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The St. John’s Review
Volume 55.2 (Spring 2014)
Editor
William Pastille
Editorial Board
Eva T. H. Brann
Frank Hunt
Joe Sachs
John Van Doren
Robert B. Williamson
Elliott Zuckerman
Subscriptions and Editorial Assistant
Deziree Arnaiz
The St. John’s Review is published by the Office of the Dean,
St. John’s College, Annapolis: Christopher B. Nelson, President;
Pamela Kraus, Dean. All manuscripts are subject to blind review.
Address correspondence to The St. John’s Review, St. John’s
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©2014 St. John’s College. All rights reserved. Reproduction in
whole or in part without permission is prohibited.
ISSN 0277-4720
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The St. John’s Communications Office
Current and back issues of The St. John’s Review are available online at
www.stjohnscollege.edu/news/pubs/review.shtml.
��Contents
Essays & Lectures
The Mutuality of Imagining and Thinking: On Dennis Sepper’s
Understanding Imagination: The Reason of Images ..................1
Eva Brann
Similarity and Equality in Euclid and Apollonius ............................17
Michael N. Fried
The Soul’s Choice of Life.................................................................41
Greg Recco
Artistic Expression in Animals .........................................................61
Linda Wiener
Poems
Troy...................................................................................................82
Hannah Eagleson
Three Poems from Les Fleurs du Mal
by Charles Baudelaire...................................................................84
Peter Kalkavage
The Second Sense .............................................................................88
Elliott Zuckerman
Review
To Save the Ideas
Book Review of Daniel Sherman’s Soul, World, and Idea:
An Interpretation of Plato’s Republic and Phaedo ...................89
Eva Brann
��The Mutuality of
Imagining and Thinking:
On Dennis Sepper’s
Understanding Imagination:
The Reason of Images1
Eva Brann
When Professor Rosemann invited me to this colloquium—small
in scale, but to my mind great in significance—I told him that I
conceived my talk on Dennis Sepper’s newly published Understanding Imagination as a sort of book review, which earned me a
wonderful possession, a copy of this magnum opus, as he called
it, rightly.
There cannot be even the hint of a wink in this appellation. It is
indeed a magnum opus, magnificent, powerful, and copious. I want
to address this last feature first, since it colors the reading of the
book.
This work takes its time. Since, to describe its thesis in a first
approximation, there is no activity homo sapiens sapiens engages
in as such that is not imaginative, Sepper ventures into all sorts of
intellectual territory and calls on a variety of theories and concepts.
The point is that instead of dropping names allusively and naming
notions abbreviatedly he takes his time in explaining what he uses,
and he does it so that a reader can follow. He needs the idea of a
field. Do we all know off-hand what a field, formally speaking, is?
1. New York: Springer, 2013. This review-lecture was written for a colloquium held on October 30, 2013 in honor of the book by the Department
of Philosophy at the University of Dallas, Irving, Texas, where Professor
Sepper teaches. Eva Brann, tutor at St. John’s College, Annapolis, was invited to be the main speaker because Professor Sepper has had close relations to St. John’s, and because her book The World of the Imagination
(Savage, MD: Rowan and Littlefield, 1991), is cited in Understanding
Imagination as a sort of predecessor in the attempt to treat the imagination
somewhat comprehensively and with due regard to the reflective tradition.
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Well, now we know. Is everyone interested in the imagination familiar with Saussurian linguistic theory? Well, a lucid exposition
is given. Does that sane remainder among us who is convinced that
opining without some grounding in the tradition of thought is like
Chanticleer standing on top of a middenheap crowing, know exactly why, and how, to study texts of the past? Well, though I come
from a school that deliberately resorts to that tradition as a treasury
of texts, yet on reading Dennis Sepper’s first introductory chapter
I felt better armed in what looks at the moment like a rear-guard
action in its defense. Let me quickly inject here that I think this is
a sufficiently winnable battle, that the last shall soon enough be
first, and that books like this one will belong to the special forces
of this fight. One element in its effectiveness is precisely that its
generalities are highly and acutely specified. What I mean by that
I’ll say before long, and I’ll even express some misgivings. But
they are the queries and doubts of a reader who has been made to
think hard.
So let me begin my review of the content of Understanding
Imagination by saying that the plenitude of notions introduced is
lucidly organized. This book knows exactly where it’s going. The
title announces the comprehensive topic of the book. (Topic, topos,
topology, topography, I should say, are not casual but carefully expounded terms of the work.) This overarching topic is the imagination and its two aspects: the activity of imagining, and its
product, images. First, the imagination is to be understood, that is,
subjected to thinking. And anyone who has ever developed an interest in this topic will know that this endeavor opens a can of
worms—particularly the problematic idea that one mental function
can be applied to another, and the implied pseudo-traditional notion that the imagination is in fact a separable faculty. (I’ll explain
“pseudo-traditional” in a moment.) The subtitle, then, implies that
this understanding will yield the “reason of images.” Now believe
it or not, the book itself contains an explication, applicable to this
phrase, of genitives, objective and subjective. Thus “the reason of
images” means both “what is the reason we have images, how and
for what purpose they come about” (objective) and “the rationality
belonging to images themselves, how images and logoi (reasons
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3
and ratios) are identical” (subjective). The main title has a similar
double meaning. The book will make good on both parts of the
promise, to elucidate both the activity and the product of images—
and, of course, these expositions will raise questions.
The organization of so large a number of mental motions must,
as I said, be lucid, and it is. I’ll first set it out summarily, then permit myself to pick out the particular aspects that got to me, and finally formulate some of the aforesaid queries. That’s as much as
to say that this is a personal take on the book, but that way of proceeding needs no excuse in respect to this work. For the author
himself has some keen observations bearing on the strenuous selfdenial of the impersonal approach, with which I have my own experience: Academic treatments of the inner life, driven by some
misguided notion of objectivity (I don’t want to say, individual inadequacy) quite often read as if the scholar had mislaid his soul
and excised his personal experience while writing on, say, the passions, the will, or the imagination. In these matters, our author
might agree, taking it personally gains something even more valuable than objectivity—call it verity.
I must say at this point what “taking it personally” shouldn’t
mean. Dennis gives the most generous praise and acknowledgment
to my own book, The World of the Imagination, which he clearly
regards as a worthy predecessor to be worthily superseded. There’s
no cause for grief in that. What better chance for an afterlife than
to find a delimited place in the next, more global treatment? At the
end, I’ll indicate briefly how the picture-making view of the imagination preferred in my book both accommodates itself and is recalcitrant to Dennis’s topology.
Chapter 1 begins by giving shape to the questions that matter
about the imagination: How do we come by the idea? Why is it
important? And it promises answers. It then goes on to a critique
of what Sepper calls “the occluded-occulted tradition” of sapient
imagining. He mounts a fair attack on what one might call the
canned version of the tradition, the “pseudo-tradition,” which is
divorced from the subtleties of the actual texts and thus set up to
miss the meaning. Here he produces a pointed answer to two questions: One, what killed the tradition? Answer: survey-type, textless
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textbook accounts. And two, what have the original texts to give
us? Answer: fresh, unstereotyped approaches to truth.
Chapter 2 offers a five-line definition of the imagination, which
is deliberately comprehensive and incidentally shows that good
books are written back to front. My students tend to think, wrongly,
I believe, that philosophy is about and ends in definitions. Yet it is
a part of the intelligent plan of this book that it begins by focusing
the mind on the topic by means of this definition. It is a risky and
arresting strategy: risky because, unlike the Socratic initiation of a
search by means of a definition that is at once popular and self-refuting, Sepper’s definition is at once demanding and conclusive;
arresting because you can tell that it is new-old, not one of the
going formulas, yet rooted in the intellectual tradition.
His ultimate aim is, as I said, comprehensiveness, initiated by
actually practicing imagining, by attending to the act. There are
guided exercises asking you to determine such aspects as how
much of imaginative remembering is reproduction, how much
detail is present, etc. There is a first engagement with various approaches, such as psychologism, which regards knowledge as
“what people in fact think” rather than “what objects actually
are,” and works on the supposition that we have similar, naturally
given, minds which have before them mental objects, and also
posits that both the mind’s thinking and its objects are accessible
to introspection. One can see that “having images”—pictures
held in or before the mind—goes well with this school of thought.
It is, however, afflicted with many quandaries. Its opponent, antipsychologism, argues that it is not from mental, thus subjective,
objects that knowledge comes but from objective public objects,
from logic, mathematics, the world. Internal objects are denied
in favor of overt behavior; mental images, at least the claim that
there are well-formed, stable mental pictures, are obvious targets
of anti-psychologism. It, too, has its difficulties.
Sepper gives notice that he will sail between these Clashing
Rocks: A mental image must be somehow based both in its situation and its forming activity—must be both public and private.
To escape falsifying fixations, we must reradicalize imagination,
recover its roots, its ontology. Sepper proposes a guiding idea
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5
that will avoid getting caught in the conventional commonplaces:
a “topology” of the imagination.
Chapter 3 could be said to set out the methodology of the book,
but that would be falsifying Sepper’s enterprise, which is premethodological. I might describe it as putting to work, for all it’s
worth, a well-found metaphor. Topos, the Greek word for “place,”
has many spaces—physical territories supporting settled locales;
reversely, mathematical fields constituted from the relations among
its elements, its sites; topological space in which expansible shapes
undergo transformations without tearing; and the index in which
rhetorical “common-places,” in Greek, topoi, can be looked up.
These are all versions of a “conceptual topology.” This rich notion
is the notable discovery, or I should say, rediscovery of the book.
Sepper finds that certain philosophers’ writings about imagination,
when directly approached, in fact employed a conceptual topology
all along.
Here is a very preliminary description of the topological approach, as exercised by people who have some preparation:
They have not acquired just a greater quantity of discrete
ideas and their associations. They have cultivated new
fields of imagination as such, as whole fields; they have
learned to mark out special positions in the field; they
have come to isolate (or section out) subfields and sometimes they learn how to relate the various fields to one
another in a new entity or a new field (94).
This much is already evident about a topological understanding
of the imagination: It will see imagining as holistic, fluid, multilevelled—and all that to the second degree. I mean that the above
is not only a description of the imagination but also of the understanding of imagination. For if the imagination is a “topography,”
a placing-in-fields activity, so much the more must its understanding
be a “topology,” an account of a topography. And conversely, if the
approach is adequate in its metaphoricity—for “place” as primarily
used and defined by Aristotle, is a phenomenon of extension—then
so must the imagination be a power of metaphorical placing. But
this is not Sepper’s explicit vocabulary; it is perhaps more an expression of my misgivings, which I’ll articulate at the end.
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Chapters 4 through 7 then do what is obviously next: give a
reradicalized reading of the deepest philosophical texts bearing on
the subject—Plato, Aristotle, Descartes, Kant.
Chapter 8, on post-Kantian treatments, displays what happens
sooner or later to anyone who tries to trace the tradition of a topic
chronologically. Eventually things fall apart into multifariousness;
one is obliged to choose a few authors out of a multitude. Sepper
concentrates on those, namely Wittgenstein (in his Tractatus) and
Saussure, who exemplify an important consequence of his own
heuristic, his topological device: that logos, far from being the antithesis of an image, is an image.
To explain the assertion that the overlapping of language with
imaging is implied in the topological approach, I must return to
Chapter 3 to introduce Sepper’s notion of “biplanarity.” It refers
to a sort of double sight by which one imaginative plane is simultaneously present with another, and the imaginer sees one in terms
of the other. It is first mentioned as a sort of dissociation, such as
happens when one distances oneself from the sense-filled experience of the world in order to see it as reason-resistant appearance,
opposed to intelligible being, if one is Socratically inclined. Or reversely, if one tends to Husserlian phenomenology, then it is real
existence that is “bracketed,” so that one may see the world as an
analyzable phenomenon. Later this relation between the planes is
called a projection. “Seeing-as” has in fact become a topos.
So logos or reason and image or picture can live simultaneously
on two planes while being, moreover, somehow projectible—that
is, in some aspect isomorphic. I have some misgivings about this
rather broad application of the notion of projection that I will offer
later on.
Now before going to those central chapters that revive the tradition and reradicalize the problem, let me just complete the sketch
of the book’s organization.
Chapter 9, the last chapter, presents the initial definition, now
endowed with enough mental material to shed the term definition
and to become a delimitation—a kinder, gentler, more inclusivesounding term. Like any thoughtful philosopher (there is, after all,
the other kind), Sepper does not in fact highly value definitions,
because they are too bare, and he says that they never deliver an
�ESSAYS & LECTURES | BRANN
7
unpackable essence. Nonetheless his now much amplified delimitation does invite an analytic reading. I will sketch out what this
reading yields, since that is the crux of the book, yet I know full
well that I’m reversing Sepper’s deliberate expansion. But what
else to do? Let me call it whetting your appetites.
So: the imagination is an activity; one might say that the imagination is nothing but imagining. This identification does an end
run around the “mental modularity” debate, which is concerned
with the problem hinted at before: whether the mind has a multiplicity of distinct faculties or is a global activity. The imagination
is neither a separate faculty nor an undiscriminable activity. This
imagining is a third something, quite positive, quite specific. It acts
evocatively, calls something forth, and that in a dual way: “abstractional” and “concretional.” Its evocative work produces on the one
hand something drawn away from, abstracted from, detached from
the original. But on the other hand, the emergent imaginative phenomenon has—this is my term now, (Sepper avoids it)—quasi-sensory characteristics, reminiscent of the embodied original insofar
as that it is a concretion, a thickening, of features. The definition
then goes on to specify this activity of imagining. First, it envisions
imaginative fields of concern with a basically potential nature, in
which the fixities of the sensory world become fluid. Second, it
exploits this potentiality to allow the projection of field upon field,
that is, of biplanarity. I have, of course, truncated this concluding
exposition and so robbed it of its subtlety.
The chapter then gathers in the topics that give the potential features form, actualize them, as it were, and so shape the field into a
topography, an expression of the field’s potentials. Recall that these
topoi or topics are figurative places, mental foci.
Here are some examples: Imagining begins with “the emergence
of appearance as appearance,” a formulation that implies “not as
appearance of a stably real thing,” and which is, by reason of this
divorce from reality, both initially placeable in the imaginative
field and essentially evanescent. Fixing this appearance, giving it
firmer shape is a further work of the imagination.
A second topic is the image as inchoate, labile, and contextual.
Contextuality in particular is a recurrent and crucial topic, since in
its shiftiness it partly explains the mobile character of images, but
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even more because context is placing, and placement is the necessary correlative of place. Further on, a topic zeroes in on imagining
as abstracting from perception. One might say “abstraction from
perception” is the preliminary activity that yields appearances as
appearances, since perception is the sensing of things as things.
But one can regard this abstraction from perception also in an opposite way: When the imagination strips the thing of its perceptual
accidents it produces a rationalized image, one having the lucidity
of reason—reason in image-shape. I think of diagrams and blueprints in connection with this.
Nine such topoi are mentioned, features both of and in the field
that have now become topics, subject-areas for future study and
theorizing, and with these “areas” the book concludes. One stems
from Sepper’s unapologetic acknowledgment that he has “cognitivized” the imagination and omitted the human depths of affectivity. He regards the future incorporation of these factors as
plausible and predicts a complex inquiry.
Another concern is the anthropological positioning of the imagination: How does the imagination fit into our humanity? Sepper
suggests that Heidegger’s Being and Time might be translated into
a more conventional philosophical anthropology, in which terms
like attunement (Stimmung) might be put to use. Here I am driven
to an aside: I would applaud this outcome, because if such a normalized derivation had been plausibly accomplished, that would
imply what some of us suspect—that Heidegger’s original existential analytic is, after all, an ordinary ontic anthropology ratcheted
up by fiat into an extraordinary ontology.
Ontology is indeed another concern. Sepper’s envisions ontological explanations that are imaginative in the sense of being fieldto-field projections, one field being the explanatory, the other the
explained field. A bonus is that this duality avoids destructive reductionism, since in the imaginative mode the field elucidated is
not collapsed into the explaining field. Simultaneity of levels is
maintained, and the object explained survives in its plane, unreduced to its explanatory elements in the underlying parallel plane.
Finally an ethics of imagination is adumbrated. Sepper speaks
of an ethos of imagination as the “inhabitable place of imagina-
�ESSAYS & LECTURES | BRANN
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tion”—how we live in its fields. Such a way of life will develop
an ethics that requires this way of life to be good. His book has
shown that thinking and imagining are inseparable. The obsession
with formal and procedural rationality and the relegation of imagination to the arts is disastrous in children’s education and, by implication, to adult practice:
The only adequate way of developing rationality is to develop our ability to imagine comprehensively; we must
start with ourselves, or we will inevitably fail our children and the future world (524).
In leaping from the first three chapters to the last, I have hollowed out the nourishing marrow of Understanding Imagination,
the “reradicalized” readings of imagination’s great philosophical
texts. I would keep you here past lunch, dinner, and nightcap, if I
attempted to fill the gap. Those interpretations are based on close
and acute textual analyses, and they take their time.
Instead I will try to say, briefly, in gist, what in each of the four
philosophers to which Sepper gives a chapter is particularly germane to the delineation of the imagination just outlined. In this
sketchy review I shall have to omit entirely the history-of-ideas
glue that holds these philosophers steady in the context of a—putatively—coherent development.
It is, incidentally, not clear to me what the actual order of discovery was: Did Sepper formulate his understanding of the imagination first and then discover previously occulted corroboration
in the textual tradition, or was it the other way around, or both simultaneously? Maybe he will tell us later.
I’m not sure whether this attempt to pinpoint the intention of an
extended exposition, to find the crux of a highly textured lay-out,
amounts to a subversion or a highlighting of Sepper’s work. Anyhow, I mean it for the latter and will try not to miss the point, but
if Dennis says I did, I will gladly yield to correction. So, then:
Chapter 4: Plato. The chapter intends a major correction of standard interpretations that downplay images in the dialogues. In fact,
“for Plato reality is mimetic,” meaning that the levels of being are
seen as a cascade of images along which the viewer rises and descends in inquiry. Moreover the image-beings produced by what I
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might call “ontological imaging” are analogically connected, that
is, by proportions constituted of logoi, ratios—as in the Divided
Line of the Republic. So they can be said to be logos-involved
(though I’m not sure that ratio-logos so readily translates into reason-logos). I also want to add that Plato calls the lowest human
thought capacity eikasia, “image-recognition,” but then puts it to
work throughout the realm of knowing, for the ascent of knowing
is through recognizing images as images.
Chapter 5: Aristotle. Next, the imagination is retrieved from a
truncated conventional account of Aristotle’s On the Soul which
suppresses two aspects—that imagination seems to be a sort of motion and that it is one aspect of intellection. The imagination’s motion is that of abstracting from the matter of the sensory object and
locating the resulting appearance in the thinking, noetic part of the
soul. There, as “intellectualized imagination” (Sepper’s term), it
functions freely over a field of shifting conformations and contexts,
over a topography. Here I want to add that Aristotle calls even the
Divine Intellect a topos eidōn, a “place of forms,” and the very fact
that this description is figurative (since the Intellect is beyond all
place) may strengthen Sepper’s claim: thoughts and images are
“concreted” in the highest reaches.
Chapter 6: Descartes. Now the topological view of the imagination is refounded in modernity, though again conventional imagination-suppressing selectivity has obscured this fact. Descartes is
a persistent practitioner of the imagination, particularly in the
mathematization of physical nature. Imagination, however, is identified as an activity of the intellect, which is capable of “remotion,”
of stepping back from its imagined figures to rethink them as
purely intellectual existences. Thus intellect exceeds imagination
so as to become, from beyond it, the source of its directed mobility,
that is, the source of its biplanarity and field-topography.
Chapter 7: Kant. Sepper precedes his exposition with an account
of the post-Cartesian occultation of the imagination by rationalism
and its revival within a new science of sensibility, aesthetics. To
these developments Kant responds with a radical epistemology—
an account, called “transcendental,” as yielding knowledge going
beyond the only conscious material knowledge possible, an account
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that traces experience to its root. This root is dual, a passively receptive sensibility “looked at” by intuition, and an actively constructive conceptuality “functioning” by understanding. The
sensibility is again dual, consisting of transcendental, that is, hypersensory space and time. Spatiality and temporality are thus with
us from the first, a priori. Into these notional receptacles flows—
from somewhere—a sensory manifold, an unstructured matter. The
imagination is a synthesizing power, a power of “placing together”
disparate elements, both at the very origin and on several higher
knowledge-producing levels of the soul. Thus imagination is, for
the first time in philosophy, productive before it is reproductive. It
is now knowledge-shaping rather than knowledge-aiding, as it was
for Aristotle, for whom it presented to thought the sensible world
without its matter. The first work of Kant’s transcendental imagination is that of informing the sense-manifold spatially and temporally, so that all sensation of the world comes to our
consciousness “in” space and “in” time, extendedly and sequentially. Mathematics, then, is a product of another imaginative synthesis, which directs thinking to invoke, to inscribe, in space
particular geometric figures, and also calls on time to develop them
progressively. Of the several syntheses, the highest and deepest,
most original, hence most mysterious, work of the imagination is
done by a procedure that is called a schematism. It “puts together,”
or rather infuses, the functions of the understanding, which is a rational power, with the space and time, the pure intuitions of the
sensibility, which is a receptive mode. On the face of it, their disparateness would seem to preclude this miracle of involvement.
But the imagination provides the ground of their union. One example: “Substance,” as a mere rational notion, is an empty concept.
When time-informed it becomes the more concrete category of that
which persists in time, a locus of underlying stability.
There are further syntheses, those that produce the ascending
ways consciousness deals with the representations before it: first,
an “apprehension,” a mere awareness of a representation as an
item; then, a “reproduction” of the representation as a memoryimage; finally, a “recognition” that by coming under concepts the
representation is now stably settled in consciousness and fully ac-
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quired by self-consciousness.
So the Kantian imagination is an activity responsible for the togetherness of analytically disparate factors. It works at the roots of
consciousness, to give it its basic constitution, and then over multiple and layered fields of knowing, by projections from the level
of mere awareness to full self-consciousness. Sepper says that
Kant, as the most consequential representative of the eclipsed tradition, “brought the . . . intelligible dynamism of imagining to a
high point that was not exceeded even by the romantics”—which
is saying a lot, and rightly.
To summarize my summary: Plato introduces an ontological
imagination, whose places are held together in a bond of logoi, ratios. Aristotle adds a psychological activity working at the crux of
human knowing, between thing and soul. Descartes conceives an
intellect that contains and directs the imagination; hence the dynamism of images—their mobility, responsiveness to context, and
biplanarity—is not intrinsic to images but is the inspiriting work
of the intellect. And Kant discovers a synthetic power merging sensibility and understanding, the two aspects of cognitive consciousness; this power originates at its unknowable root of the human
subject and works at all its levels.
These four philosophers anticipate in various degrees of prominence the two chief elements of Sepper’s analysis: the close linkage of reason with imagination and the shifting field-topography
notion of mobile imagining. And they corroborate his respect for
the tradition as a source of illumination.
Now, to do my job as reviewer, I should subjoin some misgivings—and I do mean misgivings and queries, not criticisms and
condemnations.
First, then, I’ll articulate a sort of global unease about explanatory delineations like Sepper’s efforts that make the—surely
heroic—attempt to capture the mobile multifariousness and closeup complexity of embodied beings, and particularly, of their mental
life. In one of his many helpful footnotes he explains the mental
motions of “abstracting” and “prescinding” (drawing off and cutting away), both of which are a kind of simplifying fixative; the
imagination itself, as a cooperating power of understanding works
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with these devices. If the project is to understand understanding
imagination through a descriptive analysis that preserves the flexible richness of a participating power, a certain swampy doubletalk is the penalty. So for example, a key word, topos, carries,
as I pointed out, the dual meaning of a given subject of inquiry
fitted into a topology and of a placing function of the imagination
producing a topography. And the imagination itself appears—indeed early Descartes is the predecessor here—in two forms. On
the one hand, it is a general power of figurative reconception—
whence its relation to human “creativity.” This human power is,
of course, nothing like the divine creation of the Bible that makes
a world out of chaos; it is rather a new perspective on an old situation or its reconfiguration. This general imagination is a Protean
power. On the other hand, there is also the narrower power of producing and manipulating images; it is a rather specialized capability. I wonder if prescinding, cutting away, containing, would
not be an authorial virtue here. But then again, if something, the
imagination par excellence, is by nature duplicitous, perhaps its
account must display intentional ambiguities and homonymous
doublings—never mind Occam’s Razor and its injunction not to
multiply explanatory entities.
The second item is only a specification of the first. Certain notions don’t seem to lend themselves to clarity—for example, contextualization and fusion. A context, as Sepper fully appreciates, is
logically definable by what is sometimes called an infinite judgment, as the indefinitely large negativity surrounding a place. So
“contextualization” means putting a small island in a large ocean
and calling that a placement. This misgiving, incidentally, reaches
to all those unhelpful politico-socio-economico-psychological explanations: You can’t zero in on an apprehended “this” by means
of too-big-to-know “that.” Something analogous goes for fusion,
the togetherness of word and thought or thing and image. It doesn’t,
incidentally, matter whether the cognitive union is to be of thought
with a material object or with its matter-stripped image; their mutuality is, by the very reason of being a fact, a mystery, and it might
be most incisive to call it that.
Third, this mutuality or reciprocity of intellect and imagination
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seems to me the mystery of mysteries, one attested to by the very
variety of grappling devices proposed for their union, precisely because of their structural dissimilarity. All of Sepper’s four philosophers, however they may assimilate the intellect to its object—as,
for example, when Aristotle analogizes sensing and intellection—
at the end of their ruminations admit, either explicitly or implicitly,
the existence of a non-sensing, imageless power of intellect. This
shows, I think, that in those high reaches the intellect itself is an
imageless power. How does a power which at its purest is placeless
come to govern placements?
These considerations make me wonder about the biplanar, fieldto-field-projecting imagination. It is, to begin with, a very congenial notion to me, this double-sight (for which Dennis kindly gives
me credit), in which an image over- or underlies worldly events,
lending them a resonance from other world-venues. Such are the
Homeric similes of the Iliad that alleviate the excruciating concentration of the battlefield by overlaying it with a bonding analogy
to the rest of the world, from the heavens to the household.
But that template notion presupposes some articulated similarity,
some isomorphism, and I have not quite understood on what basis
Sepper’s fields are actually projectible onto one another, how they
are homologous. For example, he says that there is something perverse in the claim that geometry is left behind in analytic, that is
algebraic, geometry. And yet there is a powerful notion, set out recently in Burt Hopkins’s extended commentary on Jacob Klein’s
work on the origin of algebra,2 that just this is the case. Symbolic
mathematics casts loose from image-mathematics and thereby
founds the very modernity Sepper is trying to reform, the world of
abstract reckoning that has suppressed concrete imagining and has
no structural relation to it and is simply not homologous with it.
Another example is word-painting, the power of language to
arouse mental images. No one knows just how words intend toward
and reach the world, nor, therefore, how they instigate its images.
So, it seems to me, the field of thinking and its articulation in words,
2. Burt Hopkins, The Origin of the Logic of Symbolic Mathematics: Edmund Husserl and Jacob Klein (Bloomington, IN: Indiana University Press,
2011). Jacob Klein was the third Dean of the New Program at St. John’s.
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this field of logos, is not, at least not obviously, in the field-to-field
relation to the imagination that the notion of a reasoning image requires—and yet I know that language often delineates pictures and
passion usually infuses words.
That brings me to a fourth and final query. Sepper quite intentionally barely touches the relation of imagining to phantasy, to
painting, and to the passions. Might it not be that in relation to
these the understanding of imagination requires different rubrics
and emphases from those in Understanding Imagination? I’ll post
brief surmises.
Cognitively useful imaging is fed from the outside face, so to
speak, of consciousness by the sensed world. Phantasy, by which
I mean fiction, presents what-is-not, and so offers a re-presentation
of no worldly original. No receptive taker-in of a fiction thinks of
it as a re-arranged reality, a reality-collage. Should one not consider
that there might be a conduit from the inside, for which the term
“unconscious” is just an evasive makeshift? Although I am here in
the company of soberly sane thinkers, I am nevertheless suggesting
that one might seriously consider what the practitioners of poetry
meant by the Muses, who live on Olympus and not in neuronal networks. The question here is, Whence comes imagining in its most
life-enhancing aspect?
When the visual arts are drawn into the inquiry, painting is apt
to come front and center, because, if a painting is (as we pre-postmoderns tend to think) an externalization of a mental image (of
course modified in its passage from quasi- to real space), then the
embodied product might in turn throw light on that immaterial
image. It might be that we are drawn to flat-medium imagery because it reminds us of our soul’s imagining—in its plane dimension
(that is, lacking volume), in its immobility (or virtual mobility),
and in what I’ll call its momentousness (its excerpting from the
banal spatial and temporal context a moment of intensified significance). The question here is, Whence issues the imagination’s
most poignant work? Even to ask that question is, to be sure, a surreptitious bit of special pleading on my part, since the answers I’ve
just suggested are the ones given in my book.
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And finally, when the imagination is properly related to the passions, from the devastating storms of erotic desire to the delicate
atmospheres of esthetic feeling, might the imagination not appear
in yet another capacity than that of abstracting from the round reality outside, or of receiving influxes from a ghostly source beyond?
I mean the capacity to transmogrify the blind shapelessness of our
most intimate psychic condition, our affectivity, into formed feeling—a phrase that surely describes some of our internal imagery.
The question here would be whether the image as an effluvium of
feeling is the same as or different from the cognitive, the art-producing, the Muse-inspired image. Thus the question of questions:
Is the imagination—be it activity, capacity, power, faculty—one or
many? Almost two and a half millennia, and we are still in medias
res. Well, I seem to have talked myself into acknowledging that
Dennis’s multiplication of entities may mirror the way things are.
Thus Understanding Imagination is a wonderfully anticipatory
waystation. So here, in conclusion, are my wishes for the book:
First, that it gain influence enough to encourage a new round of
broadly conceived image-inquiries aided by fresh, close attention
to the great predecessors and perhaps some new, ingeniously devised, imagination-informed image-research. And then, that its call
be heeded for a reform which I’ll put in my own words: There is
in our world a strong strain of relentless reductionism and blind
rationalism whose inevitable complements are mechanical creativity-mongering and thoughtless image-proliferation. One antidote,
perhaps only topically applicable—but then positive good usually
is local—would be a revivified attention to the reason of images.
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Similarity and Equality in
Euclid and Apollonius
Michael N. Fried
By Way of Introduction
My subject today is the meaning of similarity and equality in Euclid and Apollonius—and, by implication, in Greek mathematics
generally during its climax in Hellenistic times. But before I actually begin, I want to say just a few words about history of mathematics and St. John’s College, and I would like to do so by telling
a little story. I told this story the last time I spoke at St. John’s,1
but I would like to tell it again, for I still think about it and am
still unsettled by it.
Not long after I finished my doctorate, I was invited to Delphi
for a meeting of historians of ancient mathematics—a small intimate group, only slightly larger than a St. John’s seminar. During
one of the morning coffee breaks, Alexander Jones, the classicist
and historian of Greek mathematics, casually asked how I felt having made the transition from a St. John’s way of thinking to a historian’s. Like a good seminar question, I was stunned by this, and
I was not sure how to answer. This was mainly because I could not
decide whether there really was a difference between a St. John’s
way of thinking and the way of thinking of a historian of ideas,
that is, whether it really was true I had made any kind of transition
at all.
With a kind of dullness until that moment, I had no trouble, on
the one hand, claiming that in the work I was doing as a historian of
Greek mathematics I was continuing what I had learned at St. John’s,
and, on the other hand, feeling frustration, sometimes bordering on
Michael N. Fried is Professor of Science and Technology Education at
Ben Gurion University of the Negev in Beer-Sheva, Israel. This lecture
was delivered on July 31, 2013 at St. John’s College in Santa Fe.
1. At the conference Classical Mathematics and Its Transformation, held
at the Annapolis campus in 2004.
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resentment, at having to explain yet again how, despite its centering
on texts mostly written long ago, the St. John’s approach was not
historical. Jones’s question made me face the possibility that there
might be a real contradiction here. Of course the reason it still preoccupies me is not because I am overly concerned about my identity
as a Johnny, but because it raises the question of history altogether.
Let me say just a word about this.
When Alexander Jones contrasted the study of history with the St.
John’s program he had in mind, I believe, a view of history, particularly the history of ideas, in which the thought of thinkers in the past
is assumed to be conditioned by times and contexts; understanding
Euclid or Apollonius must, in that view, always be mediated. The contrast with St. John’s may have been based on a mere caricature of the
College where students deal with “eternal ideas” able to be grasped in
an unmediated way. But there is another non-historical view of Euclid
and Apollonius that involves assuming such authors can be read with
no mediation beyond a good Greek lexicon, one that is related to that
caricature version of St. John’s, while not, I hasten to add, the St.
John’s way. It is that in which one comes to mathematics of the past
through modern mathematical concepts and methods, as if the mathematicians of the past were merely writing about the same ideas in a
different language—as John Edensor Littlewood famously said, like
“fellows of another college.”2 Modern mathematical ideas, for those
who approach ancient texts in this way, do not mediate a reading of
the past, but only clarify what those older mathematicians were actually saying. Modern mathematical insight, on that view, becomes the
key to historical insight. A historian like Jones could well see that same
modern insight as obscuring what the mathematicians of the past understood.
For Jones, what the older mathematicians were actually saying is
what they did say in the body of texts they left behind. In order to recover the original meaning of those texts, if we can, one must read
them attentively and with the thought that they were meant to be read.
This unmediated reading of texts, I think, is not far from what one
tries to do at St. John’s. The difficulty here is that having read the texts
2. Quoted in G. H. Hardy, A Mathematician’s Apology (Cambridge: Cambridge University Press, 1940), 81.
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one must nevertheless interpret them—and what it means to interpret
can be interpreted in many ways! Here there can be deep divisions in
outlook.
It may be that Alexander Jones, as a historian of mathematics, is a
historicist, that is, that he truly believes mathematics to be entirely a
product of historical forces so that Greek mathematics, say, belongs
immovably to its own time. In that case he would certainly see a divide
between the way he relates to the past and the way one does at St.
John’s. But whether he really is a historicist I do not know; I never
asked him. Whatever the case, in approaching the history of mathematics, he must, as I must as well, begin at least with a working assumption that the mathematics of the past is different from that of the
present.
The subject of this lecture is not the idea of history, to use the title
of R. G. Collingwood’s famous book,3 and so I shall have to risk your
being left with the impression that this working assumption is only a
kind of maxim. However, I do want to stress that it is in fact fundamental to the way a historian must come to the past. For example, in
the chapter on historical experience in Michael Oakeshott’s Experience and Its Modes, the author distinguishes different kinds of past,
of which one is the historical past, or, we might say, the historians’
past:
The differentia [emphasis in the original] of the historical past
lies in its very disparity from what is contemporary. The historian does not set out to discover a past where the same beliefs, the same actions, the same intentions obtain as those
which occupy his own world. His business is to elucidate a
past independent of the present, and he is never (as an historian) tempted to subsume past events under general rules. He
is concerned with a particular past. It is true, of course, that
the historian postulates a general similarity between the historical past and the present, because he assumes the possibility
of understanding what belongs to the historical past. But his
particular business lies, not with this bare and general similarity, but with the detailed dissimilarity of past and present.
3. R. G. Collingwood, The Idea of History (Oxford: Oxford University
Press, 1946), which collects together the author’s works on his philosophy
of history.
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He is concerned with the past as past, and with each moment
of the past in so far as it is unlike any other moment.4
As a position regarding the way one should come to the past rather
than a position about how the past really is, this is not very different
from a good rule for listening or reading well, as we try to do at St.
John’s: you will listen better to what authors are trying to say if you
do not assume you already know what they are saying—if you assume, rather, that they are saying something different from anything
you have ever heard before.
That said, we are creatures of the present; we cannot pretend the
present does not affect us in any way. For this reason, it is at least useful, if not essential, to be cognizant of the present even while we are
trying to find a very different past. So, while my purpose today is to
try to clarify the notions of similarity and equality in Euclid and Apollonius, I want to begin with a certain aspect of how we moderns tend
to think about similarity and equality: I hope it will help to bring out
the tremendous difference and even strangeness in the ways these notions were understood in classical times.
Similarity and Equality in a Modern Context
Let me begin with a problem someone gave to me sometime before
my flight from Israel to Santa Fe (it is a long flight so it is always
good to have a mathematics problem to work on in transit). The
solution I will present is a modern one.
Let A and B be given points and let C lie on a given
circle. Let P be the centroid of triangle ABC. Find
the locus of point P.
Let E be the midpoint of AB. Then if EC is any line from E to a
point C on the circle, EP:EC=1:3, since P is the centroid of triangle
ACB. Hence, we may think of E as a center of similitude—a point
from which the plane is dilated or contracted uniformly, that is,
that the distance between points is enlarged or diminished by a
fixed ratio (3:1 in this case). The locus PP′P″ is then the image of
4. Michael Oakeshott, Experience and Its Modes (Cambridge: Cambridge
University Press, 1933), 106.
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circle CC′C″ via a contraction relative to E. Therefore, the locus
PP′P″ is a circle having a radius 1/3 that of the given circle CC′C″.
By the same argument, we can see that if C moved on any other
shape, say, an ellipse or a square, the locus of P would also be an
ellipse or a square 1/3 the dimensions of the original ellipse or
square.
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THE ST. JOHN’S REVIEW
In fact, it can be a completely arbitrary shape.
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In every case, the locus required is a shape similar to the original
shape and 1/3 its dimensions.
For our purposes, there are two things we should observe. The
first is the form of the problem, the mere question of locus. What
does it mean to “Find the locus of P”? The idea of locus, or in
Greek, topos, is not an easy one. It would require a lecture of its
own. Yet, it is related, I think, to my main subject, similarity and
equality. I shall say a word about this later.
The second thing to observe, putting the difficulties of locus
aside, is my own way of answering the question, namely, “The
locus required is a shape similar to the original shape” What allows me to speak so generally? Why is it that I need to know nothing about the original shape, none of its special properties? What
allows me, a post-nineteenth century person, to speak of the similarity of a shape I know nothing about?
The answer to this is that in solving the problem I only referred
to a relation between EC, wherever C happens to be, and EP. More
precisely, I took P as an image of C when the entire plane was
contracted by a factor of 1/3 with respect to the point E. That ABC
happened to be a triangle and that P was the centroid of ABC was
really incidental. More importantly, in the original problem, the
fact that the point C moved along a circle was incidental. I did
not, even once, refer to a property of circles!
The modern turn here is precisely to ignore any particular shape
and give all of one’s attention to the space in which it is found.
The contraction by 1/3 is of the space itself, the entire plane:
everything in it will be contracted, shrunk, by a factor of 1/3, so
whatever the shape, it will be the same, only smaller (and in another instance of course it could also be larger)—it is as if we
make a change of scale. This kind of transformation of the plane
is called a “dilation,” and, in general, we can speak about similarity in terms of a dilation combined with other transformations
of the plane that preserve distances between points, translations,
reflections, rotations (these are known as “isometries”).5 This centering on the space is crucial in almost every aspect of modern
5. In fact, it turns out to be enough to speak about reflections: translations
and rotations can be defined in terms of combinations of reflections.
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THE ST. JOHN’S REVIEW
mathematics.6 And it is what links similarity and equality, or congruence. For since a dilation is determined by the factor of contraction or enlargement, one can speak of a unit dilation where the
factor is 1. Congruence—and we shall have to confront the problem of congruence versus equality later—is only a special case of
similarity, so that if two figures are congruent they are automatically similar as well.
I want drive home the point that modern geometry is colored by
its emphasis on space by quoting a nineteenth century geometer
who is thought of as a classical geometer, that is, one whose work
is not governed by algebraic ideas—and, indeed, he is considered
one of the greatest geometers of nineteenth century. This is Jakob
Steiner. One of the ideas Steiner developed (though he may not
have invented it) was called the “center of similitude.” In the problem above, this is the point E, the point with respect to which we
dilate the plane. Steiner speaks of this in more than one work; here
is how he describes it in “Geometrical Constructions with a Ruler
Given a Fixed Circle with its Center”:
If in a plane through any point E we draw rays (lines) in
all directions EA1, EB1, EC1, . . . and by means of these
rays, so connect with one another all points of the plane
that to every point A1 on such a ray as EA1 corresponds another point A2 on the same ray; and indeed, under the condition that the distance of every two corresponding points
from the point E, and EA1 and EA2, have throughout one
and the same given ratio, as n1:n2, then such a system of
correspondence is thereby brought about that the plane is
6. I think Jacob Klein put his finger on the same tendency when he wrote,
“Descartes’s concept of extensio identifies the extendedness of extension
with extension itself. Our present-day concept of space can be traced directly back to this. Present-day Mathematics and Physics designate as
‘Euclidean Space’ the domain of symbolic exhibition by means of linesegments, a domain which is defined by a coordinate system, a rational
system, as we say nowadays. ‘Euclidean Space’ is by no means the domain of the figures and structures studied by Euclid and the rest of Greek
mathematics. It is rather only the symbolic illustration of the general
character of the extendedness of those structures.” Jacob Klein, “The
World of Physics and the ‘Natural’ World,” The St. John’s Review 28.1
(1981): 29.
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traversed twice. Or, we can also imagine that two planes,
which may be called α and α′, lie one upon the other, while
every point may be considered as belonging as well in one
as in the other plane.7
Although Steiner will use the center of similitude specifically for
circles, lines, and angles, his way of presenting it in terms of a
transformation of the entire plane—or, as we would say, a mapping
of one plane onto another—shows the generality of his conception.
So, to reiterate the main point above, similarity can be a general
notion for us since in our modern mathematics similarity refers to
such an operation on the entire plane in which geometric figures
live. And because we focus on the entire plane rather than the objects themselves, the particularity of the objects deemed similar becomes unimportant, as we have seen. It is in this way that the
conception of similarity in Euclid and Apollonius (and, I would
add, Archimedes as well) is profoundly different from that in modern, post-nineteenth-century mathematics.8
7. Jakob Steiner, “Geometrical Constructions with a Ruler Given a Fixed Circle with its Center,” trans. M. E. Stark, ed. R. C. Archibald, Scripta Mathematica 4 (1948): 222. Steiner’s diagram is slightly different from the one
included above, for there are a few more points he wants to emphasize beyond
the mere definition.
8. For this reason, comments such as this from Jeremy Gray seem to me completely wrongheaded: “The Greek geometrical proofs worked because of assumptions made about the underlying space, which are reflected in the ideas
of congruence, similarity, and parallelism.” (Jeremy Gray, Ideas of Space
[Oxford: Oxford University Press, 1979], 29.)
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THE ST. JOHN’S REVIEW
Similarity in Euclid and Apollonius
In some ways, the radical departure of the modern conception of similarity from the classical Greek conception has everything do with
how mathematicians like Euclid and Apollonius treated the plane itself. The plane, epipedon, in Greek geometry has, one might say, two
expressions, 1) as an object, and 2) as a place. As an object, it can be
considered in relation to other objects, for example, it may be inclined
to another plane, or a line may be inclined to it. It may cut another
figure, a parallelepiped as in Euclid, Elements XI.25 (“If a parallelepipedal solid be cut by a plane which is parallel to the opposite
planes, then, as the base is to the base so will the solid be to the solid”),
or as in Apollonius, Conics I.11-14 where the conic sections are produced by cutting a cone by a plane. Sometimes a plane is nearly identified with part of itself, as in the face of a solid figure (see for
example, Elements XI, Definitions 9 and 10), in which case it becomes an object in a sense not much different from the way a triangle
is an object.
As a place, it is not something manipulated: it is there, and there
are things in it—they can be manipulated, but it cannot.9 Thus in Elements I, Definition 8, “A plane angle is the inclination to one another
of two lines in a plane (en epipedōi) which meet one another and do
not lie in a straight line.” Again in Book XI, Proposition 1, “A part of
a straight line cannot be in the plane of reference (en tōi hupokeimenōi
epipedōi) and a part in a plane more elevated,” the plane is an immovable place. This phrase “the plane of reference,” or “the plane
placed under,” as a place on which things may be situated, also appears in Apollonius’s Conics I.5210 where Apollonius constructs a
parabola in a plane. Even though the plane is not the exclusive field
of action here, as it is in Book I of the Elements, and may have a relation to other objects or be constructed, it is, nevertheless, unmanipulated in these contexts, a that-with-respect-to-which other things may
be manipulated. It is also the place in which the similarity of figures
9. This idea is important in connection to Book IV of the Conics. See Michael
Fried, Apollonius of Perga’s Conics, Book IV: Translation, Introduction, and
Diagrams (Santa Fe: Green Lion Press, 2002).
10. See, for example, Apollonii Pergaei quae Graece exstant cum commentariis antiquis, ed. I. L. Heiberg, Vol. 1 (Leipzig: Teubner, 1891), 160, line 15.
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is explored. Of course the plane is a place in which the similarity of
figures is explored for the moderns as well; however, they do so by
treating the plane as a place that is able to be manipulated, as if the
place were an object. As such, it can also be compared to other planes,
as we saw in the example from Jakob Steiner.11
To return to the main point, however, the upshot of the ancient
view is that the similarity of figures must be a comparison of the figures themselves within a plane. One’s attention, therefore, must be
sharply focused on the figures and their properties. The foundation
of similarity rests in the look of geometrical figures. I use the word
“look” intentionally; it is a fair translation of the Greek word eidos,
which besides its well-known Platonic context has a mathematical
meaning of “shape,” or “form” in the sense of “shape.” For example,
in Euclid’s Data, Definition 3, we find the following explanation:
“Rectilineal figures are said to be given in form (tōi eidei), if the angles are given one by one and the ratios of the sides to one another
are given.”12 This definition is notable not only because of its resemblance to the definition of similarity in the Elements (see below), but
also because it makes clear that “similar” is related to something the
figures themselves possess,13 namely, their own look or form: for
one figure to be similar (homoios) to another means that they are in
possession of the same shape, the same form, the same look.
The shape of a person may be different from the person, but the
shape of a triangle is impossible to separate from what it is to be
a triangle. In geometry, the shape of something depends on what
that something is. There are, for this reason, as many criteria for
similar figures as there are different kinds of shapes: this is why
for the Greek mathematician there is no single governing rule for
11. See pp. 24-25 above.
12. Translation from Christian Marinus Taisbak, Euclid’s Data: The Importance of Being Given (Copenhagen: Museum Tusculanum Press, 2003), 115.
Taisbak’s book contains a deep discussion of the idea of “givenness in form”
and of Euclid’s Data generally.
13. In this connection, Taisbak points out, “The Elements compare triangles.
The Data deals with individuals [emphasis in the original], and with the
‘knowledge’ we may have of such individual triangles, within the language
of Givens.” (Taisbak, Euclid’s Data, 126-127.)
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determining similarity. In the Elements, for example, we have the
following different criteria for similarity:
Elements III, Def. 11, Similar circular segments: “Similar
segments of circles are those which contain equal angles
or in which there are angles equal to one another.”
Elements VI, Def. 1, Similar rectilineal figures: “Similar
rectilineal figures are such that they have each of their angles equal and sides about the equal angles proportional.”
Elements IX, Def. 9, Similar solid figures: “Similar solid
figures are those contained by similar plane areas
(epipedōn) equal in number.”
Elements IX, Def. 24, Similar cones and cylinders: “Similar cones and cylinders are those of which the axes and
diameters of the bases are proportional.”
Add to these other definitions from Apollonius and Archimedes:
Apollonius, Conics VI, Def. 2, Similar conic sections: “[S]imilar [conic sections] are such that, when ordinates are drawn
in them to fall on the axes, the ratios of the ordinates to the
lengths they cut off from the axes from the vertex of the section are equal to one another, while the ratios to each other of
the portions which the ordinates cut off from the axes are
equal ratios.”14
Archimedes, Conoids and Spheroids, Introduction, Similar obtuse-angled conoids (i.e. hyperbolas of revolution): “Obtuse-angled conoids are called similar when
the cones containing the conoids are similar.”
Each of these definitions demands prior knowledge of the object
to which the word “similar” is being applied; for example, one
must know that the angles contained in a segment of a circle are
all equal so that one can speak of the angle of the segment. The
necessity of such prerequisite knowledge precludes a general definition of similarity: “similar” always awaits the particular geometrical entities which are to be similar—even ratio and
14. All translations of Books V-VII are from G. J. Toomer, Apollonius Conics
Books V to VII: The Arabic Translation of the Lost Greek Original in the Version of the Banu Musa, 2 vols., (New York: Springer-Verlag, 1990).
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proportion is not fundamental, as the case of similar circular segments shows. And since “similar” for triangles is one thing and
“similar” for conic sections something else, one could not ask
whether some shape is similar to some other shape without first
assuming that they are of the same type—a polygon, for example,
or, again, a conic section.15
Thus, while Apollonius can ask whether or not a parabola is similar to a hyperbola or even an ellipse in Conics VI.14, the question
remains strictly within the context of the similarity of conic sections for which there is a general definition. And when we look at
that general definition, we see how deeply it is rooted in the foundations of conic sections developed in Book I of the Conics. Let
us restate it:
Similar [conic sections] are such that, when ordinates are
drawn in them to fall on the axes, the ratios of the ordinates to the lengths they cut off from the axes from the
vertex of the section are equal to one another, while the
ratios to each other of the portions which the ordinates
cut off from the axes are equal ratios.
15. I am referring of course to “similarity” in its strict mathematical sense, as
opposed to the use of “similar,” in a non-mathematical context, even within
a mathematical work. For example, in the preface to his Phenomena, Euclid
writes that “if a cone or cylinder be cut by a plane not parallel to the base, the
resulting section is a section of an acute-angled cone which is similar to a
shield (homoia thureōi).” (Euclidis Phaenomena et Scripta Musica, ed. Heinrich Menge and I. L. Heiberg [Leipzig: Teubner, 1916], 6.)
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So, suppose ACD and PMN are two conic sections. Let AB and
PQ be their respective axes, and let CEC′, DFD′, MRM′, NSN′
be drawn ordinatewise.
Then ACD and PMN are similar if CC′:EA::MM′:RP and
DD′:FA::NN′:SP whenever AE:PR::AF:PS.
In order to follow this definition one must understand what
an axis is and what lines drawn ordinatewise means—and, naturally, one must understand that every conic section has an axis,
or, more generally, a diameter with respect to which lines may
be drawn ordinatewise.16 Unlike the little problem with which
I began the discussion, a proposition about similarity in Apollonius’s Conics must concern conic sections and their particular properties: Conics VI, the book which treats similarity (and
equality) is, after all, a book about conic sections!
As an easy example of how Apollonius uses the definition
and how not only its formulation but also its use depends on the
properties of conic sections, consider Conics VI.11, which
proves that every parabola is similar to every other parabola.
Here is a paraphrase of the proof.
Suppose AB and GD are two parabolas, AK, GO are their
axes, and AP, GR are their respective latera recta.
16. There are other definitions, notably one implied by Archimedes for
the ellipse and hyperbola. If PQ and pq are the axes of, say, the two ellipses and AR is an arbitrary ordinate in the one while bs is an arbitrary
ordinate in the other, Archimedes says that the two ellipses will be similar if it is true that:
sq.AR:rectPR,RQ = sq.bs:rect.ps,sq
Note that nothing is said about where R and s are on the respective axes.
The condition is equivalent to Conics, VI.12, for this ratio is always that
of the latus rectum to the transverse diameter, by Conics, I. 21. I might
add that although Toomer calls this a definition, Archimedes does not:
he simply states the fact that the conics will be similar if this is so—and
that at the end of a proposition! (See Conoids and Spheroids, Proposition
14 ad fin., in T. L. Heath, The Works of Archimedes [Cambridge: Cambridge University Press, 1897], 125.) In any case, like Apollonius’s definition of similarity, this condition of Archimedes is also tied closely to
conic sections as opposed to any other kind of shape.
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Let AK:AP::GO:GR, and suppose Z and Q are arbitrary points on
AK.
Choose M and C so that they cut GO into segments having the same
ratios as the corresponding segments defined by Z and Q.
In parabola AB, draw EZI, HQS, BKT ordinatewise, that is perpendicular to AK since AK is an axis. Similarly, in GD, draw LMU, NCF,
DOX ordinatewise.
Now, by Conics I.11, BK and DO are mean proportionals between
AP and AK and GR and GO, respectively (i.e., AP:BK::BK:AK and
GR:DO::DO:GO)
Therefore, BK:AK::DO:GO, so that BT:AK::DX:GO [since
BT=2BK and DX=2DO].
Since AP:AK::GR:GO, AK:AQ::GO:GC, therefore, AP:AQ::GR:GC.
Thus, repeating the argument used to prove BT:AK::DX:GO above,
we can show also HS:AQ::NF:GC and, again, EI:AZ::LU:GM.
And so Apollonius concludes:
Therefore, the ratio of each of the lines BT, HS, EI,
which are perpendiculars to the axis [AK], to the
amounts which they cut off from the axis, namely, to
AK, AQ AZ is equal, respectively, to the ratio of the
lines DX, NF, LU, which are perpendiculars to the axis
[GO], to the amounts which they cut off from the axis,
namely OG, CG, MG.
And the ratios of the segments cut off from one of
the axes to the segments cut off from the other are
equal.
So section AB is similar to section GD.
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Again, what I wish to stress about this proof is not the details of
the argument, but the mere fact of its appealing at every step to the
specific properties of the parabola demonstrated in Conics I.
Perhaps the most striking reflection of how the similarity of
conic sections completely depends on the definition of conic sections, their geometric identity as the section of a cone, is the fact
that book ends with a set of eight constructions involving the cone
and locating conic sections within the cone, for example, “Given
a cone and given a parabola, find a cone containing the parabola
that is similar to the given cone” (Conics VI.31). Significantly,
Book VI is the only book in the Conics, besides Book I, in which
the cone appears explicitly.
We need now to move on to the question of equality. For, remember, Conics VI is not just about similarity, but also about
equality.
Equality in Euclid and Apollonius
As we noted above, with the modern view of similarity in which
similarity relates to a transformation of the space in which objects
are found, congruence becomes a completely derivative notion. And
here I should say that moderns speak about congruence and not
equality—and I think there is much to say about that—but more
often than not the use of one or the other is a matter of convention.
For example, when Hilbert comes to the axioms of congruence in
his Foundations of Geometry he more than once uses the expression
“kongruent oder gleich,” that is, “congruent or equal.” That it can
be a matter of convention is an important aspect of the modern perspective. Greek mathematicians do have a special designation,
“equal and similar” (isos te kai homoios); nevertheless, they do not
have a separate term for the relation of “congruence.” We shall have
to confront this combination “equal and similar” later, but for now
suffice it to say that there are only two basic terms “equal” and “similar.” The difficulty of their relationship cannot be swept away.
Thomas Heath’s treatment of this, for example, is quite unsatisfying.
When Euclid uses the word “equal,” isos, in a manner corresponding
to our notion of congruence, Heath just takes that to be the sense of
the word, and when Euclid then uses it in a manner corresponding
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to our notion of equal areas (Elements I.35), Heath says this is
“equality in a new sense.”17 Nevertheless, Euclid does use the same
word, isos. One cannot escape that.
For Euclid at least, equality is a very general notion, and it is certainly one of principal themes of Book I of the Elements, if not the
principal theme. As such, it is an idea that undergoes development
in the book; one might say the book develops a kind of theory of
equality. Let us consider briefly the overall direction of that development.
The theory of equality is contained in the five Common Notions
(koinai ennoiai) at the start of Book I of the Elements.18 These Common Notions are the following:
1. Things equal to the same thing are equal to one another.
2. And if equal things be adjoined (prostethēi) to the
same thing, the wholes are equal.
3. And if equals be removed from the same thing, the remainders are equal.
4. And things fitting (epharmozonta) on one another are
equal to one another.
5. And the whole is greater than the part.19
Of these, the fourth provides the basic criterion, the basic test for
equality: if one figure can be fitted exactly on top of another, then
the figures are equal (isos). It makes its first appearance in proposition I.4, which states that two triangles will be equal if they have
17. T. L. Heath, The Thirteen Books of Euclid’s Elements, Vol. 1 (New
York: Dover, 1956), 327.
18. Heiberg mentions other common notions appearing in some manuscripts; for example, “If unequals be adjoined to unequals, the whole is
unequal” and “Doubles of the same thing are equal to one another,” as
well as, “Two lines do not contain a space.” Except for the last about two
lines not containing a space—which, as Proclus himself seems to suggest,
is odd fish among the others—all of these common notions, therefore,
concern equality—and even that last common notion may be connected
to the nature of coinciding.
19. My translation.
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equal sides surrounding an equal angle. The entire demonstration,
problematic though it may be, plays on Common Notion 4: equal
lines are fitted on equal lines; the equal angle is fitted on the equal
angle; this forces the one triangle to fit on the other, so that the two
are equal.
In fact, that equal lines can be fitted on equal lines and equal angles on equal angles is not truly an application of Common Notion
4, but its converse; however, with simple undivided objects like
lines and angles, being equal and fitting on one another are treated
as identical relations.20 And in this connection we must return to
Book VI of the Conics for a moment. For Apollonius takes the criterion for equality provided by Common Notion 4 as the very definition of equality of conic sections:
Conic sections which are called equal are those which
can be fitted, one on another, so that the one does not exceed the other. Those which are said to be unequal are
those for which that is not so.
In the Elements, however, Euclid shows that the converse of
Common Notion 4 cannot be assumed in all generality. It is here
that the other Common Notions clarify why the criterion of “fitting on one another” is sufficient but not necessary for equality:
in Elements I.35, Euclid shows that things can be equal without
having the same shape, that is, without being able to fit on one on
the other.
Proposition I.35 states that “Parallelograms on the same base
and in the same parallels are equal to one another.” Thus the
proposition tells us that parallelograms such as ABCD and EBCF,
which are clearly not the same shape, may, nevertheless be equal.
It is instructive to look at Euclid’s proof of the proposition (in
paraphrase):
Since ABCD is a parallelogram, AD is equal to BC.
For the same reason, EF is equal to BC. Whence also
AD is equal EZ (by Common Notion 1); and DE is
common; therefore, the whole AE is equal to the whole
20. See Michael N. Fried and Sabetai Unguru, Apollonius of Perga’s
Conica: Text, Context, Subtext (Leiden: Brill, 2001), 228.
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DF (by Common Notion 2).21 But also AB is equal to
DC. So the two lines EA, AB are equal to the two lines
DF, DC, each to each. Also the angle contained by FDC
is equal to the angle contained by EAB, the exterior to
the interior. Therefore, the base EB is equal to the base
FC and the triangle EAB is equal to the triangle FDC
(by I.4 and, derivatively therefore, Common Notion 4];
let the common part DGE have been removed; therefore, the remaining trapezoid ABGD is equal to the remaining trapezoid EGCF (by Common Notion 3); let
the common triangle BGC have been adjoined; the
whole parallelogram ABCD is therefore equal to the
whole parallelogram EBCF (by Common Notion 2).
The parallelograms being on the same base and in the
same parallels are, therefore, equal to one another.
What we see in this proposition is no “new conception of equality,”
as Heath says; on the contrary, what we see is that the Common Notions—which comprise, as I said, the theory of equality—begin from
the basic notion of “fitting on one another” to show how equality applies also to shapes that do not fit on one another. It is an elaboration
of equality, a spelling out of the theory, not a new kind of equality. Even
Elements I.47, the “Pythagorean Theorem,” can be seen in this light,
since it shows not only how one figure can equal another of a different
shape, but also how one figure can equal two others of the same shape.
21. It is typical that Common Notions 2 and 3 are used when a single thing
is removed from two equals. This assumes that anything that can be equal
to something is always at least equal to itself. It is curious—and perhaps significant—that this fundamental fact is missing from the Common Notions.
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And, I would argue, Book II continues this inquiry with its attention to
how one or several rectangles may equal other rectangles.
This elaboration of the idea of equality demonstrates how things
can be equal even though they have far from the same shape. Conversely, things can be of the same shape and yet not be equal. Aristotle points this out, tellingly enough, in the section on motion
and alteration in the Categories (15a, 30-33): “there are things that
increase and are not thereby altered as well. For example, if a gnomon is added, a square is increased in its size but does not undergo
alteration (ēuxētai men, alloioteron de ouden gegenētai).
Thus, in both directions, equality of figures is not identical with
sameness of shape. Equality cannot be subsumed under similarity
and similarity under equality. Yet, equality has to do with shape in
some way. It is rooted in shape inasmuch as superimposition is its
basic test; and it can be used to probe shape, for example, in showing that a line through the center of an ellipse divides an ellipse
into two equal halves (Conics VI.4 and 5). But, again, because
equality does not necessarily mean sameness of shape, shape itself
cannot be its main object. That main object of equality is similarity.
Thus it is a kind of counterpoint between similarity and equality,
rather than a logical dependence one way or another, that characterizes how these ideas appear in Apollonius and Euclid.
Equal and similar
The logical disconnection between equal and similar is particularly
clear in the Conics, where propositions for similarity are kept separate from those on equality: one proposition will show when two
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sections are equal and a different proposition later in the book will
show when they are similar. Now we must return to the idea of
“equal and similar” (isos te kai homoios) in Apollonius and Euclid,
for here the two notions do come together. But it is a peculiar coming-together—not a logical joining, but only slightly more than a
mere conjunction. This has the effect of forming a new term while
leaving the independence of the original terms. There is “equal,”
there is “similar,” and there is “equal and similar.”
As a unit of meaning, Charles Mugler, in his dictionary of Greek
mathematical terminology, notes a non-mathematical use of isos te
kai homoios: he cites Thucydides’s account of the battle between
Corinth and Corcyra over the fate of Epidamnus, in which Corinth
at one point advertised Epidamnus as a colony where citizens would
be “in perfect equality” (epi tēi isēi kai homoiai).22 The two words
isos and homoios come together almost as mutual intensifiers. Greek
mathematics does not use intensifiers—“really round,” “really
straight,” “really parallel,” “really similar” don’t appear! Yet “equal
and similar” does seem to have the sense of “equal in every way.”
And this puts objects into a new class. Thus, in the Elements, “equal
and similar” solid figures makes its appearance in Book XI, Definition 10 as an independent definition after the definition of similar
solid figures quoted above: “Equal and similar solid figures are those
contained by similar plane areas equal in number and in magnitude.”
Euclid might have defined equal and similar solid figures as similar
solid figures whose faces are not only similar but equal as well—
that is, he might have subordinated “equal and similar solids” to
“similar solids,” and, therefore, also have eliminated any need for a
separate definition. Obviously there is a relationship between “similar solids” and “equal and similar solids,” but in Euclidean discourse
it is a relationship between inhabitants of distinct categories.
This understanding of “equal and similar” can also be seen in
Book VI of Apollonius’s Conics. Proposition VI.16, for example,
tells us that “Opposite sections are similar and equal.” The proof
runs as follows: in Conics I.14, Apollonius proved that the latera
recta of the opposite sections are equal; therefore, the figures of the
22. Charles Mugler, Dictionaire historique de la terminologie géométrique
des Grecs (Paris: Librairie C. Klincksieck, 1958).
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two opposite sections (the rectangle whose sides are the latus rectum
and the transverse axis) are equal and also similar; therefore, by VI.2,
the hyperbolas are equal (this is unmentioned in the text), and, by
VI.12, they are similar. The proof is simple, but there is a subtlety.
In proposition VI.2, Apollonius proved that “If the figures that are
constructed on the transverse axes of hyperbolas or ellipses are equal
and similar, then the sections [themselves] will be equal.” From this,
as I said, it follows that the opposite sections are equal, which, by
Appolonius’s definition (in contrast to Euclid’s Common Notion 4),
means they may be fitted one on the other. It would seem then an
immediate inference that they are also similar, that they have the
same shape. But Apollonius says this only after VI.12, which shows
that if the figures of hyperbolas (or ellipses) are similar then the hyperbolas (or ellipses) are similar, and what is more, he cites only
VI.12 as his justification.
Therefore, for Apollonius, to be equal—even when this means
“able to be fit one on another,”—and to be similar are different relations: the assertion that the opposite sections are “equal and similar”
demands proving that the distinction can be made. For us moderns,
who see a logical connection between “equal” and similar,” saying
“similar and equal” is understandable but redundant—like saying
“rectangular and square.”
Conclusion
Let us then go over the ground again and see where we have arrived.
The modern notion of a transformation of a plane ignores the particularity of a given object and acts only on the space within which it is
placed. Such transformations can be chosen in many ways, but, for
similarity, one can be chosen so that all distances between points in
the original space can be dilated or contracted by a fixed ratio; the
ratio, treated as a number, can be greater than 1, less than 1, or equal
to 1. In this way, similarity and equality can be taken as concepts that
are not fundamentally different, equality being the case when the fixed
ratio happens to be 1.
This way of approaching the subject of similarity and equality is
foreign to the mathematics of Euclid and Apollonius because of its
roots in specific geometric figures and their specific properties. Similarity in Greek geometry begins and ends in the sameness of shape.
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Equality begins with the sameness of shape, with superimposition, but
its special character, as seen explicitly in Euclid, is its ability to depart
from the sameness of shape. In this way, similarity and equality are
independent, so that recognizing a similarity, a sameness of shape, is
a different process from recognizing an identity, even though the
processes are tantalizingly close—should I say similar? Still, the two
processes can meet, and when they do, they create a third notion,
“equal and similar.” But, as I argued above, they create a third notion
precisely because they are not joined in logical way—they are simply
brought together.
But this presents us with a difficulty. If similarity and equality are
indeed independent notions, what then is Book VI of the Conics really
about? It cannot be exclusively about shape, as I have thought in the
past, because that, as I have argued, is the province of similarity, not
of equality. So when Apollonius describes Book VI as a book about
similarity and equality in the letter introducing the entire Conics, does
he mean to say that it is simply about two unrelated or vaguely related
topics? Perhaps.
But I think there is more to it than that, chiefly for two reasons. The
first is, as we have noted above, the reappearance of the cone in Book
VI, drawing us back to conic sections as whole, definable objects. The
second is the form of the definition of equality, which is, I believe,
more problematic than similarity, as I have implied throughout this
lecture. The difference between this definition and Euclid’s Common
Notion 4 is found in its second phrase, “Those [conic sections] which
are said to be unequal are those for which that is not so”—making superimposition the exclusive test of equality for conic sections. Thus,
when Apollonius wants to show that sections, or segments of sections,
are equal, he assumes typically that there is some point that does not
coincide with a point on the section presumed equal, and then demonstrates that contradiction follows. What I would like to bring out is
that equality has something to do with every point on the conic section.
In this way, what links similarity23 and equality is their way of looking
at a conic section, or a segment of a conic section, all at once.
23. In the Protagoras (331e), Plato has Protagoras make the remark, concerning justice and holiness, that we should not call things dissimilar just
because there is one point of dissimilarity between them. Socrates replies,
“I was surprised at this.”
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This is the connection, I believe, in which the problem of similarity and equality is related to the idea of locus, which I mentioned
in regard to the little problem with which I started. It too concerns
not an arbitrary place, but a definite identifiable place, all of whose
points have a certain property. It too, in other words, concerns in
some way the whole of conic sections, but in a less direct way.
There is no time, of course, to go into this in detail here, but I do
want to make clear that as we approach an understanding of similarity and equality, it is likely we shall also approach an understanding of other fundamental notions in Greek mathematics.
This, I might add as a final word, was the not the view of older
historians of mathematics, such as H. G. Zeuthen (1839-1920).
Zeuthen had no doubt that the modern point of view was Apollonius’s point of view, and on that basis wrote his expansive and deep
work on the ancient theory of conic sections (Zeuthen, 1886), which
set the tone of Apollonius scholarship for almost a century.24 He
could brush Conics VI aside, saying that it was “of no great significance” in the attempt to understand the Greek theory of conic sections.25 I hope that the discussion here makes that statement moot,
to the say the least.
24. H. G. Zeuthen, Die Lehre von den Kegelschnitten im Altertum (Kopenhagen: Höst und Sohn, 1886).
25. Zeuthen, 384.
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The Soul’s Choice of Life
Greg Recco
Most dreams are forgotten, perhaps even before the night has
passed. Others obtrude into daytime thought, even as their meaning
remains obscure. They haunt us, and seem to promise a rare and
precious revelation. Their coming insistently to mind implies a
faint undertone of reproach, like hearing your name repeated on
waking, before you are quite sure who you are. Such dreams seem
to call from afar, and from where we stand, they can only seem
alien. But we also suspect that we are the ones who are out of place,
and that the dream is calling us back from our wandering. In this
recollection of the unfamiliar, we sense dimly that we are tied to
what is familiar by only a specious kinship, and that our true home
lies elsewhere.
This sort of strange appeal that calls us back from estrangement
can occur not only in dreams or visions, but also in deliberately
produced works of art such as poems, paintings, and stories. In refusing to make any ordinary sort of sense, they contradict our
everyday understanding and invite us to speak along with them in
something like a foreign tongue. The dialogues of Plato, in particular, contain many examples of images or tales of this sort, beguiling works of imagination that linger in memory on the far horizon
of intelligibility. For those of us who read and talk together about
Plato with some frequency, such tales or images have become part
of the vocabulary of our thought—perhaps even a large part, just
as loan-words can come to outnumber a language’s own stock of
true-born names. Before moving on to our main theme, it will be
worthwhile to reflect briefly on a familiar example—the image of
the cave in the Republic—so that we can begin to meditate on how
such images work and what they accomplish.
Socrates asks his interlocutor Glaucon to imagine a cave in
which people are chained in such a way as to be able to see only
what is directly before them, the cave wall on which shadows are
Greg Recco is a tutor at St. John’s College in Annapolis, Maryland. This
lecture was delivered in Annapolis on 12 November 2012.
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projected by a fire above and behind them. Glaucon exclaims that
these are “strange prisoners” (515a).1 “Like us,” Socrates replies.
But then something odd happens. At the very moment when we
might expect Socrates to offer the key by which to decipher these
unfamiliar letters, he instead continues to speak in the language
of the image. The prisoners are “like us,” he continues, “for do
you suppose such men would have seen anything of themselves
or one another other than the shadows cast by the fire on the wall
facing them?” Now, this is not so strange a move as to pose an
impossible task of interpretation, especially to someone who has
thought about the image for some time. We might start with the
idea that our ordinary efforts to know are wrongly oriented and
thus largely unsuccessful, and from there move on to the idea that
this concerns not only our attempts to know the world but even
our self-knowledge and knowledge of others. That sounds about
right. But we should try to imagine what Socrates’s reply would
sound like to someone who had never heard the rest, to someone
who has not had the time to think about it, to someone who does
not know where Socrates is going. To this person, Socrates’s response must seem pretty nearly the opposite of the explanation
that Glaucon’s remark implicitly requested. After hearing it, Glaucon would probably still say that the prisoners are strange, perhaps
as a sort of polite way of saying that the man telling him about
the prisoners is strange—and it would be hard to disagree.
But whether or not Glaucon meant his remark as a reproach, and
however strange Socrates’s speech is, its strangeness does not stem
from some madness of his, some disordered state of his powers of
thought or imagination. What is truly strange here is not the image
to which he gives voice, but the situation it is intended to portray,
namely, the fact that creatures destined for knowledge should
spend their lives so unaware of, and so unwittingly cooperative
with, the powerful impediments to knowing that characterize their
situation. The proper way to hear Socrates’s response to Glaucon’s
remark about the prisoners’ strangeness is thus affirmatively—not
“the prisoners are not strange; they are like us,” but, “they are like
1. Translations throughout are lightly adapted from Allan Bloom’s The
Republic of Plato (New York: Basic Books, 1968).
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us, strange.” And his explanation is an explanation not of the prisoners’ likeness to us but of their strangeness; again, “do you suppose such men”—those described in the image—“would have seen
anything of themselves or of each other than the shadows?” Given
what Socrates is trying to accomplish, deflecting the question of
likeness and going farther into the image may be the only way to
make it work. The image presents important features of our epistemic situation that are normally difficult to discern, but that we
can come to perceive if we take up an initially unfamiliar and awkward perspective, make it our own, and then turn this view back
on what had previously gone unquestioned. In order to know, we
must learn to speak strangely.
With a few small, though significant, differences, this kind of
change in understanding is what is aimed at by the final pages of
the Republic, the so-called Myth of Er (614b-621b). It, too, is a
fantastical story that represents in figurative form an important but
overlooked dimension of our actual situation. Its fantastical character is not a product of wild genius, but arises from Plato’s rigorous attention to both the nature of human freedom and the
difficulty of discerning it from within our ordinary perspective.
In the case of the cave image our learned familiarity with it
makes it relatively easy to put a name to what it is about; unlike
Glaucon, we have read the Republic. And we get some more help
from the fact that Socrates tells us outright what the image is meant
to be an image of. “Make an image,” he says, “of our nature in its
education and want of education” (514a). The Myth of Er, by contrast, is not presented as an image of anything at all. It is ostensibly
the report of a man who returned from the dead to tell of what
awaits souls after life. Socrates presents it as the completion of the
dialogue’s investigation of justice, inasmuch as it gives an account
of the good and bad that come from being just or unjust, not in this
life, but after death.
In this connection, the story is a fitting end for the dialogue, in
that it recapitulates a theme first sounded very near the beginning.
Cephalus reports that as a young man he scoffed at the stories of
punishment in the afterlife, but old age has found him and his agemates more fearful of what is to come. They are looking back over
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lives that contain perhaps no small measure of wrongdoing.
Cephalus is thankful for his wealth, above all for the ability it gives
him to conduct the costly private rituals of expiation that his fear
has made seem prudent. Socrates’s return to this theme at the end
of the dialogue, then, seems to endorse Cephalus’s anxious piety,
at least in confirming that there is something to fear for those who
have done wrong. But the story contains much more than is necessary for this purpose and, indeed, much that does not directly or
obviously further it. Also, it is just very strange. Even with some
degree of paraphrase, it will take a short while to recount it. So
here it is.
Upon his death, the soul of Er traveled along with other souls of
the dead and came to a place where there were two openings in the
earth and two in the sky, above and across from them. Between the
pairs of openings sat judges, who directed the just to continue to
the right and upward through the opening in the sky, and the unjust
to go to the left and downward into the earth. Er himself they instructed to remain, observe, and report what he saw on his return
to the world of the living. What he saw first was this: as some souls
were going into the two openings indicated by the judges, other
souls were coming out of the others, some up from earth, others
down from the heavens. All those who had returned went off with
delight to a nearby meadow, where they made camp and engaged
in conversation. Those who had known each other in life greeted
each other and asked what it was like in the other place. So they
all told their stories, some lamenting and crying as they recalled
all they had seen and undergone in the thousand-year journey beneath the earth, the others telling of the beauty of the sights and
experiences above. In general, those who came from below the
earth said they had received a tenfold punishment for each of their
acts of injustice, once each hundred years, on the grounds that a
human life was about a hundred years long. For acts of impiety towards the gods, the penalty was yet worse. Of one particularly terrible tyrant named Ardiaeus it was related that when his thousand
years had passed and it was his turn to go up, he and other perpetrators of unholy deeds were rejected by the opening. Men standing
nearby seized them, then bound them, flayed them, and dragged
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them along the rough ground in the sight of the others, finally casting them into the pit of Tartarus, from which none return. Fear of
being rejected by the opening and subjected to this torment was
thus the last of the punishments for souls who had lived an unjust
life. The rewards for justice were said to be the counterparts of
these.
On the eighth day, the souls who had returned were made to
leave the meadow and continue their journey. In four days’ time,
they came to a place from which they could see a sort of pillar of
light stretched from above through all of heaven and earth, like a
rainbow. This light was said to bind the earth and the heavens and
be connected to a complex, interlocking arrangement of whorls
forming a sort of spindle, which belongs to the goddess Ananke or
Necessity. Her daughters, the Fates Atropos, Clotho, and Lachesis,
put their hands to the turning of these otherworldly whorls and
were associated with the three dimensions of time: Atropos, she
who cannot be turned, with the future, Clotho, the weaver, with the
present, and Lachesis, the dispenser of lots, with the past.
The souls were then brought before Lachesis. Her spokesman
gathered up the lots and patterns of lives that lay in her lap, and
then delivered the goddess’s message to the souls arrayed before
him. He said: “This is the speech of Ananke’s maiden daughter,
Lachesis: ‘Ephemeral souls, this is the beginning of another deathbringing cycle for the mortal race. A spirit shall not be allotted to
you, but you shall choose a spirit. Let the holder of the first lot
make the first choice of a life to which it shall be bound by Ananke.
Virtue is without a master; as each honors her, it shall have more
or less of her. The blame belongs to the chooser; the god is blameless.’”
Then the lots were distributed to the souls and the patterns of
lives were laid out on the ground before them, lives of all sorts—
lives of animals and tyrants, lives of the famous and the obscure—
and these lives far outnumbered the souls present.
The spokesman continued: “Even for the one who comes forward last, if he chooses intelligently and lives earnestly, a life to
be happy with has been laid out, and not a bad one. Let the first
not be careless in his choice, nor the last disheartened.”
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Since the soul’s choice of life is my theme, let me quote without
paraphrase the section that follows, which deals most directly with
that choice.
“And the first to choose came forward and immediately chose
the greatest tyranny, and, because of folly and gluttony, chose without having considered everything adequately; and it escaped his
notice that eating his own children and other evils were fated to be
a part of that life. When he considered it at his leisure, he beat his
breast and lamented the choice, not abiding by the spokesman’s
forewarning. For he didn’t blame himself for the evils but chance,
demons, and anything rather than himself. He was one of those
who had come from heaven, having lived under an orderly constitution in his former life, partaking of virtue by habit, without philosophy. And, it may be said, not the least number of those who
were caught in such circumstances came from heaven, because
they were unpracticed in labors. But most of those who came from
the earth, because they themselves had labored and had seen the
labors of others, weren’t in a rush to make their choices. For just
this reason, and because of the chance of the lot, there was an exchange of evils and goods for most of the souls.”
“He said that this was a sight surely worth seeing: how each of
the several souls chose a life. For it was pitiable, laughable, and
wonderful to see. For the most part the choice was made according
to the habit of their former life. He said he saw a soul that once belonged to Orpheus choosing the life of a swan, out of hatred for
womankind; because he died at their hands, he refused to be generated in and born of a woman. He saw Thamyras’s soul choosing
the life of a nightingale. And he also saw a swan changing to the
choice of a human life; other musical animals did the same thing.
The soul that got the twentieth lot chose the life of a lion; it was
the soul of Telamonian Ajax, which shunned becoming a human
being, for it remembered the judgment of arms. And after it was
the soul of Agamemnon; it, too, hated humankind as a result of its
sufferings and therefore changed to the life of an eagle. Atalanta’s
soul had drawn one of the middle lots; it saw the great honors of
an athletic man and couldn’t pass them by but took them. After this
he saw that of Epieius, son of Panopeus, going into the nature of
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an artisan woman. And far out among the last he saw the soul of
the buffoon Thersites, clothing itself as an ape. And by chance the
soul of Odysseus had drawn the last lot of all and went to choose;
from memory of its former labors, it had recovered from love of
honor; it went around for a long time looking for the life of a private man who minds his own business; and with effort it found one
lying somewhere, neglected by the others. It said when it saw this
life that it would have done the same even if it had drawn the first
lot, and was delighted to choose it. And from the other beasts, similarly some went into human lives and into one another—the unjust
changing into savage ones, the just into tame ones, and there were
all kinds of mixtures.”
So far the report of Er. Socrates interrupts his recounting it just
once, to emphasize the supreme importance of this choice of a life
and to point out that we really ought to devote all our energies to
acquiring the art of making this choice well. His way of talking
about what would make for a good choice is very interesting, and
I will return to it near the end of this lecture. But for now, let us reflect on the many ways in which the story gives the attentive reader
pause and does not simply supplement the dialogue’s account of
what justice is and what effect it has on souls. The story, it must
be said, does not do just what it was said to do.
In the first place, it is worth reflecting on how extravagant the
whole section on the souls’ choice of life is. The account was introduced and admitted on the pretext that it would supplement the
dialogue’s account of the power that justice has in the soul without
the assistance of reputation or other external benefits. Like other
such familiar tales, it accomplishes this by adding to whatever uncertain external benefits justice and injustice might win in life and
among humans, a certain and unerring exactitude in punishment
and reward from the gods in a sort of life after life. So, one might
reasonably inquire how this purpose is advanced at all by the elaborate account of the spindle of Necessity or the whole idea of souls
choosing their next life, not to mention the many examples of particular choices made by souls famous and unknown. At most, one
might argue that the fact that the lives for which the souls are being
rewarded or punished were of their own choosing underscores
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souls’ responsibility for their own justice or injustice, and thus
shows that the rewards and punishments are deserved. Even according to this explanation, however, the wealth of detail concerning particular souls’ choices, as well as the cosmic backdrop, would
be only so much ornament.
But of all the reasons for taking the Myth of Er as a figure for
something other than what it is said to be, the most compelling is
the fact that the rewards and punishments pointedly do not have
the character we might expect they ought to have: they are ineffectual or at least unfathomably obscure in their mechanism.
That the rewards for a just life are ineffectual we learn from the
example of the soul that draws the first lot and chooses its next life
first. It had come from heaven, and apparently a thousand years’
worth of beautiful sights and enjoyment was not enough to persuade it of anything but its own fitness to be the biggest tyrant of
all. Although it was happy enough to reach immediately for this
life, it was also particularly resistant to taking responsibility for its
own choice when it became clear that the life contained many evils.
This kind of remorse over bad choices, Socrates’s summary indicates, was not uncommon among those who came down from the
heavens.
What of the others? Those who had toiled and suffered below
the earth and had seen the toils and suffering of others were said
to choose more carefully, and thus on the whole, we are told, there
was an exchange of goods and evils for most souls. This might lead
one to the conclusion that while the rewards do not promote the
choice of justice, the punishments do.
But several things undercut the confidence we might have in the
efficacy of posthumous punishments: in particular, the fate of the
incurable or unholy, the complete forgetfulness of the living, and
above all the impossibility of adequately representing injustice to
the unjust perspective. As for the first, there are those like Ardiaeus,
for whose crimes, it seems, no finite punishment could be adequate, on the grounds that his soul was incurable, and possibly also
because of the enormity of his crimes, which transcend the horizon
of justice altogether, being not only unjust but also unholy.
A second problem with the notion that the punishments of the
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afterlife are effective in curbing injustice lies in the fact that souls
are made to drink from the river of Carelessness on the plain of
Forgetfulness before continuing into the life they have chosen, and,
as a result, forget everything. Those who have chosen a just life,
being the majority of those who completed the underground passage, will go through it and then join those who make the heavenly
passage. Now having forgotten their former labors, they are likely
to choose hastily and with misplaced confidence in their ability to
discern what is a good life. Interestingly, this “exchange of goods
and evils” for most souls was already inscribed, so to speak, in the
topography of the place of judgment: the opening that leads out of
heaven is located above and opposite the one that leads into the
earth, as the one that leads out of the earth lies below and opposite
the opening that leads back into heaven. Forgetfulness and carelessness seem to guarantee that there will be a revolution not only
of whorls, but also of souls. But forgetfulness and carelessness are
not magical effects brought about by the eponymous plain and
river. If punishment is the engine driving the motion of souls upwards and towards justice, then the beautiful sights and enjoyment
found in the heavenly passage do no less to drive them down, towards injustice. This is precisely not the image of a world-order
that uses rewards and punishments to produce justice with mechanical accuracy and inevitability, but the image of a world-order that
strongly inclines souls towards an eternal and predictable alternation of good and bad. Why should this be the purpose of the cosmos?
A third problem with the account is that it is difficult to see what
the souls must be in order for their passage to be able to teach them
anything. This difficulty is thrown into relief by a significant omission. Of the souls returning from beneath the earth, Socrates says:
“They were punished for each injustice once every hundred years;
taking this as the length of a human life, they could in this way pay
off the penalty for the injustice ten times over. Thus, for example,
if some men were causes of the death of many, either by betraying
cities or armies and had reduced men to slavery, or were involved
in any other wrongdoing”—and here I interrupt to note that just
where one might hope to learn precisely how such acts are an-
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swered in that other place, Socrates concludes simply, “they received for each of these things tenfold sufferings.” In other words,
Socrates provides us with no specific information. Plato handles
the issue of narration very deftly here, for he has Socrates preface
this section with a warning about its incompleteness; Socrates says,
“Now, to go through the many things would take a long time, Glaucon. But the chief thing is this,” and then proceeds with the summary I just read. But if the purpose of resorting to summary was
to avoid trouble, then it is difficult to understand Socrates’s choice
of examples.
In the first place, the list of specific forms of injustice by itself
leads one to expect a similarly specific list of punishments. Also,
the fact that each “cycle” of punishments is calibrated to the length
of an average human life supports the expectation that punishments
will somehow correspond to, mirror, or just repeat in inverted form
the particular wrongs one has done. But the examples of injustice
Socrates in fact offers do not fulfill any of these expectations, for
the important reason that the victims of these injustices are in each
case many in number. If a man betrays an entire city, how can his
single life (or a single afterlife) stand any chance of comprising
the myriad injustices done to his fellow citizens? If he sold dozens
into slavery, how could his life encompass suffering the same fate
dozens of times? Even if somehow it could, it would also have to
contain dozens of instances of the state of freedom that slavery destroys. And each of these would have to be in some way pristine,
so that the evil that is enslavement could have its full effect on the
soul being punished in this way—for enslaving one person twice
is not the same as enslaving two different people. In general, then,
it is unclear how a single life can have the evil it does to many represented to it effectively.
One solution to this conundrum, of course, is to take one sort of
evil to stand for all others, to serve as a kind of medium of exchange. Maybe pain could serve as such a punitive currency, repaying specific evils with generic badness. The extravagant
punishment of the soul of Ardiaeus, however, serves both as an example of this sort of thinking and as a sign of its insufficiency. The
punishment is not only of infinite duration; it is also unimaginably
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intense, and the one being punished in this way does not in any
way signal to us what his experience is. Now, it is possible, of
course, that we hear nothing from the soul of Ardiaeus because
there is no need. If his soul is incurable, perhaps his punishment is
not for him but an example to others, and in order for him to serve
as an example, all that matters is that they take his experience as
an example, whatever he himself may think of it. Consistent with
this interpretation is the presence of the guards who point out to
the others why these souls are being singled out for such treatment;
that is, it seems at least in part to be a show put on for their benefit.
Also consistent with this view is the claim that what improves the
judgment of those who make the underground passage is not just
that they have labored and suffered themselves, but also that they
have seen the labors and sufferings of others. Nonetheless, the absence of the directly suffering soul’s perspective on the single particular punishment reported to us underscores the problem,
outlined by omission in the preceding passage, of how a soul’s evil
can be represented to it—and this remains a problem.
If the soul’s thousand-year journey below the earth is to teach it
anything—as the improvement in its choice of life suggests it
does—then the soul must somehow have the evils it engaged in as
though they were something good presented to it as what they in
fact are. But in order to recognize one’s own wrongdoing for what
it is, the perpetrator must have a different perspective than was
available to him during the act, and this kind of thoroughgoing
change in perspective is, as we have learned, terribly difficult. In
the cave image, it is represented as a turning around that can simultaneously be a passage from what is darker to what is brighter
(that is, an actual improvement) and a passage from what is perceived clearly and comfortably to what is perceived only dimly
and painfully (that is, an apparent worsening). Something else is
needed: a trustworthy and trusted guide who can articulate what is
happening to the soul being forcibly turned around in this way. In
the end, pain by itself is too diffuse, too immediate, and too uncontextualized to bear the articulated meaning that would be necessary in order to effect this change, a fact that is perhaps hinted at
by the punishment’s tenfold repetition. Even the torture of the souls
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of the unholy, which might seem to stand on its own as an object
lesson in the wages of wrongdoing, is supplemented in the story
by agents standing by to explain it, which suggests that it cannot
bear its meaning within itself on its own.
In the case of both punishments and rewards, then, the report of
Er sets up certain expectations or requirements that it then pointedly does not or cannot fulfill. The rewards for a just life, we feel,
ought to reinforce the choice of justice, but instead they are presented as strongly correlated with the careless haste and entitled
self-importance that lead to a bad choice of life. As for the punishments, while they are said to have the effect they ought to, still,
the mechanism by which they are meant to accomplish this is
markedly obscure, and inquiring more closely into it only makes
the confusion more intense, particularly by directing attention to
the source of the problem: the soul and its perception of, or perspective on, the good. If the myth’s self-presentation is at odds with
its content, particularly in its central conceit, we have to turn elsewhere to discover its real import. One thing that is clear, as we
have just seen, is that the story concerns the soul. Just what is the
soul in this story?
One phrase in the description of souls’ choice of lives incidentally brings to the fore one of the key features of the myth’s portrayal of the soul. Er saw “a soul that used to belong to Orpheus”
choosing the life of a swan. The striking phrase “used to belong”
underlines something that must be assumed in order for the story
to work at all, and it does so compactly and forcefully. For the myth
to work, a soul, whatever else it may be, cannot be identical with
any named person. The name “Orpheus” must indicate the temporary composite of an otherwise anonymous soul with the singer’s
life whose story we know from myth. Any name, then, must miss
the soul and indicate only such a composite, even my name or
yours. The possessive in the phrase “my soul” becomes particularly
obscure. If I were to utter the words “my soul,” who would I be
saying the soul belongs to, and what would I be taking myself to
be that is distinct from my soul? Who or what is speaking when
the words “my soul” are uttered? Whatever we might previously
have thought it was, the story is now telling us that a soul is not
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identical with a life or a person, since it precedes and outlives both.
One possible source for this strange conception of the soul is the
discussion of its immortality earlier in Book 10 (608d-612a).
There, the question arises how the soul can be both immortal and
capable of being at odds with itself. Self-opposition (of the sort examined in Book 4) is associated with being composite, and this, in
turn, is associated with change and decay. A soul composed of
parts, it seems, could only be mortal. Instead of investigating this
dilemma, Socrates merely suggests that the view of soul that we
have—and that he and his interlocutors have had throughout the
whole of the dialogue—is like the view one would have of how a
man looks if one were to see only the statue of him that had lain at
the bottom of the sea for many years and become disfigured and
covered with shells, seaweed, rocks and so forth, as in the case of
the statue of Glaucus. The image more or less directly asserts that
our embeddedness in body, change, and manyness has made our
souls unrecognizable. This is an unpromising starting point, but
Socrates remains confident and ventures the guess that the soul’s
true nature is to be found by our looking to its philosophia, its love
of wisdom. This recalls another account of the division of the soul
that emerges from the yet earlier discussion of the terrible evils of
tragic poetry in Book 10. This account divides the soul’s philosophical, calculating, law-abiding part, which suffers misfortune
in silence and tranquility, from another part, which indulges in loud
lamentation. The latter is itself indulged by writers of tragedies,
who trick even the decent man into weeping immoderately at the
misfortunes of another on the grounds that this is at least not selfpitying, and is only a kind of play (606a-b). The gist seems to be
that the first part of the soul would do its work better without the
second. Both accounts, then, solve the problem of manyness by
making one part stand for the whole. Whatever the merits or faults
of such a solution, we should consider that if the true identity of
the soul should turn out to be only its rational part understood in
this way, then the whole drama of existence—the stories of our
lives as we commonly understand them—would be wholly irrelevant, composed entirely of a sort of encrustation of alien matter
that only serves to obscure the soul from view. By themselves, on
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this view, souls might essentially have nothing to do with lives.
While these two prior discussions of soul seem relevant to the
myth and are consonant with some aspects of its sharp distinctions
between soul and person and between soul and life, they are at odds
with others. Souls in the myth are not heartless calculating machines, but beings capable of feeling and expressing emotion.
When the souls complete their respective journeys, they go off
“with delight” to the meadow where they confer. When those who
came from the underground passage recount what they have seen
and undergone there, they cry and lament in recalling it. When
these souls are nearing the exit and see some like the soul of Ardiaeus being rejected, they experience a great fear, which they note
is only one among many they have suffered. In sum, then, the souls
in the story respond emotively and expressively to their situation,
even during this time when they are presumed to exist in separation
from body and life.
In addition to transitory affections such as a moment of fear,
souls in the myth also have longer-standing dispositions or traits
of character. The soul of Ajax, son of Telamon, bitterly recalls the
judgment that granted the arms of the departed hero Achilles to
Odysseus instead of to him, and so flees humanity. The souls of
Orpheus and Agamemnon, in turn, make their choices of animal
lives out of long-standing hatred, of women in the first case and
of humanity in general in the second. In each case, these quasi-permanent states were crystallized, so to speak, by the trauma of their
previous lives (the very ones we associate with their names, as if
their souls had become those single lives). Their hatreds and resentment are very much not the passions of a moment, as they appear to have persisted unchanged and utterly undiminished
throughout their millennial journeys. A final, most significant example of a state or characteristic of soul allowed by the myth is
that of the soul of Odysseus, which “from memory of its former
labors, . . . had recovered from love of honor.” Somehow, the soul
as portrayed in the myth is capable of being affected by its life,
and affected in such a way as to be able to learn, not just greedily
carry forward the savor of bitter memory. In either case, however,
what we see is that however distinct souls may be from lives, their
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lives affect them. In light of this, perhaps it is time finally to turn
directly to what the story must take a life to be.
This is in one way the most straightforward and familiar element
of the story; everyone knows what a life is, what it is composed
of, why it is important, what makes it good or bad, and so forth. In
another way, however, the central conceit of the myth of Er requires a life to be something that is almost impossible to understand. Recall that the life contains elements like wealth or poverty,
good or bad birth, strength, beauty, political office or rule, and indeed everything that could characterize a life, or almost everything.
For, as was explained, since the soul that lives the life must be
changed by it, the life considered by itself does not contain an “ordering” or “arrangement” of soul (taxis). If our question is what
we ought to remove in thought from our usual conception of what
a life is in order to arrive at an idea of the lives whose paradigms
lie in the lap of Lachesis, the answer is both simple and perplexing:
we must remove everything that soul is. As it has done in many
places, the dialogue is once again causing a problem by treating a
distinction as a separation. When Socrates manages to bring the
conversation to a halt of this sort, he often turns to an image or example that retroactively modifies one of the discussion’s starting
points. We could try the same, and instead of trying to proceed with
delimitation or definition in the face of aporia, we might turn to an
example of what the myth takes to be a life, which it obligingly
provides.
None of the lives is very extensively described, but the first example of a life that is chosen is among the fullest. The nameless
soul that drew the first lot—which “participated in virtue out of
habit, without philosophy” after living in “an ordered regime”—
picked the life containing the biggest tyranny straightaway, “but it
escaped its notice that eating his children and other evils accompanied this.” It escaped his notice. How strange. How can we understand this? Should we agree with the old song that “the large print
giveth and the small print taketh away”?2 Do the events or elements
of a life presented to choice differ in their prominence, such that
some would count as the large print, and some as the small? And
2. Tom Waits, “Step Right Up” (Small Change, Asylum Records, 1976).
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what would determine which appear more or less prominent? Just
what is written or figured on the paradigms of lives in the lap of
Lachesis? In the example just considered, the great tyranny looks
good at first, but when the soul “considered the life at its leisure,”
it discovered its evils, and was unhappy with its lot.
In a way, this latter portrait of a life is familiar and cogent: a life
containing an apparent good may of necessity also contain actual
evils that counterbalance or even outweigh the apparent good. But
in another way, this is an unsatisfactory way of talking about a life.
It tries to mark the badness of the life that contains one sort of fact
sometimes thought to be good (being a tyrant) by pointing out that
it also contains another sort of fact, which is generally acknowledged to be bad (eating one’s children). The whole question of
what makes a life good or bad has been reduced to the piecemeal
evaluation of particulars, and the summation of such judgments,
as in what is sometimes called a rubric.
But we really ought to doubt this soul’s assessment of its chosen
life, since we have already been told that it makes the choice affected by folly and gluttony. It could be so misguided as to be mistaken about which of the life’s elements is good and which bad. In
fact, we have already been told in Book 9 that the worst possible
eventuality for a soul that is tyrannically inclined is for it to become
an actual tyrant. Conversely, it may be that something as horrible
as eating his children is an appropriate accompaniment to the
“large print” of his being a tyrant.
But just inverting the assessment this foolish soul made of each
of these facts does not really solve the deeper problem, of which
the problem of the relative prominence of a life’s parts—its large
and its small print—is just a symptom. The component elements
of a life in the myth are subject to two seemingly contradictory demands: they must be “without an arrangement of soul,” and thus
be somehow meaningless, and they must be capable of “leading”
the soul to being just or unjust, and thus somehow have a meaning.
As for the former term of the contradiction, given that there are
good and bad among rich and poor alike, wealth, to pick one example, looks like the sort of thing that the Stoic Epictetus would
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call indifferent, something that is of no importance when compared
with the greater question of whether we are living well, and does
not by itself answer the question. As for the latter, however, the
soul that has learned the art of choosing lives well, Socrates says,
will call lives good or bad depending on whether they “lead to
virtue or vice.” But now we have to ask: how can events be said to
“lead” to virtue or vice at all unless they have within them the germ
of a sense, an incipient significance that is preserved in what it
gives rise to?
As in other similar cases, the commentary on the myth is quite
relevant and helpful, if somewhat oblique. Socrates portrays in
some detail the person who has acquired the art of choosing lives
well. He says: “He will take into account all the things we have
just mentioned and how in combination and separately they affect
the virtue of a life. Thus he may know the effects, bad and good,
of beauty mixed with poverty or wealth and accompanied by this
or that habit of soul; and the effects of any particular mixture with
one another of good and bad birth, private station and ruling office,
strength and weakness, facility and difficulty in learning, and all
such things that are connected with a soul by nature or are acquired.
From all this he will be able to draw a conclusion and choose—
while looking off toward the nature of the soul—between the worse
and the better life, calling worse the one that leads it toward becoming more unjust, and better the one that leads it to becoming
more just” (618c-e).
One of the most striking things in this passage, I think, is the intensity of its emphasis on combination. The possessor of the art of
choosing lives is said to consider the elements of lives both “separately and in combination” but all the examples are of complex
configurations. Here, then, is one way in which something can both
have a meaning and not have it in itself: it can have its meaning in
being combined with something else. Note that the myth helps us
here. The composition of elements that makes up each life is not
something chosen; the lives have already been assembled by the
time the souls have to choose them. Rather, souls are to call lives
good or bad on the basis of no element in them, but on the basis of
what living such a life will work in the soul that lives it. That is,
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what was being chosen (whether or not this escaped the choosers’
notice) was not an indifferently composed aggregate of particular
life-events or features, but something whose value lies on another
level.
Another striking feature of the passage is how thoroughly confusing it makes the separation of life and soul that lies at the basis
of the myth. In the first place, the possessor of the art is said to
know about the effects of mixtures that include elements such as
“this or that habit of soul.” This seems directly opposed to the
claim that lives are without an “ordering” or “arrangement” of soul.
Including this feature does not in itself introduce an inconsistency;
rather, it states the problem well: the soul that sets out to have
wealth or any other good thing will be changed by its pursuit, so
that there is no guarantee it will still want or be able to enjoy what
it was pursuing by the time it gets it. The one who possesses the
art would have to be able to predict what changes the living of a
life would work in the soul. In short, what makes elements of a life
part of a life that can be called good or bad is their connection with
the soul that has to live that life—the suffering, rejoicing, experiencing, remembering, expressing, and thinking being. These powers are what lend to those events or conditions whatever sense they
have. Here we see another way in which a life has a meaning, but
not in itself; it has a meaning in and for a soul.
To state the matter most generally, elements of a life are capable
of having a meaning that is not in them because that’s just what it
is to be an element of a life: to be a “Here” that is also, with all the
weight Plotinus gives the word, a “There.” The seeming paradox
is just the reality of our situation, and one that Plato has been carefully directing our attention to throughout the dialogue. We spend
as much time as we do in this dialogue on the proper organization
of an educational program not merely for the stated reason—that
we need guardians who will be both harsh with the city’s enemies
and gentle with its citizens. Rather, as the central books show and
the final myth signifies, the deeper issue is that what is most immediately apparent is always somehow a distraction from the intelligible reality of what is. But the sensible is not merely
something other than the intelligible: it is the region wherein the
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intelligible shows itself; it is where we live. The small things matter. The ball I learn to catch may be little more than arbitrary mineral, vegetable, and animal products refashioned to the measure of
a human hand, but the act of catching that this ball makes possible
is an emblem and anticipation of all sorts of future forms of mastery. The little bumps and tussles of playground life are like so
many prophetic utterances spoken to us in childhood that foretell
adult life’s disappointments—its alliances and betrayals, its kindness and its savagery—and they foretell them with both the accuracy and the obscurity that are characteristic of an oracle. Our lives
consist not in isolated events, but in pattern and paradigm, eidē on
the move.
This strange mode of being of the elements of our lives is a feature of the world of the myth of Er that also happens to be a feature
of our world; it is the literally true thing at the center of a mass of
figurative falsehoods, and around which the whole turns. It is the
true thing that seems strange to us who have become strangers to
it. The elements of lives can appear big or small, cruel twists of
fate, or irrelevant impediments to powers we find we do not need
to get by. We who live them do not experience ourselves as having
chosen them. But reflecting on the image of our souls choosing
our lives can awaken us from the dream-state in which we treat the
meanings of our lives as beings, as ta onta, as things that always
are, with no tincture of ambiguity or self-opposition, no dependence on perspective or interpretation, no horizon of possible transformation. On the contrary, we should recognize our lives in their
truth: they are the materials—somehow both indifferent and essential—out of which souls weave the tissue of meaning they first put
on and then inhabit; they are elements that stand to our souls and
hearts as those other elements—earth, air, fire, and water—stand
to the multifariously capable bodies of living beings of all kinds,
their material support and flesh. When the elements of our bodies
or lives fail us, we break, but when they cooperate, we succeed in
being something they would not be on their own, something other
and beyond.
The myth tells us that we need to learn how to cooperate with
these elements and their ways, so that we may make a good pas-
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sage in this life and the next, and perhaps in the next after that. But
what would make for a good passage? What should we hope for?
A well-deserved reward? Or a suffering that makes the soul better?
The beautiful sights and pleasant experiences that the myth sets up
as a reward for a good life carry with them the same ambiguity as
the goods of this life: many souls are not improved by them, but
turn out worse. To answer the question, we might think of the soul
that once belonged to Odysseus. Of this restless and clever soul,
we were not told whether it had come down from heaven or up
from the earth, only that memory of its former labors had cured it.
Those labors could have been carried out on earth as part of the
life we associate with Odysseus’s name—where he struggled to
regain his home after long years in foreign lands, losing all his
comrades—or they could have been performed as payment in that
place beneath the earth, some days’ journey from the spindle of
Necessity where lives are woven. Perhaps our hope and prayer
should be the same as his could have been: may we all perform
such labors, and remember them, and be cured of what ails us.
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Artistic Expression in Animals
Linda Wiener
I have three main goals in this lecture. The first, and most important, is to inspire you to be more open to and aware of the animals
all around you. The second is to give some history of a fascinating
debate on animal color and behavior that began in the early twentieth century in the United States; this will illustrate how difficult
it is to elicit any sort of Truth from the phenomena of nature. The
third is to persuade you that, at least some of the time, animals engage in artistic expression for its own sake.
Ever since Charles Darwin published On the Origin of Species
in 1859,1 by far the most popular way of interpreting the appearance and behavior of organisms has been through the theory of natural selection. According to this theory, if a mutation appears in an
animal and that mutation helps the animal survive and reproduce
better than similar animals in their environment, the mutation and
the animals that carry it will be preserved while others will eventually decline and die out. But ever since this theory was published
there has been dissent. The most well known dissents are from religious objectors, however there have always been some scientists,
naturalists, philosophers, and others who work intimately with
plants and animals who accept the theory of evolution through natural selection, but believe that it is not sufficient to account for all
the phenomena of nature. I am one of this latter group.
In this lecture, I will use the lens of artistic expression in animals
as a way of exploring this question. I begin with an example from
bird song. I was at a performance of Beethoven’s Ninth Symphony,
Linda Wiener is a tutor at St. John’s College in Santa Fe, New Mexico.
This paper is adapted from a lecture delivered at the College’s Annapolis
campus on September 6, 2013. The original lecture involved images and
some video clips. This version makes do with some photographs, as well
as links to images on the web. Be sure to open the links and look at the
images while reading!
1. Charles Darwin, On the Origin of Species, first edition (Boston: Harvard University Press, 2001.
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given by the Santa Fe Community Orchestra at the Santa Fe Opera
House in May, 2008. The opera house is covered on top, but open
around the sides. At the very beginning of the third movement, a
flock of house finches flew in and perched above the orchestra.
One male joined in singing with the music in such a way that it
seemed a part of the piece. He sang for most of the third movement
and at the very end of that movement, when the orchestra plays
four notes, the bird came in afterward, using the contact chirps of
the species, and mimicked those last four notes.
This is an example of a bird singing in his capacity as a musician. He shows that he knows something about music and can employ it appropriately outside its use for attracting mates and
protecting territories. This propensity of a least some birds to sing
outside the mating and nesting seasons was noted by Thoreau and
more recently by David Rothenberg in his book Why Birds Sing.2
David is a philosopher and jazz clarinetist. He plays his clarinet
with birds in aviaries and in the wild, sometimes with remarkable
results. As with the bird at the opera house, some birds respond
musically to his musical prompting. I particularly like a duet he
participated in with a laughing thrush; it can be heard online.3
Rothenberg concludes that birds sing because they enjoy it.
Other animals have been reported to respond to human music. I
read that crickets will approach when they hear music and start
singing. My own experiments with two species of crickets were
inconclusive; they chirped so much it was hard to tell when they
were responding to music and when they were chirping in their
natural rhythms. I have been told stories of raccoons coming on
stage during a concert. There is also record of a bear doing the
same thing (Fig. 1).
Moving on from music, probably the most famous artistic animals are the bowerbirds of Australia and New Guinea. For instance,
the satin bowerbird builds an oval shaped bower out of sticks and
decorates it with mostly blue objects. This includes flowers, berries,
and even human-made items like plastic drinking straws. Other
species have differently shaped bowers and use different color
2. David Rothenberg, Why Birds Sing (New York: Basic Books, 2005).
3. http://www.whybirdssing.com
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Fig. 1: Bear at concert4
schemes. The vogelkop bowerbird builds a conical bower and decorates mostly with red and orange objects.5 The females come
around to check out the male bowers, the males dance for them, and
then the female selects a male to mate with. She then goes off to
build a nest and raises the young on her own.
This is a classic example of what Darwin called “sexual selection” in his book Descent of Man and Selection in Relation to Sex.6
In Darwin’s account, the females have aesthetic standards and
whichever male best meets those standards is the one she chooses
as a mate.
Darwin thought sexual selection less rigorous than ordinary natural selection because it was not a life and death matter. Recently,
Darwin's view of sexual selection has been revised. Now, the
building, decorating, and dancing activities of the male are seen
as direct reflections of the actual genetic quality of the males. The
females are selecting the males not according to an aesthetic standard, but according to which are the most genetically fit. This
brings sexual selection theory more in line with the classic theory
of natural selection.
4. From Carl Marty, Northenaire’s Ginger and Her Woodland Orphans
(Park Falls, Wisconsin: MacGregor Litho, 1953).
5. http://www.duskyswondersite.com/animals/bower-birds
6. Charles Darwin, Descent of Man and Selection in Relation to Sex (New
York: Penguin, 2004).
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A group of birds called the catbirds, in the same family as the
bower birds, helps raise a few questions about this modern understanding. In the catbirds, the males and females cooperate to build
the nest and rear the young; on average catbirds rear more offspring than the bowerbirds. An alternative explanation for bowerbird behavior is that the bower birds have “chosen” in some way
to forgo their maximum reproductive potential in order to devote
energy to the creation and appreciation of art.
Closer to home, there are other collecting and decorating animals. The pack rat of the Southwestern states is one. They are
beloved by archaeologists because they collect all sorts of things
from their surroundings and store them in their nests. An ancient
pack rat nest can tell scientists a lot about the sorts of things that
were around at the time. Pack rats are also famous for being destructive when they choose to nest in your home or vehicle. Whenever I hear friends complain about a pack rat nest, I beg them for
photographs.
Pack rats have different preferences when constructing their
nests. Sometimes, it is just a bunch of sticks and a few fabulous
items they have collected. My friends Betsy and Jamie had a nest
in their vehicle with a central white fluffy nest structure, then an
attractive bed of greens with dried red chiles piled in the center
(Fig. 2a). My friends Robert and Susan had a pack rat nest in their
vehicle with a central grey fluffy nest structure surrounded by a
variety of sticks, stems, and cholla cactus pads (Fig. 2b).
Fig. 2a
Photo by Jaimie Haskell
Fig. 2b
Photo by Robert Schlaer
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ESSAYS & LECTURES | WIENER
Another friend, Pam, tells this story about a pack rat nest she
found in her truck. She was so mad when she saw the nest, she
threw everything on the ground; when she came back some time
later, it was all back in the truck. Not only that, it was back in just
the way it had been before, with each major element, stems, sticks,
and other items in exactly the same spot. This shows us that the
nest isn’t just a bunch of stuff thrown around. The pack rat arranges
her space to her own taste. Just as when someone messes up one
of your rooms, you put it back to its original arrangement, so too
does the pack rat.
Let’s look at some domestic animals. I had three ferrets over a
period of about nine years. They were all avid collectors. They had
stashes of the stuff they collected; there was a main stash usually
under and couch or in a cabinet, and smaller satellite stashes in
various locations. I noticed that they went through periods of collecting. My ferret Fennel collected soft things like beanie babies
and stuffed animals for a while and then switched to hard things
like pill bottles and vials. They also had a sense of value. If they
found something unusual, it would be hidden way in the back underneath other items in the stash, whereas a common object like a
pencil would just be thrown in anywhere.
My colleague Llyd Wells in Santa Fe has a ferret named Tomato
who makes stashes.
Tomato keeps a stash of mostly soft items in the closet in the
bedroom (Fig. 3a) and another stash of mostly harder rubber items
under the sink in the bathroom (Fig. 3b). Llyd will switch an item
Fig. 3a
Tomato’s bedroom stash
Fig. 3b
Tomato’s bathroom stash
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out of one stash into the other and Tomato is quick to “correct”
this. Tomato has organized her stashes and knows how they are
supposed to be.
If it seems like I am talking about ferret collecting in much the
same way I might talk about human collecting, it is because I am.
This brings up the bad word anthropomorphism. I am accused of
projecting my own desires, intentions, and activities onto the ferrets. However, if I see an animal acting in much the same way I
would in a similar situation, why shouldn't I, at least as a first step,
assume that it is acting with similar desires and motivations? After
all, the ferret, the pack rat, and me are all children of nature. We
have all evolved on this earth; why should we be assumed to be so
alien to one another?
Here is one more example from our domestic animals. Robby
is a dog who belongs to friends Jonathan and Barbara. He has a
basket of stuffed animals and when his people are away he makes
careful arrangements of them on the living room floor. A typical
one has four evenly spaced animals in a straight line, with one off
center (Fig. 4a). A slightly more complex arrangement has two of
the same animals, in different colors, together. There are two animals, evenly spaced on either side of these two and then down from
the ends, another animal on each side with different, but still even,
spacing (Fig. 4b).
Fig. 4a
Robby’s animals, simple
Fig. 4b
Robby’s animals, complex
Also typical of Robby’s work: the stuffed frog is in every arrange-
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67
ment. This is definitely not the work of an animal just throwing
things around because he is mad that his people are away.
A few years ago on YouTube there was a doberman who made
similar stuffed animal arrangements, though he went in more for
circular patterns. Let me take a moment to recommend YouTube
as a valuable source of information about animal behavior. Now
that most people have small video cameras or cell phones with
them all the time, an amazing variety of animal behavior has been
recorded and put online. Behaviors that I would have been called
crazy for reporting ten years ago are now accessible to everyone.
And everyone can judge for themself.
These collecting and decorating behaviors show us a range of
possibilities in nature. They are essential to the reproductive biology of the bower birds and certainly serve a utilitarian function for
them. For pack rats and ferrets these activities are typical of the
species, but do not serve any essential functions that we know of.
Robby the dog’s activities are not at all typical of the species, but
such behavior pops up now and then among dogs. I have read of
other cases in which one or a few animals engage in these kinds of
activities, though, again, they are not typical of the species. There
were a group of pigs7 who made arrangements out of shingles and
dirt and even a wolverine who made arrangements of sticks in a
chain link fence, left them up for a few days, and then made a new
arrangement.8
I suggest that the musical, collecting, and decorating activities I
have been chronicling are not always specifically evolved to serve
mating rituals or other survival needs, but may be part of a much
broader expressiveness in the natural world that can be turned to
utilitarian functions, but need not be.
When we look at invertebrates, it is a little harder to judge what
they intend, because they are not so closely related to us. Let’s look
at a few examples that might count as art for art’s sake. The decorator urchin collects various materials from the ocean floor and
7. Noel Perrin, Second Person Rural (Boston: David R. Godine, 1980).
8. Douglas Chadwick, The Wolverine Way (Ventura, California: Patagonia
Books; 2010).
9. http://www.flickr.com/photos/benjaminbull/2844381114
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puts them on top of its spines. I have read that this is for camouflage, but the photos that I have seen do not support this; they are
all highly visible.9
Harvester ants are common in the Southwestern United States.
Their nests are covered with small stones and are famous as collecting sites for various materials that people want. Some are covered
in crystals and sparkle in the sun. People know they are the place to
go to find turquoise and beads. Paleontologists find small fossils
from rodents on their nests, and scientists studying radioactive minerals go to their nests to find trinitite, the mineral formed from the
first atomic bomb test at the Trinity site in New Mexico.10
Garden spiders, also called writing spiders, build orb webs and
decorate them with zig zag patterns that are different for each
species.11 Henri Fabre, the great French entomologist, called these
their “signature.” I had, until recently, not read any plausible accounts of their function. It turns out, however, that the silk in the
“signature” is different from the web silk. It reflects ultraviolet
light and may function to attract insects into the web.
This is still untested, but does seem plausible. Even so, a further
question is why the web is decorated in just this way. Why do such
decorations seem more than is needed to fulfill the functions they
serve? This is one of the main questions that David Rothenberg,
the man who wrote Why Birds Sing, pursues in a more recent book
called Survival of the Beautiful.12
Usually when we think about animals and art, we are not thinking
about the arrangement of a pack rat’s nest or the beads on a harvester ant’s nest. We are thinking, rather, that animals are beautiful.
Humans have long appropriated bird feathers and animal skins for
our own adornment. I am an entomologist, and so I look at insects
a lot. Consider this beetle (Fig. 5)—the highly ornamented form of
the legs, the shape and texture of the thorax, the colors and patterns
on the wing covers. It is a fantastic animal and only has to be put
on a background and photographed to be easily seen as art. This is
10. http://www.flickr.com/photos/mouser-nerdbot/5334689193
11. http://en.wikipedia.org/wiki/File:Argiope_aurantia_web.jpg
12. David Rothenberg, Survival of the Beautiful: Art, Science, and Evolution (New York: Bloomsbury Press, 2011).
�ESSAYS & LECTURES | WIENER
69
Fig. 5
“Coleoptera” by Jo Whaley
one of the ideas behind a book, The Theater of Insects,13 that I collaborated on with photographer Jo Whaley.
Other insect colors are understood as serving important protective functions. The great purple hairstreak, a butterfly I see in New
Mexico, has prominent white polka dots set in a black background
on its head and thorax, a bright orange abdomen, and iridescent
scales on its wings.14 The top of the wings are a beautiful irridescent purple. The bold black, white, and orange colors are referred
to as warning coloration. Insects that are poisonous such as the
black and orange monarch butterfly, or dangerous like the yellowand-black-striped wasps and bees, have these kinds of color patterns. The theory is that predators such as birds learn to avoid these
patterns and so the animals are protected. Also, insects that are neither poisonous nor dangerous may evolve these patterns to fool
predators into refusing to eat them.
The peacock spiders, a group of jumping spiders, have wonderful bright color patterns, and special flag-like structures on their
second pair of legs.15 They do elaborate courtship dances for the
females. This again seems like a classic example of sexual selection in that the colors, patterns, ornaments, and dancing serve an
13. Jo Whaley, Deborah Klochko, and Linda Wiener, The Theater of Insects (San Francisco: Chronicle Books, 2008).
14. http://www.jeffpippen.com/butterflies/greatpurplehairstreak.htm
15. http://amazinglist.net/2013/02/the-peacock-spider-maratus-volans
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essential function in attaining a mate.
Consider, however, the radiolarians. They are one-celled animals
that live in the ocean. They are an old lineage, existing for over
600 million years. They have an amazing variety of forms, ornaments, and textures that serve no known functions.16 It seems that
as soon as there were animals, even just single-celled ones, there
was already a tendency toward elaboration. Again, I suggest that
such elaboration may be part of a basic expressive function of nature. Such appearances are not necessarily evolved to serve particular survival or reproductive functions.
Hold that thought. Now I am going to turn to the debate I mentioned earlier. Abbott Thayer was a well known portrait painter in
New England at the turn of the twentieth century. He was famous
for portraits of women with angel’s wings. He was also famous for
his theory of animal coloration. With his son Gerald, he published
a book in 1909 called Concealing-Coloration in the Animal Kingdom.17 I came across this book quite by accident about eight years
ago and was enthralled by it. Contrary to the theory of his day, and
also contrary to the theory of our day, the Thayers thought that all
animal colors were concealing.
The frontispiece of the book, a painting, shows a male peacock
with his colorful tail concealed in the colorful leaves on the forest
floor and his beautiful blue neck concealed against the sky (Fig. 6).
This vantage would be from the point of view of a ground predator
such as a fox.
More plausible, perhaps, is his photographic plate of a grouse
showing it concealed in its forest environment (Fig. 7).
Almost everyone would agree that grouse are well concealed in
the forests in which they live. But, Thayer goes further. He tells us
that if you want to know what a forest looks like, you should not go
around looking at forests because they will confuse you with their
idiosyncracies. You should look at animals such as the grouse who
must be concealed wherever they are in the forest. Thayer writes:
16. http://incrediblebeings.files.wordpress.com/2010/05/radiolarians-10species-2.jpg
17. Gerald Thayer and Abbott Thayer, Concealing-Coloration in the Animal Kingdom (New York: MacMillan, 1909).
�ESSAYS & LECTURES | WIENER
71
Fig. 6
Thayer plate of a grouse
concealed in the forest
Fig. 7
Thayer plate of a grouse
concealed in the woods
They are, in the best sense of the word, triumphs of art;
and in a sense they are absolute, as human art can never
be . . . There he will find it in epitome, painted and perfected by nature herself. Color and pattern, line and shading, all are true beyond the power of man to imitate, or
even fully to discern.18
It was this insight that led Thayer to become the father of military camouflage. He went around trying to get the U. S. military
18. Thayer, 240.
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to adopt the idea. He failed, though the French military took him
up on it. Now, of course, military camouflage is well established
everywhere.
Under the influence of this book, I was failing to see animals
everywhere. Driving in the high plains along Route 285 in New
Mexico in the early spring, I would think of Thayer’s claim that
antelope are marked so as to be concealed on the patchy background of snow and bare soil.19 I would be thinking that there were
hundreds of antelope out there, but that I could not see any of them.
The problem with this construal is that in fact you can see them,
especially if you are looking for them.
One person who read Thayer’s book and was incensed by it was
Theodore Roosevelt. In fact, he was so incensed that he published
a 120-page rebuttal in the Bulletin of the American Museum of
Natural History.20 Roosevelt writes: “It is impossible to go over
page by page the really countless erroneous statements, wild
guesses, and absurd interpretations of fact which the book contains.” He cuts the Thayers some slack because of their artistic temperaments, but finds their lack of knowledge inexcusable. As you
may know, Roosevelt was famous as a big game hunter and could
easily take the point of view of a predator. He was also an excellent
naturalist and knew the names and habits of all the small birds and
mammals that lived around him. Going back to the frontispiece,
Roosevelt points out that if the peacock is indeed concealed in the
forest environment, then the peahen—which is very differently colored—must be conspicuous in that environment.
Here is a summary of some of his main objections: First, Roosevelt says that it is our eyes, and not the colors of the animals,
that determine whether we will see them. He tells us that his native
guides in Africa could often see animals he failed to pick out. Further, cover is more important in concealing animals than their colors, motion is also more important than colors, and besides, most
predators hunt by scent and do not use their eyes until they are very
19. http://kenarcherphotos.com/p953706307/h1BF0CD15#h1bf0cd15
20. Theodore Roosevelt, "Revealing and Concealing Coloration in Birds
and Mammals,” Bulletin of the American Museum of Natural History 30
(1911):119-239.
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73
close—and by then they already know the animal is there. All these
objections have merit. In fact, Roosevelt almost, not quite, but almost, claims that all animals are conspicuously colored, the opposite of the Thayers’ claim.
Before going on I want to relate an incident that happened while
I was still very much under the influence of Thayer’s book. I was
watching mallard ducks on a pond at sunset with my daughter. The
speckled brown females were difficult to see wherever they were—
on the bank, in a tree, or in the water. The males, which Thayer
claims are concealingly colored in the pond environment, were
very easy to see.21 We were watching a particular male swim across
the pond, and at one point it suddenly and completely disappeared.
That is, its white back matched the sparkly white water of the pond
at sunset, its brown breast matched the reflection of a tree trunk in
the water, and its green head matched the reflection of foliage in
the water. It was so startling that I actually jumped. Then, a halfsecond or a second later, it swam out of that position and again
could be easily seen.
So, Thayer is only a little bit right when he claims that male mallards are concealed in their pond environment. For the most part
they are not. However, a kind of secret was revealed through this
experience. They seem somehow born of their environment. It was
as if someone had taken a piece out of a jigsaw puzzle of a pond
at sunset and turned it into a male mallard duck.
One more important participant in this debate on animal coloration was John Burroughs, a naturalist and writer from New York
state. He published an essay in 1908 entitled “Gay Plumes and
Dull.”22 In it he takes up the topic of concealing coloration. He has
his own set of objections to the theory. He points out that if concealing coloration were so important to animal survival, you would
expect all animals in a given environment to be the same color, yet
we see that they are not. Also, we would expect concealingly colored animals such as grouse to be more abundant than brightly col21. http://www.flickr.com/photos/mclap/4366013629
22. John Burroughs, “Gay Plumes and Dull,” in Leaf and Tendril (New
York: Houghton Mifflin, 1908).
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ored animals such as male cardinals and pheasants, and we would
expect the females of these last two species to be more abundant
than the males. Yet, this is not what we see. From experience I can
say that this is also the case with insects. Species with concealing
colors are not more numerous as a rule than brightly colored ones.
Burroughs writes:
Whatever truth there may be in this theory of protective
coloration, one has only to look about him to discover
that it is a matter which Nature does not have very much
at heart. She plays fast and loose with it on every hand.
Now she seems to set great store by it, the next moment
she discards it entirely.23
Burroughs accounts for the colors of the antelope and other animals like this:
Things in nature blend and harmonize. One thing
matches with another. . . . Arctic life will blend more or
less with Arctic snows, tree animals will show greater
variety in tint and form, plains animals will be dull of
hue like the plains . . . through the law of natural assimilation, like begetting like, variety breeding variety.24
He reaches for a “law of natural assimilation” to explain this,
and also reaches for another natural law to explain differences in
coloration between males and females of the same species:
His gay plumes are the badge of his masculinity . . . the
riot and overflow of the male sexual principle.25
Females being generally more dull in hue partake in a more passive female principle of nature. Burroughs still feels that the appearances have not been fully accounted for. He goes further,
speculating that:
It is like the caprice of fashion . . . exaggerated plumes,
fantastic colors, and monstrous beaks of many birds in
both hemispheres have as little apparent utility, and seem
23. Burroughs, Leaf and Tendril, 61.
24. Ibid., 80.
25. Ibid., 95.
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75
to be quite as much the result of caprice, as are any of
the extreme fashions in dress among human beings.26
Even in the animal world, there is fashion. One man who takes
up this theme, decades later, is Roger Caillois, a French philosopher who published a book in 1964 entitled The Mask of Medusa.27
Caillois was especially interested in the phenomenon of mimicry
in the insect world. The dead leaf butterfly is a good exarnple.28
The undersides of the wings are a perfect mimic of a dead leaf,
complete with leaf veins, fungal spots, and a broken stem. If this
butterfly was immobile in leaves on a forest floor, you would never
see it. However, it is not uncommon to see these insects outside of
the environment where they would be concealed, as if they are,
perhaps, showing off.
Another spectacular mimetic caterpillar is Hemeroplanes triptolemus, found in Central America.29 It looks like a regular caterpillar when it is feeding on a branch, however in the last stage
before it pupates, if disturbed, it turns upside down and comes at
you looking for all the world like a tree viper, though the “eyes”
are not real and cannot see. The theory is that birds or other predators think they are in the presence of an animal that is dangerous to
them and are frightened away, instead of eating the caterpillar. It is
thought that any caterpillar that deviates from the perfect mimetic
form will be spotted and eaten by predators until, eventually, the
most perfect mimics are “created” by this selective predation.
Many butterflies and moths are known as snake mimics. The
spicebush swallowtail, native to the United States, is one such
caterpillar.30 To me, this caterpillar looks more like a friendly
stuffed toy snake than a dangerous enemy. We need to wonder why
it is that the first mimic is so perfect if this second one is an effective deterrent of predation. Adults may also be identified as snake
26. Ibid., 90.
27. Roger Caillois, The Mask of Medusa, tr. George Ordish (New York:
C. N. Potter, 1964).
28. http://beastlyvirtues.blogspot.com/2013/03/fuxianhuia-who.html
29. http://madasamarinebiologist.com/post/16015203836/snake-mimiccatepillar
30. http://www.pinterest.com/pin/459859811920520201/
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mimics. Philip Howse, of Southampton University in England
claims that the wing of the atlas moth is a cobra mimic.30 Look at
a whole atlas moth.31 Again, we are led to wonder why, if birds are
such astute and perceptive predators, they don’t know that cobras
are five feet long and live in the rice paddies, not five inches long
and hanging in the air.
Caillois notes this “aimless delirium of perfection in nature,”
and proposes that mimicry is an autonomous force in the world of
biology that does not require utilitarian explanations. He goes further and also invokes, like Burroughs, a principle of fashion, connecting it with the phenomenon of mimicry:
But in the case of man, fashion is also a phenomenon of
mimicry, of an obscure contagion of fascination with a
model which is imitated for no real reason.32
The plant hoppers are a group of sap-sucking insects that live
on trees and shrubs. They have an astounding variety of forms.33
They may resemble wasps as one of the photos on the foregoing
site sort of does. You can see the black and white stripes, the narrow “wasp waist,” and a variety of pointed projections that may
deter a predator. Notice that the real body is underneath the wings.
The whole “wasp” is a projection of the prothoracic segment. It is
as if the plant hopper is wearing a mask or a costume. If we look
at other plant hoppers, we will be impressed that many do not seem
to be mimics at all. Their colors, shapes, and ornaments seem more
like the work of a playful, creative imagination.
So far, I have been referring to art as something like “the beautiful.” Now we are seeing, in the natural world, a different category
of art, that of mask and costume, a category that has a wide variety
of functions in the human world. Caillois was especially interested
in an insect called the lantern bug (Fig. 8). They are related to the
30. http://www.telegraph.co.uk/earth/wildlife/8082739/Butterflies-andmoths-mimic-snakes-and-foxes-to-fool-predators-claims-researcher.html
31. http://butterflycircle.blogspot.com/2012/08/the-atlas-moth-chroniclesepisode-1.html
32. Caillois, The Mask of Medusa, 41.
33. http://femtasia.blogspot.com/2010/11/membracidae.html
�ESSAYS & LECTURES | WIENER
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Fig. 8
Lantern Bug34
tree hoppers and also live by sucking sap from trees. It is a Swiss
army knife of a bug; the forewings mimic dead leaves, when they
are lifted up there are two prominent eye spots. These are generally
interpreted as looking like vertebrate eyes so that a potential predator, thinking it is in the presence of a larger predator that could be
a danger to it, will be frightened away. Best of all, it has a large alligator mask above its real head. You can see the eyes, the nostrils,
and the row of teeth. Again, we must question. Don’t the predators
know that alligators are 6 feet long and live in the river, rather than
an inch or so long and in a tree?
Caillois compares the lantern bug to a human shaman. The dead
leaf forewings are its cloak of invisibility which can be suddenly
thrown off to reveal the conscious being who had been hidden. He
writes:
Where there was nothing, there is suddenly horror. The
insect knows how to frighten; what is more it gives rise
34. James Duncan, Introduction to Entomology, Vol. 1 [Vol. 30 of The
Naturalist’s Library, ed. Sir William Jardine] (Edinburgh: W. H. Lizars,
1840), Plate 22.
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to a particular kind of fear, an imaginary terror not corresponding to any real danger . . . working through the
strange and fantastic.35
One further example of this phenomenon is the oleander hawkmoth caterpillar, Daphnis nerii.36 This caterpillar, when viewed
from a certain angle, exhibits creepy glowing eyes that do not look
like those of any animal, but evoke horror. They have the same kind
of effect as eyes painted on a shield or the bow of a ship. This suggests that birds, monkeys and other predators may be susceptible
to a kind of existential dread brought on by these false, staring eyes.
The wide range of such costume- and mask-effects in insects
mirrors the many uses of masks in human communities. There
are masks to disguise, to camoflauge, to frighten, to take on the
look and energies of another kind of creature—there are even
masks just for play. If we go with Caillois’s thought, we can see
that humans are not isolated from the rest of the natural world by
our art, our mythology, our psychology. We belong to the world
and can see aspects of these human features represented in the
behavior, or printed on the actual anatomy, of other animals.
I have been arguing that there is more going on in the world of
biology than natural selection for the purposes of survival and reproduction. Especially today, when most thinking about evolution
is connected with thinking about genes, we confine ourselves to a
narrow range of interpretation of biological phenomena. As a result,
we are continually underestimating the capacities of animals, and
this underestimation takes place before there are any data. We are
always tempted to read the capacities of animals off of their genes
or anatomy and from the theory of natural selection. No matter how
many times this is shown to be wrong-headed, these strategies are
constantly invoked. Truly, it is not possible to know what an animal
is capable of without actually observing its behavior for a long time
under a variety of circumstances.
It is assumed that bees have such tiny brains that they cannot do
symbolic reasoning, but showing that they do somehow does not
35. Caillois, The Mask of Medusa, 104.
36. http://www.flickr.com/photos/77995220@N00/9398097107
�ESSAYS & LECTURES | WIENER
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challenge the general principle. When we limit beforehand what
we believe is possible, we often cannot see what is right in front
of our eyes, or we fail to reflect about it at all because we have already sorted out the observed appearance or behavior into one of
our preset categories. One thing is warning coloration, another is
sexual selection, another is protective coloration—and we’re done.
Not only do we fail to see, we lose a language that is adequate to
the actual phenomena. We lose a sense of Nature with a capital
“N,” a nature rife with potentiality and surprises, Nature as a principle of motion and change. Only the poets still use this sort of language with a good conscience.
I’ve been using the lens of artistic expression in animals as a
way to explore this issue.
Here at the end, in the coda, I would like to switch to a different
sort of example to illustrate this point. A few years ago there
showed up on YouTube some footage of an elk, named Shooter, at
the Pocatello Zoo in Idaho, saving a marmot from drowning in a
water tank.37 There were two witnesses, a veterinarian and an educator. The whole event took about 15 minutes. The elk was pawing at the water and with his big unwieldy antlers, trying to get his
head in the tank. Finally he lifted out the marmot, put it on the
ground, and gently nudged it with his foot. In a little while the marmot shook itself and ran into its hole. It is wonderful footage.
The odd thing to me was the narrative of the witnesses. Even as
we are watching, they are explaining that elk don’t do this. They
are all about survival. They speculate that it is only because
Shooter lives in a zoo and has his needs met that he can develop
more elaborate behavior. The scientist in me immediately asks how
we know that elk don’t do this. Do we have dozens of examples of
marmots squeaking in distress as they drown in mountain lakes
while elk graze unconcernedly on the shore? We don’t really know
as we only have one example of an elk confronted with this situation. Underlying the narrative is the view that elk behavior is
generic and aimed only toward survival. I suggest that the elk and
37. http://abclocal.go.com/kabc/story?id=8211416
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the marmot, who after all live in the exact same place, know each
other. This may be an act of individual friendship, not calling for
any explanation at all in terms of natural selection.
I hope I have stimulated you to look more carefully and think
more widely when you observe animals. The world of animal appearance and behavior is wide and wonderful. The next step is for
you to go outside and start looking around for yourself.
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Troy
Hannah Eagleson
Eris
You cannot even bite into it,
Feel color burst in your mouth,
Taste nectar on your tongue.
Hard gold spinning down the table,
Stopping talk,
Clanging pitchers,
Breaking glasses.
Spilling wine
On immortal gowns.
Setting at war
Beauty, wisdom, power
Unleashing the bronze spear and gleaming chariot,
The arrows’ iron,
Drawing jagged lines.
Eve had at least the momentary taste,
Flavor widening her eyes,
Fruit in her mouth
In exchange for Eden lost.
Troy fell for an apple no one tasted.
�POEMS | EAGLESON
Judgment
Did Priam ever wonder,
Why Paris? Like a filigree circlet,
Looking fine enough, delicately wrought,
But not much use in battle.
Why not Hector, steady and strong,
Brave and to be trusted?
Why not honey-tongued Odysseus on the other side,
Or fierce Agamemnon himself?
Why should Paris be unlucky enough
To stumble near the gods’ celebration,
Fool enough to think he could judge
Among beauty, wisdom, power?
And who would choose beauty?
What good is that,
To managing a kingdom?
Does it build the walls or feed the hungry?
Does it grow the wheat or press the grapes?
Does it strengthen the gates or make the wells run deeper?
Who would have thought that epics begin
Not with the bright spear or bronze helmet,
Not even with the twist of golden hair,
But with the slight prince
Strayed to the wrong table,
Making a fool’s choice?
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Three Poems from Les Fleurs du Mal
by Charles Baudelaire
Translated by Peter Kalkavage
The Swan (to Victor Hugo)
I
Andromache, I think of you! That little stream,
Poor and gloomy mirror where once there shone so bright
The tremendous majesty of your widow’s grief,
That lying Simoïs that grew great through your tears,1
Impregnated at once my fertile memory,
As I made my way across the new Carrousel. 2
Old Paris is no more (the form of one’s hometown
Is quicker to change, alas! than a mortal’s heart);
I see but in my mind that whole camp of makeshift huts,
Those piles of capitals, rough-hewn, and column-shafts,
The grass, the massive blocks turned green by standing pools,
And shining in the panes the scattered bric-a-brac.
There a menagerie at one time was spread out;
There I saw, one morning, under skies cold and clear,
At the hour when Work wakes, when street cleaners push
A menacing storm into the silent air,
A swan that had recently escaped from his cage,
And, scraping the dry pavement with his webby feet,
Was dragging his white plumage on the rugged ground.
Near a waterless ditch, the beast, opening his beak,
1. In the Aeneid (III, 302), Andromache, now a refugee in Epirus, weeps
for Hector near a “false” Simoïs, a river near Troy.
2. The Place du Carrousel, an area near the Louvre, underwent continual
renovation in the 1850s.
�POEMS | KALKAVAGE
85
Was nervously bathing his wings in the dust,
And said, heart full of his beautiful native lake:
“Water, when will you rain? Lightning, when will you roar?”
I see this ill-starred wretch, a strange and fatal myth,
Toward the heavens sometimes, like Man in Ovid’s poem,3
Toward the heavens ironic and cruelly blue,
On his convulsive neck straining his thirsty head,
As though he were addressing reproaches to God!
II
Paris changes! But nothing in my melancholy
Has budged! New palaces and scaffoldings and blocks,
Old quarters, all turns to allegory for me,
And my precious memories are heavier than rocks.
In front of that Louvre too an image weighs me down:4
I think of my great swan, with his gestures insane,
Like people in exile, ludicrous and sublime,
And gnawed by relentless desire! And then of you,
Andromache, fallen from a great husband’s arms,
Vile beast of the field, under Pyrrhus’s proud hand,
Near a bodiless grave, bent over in a swoon;
Hector’s widow, alas! and Helenus’s wife!5
I think of the negress, all consumptive and thin,
Trudging in the mud, and searching with haggard eye
For the now-absent palms of proud Africa’s land
In the distance behind the immense wall of fog;
3. Metamorphoses I, 84-85: “All other animals look downward; Man,/
Alone, erect, can raise his face toward Heaven.” (Ovid, Metamorphoses,
trans. Rolfe Humphries [Bloomington: Indiana University Press, 1960], 5.)
4. That Louvre, i.e., the Louvre before the reconstruction in 1852 that
eliminated the old streets separating the Louvre from the Palace of the
Tuileries.
5. After the fall of Troy, Andromache and Helenus (Priam’s son) became
the slaves of Achilles’s son, Pyrrhus, who eventually let them marry
(Aeneid III, 321-336).
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Of whoever has lost what will never return—
Ever, ever! Of those who sate themselves with tears
And are suckled by Grief as by a good she-wolf!
Of skin-and-bone orphans withering like flowers!
And so, in the forest that inexiles my mind
An old Memory sounds with full blast of the horn!
I think of the sailors forgotten on an isle,
Of captives, the vanquished! . . . and many others still!
Fogs and Rains
O ends of autumn, winters, springtimes steeped in mud,
Sleepy-headed seasons! I love you and I praise you
For enveloping thus both my heart and my brain
With a vaporous shroud and a vague sort of tomb.
On that vast open plain where the cold storm-wind plays,
Where the weathercock rasps through the long drawn-out nights,
My soul, even better than in spring’s tepid time,
Will proceed to spread wide its great raven-black wings.
Nothing is more sweet to the funereal heart,
And on which for so long winter’s chill has come down,
O seasons drenched in pallor, you queens of our clime,
Than the unchanging look of your deathly-white gloom,
—Lest it be, on a night without moon, two by two,
To put sorrow to sleep on a perilous bed.
�POEMS | KALKAVAGE
87
The Vampire
You who, like a thrust of the knife,
Entered inside my plaintive heart;
You who, as mighty as a herd
Of demons, came, adorned and mad,
To make your bed and your domain
Of my humiliated mind;
—Obscene one, to whom I am bound
Like the galley slave to his chain,
Like the hard gambler to his game,
Like the wretched sot to his bottle,
Like the carrion to its vermin,
—Accursèd, accursèd be you!
I pleaded with the rapid blade
To win my freedom back by force,
And told the poison, schooled in guile,
To come and aid my coward’s will.
Alas! the poison and the blade
Both held me in disdain and said:
“You’re not worthy to be relieved
From your accursèd servitude,
Fool! —if from that empire of hers
Our efforts would deliver you,
Your kisses would resuscitate
The cadaver of your vampire!”
�POEMS | ZUCKERMAN
The Second Sense
Elliott Zuckerman
Listen: In wind and water,
the second sense
records a message for the sixth
Before our birth
only a patch of reason moved the pulse
Before the germ
of anything like melody,
maternal heartbeat set the meter’s pace
In harmony
the pulse ascends to the unheard. Though sound
is left below, compatible numbers
continue climbing
That’s why the masters of man’s sound
enthralled by breeze and shower
and friendliness of field and leaf
reiterate the triad tirelessly
sustained beyond the call of need or taste
The level field
the rising cliff or tree
are the co-ordinates of the soul
In simple chords sustained
beyond all reason
one master celebrated greenery
striding and hunched, hands clasped behind his back.
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89
To Save the Ideas
A Review of Daniel Sherman’s Soul, World, and Idea: An
Interpretation of Plato’s Republic and Phaedo. Lanham,
MD: Lexington Books, 2013. viii + 410 pages, $110.
Eva Brann
“To save the phenomena” of heavenly motions by undergirding
them with rational, that is, mathematical, hypotheses—that is said
to be the problem Plato set for astronomers in a passage from the
Republic frequently referenced by Daniel Sherman.1 His own
project is, as I understand it, the inverse one: to save the Platonic
ideas by a new interpretation of the dialogues in the title of his
book. It might be said to be the deeper and more difficult problem
to solve—and just as enticing.
But what, you may think, is the use of an inviting review, when
you blanch at the price? This book, written by an alumnus of St.
John’s (Annapolis, 1963) after a long teaching career and obviously
much study and reflection, should be kept in mind by anyone of us
who has more than a nostalgic interest in the Platonic dialogues; if
you can’t afford it, you might persuade your local library to acquire
it or get it for you on interlibrary loan.
It is surely a book not to be overlooked in any serious study of
the Platonic dialogues, not just the Republic and the Phaedo. But—
in any responsible review there must be “buts,” and I’ll get them
out of the way, the more uninhibitedly to do this huge work justice—its very volume raises some obstacles, thought-provoking
enough to induce the following little prefatory meditation on voluminousness.
There is an aphorism by Callimachus (third century BCE), the
most famous librarian of the great ancient Library at Alexandria:
mega biblion, mega kakon, which our wicked undergraduates at
St. John’s used to translate: “A great book is a great evil.” What he
actually meant is probably: “A long book is a big pain,” since he
1. Republic 528 ff. Simplicius (Commentary 2.43, 46) reports Plato’s
challenge to the astronomers.
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considered long epics to be antiquated. Having, on several occasions, inflicted such pain, I have come to think of book length as
an independently significant factor. For one thing, it is involved
with the distinction between “primary” and “secondary” literature—between a difficult, rebarbative original and its ancillary elucidation. There’s “learning’s crabbed text” and then “there’s the
comment,” as Robert Browning says in “The Grammarian’s Funeral.”
A primary text may be as long as it pleases, say, the roughly
seven hundred pages of the Critique of Pure Reason or the nearly
double that of War and Peace. But a secondary text, a commenting
explication? Well, how can it help but be a good deal longer than
the original? It is, after all, an explication or “unfolding,” an explanation or “planing-out,” an exposition or “setting-out,” an elucidation or “bringing-to-light.” Anything that is smoothed-out will
be larger in bulk than it was in its original implicitness or self-entanglement. However, the length of an exegesis that “leads-out” of
a textual complexity is a very real problem of human temporality.
Even for willing learners, since ars longa, vita brevis, if the artfulness of the text is great and the commentator tries to be adequate
to it, there is the risk of displacing it, because human life is always
short on time. Moreover, while words clarify, wordiness obscures
matters.
To my mind this means that to make up for its preempting bulk,
an interpretation has the obligation to be easier—and so, faster—
to read, and the interpreter has the obligation to accordingly be
willing to accept a loss of subtlety and depth. Although one might
say that a great text is one long aphorism, being too brief for what
it bears, surely the difference between a weighty text and its analysis is not merely that of succinctness and amplitude. In addition,
an interpretation should willingly forego that mysterious penumbra
of connotation and resonance which attends a great book and candidly admit that a great author’s scope is apt to exceed the interpreter’s perspective (not withstanding his—dubious—advantage
of an added historical distance). To say it plainly: secondary writing has a smoothing function; to it shallowness is mandatory. So
much here for one of its qualities; more about its quantity below.
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There is a now often deprecated notion behind the “primary/secondary” distinction which goes beyond that of “original/commentary,” namely, “great/not-so-great.” The one main mark of textual
greatness is just this: exposition-proneness. Whatever spatial
metaphor you may apply to the effort—illuminating the surface,
delving into the depths, unrolling the convolutions—there is always more to be said about it. The exegete may be exhausted; the
book never is. Put another way: A great book will contain many
serendipities but few inadvertencies. (Even Homer nods, but rarely.)
Thus the interpreter’s care is safely invested; there will be returns.
I have slipped from “commentary” to “interpretation” because,
while a commentary might be pretty innocent, hovering around the
factual extrinsicalities of the text, interpretations get inside it and
are fraught with potential culpability. First of these is inadequacy
to the meaning of the text: To interpret well, you have to begin
reading literally, attend to the letter of the text. Any willing student
can be trained to do that. But then it gets complicated, especially
for the Socratic dialogues of Plato. Who among the participants
understands what Socrates is asking and what he himself is saying?
What is Socrates’s intention? Where is Plato? Which words or suppressions bear the meaning of the conversation? In what sayings
or silences is its locus of truth? The effort of cluing this out is very
nearly simultaneous with the exposition of that truth or of its occlusion—here’s a version of that notorious “hermeneutic circle,” that
the parts are known by the whole, but also, inversely, the whole by
its parts.2 Inadequacy, lack of acuteness in construing the text from
both ends, here vitiates the interpretation—but that is not at all the
problem of Sherman’s book, and thus not my problem here.
Second, the pedagogic ineffectiveness of interpretative commentary: I want to frame this aspect of secondary writing as a large
problem, so to speak, that is little regarded—the problem of bulk.
Having myself perpetrated several big books, I suppose I’m qualified. Here’s the problem: In writing of that sort there are levels of
aboutness. At the bottom there is, once again, what the primary
2. The “hermeneutic” or interpretational art is named after the herald-god
Hermes, one of whose offices it was to convey plainly the meaning of
messages.
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book literally says. On top of that (or wherever it’s to be located)
there is the originating writer’s meaning—not that he failed in saying
what he intended, but that he may have reached for a new language
to convey his original notions, or that he may have suppressed complete articulation so as to involve the attentive reader. For most (no
longer all) interpreters, it is an article of hermeneutic faith that there
is such an implicit meaning, that its novel language often needs an
interpreter, that the author’s intention is often not immediately obvious—and that they’re elected to open up the book to others’ view.
So on top of that comes the secondary writer’s own understanding
of the primary text, which any candid commentator will, by that
little margin of modest doubt, know how to distinguish from its
underlying template. And now, to top it off, there is a tertiary level,
huge and growing: the more or less deviationist opinions of all the
fellow interpreters, who each have different perspectives, reconcilable and irreconcilable. And in this perspectival fecundity lies
the proof both of the primary text’s grander scope and of its human
limitations.
Secondary bulk is a real and present danger: smoothing turns
into smothering. Oddly enough, there is a device for the self-neutralization of big secondary books: the Index. For original books,
excerpted reading is a hermeneutic no-no, precisely because of the
hermeneutic circle, because the clue to the whole may lie in any
or all parts. Not so in interpretative commentaries, whose writer
should not be out to piggy-back a masterpiece on the underlying
text, but should help the user to check out names, find definitive
passages, and follow up themes. Indices affirm the secondary
writer’s modesty; a detailed index signifies the writer’s blanket
permission to spot-read, to use the interpretation in thinking about
the text thus served. Primary texts usually aren’t indexed to begin
with. Soul, World, and Idea has an index, but I wish Lexington
Books had invested in a more ample one.
“Careful” unpacking, analysis, reading, is a phrase, the favorite
one in Soul, World, and Idea, of hermeneutic virtue. Here’s the
“but”: it leads to pertinent paraphrases of the text to be interpreted,
together with commenting qualifications, modifications, cautious
retractions—in short, to lengthiness. Add to this the dutiful inclu-
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93
sion, both in the text and in long footnotes, of tertiary commentary,
in which the work comes to grips with, analyzes, critiques, or accepts a large number of contemporary interpretations by fellow
scholars. Just as the careful reading often yields welcome insights
(of which I’ll give an example a little below), the referencing of
scholarship is often helpful. Instead of just citing names and numbers, Sherman actually reproduces arguments. But it nearly doubles
the book’s length.
I am, as they say, “conflicted” about both of these efforts: the
written record of “careful reading” and the learned absorption of
“scholarship.” Who can doubt the value of carefully thinking
through a worthy text by engaging in extensive internal i-dotting
or the propriety of responsively considering others’ understandings
and making a mental note of their putative mistakes? But, then,
isn’t it the next best step to allow the bulk—not the gist—of our
own thinkings and others’ errors to pass away, unpublished, into
forgetfulness? Treat them as ephemeral, and let them die within
days of their birth (as do those eponymous ephemerids, the
mayflies) and enter forgetfulness, there to become the soil of reflection. Shouldn’t philosophy be resolutely anti-cumulative, ever
at the beginning? Absent a firm settlement of my misgivings about
bulky writings and extensive sourcing, I take refuge in a very practical solution: at least to pay attention to what is near and dear, and
certainly to the works of alumni.
So let me start with a sample of insights Daniel Sherman’s book
offers, combining close reading and responsiveness to scholarship
(p. 165). An interesting issue is “the autonomy of philosophy” seen
in personal terms, namely as the ability of ordinarily thoughtful
human beings to withstand the social order. Pierre Bourdieu, a
French sociologist, surmises that the categories imposed by the
power structure are intractable because they are unconsciously involved in the very struggle to escape them; thus even the not-soconforming characters of the Republic respond to Socrates’s
sedition with responses varying from “metaphysical fury,” through
friendly doubt, to sullen withdrawal. Against this defeatism, Sherman pits his interpretation of Platonic discourse as being very
awarely situated in medias res. Socrates indeed operates, albeit
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quite consciously, in the context of the social setting and its implicit
opinions. He employs dialogic practices to make these explicit and
to ascend, starting from within the social and natural world, to the
alternative realm of Ideas; the ideas are thus both continuous with
and opposed to the given social context, hence in a tension of critique and acceptance with respect to ordinary meanings. One might
say that Sherman saves the autonomy of thinking from circumstance by arguing that it is its very implication in the opinionenvironment of the world which, when brought to awareness,
gives it its rightful claim to independent knowledge. (P. 165.)
I’ve begun with this example, taken from the middle of the book,
because it is typical of Sherman’s saving, composing, middle-ofthe-way responses to exaggeratedly alienating views of Plato’s
project. Now it’s time to give a glimpse of the over-all structure of
the book, chapter by chapter. Keep in mind that this is a dense exposition, consisting of four-hundred meticulously argued pages, so
my summary will be skeletal indeed, and my queries will loom
larger than they would were the detail not suppressed.
The Introduction sets out the interrelation of cognizing soul,
experienced world, and Sherman’s own conception of discourseembedded ideas, in the Republic and the Phaedo. He reviews the
various values accorded by scholars to their dramatic aspect, from
mere embellishment, through an attendant enactment of philosophical life to an inextricable involvement of action and argument.
Jacob Klein3 was an early and vivid proponent of this third view,
and Sherman recalls Klein’s influence on him in the warm appreciation of his Preface. In particular, Klein’s close-to-life reading
of the dialogues is reflected in Sherman’s “most radical and challenging suggestion”: the ideas are not atemporal beings separated
from the world but have a temporal, world-implicated dimension;
consequently the Platonic account of ideal being can the better be
the operative basis of a philosophic life of learning, teaching, talking. Images and image-making—and image-recognition, I would
add—will be crucial in drawing the ideas into human cognition
and moral activity.
3. Jacob Klein (1899-1978) was tutor (1938-69) and dean (1948-58) at
St. John’s College, and teacher until his death.
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Chapter 1. The Interlocutor’s Request analyzes the problems
posed to Socrates in the Republic by Plato’s two brothers, Glaucon and Adeimantus: to show that justice is an inherent good,
hence a source of happiness. Here, I might comment, is a first
occasion for Sherman’s “careful parsing”; he delves deep into
the shallowness of Socrates’s talking partners. I think that approach, a dimension of the whole book, is a little hard on these
young men, as well as the all-but-boys of the Phaedo. After all,
they are there all night in the Republic and all day in the Phaedo,
attentive and eager; they do about as well as would any of us. If
I’d been there I wouldn’t have intruded my every mental reservation either, and, I think, that the same experience of a tacit
critical descant that Plato asks of a reader, Socrates respects in
his companions. We must supply knowing smiles, snickers,
raised eyebrows, furrowed brows, just as in a St. John’s seminar.
I think Socrates is more apt to bring out his present partners’
strengths than to expose their efforts to our cavils—if they’re
young.
To satisfy the brothers’ request Socrates sets up that problemfraught analogy between the offices of the castes of a well-constituted political community and the powers of the parts of the
soul. Sherman’s thorough expository prose obscures a little—a
dramatic hiccup would have helped—the arresting political assumption of this magnifying image, in which the individual psychology is said to be mirrored in the communal “constitution”
(whence the Greek title Politeia, “Polity”): civic justice is understood as the image of psychic adjustment. The consideration
of imaging becomes more urgent.
Chapter 2. Discourse treats of the possibility of realizing a
city so constituted. Recall here that Socrates in fact gives an unambiguous final answer: It makes no difference whether the
ideal city will ever exist or is just a model laid up in heaven; the
point is to practice our inner politics in its image—to use its politeia in turn as a model for constituting our own, individual,
psychic balance (592b). However, Sherman introduces several
levels on which the possibility question may play out. One condition for the existence of the just city is that a philosopher-king
will turn up—and, I would add, before he arrives there must be
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a pre-royal philosopher-founder—a proven unlikelihood, as is
shown by Plato’s misadventures with Syracuse’s tyrant-dynasty,
set out in his Letters. Therefore Sherman now reviews these
royal philosophers’ nature and their education, and in preparation, the underlying characteristics of degrees of cognition and
their objects. Thus the “digression of the central books” (p. 77)
is justified. Some readers may recall that Rousseau saw the center of the Republic in these books. Whatever the title may imply,
he says, it is really a treatise on education (Émile I) and, I might
add, on the constitution of the soul and the beings of the world.
Apparently, Sherman agrees (p. 137). However, he regards the
application of the ontology (the account of Being) and its realization in a program of education as provisional, incomplete.
The Phaedo is a necessary supplement. In any case, for him the
prerequisite imaging of the ideal in discourse looms yet larger.
Chapter 3. The Cave: Education and the Lack of It deals with
the Image of the Cave (the venue of human life) and the Divided Line (the gradation of beings and the ascent of cognition). Sherman takes the cave to be the city and, in clever
accord with the order of the Republic’s earlier books, where
city precedes soul, but in reversal of Books VI-VII, where the
enabling ontological line precedes the consequent civic cave,
manages neatly to insinuate his main thesis, the implication of
the Ideas in the human experience and knowledge of the world.
A bonus is Sherman’s account and critique of Heidegger’s interpretation of the Cave Image as embodying a loss of openness to the direct presence of beings, a receptivity still retained
by the Presocratics. Sherman shows that Heidegger himself actually appeals to the “ungrasped essence,” said to be deformed
by discourse, an appeal that vitiates the purity of his cherished
immediacy. Since Sherman himself supposes that beings come,
so to speak, into Being only in thinking and its speech, he argues that Plato’s image-dynamics more adequately facilitates
the sharing of Ideas between soul and world than does Heidegger’s hope of “unhiddenness.”
Chapter 4. The Divided Line and Dynamic of Ascent gives a
dynamic interpretation of the Divided Line, as an ascent and
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descent, turn and turn-about, of living thinking, whose motor,
so to speak, is imaging: the Divided Line represents the cosmos, both its shifting appearances and its stable beings, as a
top-down cascade of images and a bottom-up effort of imagerecognition.4 Sherman begins with the triple causation attributed to the Idea of the Good, which is off the line, “beyond
Being.” It is a hyper-principle that brings things into being, allows them to flourish, and makes them knowable (as its image,
the sun, causes birth, growth, and visibility). Sherman deals
with a scholarly claim (Annas’s) that the Good is too impersonal and offers no human fulfillment thus: As the source of
the world’s intelligibility it is surely good for human beings. I
would add that the Good was in Plato’s “Unwritten Doctrines”5
named the One; thus it is a principle of unification, hence responsible for all human community, be it the civic union of
politics or the private bond of friendship; that is why it is introduced in the Republic.
There follows a close reading of the Line as a ladder of dialectic
ascent, which cannot be thrown away—“a serious claim” (p. 134)
moving toward Sherman’s interpretation of the Ideas as tied to psychic activity. The problem of images comes ever more front and
center in a critique of one scholar’s (Patterson’s) analytic treatment
of the sort of things the original Forms (Ideas) must be if worldly
things are their images: The Form is what its name says it is, but
not as having the qualities its namesake images possess. This
makes more sense than you’d think (though like all analytic expla4. “Image-recognition,” which is the mode of ascent along the Divided
Line, is Jacob Klein’s rectifying translation of eikasia, often understood
as a mode of guessing, conjecturing (as by Sherman himself, p. 151). Thus
the ability to distinguish between original and copy becomes the basic and
pervasive ontological capacity. Images, the objects recognized by imagerecognition, the central problem of Plato’s Sophist, present a never-ending
enticement to ontological reflection, some of which is being carried on in
issues of this journal: Review of Eva Brann, The World of the Imagination
(1991) by Dennis Sepper, The St. John’s Review 42.1 (1993): 1-19; review
of Dennis Sepper, Understanding Imagination (2013) by Eva Brann in
this issue, 1-16; and now this review of Sherman’s book.
5. Plato’s oral speculations, reported first by Aristotle.
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nations it’s flatly clarifying rather than brightly illuminating): A
Horse-Form is what a horse in truth is, but it’s not for riding. Sherman must object. Whatever this analysis of being a form means, it
implies that forms, ideas, are quite separate in kind from their physical images; he is preparing to bring forward a way of understanding the (moderated) separateness of Ideas from Soul and World
that requires their (ultimate) interdependence. The rest of the chapter concerns the soul’s different cognitive relations to the rising reality of the objects represented by the upright Line.
Chapter 5. Education and the Mind’s Eye attends to
Socrates’s filling in the lack of education in the Cave with the
education for the philosophic rulers. Sherman dwells on the
significance of Socrates’s beginning the program of study with
arithmetic—not the technique of numerical calculation but the
science of the nature of numbers.6 This science, beginning with
the unit, the one that constitutes each of the unit-assemblages
called arithmos, has special powers of philosophical levitation.
The “one” that is the beginning of counting-up, of generating
numbers, is, one might say, the inverted image of the One that
is the principle of the unity of all that is, the Good: the least
constituent mirrors the whole constitution.
From the first study I pass directly—Sherman leaves no such
lacuna—to the final one, dialectic, which dwells on the Ideas:
“Dialectic, then, produces the image of discourse [my italics]
as the song of reason of which the relations of Ideas as a harmony of the whole is the ultimate objective content” (p. 198).
Sherman means this literally: the identity of Ideas is inseparable from the relations among them, and those relations are insubstantial, it would seem. By “insubstantial” I mean that
normally relations emanate from and terminate in beings,
6. He takes his departure from Jacob Klein’s Greek Mathematical
Thought and the Origin of Algebra (Mineola, NY: Dover, 1992). Alumni
of the St. John’s Program will recognize all the elements of Socrates’s
program of learning, but will want to ponder the fact that we begin our
mathematical studies with Euclid’s geometry, with shapes and magnitudes
rather than with numbers and multitudes. I’d like to hear speculations
about, and opinions of, this pedagogic reversal.
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which is why humans have to be somebody to relate to somebody. It’s not that existence as a mere node of relations is unthinkable, but rather that it’s demeaning. However, since the
treatment of the objects of dialectic, the Ideas, is deliberately
inexplicit in the Republic, it is in any case insufficient for a
persuasive theory of ideal being, and that deficiency makes
room for Sherman’s speculation.
Chapters 6-8. The Phaedo’s Arguments for Immortality, The
Problem of Wrong Beginnings, From Logos to Idea—these
chapters bring in the Phaedo’s fuller account of the soul as capable of learning and its more direct treatment of the Ideas as
necessary hypotheses; “image” and “separation” (chorismos)
are the concepts to be further clarified (p. 211).
In Chapter 6, the issue is whether the separation of the soul
from the body that the Phaedo appears to propose, be it as a
means of moral purification or as a condition of immortality,
is to be taken literally or imagistically, whether it is logos or
mythos (p. 221, though as it turns out logoi are also “images”).
Sherman prepares for his denial of this separate existence of
the soul and that of the Forms, whose separation is implicated
in the immortality and thus in the separability of the soul, by
arguing that if the reading of the text is properly dramatic, separation will always appear as “mythical” (p. 256), that is to say,
figurative—and that the naive boys of the Phaedo are not up
to the image-recognition required by Socrates’s myths.
It is a little absurd to balk at a book’s bulk and then to ask
for more. But, by concentrating on the boys’ inept literalism,7
an image-ontology, though projected in Chapter 7, is displaced
by a critique of the interlocutor’s powers of image-recognition
and interpretation. Such an ontology would, I think, give an
account of two aspects of image-being: 1. whence comes the
difference in plenitude of being that distinguishes an original
from its image, that admixture of being and non-being which
7. I keep saying “boys.” Simmias and Cebes are neaniskoi (Phaedo 89a),
adolescents with incipient whiskers or youths with first beards. To me
they seem the age of freshman, boys and men in turn.
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makes an image a mere image to the detriment of its dignity
(as set out in Plato’s Sophist);8 and 2. what is that similarity,
that admixture of sameness and difference, that connects an
image to its original—a far more complex question. It is this
second inquiry that would seem to me pertinent to Sherman’s
central thesis, which will involve a right reading of imagistic
logoi or rational mythoi. Here is how the philosophical problem
of similitude presents itself to me: Can objects from realms that
are conjoined by no exhibitable “isomorphism,” no structural
identity, have an image-relation? How far can the ordinary
word “image” be stretched, salva significatione, with its meaning being saved?
But perhaps before ontology should come phenomenology, an
account of the way imagining works and images appear.9 Sherman
puts to use a long passage from Proust’s Remembrance of Things
Past (p. 236), a practice I like very much because good novelists
are master-phenomenologists—it’s their métier. Marcel is enamored of a black-eyed woman, but every time he re-envisions her
the memory presents her as blue-eyed—as he says, because she
was a blonde. Perhaps, he perversely concludes, if her eyes had
not been so strikingly, intensely black, he would not have been so
particulièrement amoureux with her as blue-eyed. Sherman understands Proust’s passage—due notice being given to its perversity—
to illuminate a kind of “recollection,” here of dredging up those
image-memories from the soul in which the image of an object
brings with it the image of a person, as in the Phaedo a lyre is associated with its owner, a beloved boy. His point is that this boyimage lacks observed detail; it is of a “total person,” and the details
8. Generally the original is distinguished by several primacies: in time,
dimensionality, functionality, reality. Not so in representative art: A
mound of two-dimensional, inedible, unreal apples, painted by Cezanne
from a prior arrangement, is generally regarded with more respect (and
certainly costs more) than a bag of Pink Ladies bought by anyone at the
supermarket. That’s the valuation Socrates wants, on ontological grounds,
to forestall in Republic X.
9. As Sherman comes near saying (p. 388). For if human discourse is
image-making, then its interpretation is image-recognition (p. 391).
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may well be mistaken. But—here’s the difficulty—Marcel is not
making a mistake. He knows, first and last, that the woman is
black-eyed. He is engaging in deliberate perversity: the imaginative potentiation by willful modulation of an observed reality that
is too opaquely positive for a languid sensibility. More simply put:
Marcel rearranges reality on the slight excuse of blondness to make
it his; so adjusted, it furnishes the object of his self-pleasingly
repetitive daydreams (je repensai); you might call it bed-ridden
love.10
I’ve picked on the Proust passage because Sherman infers from
it a solution to the problem of similarity I posed just above:
The picture does not look exactly like its original, but
then neither does the lyre look like the young boy, yet
we bridge this difficulty by our ability to respond to the
image as image. The sense of both “like” and “unlike”
is in fact multiple; it can be both in order of vivacity (picture vs. object) and visual resemblance (lyre-person).
And this is true of relations of the non-visible of “resemblance” and recollection (p. 237).
Sherman concludes that in the lyre-boy passage Plato is stressing
the possibility of such non-similar resemblance (I’ve intentionally
put it as a contradiction in terms), and that is what I want to question: When push comes to shove, how far up the ascent to Being
can image-recognition take you without obscuring the very nature
of the objects, the Ideas, which you want to attain?11
10. Proust’s way with love meets its refutation in a charming movie, It
Happened in Brooklyn, a 1947 film directed by Richard Whorf, starring
Frank Sinatra, Peter Lawford, and Jimmy Durante. The Sinatra character
takes his girl for granted, Lawford’s is really in love with her. Durante
(Brooklyn’s wise man) tests Sinatra: What’s the color of her eyes? He
dithers: perhaps blue? And so with other detail. Lawford knows on the
instant: brown. Q.E.D.: True love is hyper-observant; in fact that’s its
hallmark: acutely observational concentration.
11. Sherman has certainly considered, but apparently without consequence, the notion that for the highest thought, for noesis, the imagelogos might fail (p. 392, n. 1); but perhaps it is fairer to say that because
he gives so much “a wider interpretation” of images and image-making,
he considers the restriction overcome.
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In Chapter 8, From Logos to Idea, Sherman’s thesis is fully developed, once again with the aid of the Phaedo, where on his last
day Socrates himself says more about the Ideas than anywhere
else.12 Socrates recounts his taking refuge in the use of of logoi for
looking at the truth of beings, lest his soul be blinded by sensory
looking. To pursue this way Socrates has recourse to hypothesizing
(literally, “sup-posing”), a way of proceeding by hypotheses,
namely Ideas, such as the Beautiful Itself (Phaedo 100a ff.). Sherman observes helpfully that a Socratic hypothesis is not, as for us,
a theory to be verified by being tested against experience, but the
converse: experience derives such being and intelligibility as it has
through some sort of presence in it of the forms (pp. 294-5).
But to test (worldly) things against the (transcendental) idea
means—and here I am not certain I follow (that is, understand
rightly or, if I do, agree)—to test them against the “idea functioning
as a logos” (ibid.). Moreover, it now turns out that “the hypotheses
as the particular idea expressed as a dianoetic [discursive] logos is
the idea at work,” and that this logos-idea is in fact to be verified,
not to the detriment of the idea but to the logos which may have
applied it wrongly by misclassifying the things of which it meant
to give an account. This human action (praxis) is, then, “a verification of the idea as logos, that is to say, as a hypothesis which is
an image of its idea” (p. 299; I’ve italicized the last clause). But
Socrates has already said that his images are both deficient and not
logoi: “for I don’t at all concede that somebody who looks into beings in accounts [logoi] looks at them in likenesses [images] to a
greater extent than one who does so in actions” (Phaedo 100a)13—
namely, does not look at them at all.
12. Along with his first appearance, as a boy in the Parmenides, so that
they are shown to preoccupy him first and last as problems; the Socratic
Ideas are ever works-in-progress. In the Symposium and the Phaedrus the
vision of the Ideas is imaginatively consummated.
13. I’ve taken this rendering from Plato’s Phaedo, trans., with introduction
and glossary by Eva Brann, Peter Kalkavage, and Eric Salem (Newburyport, MA: Focus, 1998). We thought that “in actions” means something
like “in sensory reality” (p. 14). My own sense, expressed elsewhere, is
that the Phaedo’s blatantly unpersuasive arguments for the immortality of
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The clearest formulation of Sherman’s thesis I found is this:
“The subjective form reflected in a logos must be seen as an image
of the objective Idea: the form is a rational image” (p. 217). The
soul’s ability to make and read “noetic images”14 is its very immortality, and the ideas it images are correspondingly eternal (p.
320). The logos-involved soul, that is, the form-informed soul and
the ideas share an ontology because they are interdependent;
“though something more than concepts, ideas do not have any real
independent existence outside this human dialectical triad of world,
soul and idea” (p. 387). And, as the logos-soul, the soul of the subjective form, is immortal and atemporal in the act of knowing in
which it accepts the eternal idea, so, reciprocally, the objective
ideas are timeless because they are congruent with the soul, not
because of some otherworldly stability (ibid.).
This account, if I have it correct, is certainly circular,15 which is no
argument against it. The most invulnerable philosophical accounts
are circular; they are ontological mirror images of the above-mentioned hermeneutic circle: Grounds “cause” consequences, consequences “confirm” grounds; inquiry requires pre-knowledge,
knowledge comes from inquiry. But in this perfect mutuality of
soul and idea, the outside third, the world (and the Idea of the Good
that makes the world intelligible) have somehow dropped out; how
are worldly things, which ideas were to serve both as causes
(sources of existence) and as reasons (sources of intelligibility),
actually involved in the triad?
the soul are each occasions for Socrates’s formulating the questions he is
leaving behind; he is handing on his forms as works-in-progress, as problems for future philosophy.
14. Sherman apparently identifies “rational” (dianoetic, discursive) and
“noetic” (intellective, directly beheld); they are, however, different segments
on the Divided Line.
15. While circularity—certainly no venial sin in secular argumentation—
is excusable in philosophical discourse, equivocation is, except in deliberate, inspired double-speak (such as Socrates’s “invisible looks,” the
Ideas) not so acceptable. I think some of my difficulties stem from subtle
meaning-shifts in key words such as image, separation, soul, rationality—
shifts away from common usage and also variations of use within the book.
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There is surely much at stake here for those of us who have the
sense that the explication of these matters might be, in all unhyperbolic sobriety, a matter of life and death. The reason is that, if we
believe that philosophical reflection (even if only occasional) makes
life more—and death less—real, this is an ever-present question:
Are there supersensible realms for us but also beyond us, attainable
but not just yet? And Sherman is surely speaking to just that question, but perhaps not altogether clearly.
Chapter 9. Closing the Circle. Now Sherman “closes the circle”
by returning to the Republic, to its last book. On the basis of his
theory of thinking as primarily image-recognition, he defends
Socrates’s condemnation of the imitative arts as practiced primarily
by painters and also poets against various scholarly critiques:
Socrates is not simply against the fine arts and their ways with reality, but he, in fact, has knowledge of a more veracious imagemaking and a more truth-telling myth-making (p. 349). So
Sherman ends by recurring to the inadequacy of the conversation
partners here, especially the vein of reward-seeking he discerns in
Glaucon (which is, in accord with the pervasive human theme of
the Republic, the happiness to be gotten from practicing justice
even incognito). Finally he resumes his own hermeneutic preoccupation by interpreting in his own mode the final myth, the myth
of Er, who returned from the Afterworld: It requires us “to see
through our images to the invisible in this life” (p. 379).16
Although it is not Sherman’s modus scribendi to collect his theses in one place succinctly and crisply as he goes, the Conclusion
does contain some summations, and therefore I may properly park
my three main queries under its title, ready to withdraw them if
I’ve misread the text.
16. That sounds just like our understanding in the Phaedo translation: the
Socratic invitation to practice death in this life (61c ff.) intends us to rise
in thought to the invisible realm here and now (and, of course, now and
then). But we did not mean that the realm of invisibility is somehow subjective, that is, only equivocally objective, psychically objective, so to
speak, or, on the other hand, that human beings come within actual sight
of it—except perhaps Socrates in the several episodes mentioned in the
dialogues, when he seems to be enraptured (e.g., Symposium 175b, 220c).
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1. This three-pronged question eventually arises in reading Platonic texts: Do the thirty-six dialogues form a somewhat organic
corpus, are the dialogues parts of a whole, or is each dialogue its
own dialectic universe, a conversational world of its own? In reading dialogues, we should, I have no doubt, begin with the latter
supposition. But for a global interpretation it seems necessary to
take notice of the ensemble. Sherman leaves the erotic dialogues,
the Symposium and the Phaedrus, out of account, and in these (as
well as in Plato’s Seventh Letter) the ascent to the Ideas is a work
of love, the virtues are practiced to disencumber the soul from the
world, the logos ceases as the soul comes within sight of the Ideas,
and the sojourn with them has an ecstatic element. In fact, in the
Symposium it is said explicitly of the paradigm form, Beauty, that
it is “neither some logos nor some knowledge” (211a).17 So I think
that Sherman’s sort of implication, his dialogical immanence, has
to be balanced, reconciled—whatever—with the other-world separateness of the Ideas as desirable and distinct objects. And, to be
sure, that is practically impossible within the constraints of “careful” dissection, scholarly respectability, and the effort to keep Plato
plausible to contemporaries. For it requires a certain—rightly suspect—suspension of scrupulosity.18
2. I have misgivings about a Socratic (though not so much about
a Platonic) ontology of the soul. To be sure, Socrates is a master
of psychology, of the soul’s phenomenology. But it seems to me
that in the Socratic dialogues, and so in Plato’s view of Socrates,
the human soul hovers outside and around the structure of beings
and Being. As Sherman flips the Socratic sequence of Divided Line
and Cave, to give preeminence to the human context, so he seems
to me to have flipped the Divided Line laterally, so to speak. Reading left to right, the four line segments representing objects of
17. However, the logos—not as thinking but as uttered language—is
imaged, “as in a mirror,” namely, in sounds (Theaetetus 206d).
18. It is a fair question what role the very desire for a beautiful Beyond
plays in making it plausible. One side might well say that such longing
vitiates sober inquiry. The other may counter that, on the contrary, the
desire is itself a testimonial to transcendence, since it is fed by veracious
intimations.
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knowledge come first, on the left side, together with their inherent
kind of knowability. The four corresponding human capacities, including image-recognition, are appended in one sentence (Republic
513d) to the right—an afterthought, as it were. But Sherman gives
them priority. Perhaps the thoughtful soul’s standing among beings
remained a rousing enough problem in the Platonic Academy for
Aristotle to center his own philosophy around its solution, achieved
by setting up the unmovable moving divinity of his cosmos as Nous,
“Thought” or “Intellect,” whose activity is noesis, “intellection,”
the highest power for Socrates. Thus Aristotle made possible an integration of soul and being—and a soul-ontology. For now beings
do not one-sidedly inform the soul, but intellect reciprocally moves
the world into its own being, its fulfillment.
But if it is the case that the soul for Socrates is not within but
about being, then it may be difficult to make it the part-parent of
the Ideas. And even if the soul is a being among beings, I don’t
grasp just how the Ideas can be in their relation to it dependent and
also in themselves independent, in short, how they can be both subjective and objective. I am all for paradoxes; I think our world is
such that they are its most adequate type of speech—provided the
inner nature of the beings that elicit them is first clearly worked
out, so that paradoxical speech is summary speech, language that
collects necessarily disparate insights. That is why I here conclude
with queries rather than with counter-claims—because I’m not sure
how the “both/and” is justified, what mental incongruities I must—
and would willingly—entertain to get the good of the duality.
3. Now comes the more technical crux of these inquiries. Just
how is logos imagistic? Out of the welter of uses for the word
logos, let me choose the two most prominent ones: word (or noun)
and rational discourse (or thoughtful speech). One word names,
intends (how is unknown) numerous instances, distinct in time,
place, or shape (morphe) and yet the same in some respect (or we
would not have a natural inclination to use this logos collectively);
that something “same” in all of them is what a logos picks out and
names; it is Socrates’s form (idea). A word conveys (how is unknown) the idea without being in any normal sense a likeness: I
think it is impossible to detect any image-function in this naming-
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logos without stretching the meaning out of all recognition. I shall
say why.
“Rational discourse” consists largely of propositions conveying
meaning. Some of these sentences are descriptive and raise mental
images (how is unknown), and such logoi are indeed image-making
(Plato, Sophist 234c). Others, however, are not descriptive but dialectic or “dianoetic;” they “think through” the thought-structure
of appearances and beings, and such logoi are only forcibly imagistic. To be sure, in the lower reaches, some logical arguments can
indeed sometimes be represented in spatial diagrams19 (how is unknown), because the logic-diagrams image not the proposition but
a mental image, a quasi-spatial corralling of class-members: Visualize “All bulls are bovines” as a herd of cattle, enclosed in a
barbed-wire fence, which includes a round pen just for the uncastrated males; then erase the cattle and retain the spatial schematism.
So, if, going from the second to the third part of the Divided
Line, I recognize by the power of dianoetic (thoughtful) imagerecognition that a geometric sphere is the true, more being-replete
original of a soccer ball (quite a feat, since to ordinary thoughtless
image-recognition the ball is surely more real), it is not because
the logos is an image but because it isn’t; it’s about images; it comprehends them. In other words, insights of image-recognition (eikasia) seem to be expressible in logoi, but they aren’t images.20 I have
a suspicion why that is: The logos has a negative capability: not or
non-, while images have no inherent negativity. They have the
same thoroughgoing positivity as the spatial world. It takes words
to dub any aspect or space, even emptiness, as a not-this or an absence. As I said, with Sherman I like to see the novelists bear me
out: The fatal Marabar Cave, in Forster’s Passage to India (Ch.
XIV), is the venue of negation in words, but in experience it is a
resounding “boum”—for negation has no sensory image as such,
and so propositions that are negated can’t be wordlessly imaged.
19. Such as Euler diagrams.
20. Sherman actually speaks mostly of image-making rather than imagerecognition. But I think the logos penetrates rather than produces images.
The difficulty may be located just here: What, in Sherman’s view, is the
work, what are the processes proper to logos?
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In sum, I’m not sure whether language intends, symbolizes, or represents,21 but it doesn’t seem to be at all isomorphic with sensible
objects so as to image them. And when it comes to speech about
the Forms, verbal, expressible thinking seems to fail, as Sherman’s
helpful report of scholars’ battles, for example, with self-predication22 amply shows.
****
These queries have been about Sherman’s unquestionably
thought-arousing interpretation of the Republic and the
Phaedo, or rather, about its philosophical consequences; indeed
they are the very proof of its interest. But Sherman also has,
besides the intention of doing the texts justice by reading them
as conversations among differently inclined and diversely responsive human beings, a motive, a hoped-for effect, which his
interpretation is to serve: to let us, with Socrates, “see ourselves as essentially engaging collectively in a discourse that
brings us together rather than drives us apart” (p. 392). And
that aim is beyond querying; what is an open question, one on
whose terms Sherman’s opus focuses the mind, is this: Do we
come closer to the way things are by recourse to the workinghypothesis of Ideas, unattainable in this life but informing the
soul from beyond with expectant desire and responsive logoi?
Or do we do better by means of Sherman’s thesis of a human
rationality so inseparably involved with the Ideas that they are
“not manifest” outside this union, within which they are interpretable “as essentially atemporal experience wholly in this
21. I half suspect that Sherman would answer my difficulty by saying that
he has enlarged the meaning of “image” so as to mean representation, a
way of re-presenting something, of recalling, of standing-for a thing, that
requires no similarity. I think it would still be necessary to show how
logos “represents.” The proper naming of logos’s relation to the things it
is about is, I think, the perplexity of language.
22. For example is the Idea of Justice itself just? The problem is a version
of the question raised in a note above: Is “similarity” reciprocal between
an idea and its copy? I should say that to me philosophy becomes wonderful just when “rational speech” (actually a redundancy: logikos logos)
fails, becomes para-doxical, “counter-credible.”
�ESSAYS & LECTURES |
109
life” (p. 386)—as our experience, it seems, not as unequivocally separate Beings?
Has Daniel Sherman saved the Ideas and if so, are they
Socrates’s Ideas? I leave that question open. But he has surely
done his part to see that the “myth was saved” (Republic, 621b)
and is now before us to consider—just as Er did by not drinking of the River of Forgetting.
�
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<em>The St. John's Review</em>
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<em>The St. John's Review</em><span> is published by the Office of the Dean, St. John's College. All manuscripts are subject to blind review. Address correspondence to </span><em>The St. John's Review</em><span>, St. John's College, 60 College Avenue, Annapolis, MD 21401 or via e-mail at </span><a class="obfuscated_link" href="mailto:review@sjc.edu"><span class="obfuscated_link_text">review@sjc.edu</span></a><span>.</span><br /><br /><em>The St. John's Review</em> exemplifies, encourages, and enhances the disciplined reflection that is nurtured by the St. John's Program. It does so both through the character most in common among its contributors — their familiarity with the Program and their respect for it — and through the style and content of their contributions. As it represents the St. John's Program, The St. John's Review espouses no philosophical, religious, or political doctrine beyond a dedication to liberal learning, and its readers may expect to find diversity of thought represented in its pages.<br /><br /><em>The St. John's Review</em> was first published in 1974. It merged with <em>The College </em>beginning with the July 1980 issue. From that date forward, the numbering of <em>The St. John's Review</em> continues that of <em>The College</em>. <br /><br />Click on <a title="The St. John's Review" href="http://digitalarchives.sjc.edu/items/browse?collection=13"><strong>Items in the The St. John's Review Collection</strong></a> to view and sort all items in the collection.
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thestjohnsreview
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The St. John's Review, Spring 2014
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2014
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Pastille, William
Brann, Eva T.H.
Hunt, Frank
Sachs, Joe
Van Doren, John
Williamson, Robert B.
Zuckerman, Elliott
Arnaiz, Deziree
Sachs, Joe
Fried, Michael N.
Recco, Gregory
Wiener, Linda
Eagleson, Hannah
Kalkavage, Peter
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Volume 55, Number 2 of the The St. John's Review. Published in Spring 2014.
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St_Johns_Review_Vol_55_No_2_Spring_2014
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St. John's Review
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