathematics in Advancing the Goals of a Liberal Education
by
Robert Blumenthal
Mathematics appears in some form or other in the core or general education requirements
of most colleges and universities, and a lot of energy is often expended regarding the specific
form this requirement should take. For example, one thorny issue is just what level of
mathematics should be required. Should it be sufficient merely to demonstrate proficiency in
algebra thus basically requiring of students no more than they were supposed to learn in high
school? Or should every student be required to take a bona fide college level course like
calculus? Furthermore, what do we want the students to take away from the required course? Is
our goal to demonstrate just how useful mathematics is in dealing with worldly matters and how
indispensable it is with regard to understanding and interpreting real-world data and solving realworld problems?
With regard to the first question, namely, is proficiency at the high school level sufficient
for meeting the core math requirement at a university, the answer has to be no. Certainly, we
would hope to provide students with content and approaches which do more than merely
replicate the high school experience. A student who has had four years of high school
mathematics and who, therefore, has taken geometry, algebra, and in most cases a course
covering standard precalculus topics should be offered an opportunity for intellectual growth
which goes beyond a mere rehash of techniques studied in high school. Which leads to the
question: just what type of intellectual growth are we talking about? Yes, mathematics is useful.
Yes, it solves all sorts of technical problems. Yes, it enables us to analyze and interpret various
kinds of real-world data. Yes, it enables us to model real-world situations and to understand and

�Blumenthal 2

address a large variety of real-world issues. Is this the focus which we wish to emphasize in our
core mathematics experience, or is there perhaps another direction we might take with regard to
intellectual growth and development, particularly in a liberal arts institution?
I have repeated the phrase real-world because I think we do our students a disservice by
focusing exclusively on the worldly aspects of mathematics. As Wordsworth reminds us, “The
world is too much with us…” And he concludes:
For this, for everything, we are out of tune;
It moves us not.--Great God! I'd rather be
A Pagan suckled in a creed outworn;
So might I, standing on this pleasant lea,
Have glimpses that would make me less forlorn;
Have sight of Proteus rising from the sea;
Or hear old Triton blow his wreathed horn. (Appelbaum 28)
It is that phrase, glimpses that would make me less forlorn, which is the key. At its heart,
mathematics has nothing to do with the world. Its efficacy in understanding the world and in
solving real-world problems is a fact, but this utility is a by-product rather than the central
motivation behind the creation of mathematics. Mathematics offers glimpses - glimpses of the
reality which underlies the physical realm, glimpses of the way in which our minds function and
the ways in which we process ideas and the relationships between those ideas, glimpses of the
role and limitations of language as vehicles for thought and the expression of ideas, glimpses of a
beauty unlike any other leading to an aesthetic experience which rivals that of anything offered
by the other fine arts.

�Blumenthal 3

What do we mean when we say that mathematics has nothing to do with the world? This
requires some attention. First, what is mathematics? Definitions can be tricky things. A
colleague once suggested to me that “mathematics is what mathematicians do.” The English
biologist T.H. Huxley offers a definition which is a bit more enlightening by noting that
“[mathematics] is that [subject] which knows nothing of observation, nothing of experiment,
nothing of induction, nothing of causation” (qtd. in Moritz 26). Notice that this definition
describes mathematics by telling us what it is not. Observation, experiment, inductive reasoning
(drawing general conclusions from specific cases) -- these play no role in mathematics. In a
word, mathematics is not science. The truth claims of mathematics in no way depend on
observations of the world. Rather, the reasoning involved is deductive (reasoning from the
general to the specific) and depends only on our rational faculties. This leads to a very
provocative definition formulated by the English mathematician J.J. Sylvester who, in
contrasting mathematics and science, states that “the object of pure Physic is the unfolding of the
laws of the intelligible world; the object of pure Mathematic that of unfolding the laws of human
intelligence” (qtd. in Moritz 7). In other words, mathematical knowledge is self-knowledge. It
tells us something of how we as human beings think, how our minds work, how we process
ideas, and it demonstrates our natural propensity for finding connections between seemingly
unrelated concepts.
At its root, mathematics deals with the most basic of human propensities, namely,
collecting things and thereby forming a collection. Mathematics is about collections, and the
mathematical term for this is set. A set is a collection of objects, and we can then think of the set
as a single entity. Forming a single entity out of a disparate collection of objects is the essential
mathematical act. E Pluribus Unum. Out of many, one. Every mathematical concept, including

�Blumenthal 4

numbers, rests upon the notion of a set. There are two kinds of sets: finite sets and infinite sets,
and infinite sets are central to just about every important mathematical theory. The simplest
infinite set to grasp of the set of all positive whole numbers, what mathematicians call the natural
numbers, N = {1, 2, 3, …}.
In a series of papers published in 1874, the German mathematician Georg Cantor
undertook the first serious attempt to understand the nature of infinite sets. In particular, he
wanted to understand whether or not we could meaningfully talk about the size of an infinite set
and whether it is possible to compare the sizes two infinite sets. He asks whether all infinite sets
have the same size, and, as a first step in addressing this question, he looks at the natural
numbers and the seemingly larger set of all whole numbers (positive, negative and 0), known as
the set of integers. Via a very simple and elegant argument, Cantor demonstrates that the set of
integers is no larger than the set of natural numbers. It appears to be a larger set, but that is an
illusion. In fact, these two sets have the same size.
Cantor then turns his attention to the set of rational numbers, namely, the set that consists
of all whole numbers together with all fractions. This appears to be an incredibly huge set and
one which certainly dwarfs the set of natural numbers. However, in one of most remarkable
proofs in all of mathematics, Cantor shows that this apparent disparity in size is again an illusion
and that the set of rational numbers has the same size as the natural numbers. This result and
proof is one of the most famous and beautiful results in all of mathematics.
At this point, it is beginning to look as if the answer to Cantor’s question is yes, all infinite
sets have the same size. However, Cantor’s most celebrated result, and the one which has deep
implications for mathematics and philosophy, is that the answer is in fact no. He exhibits a set,
namely the set of real numbers, which is so large that it no longer has the same size as the natural

�Blumenthal 5

numbers. Infinite sets come in different sizes. There is not a single undifferentiated notion of
infinity since some infinite sets are truly larger than others. This result completely changed
theory of sets and, since sets lie at the heart of mathematics, all of mathematics as well. Prior to
Cantor, going as far back as Aristotle, the very idea of an infinite set was rejected. The idea was
rejected because it led to various unpleasant consequences, like the fact that a part can be
equivalent to the whole. This is nonsense and so the very idea of the existence of infinite sets
must be nonsense.
However for Cantor, infinite sets exist. The set of natural numbers exists as an actually,
not just potentially, infinite set, and we can hold in our minds in a single instant of time the
collection (i.e., set) of all natural numbers. Yes, this leads to certain startling consequences like
the fact that a part can be equivalent to the whole. But the reason we are startled is because we
are expecting infinite sets to behave the same as finite sets. This is an unreasonable expectation.
Infinite sets are fundamentally different from finite sets and we can’t expect them to behave in
the same way. We are in a brave new world where a part can be equivalent to the whole and
where some infinite sets are truly larger than others. This is not unlike the situation ushered in
by the theories of general relativity and quantum mechanics where we are confronted with
behavior which runs contrary to common sense and everyday experience.
Having proved that the set of real numbers is of a truly larger size than the natural numbers,
Cantor wondered just how much larger it is. Is the set of real numbers the next largest set after
the natural numbers or is there something in between? In other words, is there a set which fits in
between the natural numbers and the real numbers in the sense that it is of a larger size than the
natural numbers and of a smaller size than the real numbers? Cantor spent the rest of his life
looking for the answer to this question. He felt strongly that the answer is no, but he was unable

�Blumenthal 6

to prove this conjecture. This question, which is known as the Continuum Hypothesis, was
singled out by the German mathematician David Hilbert at the International Congress of
Mathematicians held in Paris in 1900 as the most important question which mathematicians must
address in the new century (413).
And address it they did, although the eventual outcome of this endeavor was something
which no one had expected or even considered. Results proved by Kurt Gödel in 1940 and Paul
Cohen in 1963, taken together, show that the Continuum Hypothesis can neither be proved nor
disproved. In other words, the Continuum Hypothesis is undecideable within the present
axiomatic foundation of mathematics. Thus, while opening up whole new areas of human
thought with his theory of infinite sets, Cantor’s work forces us to confront the fact that there are
certain fundamental limitations on our capacity for understanding and that the answers to
compelling foundational questions are simply unknowable by the human mind.
One of the weaknesses of many of the courses aimed at the general student is that all too
often they morph into either a math appreciation course or a math history course thereby
transforming the experience into something other than a course in mathematics. Even if this
situation is avoided, another pitfall is that many such courses are survey courses organized
around a multitude of topics. As such, each topic receives only superficial treatment and the
student misses the essential experience of delving deeply into an important mathematical theory.
I have sought to avoid both of these situations and have taught for many years a course organized
around a few (at most three) selected topics in advanced mathematics.
These topics must be chosen carefully and, in my experience, need to meet several criteria.
Each topic must be one which the students have not encountered before and must represent a
truly important mathematical idea. Each topic should be modern in the sense that it originated

�Blumenthal 7

relatively recently and is an active area of continuing research. Finally, each topic must be able
to be presented to the general student without loss of mathematical rigor. This last point is
particularly important since the whole point is to convey a meaningful sense of the mathematical
experience. I have had considerable success in this course with topics chosen from number
theory, group theory, and Cantor’s theory of infinite sets.
Most of the students react very well to this course for two reasons. First, it is so unlike
anything they expected from a mathematics course (this comment appears often on the course
evaluations), and secondly they realize, especially from the discussion of infinite sets, where they
are challenged to abandon certain of their preconceived ideas about reality, that mathematics has
profound things to say about questions which have been raised for thousands of years by various
important thinkers.

Works Cited
Appelbaum, Stanley, ed. Great Sonnets. New York: Dover Publications, 1994.
Cantor, Georg. Contributions to the Founding of the Theory of Transfinite Numbers. New York:
Dover Publications, 1955.
Cohen, Paul J. Set Theory and the Continuum Hypothesis. New York: W.A. Benjamin, 1966.
Godel, Kurt. The Consistency of the Continuum Hypothesis. Princeton: Princeton University
Press, 1940.
Hilbert, David. "Mathematical Problems." Bull. Amer. Math. Soc. 37 (2000): 407-36.
Moritz, Robert Edouard. On Mathematics. New York: Dover Publications, 1958.

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t

MINUTES
/Of a Meeting of Descendents of Francis Scott Key
and Mary Tayioe Lloyd held at St. John's College, Annapolis,
Maryland, on May 2Z, 1959.
9^ * * * * i|t * * * « * * 413|i # :(i # * *1)1 ** *

Invitations to the dedication of the FRANCIS SCOTT KEY MEMORIAL
HALL on the Campus of St. John's College, Annapolis, Maryland, having

been sent to 123 addresses of descendents by the College, the following
assembled at that place on May 2

Miss Ellen Key Blunt
Miss Elizabeth Blunt
Col. &amp; Mrs. Wilfrid M. Blunt
Col. &amp; Mrs. Arthur T. Brice
Gen. &amp; Mrs. Richard W. Cutts
Mr. George Washington Dobbin
Mrs. Robert A. Dobbin
Mrs. William Harvey Doyle, Jr.
Mr. Howard rfay Doyle
Mrs. S. Wilson Heaton
Mrs. William Tabor Jarvis
Mrs. John Forsyth Joline, Jr.
Mr. Laurence Turnbull Joline
Mr. Christian Albert Keller
Mr. &amp; Mrs. Francis Scott Key 1/

1959:
Mrs. Herrick Faber Kidder
Mr. Edward Lloyd
—-—
Mrs. Josephine Browne Masi
Mrs. James Edward Palmer
&lt;Mr. Gilbert Key-Smith
Mr. Robert H. Key-Smith
Mrs. Mlles P. Standish
Mr. JohnT. Wainwright
Miss Mary Katherine Weld
Miss Katherine Key-Smith
Mrs. Morgan Burdette Schille
Miss Mary Howard Lloyd

After an impressive dedication ceremony which was attended by
The President of the United States - Dwight D. Eisenhower - and a buffet

luncheon served on the College Campus - all of the above-listed members of

the Francis Scott Key family - with the exceptions of Mrs. Palmer, Mr. Keller
and Miss Lloyd, - assembled in a conference room of the Memorial Hall

The purpose of the meeting, as outlined in the call to assembly, was

to consider the formation of a permanent Key Family Society to establish and
maintain in the St. John's College Library complete genealogical data and
records of the Family.
The meeting was opened at approximately 2:30 PM by the President of

St. John's College, Dr. Richard D. Weigle, who welcomed the descendents

�MINUTES- - - ------------- -{2)

of Francis Scott Key, Class of 1796, to the College.

Dr. Weigle stated that,

ever since his advent to St. John's College a decade ago, he had hoped for a

memorium to that honorable and distinguished gentleman and alumnus - our
ancestor « that would be of a permanent nature; and that he had also hoped for

the establishment of a Key Family Society that would be related in some way

to the College.

He reported that, as a result of the efforts of the Old Dominion

Foundation, the Maryland Historical Society, the Board of Governors of the

College, and the friends and alumni of the College, the ground-breaking for
the memorium had taken place in October, 1956.

He offered to the proposed

Key Family Society the freedom of the Memorial Hall, the use of the St. John's

College Library, and secretarial service and assistance to facilitate the collec-tion and maintenance in the Library of complete genealogical data and records of

the Society and Family.

Dr. Weigle also brought tolhe attention of those present

the fact that the interior decoration of the Ijobby of the Memorial Hall had not

been completed, and that the College would like to have a memorial plaque,

tablet, or bas-relief for the space above the fountain in the entry, covered at
the time by a United States Flag of 1815.

Dr. Weigle withdrew, and the meet­

ing was turned over to Col. Brice - (Cousin Arthur).
Cousin Arthur explained how the idea of a Key Family Society had come
up in his immediate family, and told of the work that had been done by himself

and his wife (Cousin Alice) - Mrs. Joline, his Sister (also a Cousin Alice) -

Col. Blunt (Cousin Wilfrid) - Mr. Donald Key King (a professional genealogist

but not in our direct lines) - the Library and Secretarial Staff of St. John's College and others - toward compiling a complege genealogy and directory of living

�MINUTES.................................... (3)

descendents.

He told how he and Cousin Alice, when his Mother, Cousin Jeannie,

was confined to a wheel chair in her old age, as something to occupy her time

and thoughts, had set her about the task of listing her "100 First Cousins ' -

which she had often mentioned, not .juite believing that she could do it, and how she
had recalled from memory by name 75 of them, with some of whom a correspon ­
dence was started, family interest aroused, and ancestral diggings begun.

Cousin jeannie died at age 90 in 1950, and Cousin Arthxxr - hoping to amass for
himself the 100 cousins, as his Mother had, and he had not - had continued the

work and correspondence from that time - thinking at the same time that it
might be nice for all of us to know each other better so that we might all be able

to claim 100 or more cousins.

He concluded his report and remarks by stating

that finally - thanks to the help of those mentioned - he had discovered that the

St.

John's Library had compiled a list of 118 of us - just the right number to

fill one of the new jet passenger airliners by which he expected to return to

California after the meeting.

The meeting was then turned over to Col. Blunt

(Cousin Wilfrid).
Cousin Wilfrid stated that he had been very pleased by the number of

descendents who had responded to the notice sent to them all; and that out of

118 sent, only 8 were returned undelivered - indicating that the St. John's
mailing list is essentially correct as to addresses.

He informed us that he had

conferred with President Weigle and advised that a perpetual record of the

Key Family could be established and maintained in the Library of St. John's
College in the event that we might decide to form a permanent Key Family
Society.

As a matter of genealogical interest he reported that the record of

�MINUTES -.................................. --(4)

service of John Ross Key as an Officer in the American Revolution had been

lost - so that any of us who might wish to establish eligibility for membership
in the Society of the Cincinnati through lineal descent from John Ross Key , 1754 -

1821, would be disappointed.

Mrs. Standish, at this juncture, stated that a record

of John Ross Key's service as an Officer in the Revolution existed in I aunce's
Tavern in New York City, and volunteered to look it up on her way home to

Connecticut.

The meeting was then turned back to Cousin Arthur.

Cousin Arthur called for discussion from the floor, and suggested that we
might appoint an "Acting Board of Regents

of seven or eight to study the problem

of establishing a permanent Society and report to the Family as a whole at a future

meeting.

He mentioned that Mr. Foster, the Director of the Maryland Historical

Society, had offered the use of the Key room of that Society in Baltimore - in its

present building or in the larger room in their proposed new building expected

to be started during the next five years - to any such permanent Key Family
Society that might be formed.
There was a general discussion from the floor on the question as to whether

or not any such permanent Family Society should be formed.

Cousin Arthur

pointed out that we would have to establish certain rules of eligibility for member­

ship, and stated that he would favor not more than two classes of membership -

' Hereditary , for all direct lineal descendents,-and Associate , for husbands and
wives only of direct lineal descendents.

this time.

He also made small mention of dues at

Cousin Laurie Joline suggested that we consider what kind of a

Society we might have in mind - whether of a sophisticated type with annual dues,

or of simpler type merely for the purpose of keeping up the genealogical record.

�(5)

MINUTES

It seemed the concensus of opinion that the primary purpose of the Society

should be for the establishment and maintenance ox complete genealogical
records - although no vote on this question was taken.

It was pointed out that

almost all of us have Key memorabilia of one kind or another &gt; letters* docu­
ments, portraits, and other physical property of our ancestor, which few of

us would be willing to part with.

Mrs. Jarvis (Cousin Edith) suggested that a

temporary Secretary should be appointed .

A voice vote on the question was taken and passed in favor of forming a
permanent Key Family Society.

Since he lived in Baltimore, and knew Mr. Foster of Maryland Historical
Society personally, Mr. George Washington Bobbin, Jr.(Cousin George) was nominated

and accepted the appointment to act as Secretary and representative of the group

to it's sponsors designated as St. John's College, of Annapolis, Md., and the
Maryland Historical Society, of Baltimore, Md.

The question of rules of eligibility for membership « whether
an^/or "Associate"

Hereditary

or other was again raised and discussed briefly.

Since there

were only approximately 21% of the known living descendents on the St. John's
College mailing present, it was moved and passed that this question be tabled
until a latter date; and suggested that a write-in vote by mail on it could be

allowed.

Mrs. Jarvis (Cousin Edith) suggested that someone should study the structure
of some of the old Boston Family Societies, which could be of use to us in

patterning our own.

Cousin Arthur requested her to undertake such a study, and

agreed to act as temporary chairman of a planning Committee or

Acting Board

�MINUTES . . . ............................ *(6)

of Regent®” for the B’amily.
Committee.

He called for volunteers for members of such a

The following accepted nominations and were appointed:
Gen. Cutts (Cousin Dick)
Kir. Dobbin (Cousin George)
Col. Blunt (Cousin Wilfrid)
K^r. JLloyd (Cousin Edward)
Mrs. Jarvis (Cousin Edith)
Mrs. Schiller (Cousin Elizabeth)
Mr. Key (Cousin f rank)
Mrs. Wm. Ward Clore (Cousin Catherine - in
absentia)
Mrs. Masi (Cousin Josephine)

There was general discussion as to the proper time and place for the next

meeting - to be for the purpose of acting on the recommendations of the Planning

Committee.

Cousins Dick Cutts, Eaurie Joline, and John Wainwright, pointed

out that commencement time at St. John's College would be an imposition on the

President of the College, having so many other matters of importance to attend

to at such a time.

Photographs of a portrait of our ancestor Francis Scott Key painted by the
well known Artist Charles Wilson Peale during the year 179b in which he graduated
from St. John's, and now in the possession of Cousin Arthur were shown, and

there was brief discussion on the possibility ot having a bronze bas-relief done

from it by a recognized sculptress in California.

No decision was reached.

As it was getting late and some of the Cousins had some distances to go to

reach home, the meeting was adjourned at about 5:00 PM - (sine die).
SS*SSSS&gt;ii*3»iS««*:|t:)&lt;********&gt;t&lt;*S*iK***

As the meeting was of an informal nature - many of the Cousins were meet­
ing each other for the first time - no agenda or order of business had been pre­

scribed, and there was confusion at times - apologies are hereby extended to those

who may have taken part in the discussions or made recommendations or suggestions
and whose names may have been passed over by your reporter.

ELLEN KEY BLUNT

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                    <text>Liberal Education and STEM Education
St. John’s College 50th Anniversary Conference Presentation
Michael J. Bolin, Wyoming Catholic College
September 15, 2014
Abstract:
One of the single biggest obstacles to the proliferation of liberal education is the modern
tendency to consider STEM fields as the most or only important fields of study. I argue, to the
contrary, that the beneficial cultural effects of progress in the natural sciences and related fields
depend in part on a foundation of liberal learning both in scientists themselves and in the broader
populace. In a post-Baconian scientific world, scientific progress has both a
technological/practical aspect and a philosophical/theoretical aspect. Success with regard to the
first aspect is necessarily defined in terms of one's conception of human flourishing, the
philosophical debate over which is behind disputes over, e.g., energy, nuclear, and agricultural
policy. Interpretations of the second aspect inevitably influence the first, as is seen in the
tendency of physicists to extrapolate from their scientific research to broader conclusions about
its implications for human nature and existence. It is not a foregone conclusion, then, that
education in STEM fields will achieve the goods at which it aims, unless the resulting knowledge
is first recognized as fundamentally human and therefore necessarily understood in the broader
context of the human good. Establishing this context is one of the fundamental tasks of liberal
education, upon which the good of specialization thus depends.
Presentation:
In a 1944 letter to Robert Thornton, then a new professor of physics at the University of Puerto
Rico, Albert Einstein wrote the following in response to Thornton’s desire to introduce the
philosophy of science into his classroom:
I fully agree with you about the significance and educational value of
methodology as well as history and philosophy of science. So many people
today—and even professional scientists—seem to me like somebody who has
seen thousands of trees but has never seen a forest. A knowledge of the historic
and philosophical background gives that kind of independence from prejudices of
his generation from which most scientists are suffering. This independence
created by philosophical insight is—in my opinion—the mark of distinction
between a mere artisan or specialist and a real seeker after truth.1

1

Einstein to Thornton, December 7, 1944 (EA 61-574).

1

�The generational prejudice, the seeing of the trees but not the forest that Einstein
described seems to me to be a common consequence of contemporary education, in large part
because of our society’s focus on STEM education and corresponding disinterest in liberal
education. My intention in this talk is to show how the task of fully reaping the fruits of STEM
education cannot be separated from the project of liberal education, and that the latter is essential
both on the part of scientists themselves and on the part of the broader populace if the former is
to be achieved. In the interests of time, I shall focus primarily on the “science” part of STEM
education.
After the early modern era in which Francis Bacon declared that knowledge and power
are really the same thing, science came to be seen by many as fundamentally oriented toward
technological and practical application. In the modern era, this idea has taken such strong root
that scientists have had to deal with politicians wishing to restrict public funding of scientific
enterprise to areas that will have a significant practical application, as if this could always be
known in advance. Disciplines in the humanities, such as philosophy, or liberal education in
general, are ridiculed as a waste of time, their critics saying such things as “If it’s not producing
food, I’m not interested.” Higher education has come to be seen as just being vocational training,
with programs such as the St. John’s College liberal arts program considered outdated at best,
almost a relic of a pre-scientific age.
These sentiments lead us into the first issue I shall discuss. What such critics are really
saying is that one ought not devote one’s life to activities that are not in some way conducive to
human flourishing. Supposing that this is true, the conclusion that one ought not devote one’s life
to the humanities or to liberal education does not immediately follow, since we cannot know
whether this is conducive to human flourishing until we have established what human flourishing
2

�is. For example, the only we reason we care whether a discipline is producing food is because we
care about food. But why do we care about food? Unless we are hedonists, it is principally
(though not only) because we need food to live. But why do we care about living? Presumably
because we wish to do something with our lives that goes beyond eating. Thus, it is clear that
whatever this “something” is, it is worth doing even if it is not producing food.
This example is an instance of a more general observation, namely that the extreme
position that maintains that only what is useful is good is implicitly a contradiction in terms. For
the useful is by definition useful for something, for the sake of another good; and the ultimate
good, also by definition, cannot be for the sake of another good. In the human sphere, the
ultimate good is the human good, human flourishing. Thus, again, it is pointless to criticize some
branch of learning for not being useful unless we first know what human flourishing is.
This issue arises in many concrete contexts, not just in abstract philosophical discussions.
It lies behind the desire of some public figures to reduce funding for NASA, on the grounds that
much of NASA’s research is not useful, or at least not obviously so. In a similar vein, sometimes
people object to the production of GMO crops not just because they believe them unhealthy but
also because they maintain a particular view of the human race’s relationship to nature and what
constitutes the good of this relationship.
The foregoing may give the impression that I see the role of liberal education to be
restricted to the study of ethics and politics, in which the notions of human flourishing and the
common good are considered. But the debate over human flourishing itself depends on prior
theoretical philosophical questions, such as what it means to be human in the first place, and
what the relationship of human beings to the rest of nature is. These questions cannot be escaped
if one is to have a complete account of reality. And if one assumes from the start that one’s own
3

�discipline ought to yield such an account, one will naturally attempt to answer these questions
from the perspective of that discipline. Thus we have the phenomenon of physicists, biologists,
and other practitioners of the sciences lecturing the public on the “meaning” of their discoveries
for human nature, the nature of the universe, and of existence itself.
I do not mean to suggest that scientific inquiry never has relevance to these questions.
Rather, I mean that the kind of relevance it has is subtle and difficult to discover, and one cannot
hope to judge well of it without much learning and practice. The learning required, however, is
not training in the hard sciences but rather liberal learning, which teaches one to consider human
knowledge as a unified whole and to distinguish accurately the scope, nature, and limitations of
each of its parts. This is why interpretation of the results of scientific inquiry is naturally
posterior to liberal education.
Here is a concrete example of what I mean. Physicist Sean Carroll, in a thoughtprovoking article entitled “Abortion and the Architecture of Reality,” writes about the types of
issues that arise in debates over abortion, such as the notions of life and personhood, and argues
that it would be foolish to think that scientific knowledge of the world cannot bear on questions
such as these. Regarding this general claim, I think Carroll is quite right. But, as is typical in
such cases, when he attempts to apply the general principle to specific cases, he mistakes his
philosophical presuppositions for the conclusions of science. Science, he writes,
tells us that there is no magical moment at which an incorporeal soul takes up
residence in a body. Indeed, the concept of a “person” is not to be found anywhere

4

�in the natural world; it’s a category that is convenient to appeal to as we try to
make sense of the world.2
Now, physical science does strongly suggest something relevant to the concept of soul, which is
that (as Carroll himself points out) however closely one inspects the matter of living things, one
will not find it following physical laws different from those followed by inanimate matter. But
soul is a fairly nebulous concept, and there is still a long way from the claims of physics to
Carroll’s interpretation of them. Likewise, that “person” is not a concept in physics is not much
more significant for debates over abortion legislation than the fact that the same could be said of
“tax return” is significant for economic policy debates.
The general point is that it is actually very difficult to delineate precisely what
philosophical, ethical, or otherwise humanitarian implications the scientific worldview ought to
have for our broader human worldview. And it is exceedingly unlikely that one will be able to do
this well if one has never even studied that broader worldview and the writings of the thinkers
who formed and influenced it. Yet this is implicitly what we expect when we encourage students
to pursue careers in STEM fields without first exposing them to the liberal education that will
allow them to understand what they are actually doing in those fields and how it relates to their
lives as human lives and not merely as employees.
What does all of this mean concretely? I am aware, of course, that universal liberal
education is not in the cards for the foreseeable future. A more plausible first step is the
recognition of disciplinary boundaries. Someone need not be an expert in physics to recognize

2

Sean Carroll, “Abortion and the Architecture of Reality,” Discover Magazine,

http://blogs.discovermagazine.com/cosmicvariance/2009/06/04/abortion-and-the-architecture-ofreality/#.VBeNaBagv-o (accessed September 15, 2014).

5

�that the physicist is stepping outside of his discipline when he speaks about free will, or the soul,
or the meaning of life; or to see that medical training does not automatically render a person
competent to speak about ethical matters. Yet questions about these things arise perennially, and
if the scientist as such is not the expert on them, someone else must be. Until we are able to
distinguish between questions that the hard sciences can and cannot answer, we will be unable to
see the value of the education that actually does teach one to answer the questions that STEM
cannot, nor even see the true value in STEM itself.
I want to conclude by saying a few words on that last topic, lest I seem to belittle or
denigrate the natural sciences, which I in no way intend. Though a philosopher, not a scientist,
by profession, I have an amateur’s (in the etymological sense of that word) interest in natural
science and have the honor of teaching it via my own institution’s interdisciplinary program. In
the process, I have come to realize that the profundity of the modern scientific worldview faces
severe impoverishment if it is approached without a background in liberal education. The
significance of the historical shift from geocentrism to heliocentrism simply cannot be
appreciated by one who has never dwelt on the thoughts of generations to whom the evidence of
heliocentrism was unavailable. I am told that something close to forty percent of Americans
reject the biological theory of evolution. This is true even of many who are well-educated, which
suggests that a lack of scientific training is not the root cause. For many, religious issues are at
stake, but I suspect that this is only a special case of the more general problem I have been
describing, which is that we have lost the habit of understanding scientific discoveries in the
context of our broader worldviews. As a result, the public frequently receives ideas such as
evolution alongside shallow and ill-informed explanations of their “true meaning.” Richard
Dawkins is a well-known culprit in this regard. Dawkins is a fine biologist, but he is not a great
6

�philosopher—he is a scientist who suffers, as Einstein said, from the prejudices of his generation,
seeing the trees but not the forest. This sort of behavior is ultimately detrimental to science itself,
which is really much richer than is suggested by presentations of it stripped of human context.
Though superficially science may seem to be more exalted by a culture that has lost its sense of
the importance of liberal learning, in the end it cannot help but be degraded by the same.

7

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                    <text>THE QUESTION OF FINAL CAUSALITY IN ARISTOTLE'S PHYSICS

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David Bolotin
I • I
St. John's College, Santa Fe
April 3, 1992

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�From the time that I first read Aristotle's Nicomachean Ethics as a sophomore in
college, I fell in love with it, and I looked to it for guidance as to how I should live. It appealed to me by its presentation of the moral life as a life of fineness, rather than of
mere obedience to law, and also by its encouragement to the striving for excellence.
was intrigued by its suggestion, so unlike anything I had heard before, that taking pride
in one's excellence is not a vice but a virtue, which as such can coexist with and.which

(
even enhances the comprehensive social virtue of justice. And above all, the E1b.ics.
struck a chord in me by its claim that activity in accordance with virtue is both the natural
end of man and the core of happiness; for although I scarcely understood this claim at
the time, I was moved by its promise of a meaningful and happy life, a life that seemed
beautifully reflected, moreover, in the discussions of friendship and contemplation with
which the book concludes. But as I continued to study, and became more and more
persuaded by Aristotle's teaching about human life, I began to be troubled by the fear
that this teaching might depend on an obsolete and indefensible view of nature. For
how can virtuous activity be the natural end or purpose of human life if, as I had been
1
\,.

taught to believe, modern natural science has shown that there are no such things in
nature as ends or purposes? Must we not say, therefore, that ends are not given to us

�2
by nature, but that we give ourselves our own ends and create our own meanings? For
a time, I tried to ignore this difficulty by telling myself that natural science was not
relevant to an understanding of human life, and by giving it, accordingly, as little thought
as possible. But this evasion could not go on forever, and I eventually had to face the
challenge that modern, natural science presents for anyone who wants to return to the
Aristotelian teaching about man. I therefore welcomed the opportunity as a tutor at St.
John's to study this science in some detail. At the same time, I began to study Aristotle's Physics, and in particular his arguments for the existence of ends or purposes in
nature, to try to see whether his natural philosophy, on which his moral philosophy at
least in part seems to depend, might possibly be true.

.

But enough of this talking about myself. Instead, let me proceed by discussing
the question of natural ends - or_of teleology, as it has come to be called - directly. My
discussion will focus primarily on Aristotle's treatment of this question in his Physics.
For the modern objections to teleology are already present, and responded to, in the
Physics itself. And modern science, it turns out, has nothing conclusive to say about the
matter. Contrary to what I had been told in school, modern science has nm shown that
there are no purposes in nature. Indeed, it has not even attempted to do so. What it
does, rather, is systematically to disregard the possibility of their existence. As Jacques
Monad, a Nobel Prize-winning biologist, has written in his work Chance

and. Necessity,

The cornerstone of the scientific method is the postulate that nature
is objective. In other words, the systematic denial that "true" knowledge
can be got at by interpreting phenomena in terms of final causes -- that is
to say, of "purpose." An exact date may be given for the discovery of this
canon. The formulation by Galileo and Descartes of the principle of inertia

�3

laid the groundwork not only for mechanics but for the epistemology of
modern science, by abolishing Aristotelian physics and cosmology. .....
science as we understand it today ... required the unbending stricture
implicit in the postulate of objectivity -- ironclad, pure, forever undemonstrable. For it is obviously impossible to imagine an experiment which
could prove the nonexistence anywhere in nature of a purpose, of a
pursued end.
But the postulate of objectivity is consubstantial with science; it has
guided the whole of its ~ digious development for three centuries. There
is no way to be rid of it, even tentatively or in a limited area, without
1
departure from the domain of science itself.
I will not bother to quarrel here with Monad's contention that the systematic denial of
purposes in nature is a requirement of science. What is important, rather, is his clear
awareness that this denial is merely a postulate of modern science, not the assertion of
an evident truth. And Monad's statement to this effect, far from being the unmasking of

(

a hitherto unseen limitation of modern science, is only the restatement of a thought that
was well understood by its originators.
Indeed, some of the founders of modern science appear personally to have believed in purposes in nature, even as they excluded all reference to them from their
strictly scientific work. As Descartes put it in his Fourth Meditation, in addressing the
question whether it is for the better that God made him subject to error,

l

... it occurs to me in the first place that I should not be astonished if my
intelligence is not capable of comprehending why God acts as he does; ...
knowing that my nature is extremely feeble and limited, and that' the nature
of God is on the contrary immense, incomprehensible, and infinite, I have
no further difficulty in recognizing that there is an infinitude of matters in
His power, the causes of which transcend my knowledge; and this reason
suffices to convince me that the species of cause tem,ed final finds no
useful employment in physical [or natural] things; for it does not appear to
me that I can without temerity seek to investigate the [inscrutable] ends of
2
God.

�4

Now questions have been raised about whether Descartes' professions of piety are
wholly sincere. But at all events, his argument against the attempt to explain natural
things in terms of ends or purposes is compatible -- to say the least - with there being
such purposes in fact. Or to take another example, Newton himself, whose account of
the motions in the solar system remainsu ne of the greatest achievements of modern
science, claimed that the solar system was originally put together by an intelligent God
acting for a purpose. For although the planets and the comets, he wrote,
may, indeed, continue in their orbits by the mere laws of gravity, yet they
could by no means have first derived the regular position of the orbits
themselves from those laws . ... This most beautiful system of the sun,
planets, and comets, could only proceed from the counsel and dominion of
3

an intelligent and powerful Being.

Newton's claim, however, about the origin of the solar system appears only in a General
Scholium that he appended to his Principia twenty-six years after its first publication.
And these theological reflections play no role in the body of the work, just as they have
played no role in the subsequent history of modern physics.
More generally, modern science from the beginning has sidestepped the question
of ends or purposes in nature, while encouraging people to take less and less seriously
the possibility of their existence, by trying to formulate laws that would encompass as
many phenomena as possible without any reference to such ends. And even in the
case of those phenomena that it does encompass, the claim that it has understood them
adequately is dubious. For its laws are mathematical idealizations, idealizations,
moreover, with no immediate basis in experience and with no evident connection to the

�5
ultimate causes of the natural world. Newton's First Law of Motion, for instance, the law
of inertia, requires us first to imagine a body that is always at rest or else moving
aimlessly in a straight line at a constant speed, even though we never see such a body,
and even though according to his own theory of universal gravitation it is impossible that
there could be one. This fundamental law, then, which begins with a claim about what
would happen in a situation that never exists, carries no conviction except insofar as it
helps to predict observable events. Thus, despite the amazing success of Newton's
laws in predicting the observed positions of the planets and other bodies, Einstein and
lnfeld are correct to say, in I.he Evolution Qf Physics, that "we can well imagine that

(

·

another system, based on different assumptions, might work just as well." Einstein and
lnfeld go on to assert that "physical concepts are free creations of the human mind, and
are not, however it may seem, uniquely determined by the external world." To illustrate
what they mean by this assertion, they compare the modem scientist to a man trying to
understand the mechanism of a closed watch. If he is ingenious, they acknowledge, this
man "may form some picture of a mechanism which could be responsible for all the
things he observes." But they add that he "may never be quite sure his picture is the
only one which could explain his observations. He will never be able to compare his
picture with the real mechanism and he cannot even imagine the possibility or the
4

meaning of such a comparison. " In other words, modern science cannot claim, and it
will never be able to claim, that it has the definitive understanding of any natural

�6
phenomenon. And accordingly, we should not allow ourselves to be so dazzled by it as
to suppose that it has refuted Aristotle's teaching about natural ends.
Let me now turn to my discussion of Aristotle and begin by reminding you of his
doctrine of the four causes, among which the end or final cause is included. In trying to
explain anything, or to answer the question "why?" about it, there are four ways, according to Aristotle, that we can respond. These four kinds of responses , these four ways of
saying "because," are each a kind of cause of the matter in question. In one sense, we
speak of the cause of something as the constituent or constituents from which it comes
into being and of which it is composed. Thus, for instance, we call the bronze in a
statue a cause of it, because the statue could not exist without the bronze that it is made
of. In another and more important sense, however, we say that the cause of something
is its form, since it is the form, rather than the constituent material, that explains why the
being is what it is. Thus the bronze constitutes a statue because it has the form of a
statue, not because it is bronze. And by the "form" of a being we do not mean its visible
shape alone, but rather its whole character, a character that we may not be able to
articulate clearly at first, but that we must already understand to a considerable degree
simply to identify the being as what it is. To take our example again, we call a statue a
statue because of its form , by which we do not mean its shape alone, but more impertantly its being the sculpted image of some other being, such as a man or a god.
Similarly, we call a human being a human being because of its form, by which we mean

�7
above all that we are animals capable of reason. Now in addition to the constituent
cause and the formal cause, a third kind of cause, which helps to explain coming into
being as well as all other changes or motions, is the source from which a given change
begins. Hence, for example, the sculptor is a cau·se of the statue's coming into being,
and therefore also, in a sense, of the statue itself, as the parent is a cause of the birth of
its offspring and the wind is a cause of rustling in the leaves. This principle of change,
which Aristotle sometimes calls the moving cause, can also, however, be a cause of a
state of rest, as when a man decides to stop running and to remain still. Finally, a fourth
kind of cause is the end or purpose for which something comes into being or for which it
exists. Thus health, for instance, can be a cause of walking by being the purpose for the

(
sake of which someone might take walks. Or to return to our first example, giving honor
to a god or perhaps pleasure to the human beholders might be the end - or the final
cause, as it is also called - for the sake of which the sculptor produced the statue.
To focus specifically now on final causality, the examples I have just given, like
those that Aristotle gives himself, suggest a definite manner in which the end of a motion
operates as a cause. First, it is present in thought to the agent who begins the motion,
and it is thought of as being good, and as being attainable by his own efforts. And as a
consequence, the agent proceeds to try to realize in deed the end that he originally had
in mind. In these cases, then, the final cause is itself a factor, together with what we
have called the moving cause, in initiating the motion that leads up to it as an end. And

�8
most of us would agree, I think, that this is a true account of such motions as that of a
statue being sculpted, for it is the craftsman's anticipation of the completed work that
directs his hands and tools. But Aristotle says explicitly that the end is a cause of
natural motions, such as the growth and reproduction of living beings, and not only of
motions initiated by human art.

5

Indeed, he justifies his use of analogies from the arts

to help explain natural processes by claiming that art imitates nature; and he means by
this not merely that some arts are representational, but more broadly that all the arts
6

derive their own directedness toward ends from that already to be found in nature. He
even goes so far as to speak of Nature herself as a kind of artisan who makes all things
for a purpose and nothing in vain.

7

Yet we have no clear evidence to suggest that na-

ture is an intelligent or even _a con~c_ic,us being, and so it is difficult for us to understand
how it can act for a purpose. Nor is it easy to conceive of a way, other than as the
object of intelligent forethought, that the end of a motion could play any role at all in first
bringing that motion about. So couldn't it be, instead, the result of accident that natural
processes often turn out in a manner that seems to suggest motion for the sake of an
end? Now this is not, as it might appear, an anachronistic or post-Darwinian question,
but is in fact a central question that Aristotle explicitly confronts throughout his account
of purposes in nature. To see how he responds to it, let us look more closely at the text
of the Physics itself.

�9
Aristotle discusses accidental causation immediately after his account of the four
causes, and he indicates the tremendous scope of the question about it by noting that
some men had attributed the existence of this world, and indeed of all ordered worlds, to
chance. Now by "this world" Aristotle does not mean the hypothetically expanding uni~

verse of contemporary science, but rather this perceptible world, the world in which we
live, along with other animals and plants, upon the earth and under the heaven. The
beauty and grandeur of this world have always aroused in men a sense of wonder, and
many have felt, as Newton did, that it must be the product of intelligent forethought.

8

I
Yet according to some of the early philosophers, this world of ours came into being, like
many other worlds, merely by chance. Now in response to these philosophers, Aristotle
begins by saying that their claim is worthy of wonder. For those, he says, who attribute
the world and the most divine of the manifest beings (L.e..., the stars) to chance do not
speak of animals and plants as coming into being by mere luck, but rather by nature or
mind or some other such cause, on the grounds that each kind of seed typically produces some definite kind of result. And on precisely these grounds, he continues, what they
say about the world as a whole is especially strange, since we see nothing in the
heavens coming into being by chance, whereas we see many things resulting from luck
9

among the perishable beings here on earth.

Now at this point, it would certainly be

possible for us to raise objections to Aristotle's argument, and some of these may have
occurred to you already. But I would suggest that we defer our objections and consider

�10
instead that Aristotle has not said, at least not yet, that those who attribute the world to
chance are wrong, but merely that their assertion is wonderful and strange -- as I
venture to say it is. And he adds that if what they say is true, this very fact deserves
careful attention, as indeed it does. Rather than assume, then, that Aristotle has already
rejected the view in question about the origin of the world - whether on adequate or on
inadequate grounds - we would do better to follow him as he goes further into the
matter by investigating more generally what chance is and what its relation is to nature.
Aristotle begins his account of chance by first discussing what he calls luck, and
by observing that we do not speak of luck as a cause of those things that come into
being always or for the most part in the same way, but rather of those that come about
contrary to any such necessary or usual patterns. Yet it is not simply the unusualness of
an occurrence that makes it a case of luck. It is also necessary that it be the kind of
occurrence that mi.gb1 have been brought about for the sake of something and from
intelligent choice. Such a result, when it comes about, however, merely by concomitance, is what is properly said to be from luck. Aristotle offers an example to help clarify
what he means in saying that luck is a cause of its results by mere concomitance. A
certain man, he says, would have gone to the marketplace to recover the money he was
owed if only he had known that his debtor was there. But he did not know, and so he
did not go to the market for that purpose; it was merely a concomitant of his going for
some other reason that his trip served the purpose of recovering his debt. Thus, the

�11
result came about from luck, and the man is said to h~ve gone to the marketplace from
luck. If, however, he had chosen to go to the market for the sake of this result, or if he
always or for the most part recovered money when he went there, neither his going nor
its result would be from luck. To speak of luck as a cause, then, is not to deny that there
must always be some definite, particular cause of a lucky result. Indeed, in keeping with
the fact that luck is responsible only for the kinds of outcomes that might have resulted
from intelligent choice, only agents who are capable of such choice can be said to act
from luck. But we attribute the result to luck when the agent's action merely happens to
serve a purpose without his having intended it to do so.
After preparing the way with this account of luck, which has the merit of being

(
immediately intelligible, Arist~tle turns to the discussion of chance, or spontaneity, as we
'

might also translate the Greek term. Chance is a broader class that includes luck as a
subclass. Like luck in particular, chance in general belongs to the over-all category of
moving causes. 10 And it too is a cause of something which, while it is the kind of thing
that might have been brought about for a purpose, does not in fact occur for the sake of
what results. The greater extension of the term "chance" is due largely to the fact that
the particular cause of what we call a chance outcome need not be an intelligent agent,
as it must in the case of luck, but can be any being, whether animate or even inanimate.
Yet Aristotle suggests more of a difference between chance in the wider sense and luck
in particular than this. He also suggests that chance results need not be of such a kind

�12
as even normally to require an intelligent agent, but that in some cases they are ones
that might have been brought about by nature, where nature is understood as a power,
distinct from intelligence, that nevertheless also acts for a purpose.

11

This suggestion,

however, is a difficult one. For as I have already mentioned, it is hard to see what it can
/4,.

mean to act for a purpose if not to act from intelligent forethought, and so it is hard to
understand what that nature could be that Aristotle is contrasting with chance. The
examples, moreover, that he gives as illustrations of chance serve to highlight this difficulty. Let me mention only one of these examples, in which the difficulty becomes
explicit. Aristotle says that a stone fell by chance when it hit a man who was passing by
below; and the reason he gives for attributing its fall to chance is that it might have fallen
•·through someone's agency, and for the sake of striking the man, although in fact it did
not. In other words, to explain what he means by a chance event, he contrasts it, not
with one that might have come about from nature, but with one that might have been
chosen by an intelligent, if in this case an unfriendly, being. 12
Now Aristotle is aware that his examples do not fulfill our expectation that chance
results are sometimes to be contrasted with what nature, as distinct from intelligence,
might have brought forth. And so he adds that chance in the wider sense is most
distinct from luck in the sphere of natural generation, when an animal or plant comes
into being contrary to nature, i.£, maimed or with some deformity. In such cases, he
says, we do not speak of luck, but rather of chance, and this not merely, it seems,

�13
because these particular beings have not been produced by intelligent agents, but also
because the nature that might have produced them, and done so for a purpose, ·is itself
not an intelligence. Aristotle adds, on the basis of a consideration that we will come
back to later, that these impairments and deformities are not precisely even from
chance. Nevertheless, his reference to them serves to support the suggestion that
chance, as distinct from luck, can be a cause of what might have arisen from the
purposive action of nature.
The question remains, however, of what it can mean for nature to act for a
purpose. And Aristotle again calls our attention to this difficulty, in the course of a
renewed attempt to answer the question about the cause of the world. What he says is
this: since chance and luck are causes by mere concomitance of what either mind or
nature might have caused, they cannot be prior to mind and nature themselves; so that
even if chance is responsible for the world, mind and nature are necessarily prior
causes, both of many other things and of this whole.

13

, Now

it is not immediately clear,

of course, how Aristotle arrives at this conclusion, or how it is to be understood. But

what I would first like to emphasize is his claim that b.Q1h mind and nature must be prior
to chance, even on the assumption that chance is responsible for the world. That he
makes this claim about mind, in particular, comes as a surprise. For the assumption
about a chance origin of the world can refer, and almost certainly does refer, to chance
in the wider sense, as distinct from luck. After all, the philosophic position to which

�14

Aristotle is responding claims that our world came into being through the blind interaction of the elements, not from the lucky or unlucky actions of an intelligent being. Yet if
we assume that chance in this sense is responsible for the world, one might have
supposed,· perhaps, that nature is a still prior cause, on the grounds that chance is a
cause of what might have been produced by nature, which must, therefore, already be
at work. But what Aristotle says, to repeat, is that nature arui mind must b.Q1b. be prior
causes of the world. And if mind, as well as nature, must already exist for there to be
chance in .the wider sense, this would seem to imply that nature is not capable of acting
for the sake of ends - those ends that are presupposed whenever we speak of chance
- unless it is somehow accompanied by intelligence. And however much this view of
nature might help us to understand how nature can act for a purpose, it is at odds with
Aristotle's earlier suggestion that it can do so on its own.
And yet perhaps this new suggestion, that nature depends on intelligence in order
to do its work, is an intentional modification of the earlier one; and in fact, the very next
chapter tends to support this modified view of nature. Aristotle says there that a natural
being has two sorts of moving causes, one of which is not natural itself, since it is wholly
unmoved. He then identifies this unmoved mover with the being's end, or final cause,
and also with its form; but the form he is referring to cannot be the form as it exists in
perishable beings, since we have already been told that these forms are perishable
themselves, and hence not entirely unmoved.

14

The reference must therefore be to

·,

�15
some other kind of form, and the only other kind that Aristotle believes to exist is the
form as it exists in thought, whether in human thought or divine thought. If natural
change, then, is to be initiated in part by final causes that are also unchanging forms, it
seems that these forms must be present in a divine mind, a mind that somehow solicits
natural beings to move to~ard the perfection of their exemplars.

15

And indeed, Aris-

totle has already suggested something like this earlier in the Physics. where he said that
the two highest principles of nature include one that is divine and good and aimed for
and another that naturally aims for and reaches toward the first one.

16

And there are

quite a few passages scattered throughout Aristotle's works that speak of a divine mind
as the prime mover and ultimate source of all life and nature.

17

(
And yet despite the attractiveness of this suggestion about the subordination of
nature to a divine mind, it does not yet allow us to see how natural motion as such can
be for a purpose. For purposive motion, at least as we understand it, presupposes more
than the mere existence in some mind of the form that is to be aimed for as its end. It
also presupposes that this form exist in the mind of an agent, such as a craftsman, that
can set itself in motion with a view to that end. Thus, for instance, if the heavenly
spheres are intelligent, living beings, as Aristotle says they are, it is at least conceivable
that they might set themselves in motion in order to approximate the perfection of the
divine forms.

18

But unless even the seeds of natural beings here on earth are self-

moving, intelligent agents, or unless they are tools in the hands of some other such

�16
agent, the assertion that the forms exist in a divine mind does not yet make it intelligible
how natural growth, for instance, can be purposive. Perhaps, then, the claim that led us
to these speculations about the divine mind, the claim that .Q.Q1b. mind .and. nature must
necessarily be prior to chance, allows for another interpretation. In particular, in saying
that mind. must be prior to chance, even if chance is responsible for our world, Aristotle
may not be trying to help us to see how nature could act for a purpose,

Le.., in conjunc-

tion with mind, but rather to indicate something about mind and chance in themselves.
And in fact, there is such a way of interpreting the claim about mind being prior to
chance. For according to Aristotle, there are different senses of priority, not all of which
need apply to the same member of a given pair. In particular, if knowledge of one thing
• is presupposed by that of another, the former is said to be prior in terms of knowledge,
and yet it is not necessarily prior in other senses, such as that of existing earlier in
19

time.

Thus, if we assume, as Aristotle invites us to do, that the world emerged

through chance, it might still be true, as he claims, that mind must be a prior cause of it;
but perhaps this is only because of priority in terms of knowledge. At all events, Aristotle
would have good grounds for saying that mind is prior to chance in this sense, for
chance results are defined as those that might have been brought about for a purpose,
and we understand purpose as that for the sake of which an intelligent being would act.
Knowledge of chance, then, presupposes a prior knowledge of mind, or, more precisely,
of the kind of minds that are capable of choice.

20

Moreover, if being in the paramount

�17
sense is what is true, or what is truly understood by some intelligence -- and Aristotle
makes this claim in the Metaphysics - then this priority of mind to chance in terms of
21

knowledge also implies a certain priority in terms of being.

Chance would not be fully

what it is if it were not understood, understood, that is, in its relation to the ends pursued
by intelligent beings. And to say all this is indeed compatible with the possibility that
such intelligent beings may have come into existence, as our world itself may have
done, through chance.
In trying to account for the priority of mind to chance, I said that the definition of
chance contains the notion of purpose, and that purpose is understood as that for the

(

sake of which an intelligent being would act. And yet we cannot forget Aristotle's earlier
suggestion that what is for a purpose is what might have been done filthfil from intelligence .Q.C ~ from nature.22 Thus, it seems that I have been ov.erhasty in claiming that
we need to understand intelligent choice, as distinct from nature, in order to understand
chance. However, the difficulty of even conceiving what it can mean for nature to act for
a purpose has been our chief puzzle all along. And so let me suggest that natural ends
themselves, like the ends that just happen to result from chance, can not be understood
without a prior understanding of those ends that are pursued through intelligent •
23

choice.

l

Now it is true that when Aristotle first speaks of purpose in the Physics, he

makes no explicit reference to intelligence or choice. What he says, rather, is that "nature," by which he means the form of a natural being, "is an end and [that] for the sake

�18
of which; for in the case of those beings whose motion is continuous and has some end,
this last stage is also that for the sake of which. "

24

And yet he has to add immediately

that not just .a.D¥ last stage of a being's continuous motion is a true end or purpose; after
all, he observes, it was ridiculous of the poet - presumably a comic poet -- to say that

•

death was the purpose for which a certain man had been born. Aristotle goes on to
explain that only the best kind of last stage wishes to be an end; and he speaks
repeatedly of ends or purposes as being, or as wishing to be, what is better or best.

25

But to be better or best presupposes a range of alternatives, and some being with the
intelligence to compare these alternatives and to choose among them . Accordingly, all
knowledge of what it is to be an end, including a natural end, depends on knowledge of
the features of intelligent choice.
My argument has now shown, I think, how Aristotle could justify his claim that
even on the hypothesis that our world emerged through chance, mind would still be prior
in causality to chance. But it has not made sense of the other half of Aristotle's claim,
namely, that nature would also, on this hypothesis, be prior to chance. For I have not
relied on the assumption that nature, as distinct from mind, acts for the sake of ends.
But unless nature does act in this way, it is not even clear how it differs from chance, let
alone how it must be prior to it. After all, chance happenings themselves are of such a
kind that they m.igb1 have come about for the sake of ends. Now there is one difference
between nature and chance, which I alluded to earlier, when I said that congenital

�19

impairments and deformities in natural beings are not precisely from chance. For Aristotle's definition of chance included a criterion that I have not yet mentioned, namely,
that the causes of chance results must be external.

26

Congenital impairments and

deformities, by contrast, are said to have an internal cause. And it is not only such
h

deformities in natural beings that can be distinguished from chance results on the basis
of this criterion. Their normal development is also said to originate from a cause within
themselves.

27

Thus, the normal growth of living beings is said to be from nature, rather

than chance, since it begins from a parental seed, which has within itself, as the parent
did already, the power to initiate those motions that lead to a mature animal or plant. On
the other hand, Aristotle thinks, rightly or wrongly, that in some species of living beings
the usual mode of generation is spontaneous, La., from chance. Such generation
comes about, he says, because the material, such as putrefying slime, from which these
animals or plants begin their development can be moved by itself with the kind of motion
that more typically must be caused in maternal residue by a paternal seed. 28 In generation from chance, then, the original source of motion is something other than the kind of
being that results from it; and in general, we can distinguish nature, as an internal
-source of change, from all external causes such as chance. Still, however, this criterion
by itself does not suffice to explain why natural motion is said to be for a purpose. And
neither does it allow us to understand Aristotle's claim that nature must be prior to
'--.

chance. Indeed, the view that nature is only an internal cause of motion adds an

�20
additional reason for doubt on this score. After all, the survival, growth, and reproduction of natural beings are dependent on a great many external conditions. Accordingly,
nature, or at least the nature of each kind of perishable being that we know of here on
earth, must depend for its very existence on something else - either on some higher
&amp;&gt;
29

principle of order or else on chance.

And on the hypothesis that our world as a whole

emerged through chance, chance would seem to be prior to nature, rather than the other
way around.
If, moreover, one holds that the world as a whole emerged through chance, it
becomes all the harder to see how there could be a purpose behind the internal development of particular natural beings. And some of Aristotle's philosophic predecessors
had in fact argued that there was none. Aristotle recasts their argument in the form of a
perplexity, as follows. Zeus does not cause rain, the argument begins, in order to make
the crops grow, any more than it rains in order to damage the crops on some poor
farmer's threshing-floor; rather, the rain falls by necessity as the evaporated moisture
rises and then cools, and it just happens to be advantageous or harmful for human
beings. And if such blind causality is the truth behind the apparently benevolent order of
the world as a whole, what prevents there being the same kind of causality at work in
the formation of particular natural beings? This argument acknowledges that the parts
of organic beings are suitably arranged for the activities through which they survive and
reproduce. But it claims that these arrangements first originated from blind necessity, as

�21
did many others, and that it merely turned out that these were serviceable, as the others
were not, for survival and reproduction. The animals and plants that we see around us
continue to survive because their parts turned out as. if they had been organized for a
purpose; but they were not organized for any purpose in fact.
Aristotle admits that one might be perplexed by this attempt to explain away the
apparent purposiveness in the structure of organic beings, but he denies that things
could have happened in the way that it suggests. He offers in rebuttal a whole series of
arguments that nature is truly a cause for the sake of something. And at least the first of
these arguments suggests that natural purposiveness is not limited to the internal

(

structure of organic beings. For instead of granting the premise that the causes of rain
are indifferent to good and bad, and arguing that the parts of living beings are nevertheless arranged for a purpose, he disputes even about the rain, or at least about its
seasonal pattems.

30

Apparently, then, he agrees that it does not make sense to think

of nature as acting for a purpose within a limited realm unless the world as a whole is
ordered for the sake of ends.
Unfortunately, however, this first in his series of arguments for natural' purpose is
extremely problematic. And yet partly for this very reason, it is of such importance that I
wish to go through it in detail. Aristotle begins by saying that "these things, and indeed
all things that are by nature, come into being either always or for the most part in the
same way," but that "nothing that is from luck or from chance does so." In support of

�22
this assertion about luck and chance, he adds that "it is not believed to be from luck or
from coincidence" - which latter term appears to be a synonym for chance -- "when
there are frequent rains in winter, but [only] if they come during the dog days [~. in
summer]." Similarly, he says, "heat during the dog days is not [believed to be from luck
or from coincidence], but [only] if [it happens] in winter."

31

Now it is noteworthy that the

explicit basis for Aristotle's claim that normal weather patterns are not from coincidence
is what is commonly believed. For those who make the argument against him, and who
speak of a temporal origin of the various species of living beings, would object that
common opinion has too limited a time frame, and that the patterns whose regularity it is
struck by exist only for a short time, in the light of eternity, as does our world itself. 32
They would say that even if the persistence of these regular patterns is not merely
coincidental, but a necessary consequence of the elements in their juxtaposition, the
whole order within which these patterns exist is the temporary and unintended aftereffect of an original coincidence. And yet despite the obviousness of this objection,
Aristotle does not even attempt to justify, at least not here, his reliance on the common
perspective regarding the permanence of our world; and by being explicit about this reliance, he calls attention to the question of whether that perspective is adequate.
Aristotle continues his argument as follows: "If, then, [things] are believed [to be]
either from coincidence or for the sake of something, and if it is not possible for these
things to be either from coincidence or from chance, they would be for the sake of some-

�23
thing."

33

Now this conclusion follows, of course, if its premises are sound. But the

premise that things must be either from coincidence or else for the sake of something is
open to doubt. For what about the bad things that happen always or for the most part?
In particular, what about the death that comes inevitably to all living beings here on
earth? The fact that birth is followed by death is no mere coincidence, if anything is not,
and yet it is hard to see a purpose for it. Aristotle helps us, moreover, to see the
dubiousness of the claim that being from coincidence or else being for a purpose is an
exhaustive alternative by explicitly basing this premise too on common opinion. And a
further sign that he is aware of its weakness is that he dqes not go on to claim that

everything by nature is for a purpose, even though he had begun his argument by
asserting that everything by nature comes about always or for the most part in the same
way. For if nothing that happens with such regularity can be from coincidence, as he
asserts, and if being from coincidence and being for a purpose are the only alternatives,
it would follow that everything by nature is. for a purpose. And yet, to repeat, Aristotle
does not even claim that this is true. What he says, rather, is that if the particular things
in question, such as normal weather patterns or the arrangement of parts in living
beings, cannot be from coincidence or from chance, then ~ things would be for a
purpose. By thus retreating from the full implications of his argument, Aristotle suggests
that this more limited conclusion, regarding the parts of organic beings and the like, is
not meant to rely wholly on the reasons that have been made explicit. Finally, Aristotle

�24
concludes his over-all argument by observing that all such things are by nature, so that
there is purpose, or "the for the sake of something," among the beings that come into
being and that are by nature. But this final conclusion, since it is based on the previous
one, can also not be justified by the explicit argument alone.
The disregard, in Aristotle's explicit argument, of natural evils such as death is
closely related to its other difficulty, its failure to respond to his adversaries' contention
about the origin of the world. For whatever weaknesses there may be in the doctrine
that our world order, and in particular its species of living beings, emerged through
chance and ne_cessity alone, this view certainly allows for a straightforward account of
death and other natural evils. And so by pointing to his awareness that he has failed to
acknowledge these evils in his own argument, Aristotle calls still further attention to his
having left it open, at least for now, that his adversaries might be right about the
question of ultimate origins.
But what, then, is the basis for Aristotle's emphatic assertion, throughout this
whole series of arguments and elsewhere, that the end or purpose is a cause of natural
development? For if there is no evidence that such development is initiated by a selfmoving, intelligent agent, and if the possibility must even remain open that life itself first
emerged through chance and blind necessity alone, how can he speak with such
confidence of purposes or ends in nature? Now to answer this question, we must begin
by noting that whatever the origin of life, if it had an origin, and whatever the more

�25
immediate moving causes of natural development may be, it remains.true.that this
motion issues regularly, throughout human experience, in living beings whose parts
work wonderfully well together in carrying out their life activities. These activities, such
as nutrition, reproduction, perception, locomotion, and thought, are the manifestations of
the form, or soul, of the being in question, and this form cannot be understood in the
light of its material conditions alone. Rather, it is only in the light of the form that the
material conditions can be seen as what they are. The bodily organs of a living being
must be seen as instruments for performing its characteristic activities, activities. without
some of which, at least, the body itself would cease to exist; and even the more ultimate
conditions of life must be understood, at least in part, in the light of their contribution to

(
this end.

34

Accordingly, even if in general the term of natural development plays no

role at all in initiating it, as it would do if.it were a purpose in the strict sense, the notion
of purpose, or of what something is good for, remains central to the proper understanding of natural beings. And since living beings become what they most truly are by
attaining their mature form, their typical growth toward maturity must also be seen in the
light of this end. This is not to deny that mature development may indeed result from the
same kind of blind necessity, given certain conditions, as does deformity or premature
death, given certain others. But as words like "deformity," "mature," and "premature"
themselves already suggest, we nonetheless see·these outcomes either as successes
or as failures of a tendency toward a natural goal. We can disregard, or pretend not to

�26
notice, this privileged status of the mature form; but it remains an inescapable fact of the
world as it presents itself to our experience.
Now these conclusions, to repeat, are independent of the question whether the
world as a whole emerged through chance. And thus the centrality of form to the
understanding of natural beings also allows us to make sense of the claim that even if
the world did emerge through chance, nature would still be a prior cause of it. For the
world consists primarily of natural beings, and of living beings in particular, which are
properly seen as what they are in the light of their forms. Hence knowledge of these
natural forms, and of these forms as the normal ends of growth, is presupposed by the
very question of whether the beings they characterize, or even the world as a whole, first
.originated through chance. Nature as form and as the end of motion is necessarily prior
to chance, at least in the sense that chance can not be understood without a prior
knowledge of this nature, just as we saw that it could not be understood without a prior
knowledge of the features of intelligent choice.

35

This notion of the mature form as the end of natural development is a far cry from
the strict sense of purpose, according to which the end is anticipated by thought and
thus helps to initiate the motions that lead up to its realization. And much of the difficulty
in understanding Aristotle's account stems from the fact that he has blurred the distinction between these two senses of final cause. Now it would have been easy enough for
him to insist on this distinction, and so I conclude that he chose not to, even though it is

�27
only the weaker sense of final cause that he regards as being applicable to nature in
general. In other words, I contend, he consciously wrote in such a way as to mislead his
readers. Now I know that it will strike many of you as an odd suggestion that Aristotle
would thus mislead his readers, and especially in what seems to be a purely theoretical
account of the natural world. And yet there is considerable support for this suggestion,
at least in general, among the ancient and medieval commentators. Themistius, for
instance, writing in the fourth century of our era, practically begins his paraphrase of the
Posterior Analytics by saying that "many of the books of Aristotle appear to have been
36

contrived with a view to concealment ...."

Simplicius, writing two centuries later,

concludes the introductory section of his commentary on the Physics with a fuller
statement of the same thought. He says, and I quote, that
[Aristotle's) writings are divided into two classes, into the exoteric ones,
such as those in the form of inquiries and dialogues and in general those
that are not concerned with the highest accuracy, and into the esoteric
ones, [or those that are meant for hearing onlyJ, which include this treatise
[i..e.., the Physics]; and in the[seJ esoteric ones, he deliberately introduced
obscurity, repelling by this means those who are too easy-going, so that it
might seem to them that they had not even been written. 37
And still later, in the tenth century, the Islamic philosopher Alfarabi wrote in his "Harmonization of the Opinions of Plato and Aristotle" that
whoever inquires into Aristotle's sciences, peruses his books, and takes
pains with them will not miss the many modes of concealment, blinding
and complicating in his approach, despite his apparent intention to explain
and clarify.38

�28
This consensus, then, across the centuries, that Aristotle deliberately concealed some of
his thought should help make it at least conceivable that my interpretation of his account
of natural purpose is correct.
But why, you will ask, would Aristotle write books in which he deliberately
concealed his thought? Now the primary answer to this question, an answer that will
seem surprising only to those who are unfamiliar with political conditions in the ancient
world, is the fear of persecution. We are told, in fact, that despite all his precautions,
Aristotle was indicted on the charge of impiety late in his life and that he had to flee
Athens in order to escape the fate of Socrates. And underlying this charge against
Aristotle is the fact that the study of nature was not in his time a respectable pursuit.
Those who devoted themselves to natural philosophy were suspected of being atheists
and corruptors of the young, and even Plato's Socrates did not try to dispel this suspi•cion at his trial, choosing instead to deny that he had ever been a natural philosopher
himself.

39

Now in this precarious situation for the study of nature, Aristotle undertook

the project of trying to make it a permissible, and even a respectable, activity. And
largely for this reason, I think, he exaggerated the extent of his agreement with popular
beliefs about the world - such as the popular belief that things happen, in general, for a
purpose - and he concealed from his less careful readers much of his deepest thought
about nature and the divine. He was, moreover, quite successful in this project of
_winning respectability for the study of nature. One measure of his success is the
unbroken tradition of commentary on his works that extended for several millennia after

�29
his death, a tradition to which we largely owe the little that still survives from the writings
of his predecessors in natural philosophy.
However, fear of persecution and concern for the respectability of natural science
are not the only reasons for Aristotle's willingness to accommodate the expression of his
thought to popular opinion. T~'1ere are also educational reasons, which stem from his
insight that natural science, unlike mathematics, is necessarily an ascent from what is
more familiar to us, in all its confusion, toward what is clearer or more knowable by na40

ture.

Given our remoteness from the ultimate causes of things, natural philosophy

can not be taught as a deductive science, but must begin, at least, as an ascent from
common opinion. Thus, for instance, insight into the truth that natural beings become
what they most truly are by attaining their mature form emerges more or less directly as
a refinement of the common belief in higher purposes. 41 And one of the surest ways to
prevent access to this insight is dogmatically to reject that common belief or dogmatically to pretend that it doesn't matter whether its claims are true. For these reasons as
well, then, Aristotle first presents himself as being in fuller agreement with that belief
than he really is.
In conclusion, let me return briefly to the question of the origin of the world. For
although my account of why Aristotle speaks of nature as an end is compatible - as is
the bulk of the Physics - with the possibility that our world emerged through chance, the
fact remains that the final book of the Physics and the first book of Qn the Heavens
contain elaborate arguments for its being eternal. And since Aristotle also claims, as I
mentioned earlier, that the highest principle of the world is a divine mind, he holds out

�30
the hope that natural motion is somehow, in a way that we may never perhaps be able
to understand, activity for a purpose in the strict sense of the word. Yet I do not think
that Aristotle himself could have placed much stock in a suggestion that anything other
than a self-moving, intelligent agent - which the divine mind of his theology is not - can
act for a purpose in the strict sense.

42

And at all events, there is a more importanF

reason for his attempt to show that the world as we know it is eternal, and dependent on
an intelligence more or less like our own. For if it is not, this does not necessarily mean
that it is the product of natural elements that have come together by chance; there is
also the possibility that it owes its existence to the will of a mysterious god or gods. And
in that case, what we call nature would be at most a subordinate order whose continuance depends on the sufferance of this god or these gods;

43

and so science, or the

attempt to understand nature in the light of its intelligible principles, would be a questionable and perhaps even a wholly misguided_pursuit. Accordingly, Aristotle's own
theology, and the associated doctrine of the eternity of the world, serves above all as a
response to this radical challenge to the scientific enterprise. It is not, however, an
adequate response to it, since his arguments for the eternity of the world, at any rate,
are inconclusive. Indeed, some of the deficiencies in these arguments are so manifest,
it seems to me, that Maimonides must surely be correct to say, in The Guide Qf too

Perplexed, that Aristotle himself did not regard them as genuine demonstrations. 44
Aristotle either had some other way, then, of justifying the life of science, and its first
premise that the world is a natural one, or else he too must have been perplexed by this
fundamental question.

�31

ENDNOTES

1. Chance aruf. Necessity. Jacques Monod, translated from the French by Austin Wainhouse (New York: Vintage Books, 1972), p. 21. The claim made in this passage is
significantly qualified on p. 41 (which should be read in connection with p. 104, along
with the slightly more tentative remarks on pp. 112-113). The original claim is restored,
however, on pp. 176-177. Note also the quotation marks around the word "true" on pp.
21 and 176.
2. Ib.e Philosophical Works Qf Descartes. translated by Elizabeth Haldane and G.R.T.
Ross, Volume One (London: Cambridge University Press, 1972), p. 173; contrast.
however, p. 194.
3. Principia. Volume ll, JJN System Qf ~ Wfill.d., Motte's Translation Revised by Florian
Cajori (Berkeley: University of California Press, 1934), pp. 543-544. Compare p. 546
and pp. 668-670.
4. Ihe Evolution SJf Physics, Albert Einstein and Leopold lnfeld (New York: Touchstone
Books. 1966), p. 31 .
5. See, for instance. Qn ~ Sm!.l 415a22-b21; Qn 1lle. E.ar1s. Qf Animals 641 b23-33; Qn
~ Generation Qf Animals 730b8-32; Physics 199a20-b14.
6. Physics 194a21-22; 199a 15-17.
7. Qn ~ J:.am. of Animals 641b10-12; Qn ~ Heaven 291b13-14, 271a33; Politics
1256b20-22; Posterior Analytics 94b36.
I

8. See Qn ~ Eans. Qf Animals 641 b10-23; compare Plato, Philebos 30a9-c8; ~
885e 7-886a4.
•
•
9. Physics 196a24-b5.
10. Physics 198a2-4.
11 . Physics 196b21-22; 198a3-6; cf. 197a5-6 and 197b18-22.
12. cf. Aristotle's "Physics" (Books 1aruf.11), translated with introduction and notes by W.
Charlton (London: Oxford University Press, 1970), pp. 109-110.
13. Physics 198a5-12.
14. Physics 192a34-b1; 198b1-4 (but contrast 224b5-6).

�32

15. Physics 194b26; Compare Charles H. Kahn, "The Place of the Prime Mover in Aristotle's Teleology," in Aristotle .Qil Nature and .LMng Things: Philosophical and Historical
Studies Presented tQ D.aYid. ~ Balme (Pittsburgh: Mathesis Publications, 1985), pp.
182-205. See also Thomas Aquinas, Summa Theologica I, 0 .2, A.3; 1-11, O.40, A.3.
16. Physics 192a16-19.
17. See, for instance, Metaphysics 1072b13-14; Qn the Heaven 279a22-30.
18. Qn too Heavens 292a14-22; 285a29-30; Qn the Motion Qf Animals 700b25-32;
Metaphysics 1072a19-b4; 1073a22-b1.
19. Compare Metaphysics 1018b14-37; Categories 14a26-b8.
20. Compare Wolfgang Wieland, Qie. aristotelische Physik, 2nd edition (Gottingen:
Vandenhoeck and Ruprecht, 1970), pp. 259-260.
21. Contrast Metaphysics 1051a34-b6 with 1027b18-1028a6. See also Qntb.eSo.ui
426a15-26; 430a19-22; 431a1-4; and compare Physics 223a16-29.
22. Physics 196b21-22; cf. endnote 10.
23. Physics 194a28-30 ff. Translations from the Greek are my own.
24. Physics 194a32-33; 195a23-26; 198b8-9; 198b16-17.
25. Physics 197b18-22; 197b35-37; 196b34-197a2.
26. Physics 192b8-32: 199b14-17; and contrast 197a1-2.
27. Metaphysics 1034b4-7; cf. 1032a25-32; Qn the Generation of Animals 715b25-30;
762a8-763b16; History of Animals 539a21-25; 547b18-23.
28. Consider Posterior Analytics 95a3-6.
29. Cf. David Furley, "The Rainfall Example in Physics ii 8," in Aristotle QD Nature and
.Living Things: Philosophical and Historical Studies Presented tQ DaY.k1 ~ Balme
(Pittsburgh: Mathesis Publications, 1985), pp. 177-182.
30. Physics 198b34-199a3.
31. John M. Cooper claims that Aristotle's argument is based on the premise of the
eternity of our world. See his "Hypothetical Necessity and Natural Teleology," in ebikc
sophical Issues in Aristotle's Biology, ed. Gotthelf and Lennox (Cambridge: Cambridge
University Press, 1986), pp. 243-274, especially pp. 246-253. Compare, however,
Meteorology 347a5-6, where Aristotle himself says that the season.al cycle of the rains

�-'

•,::-_...
~

33

merely "wishes (emphasis mine) to be perpetual in its order," ... Kat TouT' iv8EAEXES
l0EAEL -yt-yvEa0at KaTci 'YE

TTJV Tci{tv.

32. Physics 199a3-5.
33. Physics 199b34-200a32. See also 199b5-7.
34. Cf. Qn 1b.e .P.ar:ts. 2f Animals 646a8-647a3.
35. See above pp. 16-18.
36. See above p. 15. Cf. Maimonides, The~ .Qf tw Perplexed, translated by
Shlomo Pines (Chicago: University of Chicago Press, 1963), Part II, Chapter 20, pp.
313=314.
37. TTOAA.a µev oov EOLKE TWV 'AptaTOTEAOIJS' ~l~AlWV ELS ETTlKpU!pLV µEµT)xavficr0m ...
Themistius, Analyticorum Posteriorum Paraphrasis, in Commentaria in Aristotelem
Graeca, Volume 5, Part 1, ed. M. Wallies (Berlin: 1900), p. 1.
1

38.
ALxfj 8€ 8t1JpT)µEVWV airrou TWV crunpaµµciTWV ELS TE Ta E~WTEPLKCl ola
TO. 'taTOpLKCl Kal Ta 8taAO)'LKCl Kat CAWS Ta µT) aKpas rucpt~Etas cf&gt;poVTL(OVTa Kai. ElsTa ciKpoaµanKci, wv Kal OVTTJ foTlv ,; rrpayµaTEta, lv To1s dKpoaµaTtKo1S
cia&lt;icf&gt;ELaV ETTETT}8EUOE Sta TOUTTJS TOUS p&lt;;t6uµOTEp01JS' QTTOKpouoµEvos-.
rrap'

ws

Simplicius, 1n Aristotelis Physicorum Ubros
Quattuor Pciores Commentana, in Commentana in Aristotelem Graeca. Volume 9, ed. H.
Diels (Berlin: 1882), p. 8.

lKetvots µT)BE -yEyp&lt;icf&gt;0m 8oKE1v.

39. Alfarabi, "Harmonization of the Opinions of Plato and Aristotle," unpublished
translation by M. Galston, p. 9. Quoted with permission of the translator.
40. Plato. Apology of Socrates 18b4-c3; 19b2-d7; 26d 1-e2; contrast, however, Phaedo
96a6-99d2 ff.
41 . Physics 184a16-21; cf. Posterior Analytics 71 b33-72a5; Topics 141 a26-142a 16.
42. Compare the relation between Socrates' youthful hopes that he would learn from
Anaxagoras how nature as a whole is ordered for the better and his mature effort to
understand the beings in the light of their forms; Plato, Phaedo 97b8-1 00a 7.
43. Given the political constraints that I mentioned earlier in the text, and in the light of
Aristotle's project to make science respectable, the evidence that he had a genuine
concern with this radical alternative is necessarily sketchy. But one might note an
astonishing example that he gives in Book One of the Physics to illustrate his response
to those philosophers who had denied the possibility of becoming. The difficulty that led
to their denial arose on the basis of a premise that Aristotle speaks of as being common
to all the students of nature, namely that nothing comes into being from non-being. For

•: . .

�.,.

34

the only other alternative is coming into being from being, and yet this too seems
impossible, since being already is. Aristotle's first response to this argument is that
becoming is neither from being nor from non-being, except by concomitance; what
comes into being does so from a being, to be sure, but not insofar as that being is a
being, but rather insofar as it is not the being that comes from it. This is, of course, a
plausible claim. But to illustrate it, he gives the example of a dog coming into being from
a horse, and the example is so fantastic that modem editors have surmised, with no
manuscript support except for a single variant reported as such by Simplicius, that the
text needs to be emended. What I suggest instead is that Aristotle uses the strange
example on purpose, in order to hint that this first, or "formal," attempt to show that
becoming is possible fails to meet the underlying challenge, which is to show, rather,
that becoming is limited to what is possible by nature. At any rate, he goes on to
supplement this first argument with a second one, based on the distinction between
possibility and actuality, and he adds that he has given a more precise account of this
distinction elsewhere. [See Physics 191 a23-b34, ·especially 191 b20-21 , and compare
187a26-b1 and 188a31-34. On the distinction between possibility and actuality, see
Metaphysics e.J
Another indication of Aristotle's concern with the theoretical challenge that the
question of the gods presents for science is found in the first chapter of Book Two of the
Posterior Analytics, at the beginning of a long and difficult discussion of how we come to
know the first principles of science or demonstration. Aristotle includes in that chapter,
seemingly as a mere example of the "what is?" questions that must be answered for
there to be science in the strict sense, the question "what is a god?" [See Posterior
Analytics 89b23-35.J
44.

Ib.e. Guide Qf ~ Perplexed, Part 11, Chapter 15, pp. 289-293.

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            <name>Language</name>
            <description>A language of the resource</description>
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            <description>An unambiguous reference to the resource within a given context</description>
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        <name>Friday night lecture</name>
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