Knowledge and Self-Knowledge in Plato's Theaetetus

Classical Studies | Philosophy

Andrea Tschemplik is assistant professor of philosophy at American University.

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Tschemplik

“I particularly admire and concur with Andrea Tschemplik’s central thesis that even in the Theaetetus the general problem of knowledge cannot be divorced from the Socratic notion that all knowledge is selfknowledge. What makes this reading so forceful in its contribution to the scholarship is that it successfully refutes the oft-claimed notion that in Plato’s later dialogues (such as the Theaetetus) he broke rank with Socrates and developed a theory of knowledge that stands on its own apart from the conversion of the soul that was a key component of Plato’s early dialogues. Tschemplik’s arguments and the evidence she mounts that no such break is evident in the Theaetetus has far ranging implications for a holistic reading of the Platonic dialogues that does not assume a straightforward philosophical division between the early and late dialogues.” —WALTER BROGAN, Villanova University

Andrea Tschemplik

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“A striking study of crucial themes in Plato’s thought. Erudite, insightful, and imaginative.” —STEVEN M. CAHN, City University of New York Graduate Center

Knowledge and Self-Knowledge Plato’s Theaetetus

“Andrea Tschemplik’s monograph emphasizes aspects of the Theaetetus that are often overlooked (e.g., knowledge of ignorance) and aspects of dialogue construction that are not widely understood (e.g., their dramatic and literary frames). She has an answer to the rarely discussed but valid question of why it takes Socrates so long to give a refutation of Theaetetus’s second account of knowledge, when that refutation could have been given in the first place. This is a welcome contribution to the new Platonic scholarship that seeks to understand the dialogues holistically, with equal sensitivity to the arguments and to their literary and dramatic nuances. The volume is important reading for students of the Theaetetus and of Plato generally.” —GERALD A. PRESS, Hunter College and City University of New York Graduate Center

Knowledge and Self-Knowledge in Plato’s Theaetetus

7/18/08 12:25:57 PM

Knowledge and Self-Knowledge in Plato’s Theaetetus

Knowledge and Self-Knowledge in Plato’s Theaetetus Andrea Tschemplik

LEXINGTON BOOKS

A division of ROWMAN & LITTLEFIELD PUBLISHERS, INC.

Lanham • Boulder • New York • Toronto • Plymouth, UK

LEXINGTON BOOKS A division of Rowman & Littlefield Publishers, Inc. A wholly owned subsidiary of The Rowman & Littlefield Publishing Group, Inc. 4501 Forbes Boulevard, Suite 200 Lanham, MD 20706 Estover Road Plymouth PL6 7PY United Kingdom Copyright © 2008 by Lexington Books All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of the publisher. British Library Cataloguing in Publication Information Available Library of Congress Cataloging-in-Publication Data Tschemplik, Andrea, 1961– Knowledge and self-knowledge in Plato's Theaetetus / Andrea Tschemplik. p. cm. Includes bibliographical references (p. ) and index. ISBN-13: 978-0-7391-2573-1 (cloth : alk. paper) ISBN-10: 0-7391-2573-7 (cloth : alk. paper) ISBN-13: 978-0-7391-3033-9 (electronic) ISBN-10: 0-7391-3033-1 (electronic) 1. Plato. Theaetetus. 2. Knowledge, Theory of. 3. Self-knowledge, Theory of. I. Title. B386.T74 2008 121—dc22 2008018521 Printed in the United States of America

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To my friends and colleagues in the Department of Philosophy and Religion at American University

Contents

Acknowledgments

ix

Introduction

1

1 Framing the Question of Knowledge and Self-Knowledge

11

2 Intellectual Midwifery, Intellectual Pregnancy

41

3 Perception and Knowledge

67

4 Doxa-Logy

103

5 Mathematics and Beyond

141

6 Conclusion

165

Works Cited

171

Index

179

About the Author

183

vii

Acknowledgments

M

any midwives assisted in the prolonged birth of this idea. Steven M. Cahn encouraged its first coming to light as my dissertation advisor, and Charles Landesman and Joan Stambaugh gave important assistance on its way to fruition. Different parts of different chapters were presented at the Society for Ancient Greek Philosophy, as well as the Ancient Seminar at George Washington University. The project has taken on its present form during my past three years at American University, where friends, colleagues, and students encouraged and supported my work. I wish to thank the College of Arts and Sciences of American University and Dean Kay Mussell for arrangement and granting of a junior leave. Special thanks go to “super-midwife” Ellen Feder, who not only read and commented upon the entire manuscript, but also kept me fit with “breathing exercises.” Jeffrey Reiman cast his expert critical eye upon the whole and convinced me that I had not produced a wind egg. Amy Oliver and Shelley Harshe read substantial sections, made helpful comments, and always gave practical and personal support. Of course, none of this would have happened without students. I particularly thank Jim Ambury, my research assistant, and all those students who have kept me from becoming sterile and barren. Finally, thanks go to my husband, Jim Stam, who suffered with me through all the labor pains.

ix

Introduction

I

n the Apology Socrates puts forward that he has “a certain kind of wisdom,” “human wisdom,” consisting in the fact that he knows that he does not know (20d). His claim to such wisdom, he says, is based on the answer that the oracle at Delphi had given to his friend Chaerephon, that there was no man wiser than he, Socrates, and which he then put to the test by means of dialectical interrogation of his Athenian fellow citizens (20d–23b). Although Socrates makes various claims to knowledge and particular kinds of expertise in the dialogues, the Delphic injunction to self-knowledge is never abandoned. The Platonic dialogue most explicitly devoted to the definition of knowledge, the Theaetetus, runs headlong into questions of the limits of knowledge. This book will examine the interconnected questions of knowledge, self-knowledge, and the limits of knowledge in Plato. I will keep the Theaetetus in continuing and primary focus, but I will also investigate the Symposium, Charmides, Meno, and Republic. Other dialogues and themes will be brought into the discussion as they prove relevant along the way. All of these dialogues will be brought into the discussion because they are specifically related to the themes of the Theaetetus, and sometimes as they are specifically related to its dramatic or literary framework. The Charmides and Theaetetus both present Socrates looking for someone who is exceptional in either wisdom or beauty; the Symposium and Theaetetus have an outer frame in which the veracity and reliability of the account is called into question, and in addition, there is the connection between intellectual pregnancy as discussed in Diotima’s account in the Symposium and Socrates revealing his skill as an intellectual midwife in the Theaetetus; 1

2

Introduction

the Meno and Republic both deal with accounts of knowledge that seem to avoid the impasse confronted in the Theaetetus. The Theaetetus is in many regards a puzzling and mysterious work: a dialogue between Socrates and two famous mathematicians, which involves technical and philosophical expertise, an array of complex philosophical arguments concerning the nature of knowledge and, at the same time, it is a conversation ending in an impasse or aporia, the mark of socalled Socratic or early dialogues. As an aporetic dialogue it raises the same questions that other aporetic dialogues do: whether the aporia is a sign of the limits of knowledge, or whether it is the result, perhaps only a temporary or provisional result, of the interlocutor’s incompetence or of other failings or circumstances. The Meno, Gorgias, and Republic, book 1, for example, bring on the “stage” interlocutors who are recalcitrant, even obstreperous, and whose attitudes seem to have a decisive impact on the outcome of the dialogue. Theaetetus, in contrast, is a much more compliant interlocutor, who tries his best to accede to Socrates’ demands, who only occasionally stumbles into the trap of trying to figure out what it is that Socrates himself believes, rather than articulating and clarifying his own thoughts. To a significant extent, in fact, Theaetetus thinks along Socratic lines: He is ready to engage in the elenctic procedure and is willing to engage in a Socratic type of review. Socrates explicitly thanks him for his helpfulness at 185e ff. where Theaetetus by himself discovers the role of soul in grasping the commons things like “same” and “different” and spares Socrates the arduous task of proving this. It can be said that Theaetetus is one of the “most Socratic” of interlocutors in the dialogues.1 The aporia regarding knowledge is initially introduced by Socrates, who, after arguing that wisdom and knowledge can be identified, states: “Well, this is the very point about which I’m perplexed (aporo¯) and I am incapable of grasping it adequately by myself, whatever knowledge is” (145e). Socrates does not reiterate his perplexity at the end of the dialogue, however; instead he declares that the process of examining Theaetetus’s answers to the question has come to a successful conclusion, because Theaetetus has given birth to all that was within him—and more, according to Theaetetus (cf. 210b). They agree that they have been able to refute Theaetetus’s earlier claims that knowledge is identical to perception, to true opinion, or to true opinion plus logos. It is thus not clear whether Socrates would say that he is in the same state of aporia as he was earlier in the dialogue. By the end of the Theaetetus we have come to a far clearer understanding why it is that we cannot arrive at a final answer to the question of knowledge as such: We can offer criteria that must be met for something to count as knowledge, but our list always comes up incomplete when we are investigating knowledge as a whole rather than knowledge of some particular expertise or special subject matter. Method plays an im-

Introduction

3

portant role when considering scientific and mathematical knowledge, and following established procedures validates what is to be considered as knowledge within a given discipline. Socrates is not concerned with a particular kind of knowledge, however, but with knowledge as such. Socrates never calls into question the possibility of knowledge as such. The failure to arrive at an adequate definition of knowledge is not tantamount to abandonment of the project of defining knowledge. Early in the dialogue Theaetetus listed various branches of knowledge, as he saw them, and those continue to stand as far as they go. Nor is the conclusion an automatic commitment to skepticism. Socrates never doubts that Theaetetus and Theodorus, his two mathematician interlocutors, possess knowledge of some kind. Rather it is precisely the limitations of this knowledge and of the definitions of knowledge which here come to the fore. Very early in the dialogue, after Theaetetus is introduced to Socrates by Theodorus, who comments on the similarities between Theaetetus’s and Socrates’ facial features and pronounces them both not beautiful, Socrates wonders whether Theodorus’s expertise is such as would allow him to make such a judgment. (143e–145a). The limits of knowledge are thematized after the frame and at the very beginning of the actual dialogue; and the limitations in transmitting knowledge are problematized by a frame conversation between Terpsion and Euclides, the self-confessed “author” of the dialogue proper. Mathematicians transmit their knowledge in the form of proofs and demonstrations. The fruitfulness of such a method is illustrated in the exchange about Theaetetus’s solution of the problem of the surds: He had been studying the geometrical proofs that Theodorus had constructed for irrational numbers up to 17, and on the basis of that Theaetetus was able to discern something which Theodorus had overlooked. Theaetetus thereupon formulated a procedure that was applicable to all irrational numbers. The question before us is how and to what purpose such methods would play out in considerations of philosophical knowledge, whether there are comparable procedures. Both the issue of the limitations of knowledge and the uncertainty of its transmissibility in the context of philosophy are related to the importance of self-knowledge as a goal of philosophy and of philosophical education. Socrates defines his philosophical mission in his defense speech (Apology 21a) by referring to Chaerephon’s visit to the oracle at Delphi. Visitors to Apollo’s shrine were always reminded of the admonition to “know yourself”—gnothi s’auton. As we learn from the next section of the Apology Socrates interprets the news that he has no peer in wisdom as an invitation to examine his fellow-citizens in Athens—poets, politicians, craftsmen—either to find someone who is wiser, or to come to know something about himself. What he comes to know through this process is that knowing what one does not know is a stride in the direction of human wisdom

4

Introduction

and self-knowledge. That self-knowledge is an overriding goal for Socrates is clear from many dialogues, but nowhere is he more explicit than in the Phaedrus, where he asserts that no other knowledge matters unless it is grounded in self-knowledge (229e–230a). Demythologizing nature and developing a scientific account of its events and workings is secondary to self-knowledge for Socrates. Knowledge of ignorance is an accomplishment of philosophical inquiry and it addresses very directly the problem of the limits of knowledge. Knowing that one does not know is a claim to knowledge and simultaneously the recognition of the need to inquire and search. Theaetetus develops a procedure and solves a problem that his teacher could not work out. He has reason to be satisfied with the knowledge he has gained and shared. But what Socrates will teach Theaetetus in their conversation is a recognition of his ignorance, that crucial initial step toward self-knowledge. It is common enough for Socrates to be associated with the philosophical project of self-knowledge, but the specific content of that project is not so easily identifiable. We must, first of all, rid ourselves of the usual modern conceptions of self-knowledge which, beginning with Descartes, are associated with intense introspection, and proceed under the assumption that we have direct and unmediated access to our own mental states. Although both Kant and Hegel called into question the possibility of having an “inner” without an “outer,” a “self” without an “other,” many twentiethcentury analytic philosophers still examine self-knowledge from a basically Cartesian vantage point. In contrast, Socrates presents his quest for self-knowledge as a task that necessarily involves other interlocutors who are willing to engage in dialogue with him. It is safe to say, I believe, that Socrates’ primary concerns do not involve his own mental states; rather he is concerned with finding out what kind of a person he is, wondering whether he is approximating a simple, divine nature or a rather complex, monstrous one.2 The kind of life that someone leads is the best indication of who she is; living and acting provide the materials for the appropriate reflection that might yield self-knowledge. Both in the Republic and in the Phaedrus Socrates presents his listeners and readers with images of the soul that clearly indicate that it is complex rather than simple. It is this complexity—whether dual, tripartite, or otherwise multiple—which presents for us the challenge of living a harmonious life. Socrates’ question regarding self-knowledge is best understood as an ethical question rather than an epistemological or ontological or, for that matter, a psychological one. His hypotheses and images representing possible ways of understanding the structure of the soul reflect the experience of dissonance, both wanting and not wanting something. It is knowing how to resolve this conflict that constitutes an essential feature of Socratic self-knowledge.

Introduction

5

Another feature of the Socratic quest for self-knowledge is concerned with the issue of the limits of knowledge, which requires constant examination. Self-knowledge is both central and elusive in Socrates’ philosophical quest. When he talks about his overarching concern with self-knowledge in the Phaedrus, he links it directly with knowledge of soul: He wants to know whether his soul is simple and divine, or whether it is monstrous and typhonic.3 It is in his second speech on ero¯s, the so-called palinode, that Socrates links the erotic with the theme of self-knowledge, explaining how one can come to know oneself through self-recognition in the other. Socrates offers a similar analysis in the Alcibiades I, where he proposes that we can come to know ourselves by seeing our image in the pupil of another’s eye (132d–133e). The quest for self-knowledge depends on the presence of an other and the question arises whether the same can be said about knowledge. Is it possible to reach knowledge by ourselves without depending on others? From a modern Cartesian perspective, we might well be tempted to answer in the affirmative; but even Descartes sought out the approval of friends to confirm his findings: For Descartes, it is only through doubt of the other that we can find the self. We are not capable by ourselves of ensuring that things of which we are convinced, and which we take to be true, are actually the case. The most haunting depiction of the dangers of self-reliance is offered in Republic 2 (382a–c), where Socrates discusses the “true lie,” which “all gods and human beings hate,” the lie in the soul that happens when people replace “things that are” with lies. The “true lie” is self-deception, an absence of self-knowledge. We must also examine ourselves with respect to all those things that we take to be “certain” knowledge. The quest for knowledge of any “other” leads us back into inquiry into ourselves. “I searched into myself,” said Heraclitus (D–K 101). The philosophical concern with self-knowledge makes the issue of the writing and transmission of philosophy very pertinent indeed. The critique of writing by a writer is not unique to Plato, but it is a major irony that Plato should put in the voice of Socrates such explicit critiques of philosophical writing. Plato writes about the difficulty and limitations of philosophical writing most explicitly in the Phaedrus and in the Seventh Letter. In the Phaedrus he alleges that writing is inherently nondialectical and unphilosohical: A written text says what it says, unable to make adjustments for its readers. It cannot take into account their individual characters, states of mind, and stages of learning. More specifically, Plato explains in the Seventh Letter why philosophy cannot be written down: “No sensible man will venture to express his deepest thoughts in words, especially in a form that is unchangeable, as is true of written outlines” (343a). And a little later: Anyone who is seriously studying high matters (spoudaios to¯ n onto¯ n spoudaio¯ n) will be the last to write about them and thus expose his thought to

6

Introduction the envy and criticism of men. What I have said comes, in short, to this: Whenever we see a book, whether the laws of a legislator or a composition on any other subject, we can be sure that if the author is really serious, this book does not contain his best thoughts; they are stored away with the fairest of his possessions. (344c)

These assertions must give pause to any self-aware reader of Plato’s works, because Plato suggests that the most we can expect from his dialogues is pointers in the direction of inquiry, rather than definitive and final answers about these “high matters.” The best we can hope for is to achieve some kind of illumination after repeatedly “rubbing” our best effort against the text (344b). I will examine in this book ways in which the frames of Platonic dialogues illuminate the “official” subject of the dialogue, bringing to light connections which are not always apparent in the main and direct discussion. The Theaetetus is framed by a discussion between two gentlemen from Megara, one of whom, Euclides, claims authorship of the dialogue. It is his chance encounter with Terpsion that provides the occasion for the reading of the written dialogue by a servant. Reflection on the passages concerning the limits of writing helps us to understand why it is that Plato’s dialogues abound with images and metaphors, why the most important claims are often formulated as analogies, sometimes elaborate analogies, with one or more missing terms. In the Republic, for example, Socrates identifies the study of the Good as the highest object of inquiry, but at the same time he assures his listeners that he cannot speak about the Good directly, but must resort to images and analogies. We can see how Plato is trying to transcend the limits of writing, by writing in such a way that his readers are forced to work out the details of the analogy for themselves. Plato induces his readers to philosophize themselves and he simultaneously withholds his “fairest” possession. Whatever we may take away from a Platonic dialogue is to a certain extent our own possession: We are as much responsible for the outcome as is Plato. Every dialogue presents us with the challenge of disentangling the analogies, and the Theaetetus is no exception. Throughout the dialogue we encounter images and assertions that are far from self-evident, which often leave the reader puzzled and perplexed. In my reading of the Theaetetus I pay particular attention to these images and offer interpretations that are consistent with the text at hand as well as other Platonic dialogues. It was in many cases helpful, even crucial, to consult other dialogues so as to get a proper perspective on a particular image, such as the linkage I see between the passage about intellectual midwifery in the Theaetetus and Socrates’ discussion of ero¯ s and Diotima’s explication of intellectual pregnancy in the Symposium.

Introduction

7

Writers dealing with the limits of knowledge are virtually compelled to speak indirectly themselves. Were we on the other side of those limits and able to talk straight concerning them, they would not be limits at all. If self-knowledge could be formulated with the objectivity of modern scientific language, then the self would have to be an object and thus not a self at all. Something might be captured thereby, but it would not be reflexive and it could not be a subject. Plato’s frequent use of analogies leaves his interlocutors free to wonder and figure and philosophize. Since analogia is the Greek term for a mathematical proportion, some sort of parallel structure is implied between philosophical knowledge and mathematical knowledge and procedure. But it also leaves the limitations and indirection in place for the reader to see and try to understand. Plato links the fulfillment of our desire to know with our nature (physis), insisting that there is a kinship between the knower and the object of knowledge. It is only someone naturally inclined toward justice who can come to know and grasp what justice is (Republic 4, 443e–444b). This claim, startling on the face of it, is actually born out in the dialogues: Critias was a future prominent member of the “Thirty Tyrants” and Charmides was a member of “The Ten” whom the Thirty appointed to rule the Piraeus. Both were involved in the tyrannical rule of Athens after its defeat in the Peloponnesian War. They were also principal interlocutors in Plato’s Charmides, who cannot come up with a definition of moderation or sound-mindedness, as that dialogue ends in aporia. Meno, the mercenary foreigner, cannot state what virtue is and that dialogue similarly ends in an impasse, though Socrates offers a provisional answer that virtue is a gift from the gods. Their natures are not in tune with the relevant subject matter. The Theaetetus also adheres to the principle that there must be harmony or kinship between the knower and the object known. It does so in two ways: (1) The reader entering upon the dialogue likely presumes that mathematicians are closely related to episte¯ me¯ —science, knowledge—and that they may well claim to possess it. The interlocutors are uniquely equipped to tackle the question of knowledge with Socrates; (2) At the same time it turns out—as we will see in the latter half of the book—that the mathematician is also limited by his nature and needs to be guided by Socrates to the recognition that knowledge and opinion differ. And that leads the mathematician to a knowledge of his ignorance and to the edge of philosophical knowledge. To accomplish this goal Socrates leads Theaetetus through three definitions of knowledge to an apparent impasse. And yet all is not lost: The aporetic ending is not merely negative.

8

Introduction

OUTLINE OF CHAPTERS In the first chapter, “Framing the Questions of Knowledge and SelfKnowledge,” I examine the frame of the Theaetetus and compare it to the frames of the Symposium and the Charmides, remarking on the fact that all three dialogues make a statement about the difficulty of the transmission of philosophy. The Theaetetus is explicitly a written dialogue; whereas the other two are narrated, one by Socrates and the Symposium by Apollodorus. The significance of framing dialogues is that it calls into question the possibility of objective accounts—that is, everything said or written carries with it the burden of perspective. The issue of perspective adds a particularly thorny issue in any discussion of knowledge, because it gainsays the possibility of detaching the account of knowledge from the position of the knower. I argue that the literary frame of the Theaetetus invites us to ask the question as to the “proper” frame of knowledge, which I suggest to be self-knowledge. In the second chapter, “Intellectual Midwifery, Intellectual Pregnancy,” Socrates’ self-ascribed techne¯ of midwifery and his expertise in erotics are examined. Socrates reveals that he has been divinely ordained to assist young men in giving birth to their thoughts and opinions, and to examine whether or not the offspring of such pregnancies are viable. The claims Socrates makes are startling, for he points both to his own sterility and barrenness, while at the same time claiming to be the measure of what is true and false. The very notion that young men can be pregnant in their souls needs clarification and can best be understood in light of Diotima’s discussion of ero¯ s in the Symposium. Diotima’s emphasis on beauty in the process of pregnancy and of birthing is a lesson well-learned by Socrates, which he demonstrated by repeatedly calling Theaetetus and his answers “beautiful,” denying Theodorus’s previous assessment of both Socrates and Theaetetus as ugly. In “Perception and Knowledge,” the lengthy investigation into Theaetetus’s first definition of knowledge as perception is reconstructed in the light of Protagoras’s dictum that “Human being is the measure” as well as the doctrine of the flux attributed to Heraclitus. The connection between Heraclitean ontology and Protagorean relativism is examined so as to reveal why Socrates introduces these two giants into the discussion, that is, to investigate their maieutic function. I will argue that Heraclitus’s flux fragment inspires Socrates to give an account of perception through the “myth of twin motion,” which can withstand the refutations of Protagoras and extreme Heracliteanism. In the “myth of twin motion” Socrates describes perception as an interactive process between the perceiver and the perceived, such that both are active and passive. This dual motion between perceiver and perceived can be seen as an initial para-

Introduction

9

digm for knowledge, one that recognizes the contribution of both knower and the object to be known in the construction of knowledge. In the concluding section I will argue that the “myth of twin motion” mirrors Socrates’ description of erotic encounters in the Phaedrus. In the fourth chapter “Doxa-Logy” I set out to analyze the last two definitions of knowledge as true opinion (doxa) and true opinion accompanied by a logos. The first section details why Socrates turns to false opinion when Theaetetus offers true opinion as the definiens for knowledge. Particular attention is given to the fact that Theaetetus is offering the false opinion that true opinion is identical with knowledge. I argue that Theaetetus’s answer can best be understood as the result of his mathematical training, insofar as there is no distinction between knowledge and true opinion in mathematics. In the second part I analyze whether the two images employed by Socrates to explain false opinion, the wax and the aviary, can in any way account for Theaetetus’s mistake. Here I offer an interpretation of the aviary in light of the discussion of the “knowledge of knowledge and non-knowledge” in the Charmides. The whole concept of nonknowledge is discussed by Socrates in just these two dialogues, which invites a comparison of the way nonknowledge is handled in each. I show that the skills involved in distinguishing the knowledge of knowledge from nonknowledge are identical to those Socrates attributed to himself as a midwife. The final section discusses the significance of logos: Although Socrates claims that their discussion has come full circle, it becomes evident that it is not a vicious but a virtuous circle. The need to articulate one’s opinion is not only the first step to knowledge but also an exercise in self-knowledge. In the final chapter “Mathematics and Beyond” I return to the central section of the Theaetetus, where Socrates and Theodorus are engaged in comparing philosophical and nonphilosophical lives. The depiction of the philosopher as one who is patterning his character and life in accordance with the divine, provides the segue for a comparison between the philosopher-king of the Republic and the mathematician of the Theaetetus. The nonphilosophical lives discussed in the digression are those of the sophist and orator, but the juxtaposition of the Republic books 5–7 with the discussion of knowledge in the Theaetetus offers a comparison between the philosopher and the mathematician. Concentrating on Socrates’ critique of mathematics as a discipline that is incapable of questioning its own starting points, I show that it is the absence of self-knowledge that disqualifies mathematics as the paradigm for philosophical knowledge. To further illustrate this point I examine the images of the sun, the line, and the cave to arrive at a clear understanding of philosophical knowledge. I argue that what Socrates provides through images in the Republic he works out dialectically in the Theaetetus: the ascent illustrated in the cave

10

Introduction

is accomplished in the Theaetetus and Socrates leads the mathematician out of the cave by getting him to the precipice of the knowledge of ignorance. That is why Socrates concludes the Theaetetus with a sense of accomplishment—he has done all midwifery can do—and words of encouragement to Theaetetus. Even if the Theaetetus is at one level an aporetic dialogue, the aporia is not entirely negative.

NOTES 1. Ruby Blondell, The Play of Character in Plato’s Dialogues (Cambridge: Cambridge University Press, 2002), 252–60. 2. See Phaedrus 230a. 3. See Phaedrus 230a.

1

O Framing the Question of Knowledge and Self-Knowledge

E

very logos is framed in multiple ways. Whether understood as argument, speech, or account, every logos is spoken, written, or otherwise communicated by someone to someone else about something. Even the most specialized scientific reports or the most abstract mathematical proofs and conjectures are addressed by authors to audiences. Assumptions are made about what that audience already understands, needs to have clarified or defended, is likely to doubt or dispute. Since all knowledge is conveyed through logos, we must necessarily confront the issue of the framing of knowledge also. Some Platonic works are direct dialogues, plunging in medias res; others are framed by the comments of a narrator or by some secondary dialogue; still others have multiple frames. The frames of dialogues indicate the viewpoint of the narrator, the temporal relation to the main event and the relation of the narrator to the main characters, and thus both the limits of his knowledge and any special access he might have to the persons and topics under discussion. Wherever there is narration or framing of conversation, we have to look beyond the simple or apparent neutrality and “objective” detachment of the presentation. Sometimes a dark frame borders a picture of clearer lines, sometimes a seeming transparent edge is the margin for the more obscure. A frame can reveal the absence of serious knowledge or self-knowledge on the part of a narrator—or potentially, surprisingly and ironically, the reverse. In this chapter I will examine the dramatic settings and framing of the Theaetetus, the Charmides, and the Symposium—in which Euclides, Socrates, and Apollodorus respectively are the narrators—as demonstrations of the 11

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Chapter 1

way that Plato “problematizes” the very activity of writing dialogues. There are both thematic and dramatic links between the Theaetetus and the other two. The Symposium advances the notion of intellectual pregnancy in the general context of ero¯s, while the Theaetetus discusses intellectual midwifery in the context of knowledge and learning. Both of these have double frames, a frame within a frame, but the outer frame of the Symposium is narrated, whereas that of the Theaetetus is in direct dialogue form. The frame of the Charmides and the inner frame of the Theaetetus both see Socrates searching for a philosophically inclined young man; whereas the argument in the Charmides will finally lead to the question of a “knowledge of knowledge” parallel to but different from the logos of knowledge analyzed in the Theaetetus. Both the Charmides and Theaetetus present postwar scenes at the outset; both the Theaetetus and Symposium raise at the outset questions as to their precise dramatic timing: “Just now, Terpsion, or a long time ago from the country” (142a) is the mystifying opening of the Theaetetus. In each of the three cases it turns out that the recording or narrating of the original conversation adds a perspective that might involve, consciously or unconsciously, a distortion of what was being said. Euclides, as the purported “author” of the Theaetetus, openly discusses his editorial work, justifying his activities in the name of ease of reading. Socrates, in his narration of the discussion he had with Charmides and Critias, reminds the auditor-reader throughout of his own subjective experiences. And Apollodorus, in the Symposium, happily identifies himself as a “maniac,” who is completely devoted to Socrates, before he recounts the speeches he has heard from Aristodemus. In each case Plato forces us as readers to question the reliability and “objectivity” of these accounts and along with it the reliability of Platonic dialogues as a whole. Thus we must look for the links between the framing of logos, accounts and arguments, and the framing of knowledge itself. In his Letters as well as in the Phaedrus, Plato suggests that philosophy, as he understands and undertakes it, cannot be written, and yet he himself wrote dialogues that lead many readers to become, if not philosophers themselves, at the least students of philosophy. The frames of the three dialogues here under investigation also raise the question of the transmissibility of philosophy, and not just as speech that happens to have been written down. The youth that Socrates is seeking out would be potential successors, possibly able to keep philosophy alive when it is threatened. The problem of transmission is not limited to philosophy: We need only consider the writings of Herodotus and Thucydides to become aware of the difficulty of assessing the veracity of accounts.1 Both acknowledge the role that they as investigators played in shaping the accounts of historical events they offer. Thucydides even sees his own firstperson account as problematic: “And with reference to the narrative of

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events, far from permitting myself to derive it from the first source that came to hand, I did not even trust my own impressions, but it rests partly on what I saw myself, partly on what others saw for me, the accuracy of the report being always tried by the most severe test possible” (1.22, italics mine). If history is an attempt to portray the unfolding of events that are shaped by humans—such as war—and, if this endeavor is beset with difficulties of interpretation and so noted by its authors, it should not be surprising that Plato disclaims the possibility of writing philosophy in letter 7: So much at least I can affirm with confidence about any who have written or propose to write on these questions, pretending to a knowledge of the problems with which I am concerned, whether they claim to have learned from me or from others or to have made their discoveries for themselves: it is impossible, in my opinion, that they can have learned anything at all about the subject. There is no writing of mine, nor will there ever be one. For this knowledge is not something that can be put into words like other sciences (mathe¯mata) (341b–c).

And so, when it comes to a written philosophical account, we have to proceed cautiously in trying to determine what the subject matter really is and what the dialogue is all about. This is especially apparent when we take into account that self-knowledge is, for Plato, one of the goals of philosophical activity and that is something that cannot be written down and transmitted with uniformity or finality, since every person must come to know him- or herself and each of us must strive for a renewed selfknowledge as we grow and change. But by paying attention to the frames of the accounts we gain entrance into some of these things. Many students of Plato consider the Theaetetus to be among his most enigmatic and mysterious dialogues: Why should a dialogue end in aporia, when its explicit theme is knowledge and its interlocutors are Socrates and two mathematicians? And why is it that the dialogue does not introduce the forms as the object of knowledge? Is the absence of the forms the reason why the Theaetetus comes to no satisfactory definition of “knowledge,” as Francis Cornford has proposed?2 In this study I will attempt to answer both of these questions. Provisionally we can say: The dialogue is about self-knowledge as well as knowledge and, precisely because it is a discussion with mathematicians, it is unnecessary for Socrates to introduce the forms. A mathematician’s attempt to formulate a definition of knowledge is an exercise in self-knowledge. This claim can most easily be understood through Kant’s argument that mathematical propositions are synthetic, not analytic. In the Critique of Pure Reason Kant explains how mathematics developed from a techne¯ to an episte¯ me¯, from a skill to a science, the moment that mathematicians recognized their own role in the

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construction of mathematical truths: “And [the mathematician] found that in order for him to know anything a priori and with certainty about the figure, he must attribute to this thing nothing but what follows necessarily from what he himself put into it in accordance with his concept.”3 I will not argue that Plato is best understood as a “transcendental idealist,” but rather that the quest for knowledge is intertwined with the problem of self-knowledge. The connection between self-knowledge and knowledge is also crucial for an interpretation of the Charmides, where Socrates investigates moderation (so¯phrosyne¯ ) with two future tyrants.4 In that dialogue the problem of self-knowledge is in the forefront and the interlocutors end in aporia, when it turns out that self-knowledge without knowledge of the good is hollow and meaningless. Knowledge of knowledge is desirable to the tyrant Critias, because he understands it to be a tool that would allow complete control, a rational science ruling over all sciences, determining what does and does not count as science. If Critias had been able to provide any content to his formalistic science, he would have anticipated Aristotle’s hierarchy of sciences in book 1 of the Nicomachean Ethics, where political science is identified as the ruling science: “For it is the one that prescribes which of the sciences ought to be studied in cities, and which ones each class in the city should learn, and how far” (1094a–b).5 What legitimates politike¯ as a ruling science is the object of its study, which, according to Aristotle, is the highest good. Self-knowledge is a knowledge of knowledge, but one that is mediated by the good. Insofar as the good is the cause of knowledge, knowledge of the good would be knowledge of the cause of knowledge and hence knowledge of knowledge. But the same passage in the Republic that identifies the good as the cause of knowledge also puts the good beyond knowledge and beyond being “in dignity and power” (6.508e–509b). Given the schematism of book 5, according to which knowledge is of being, rather than of becoming or nonbeing, then the good, which is beyond being, must also be beyond knowledge. To that extent we are necessarily ignorant of it. Hence self-knowledge is Socrates’ knowledge of ignorance. While the focus of the immediate investigation is to establish the connection between the Theaetetus and the Charmides, and to first analyze their respective frames, the themes and problems raised in these dialogues will often lead us to consult other dialogues as well. For discussion of the dialogue frames, the Symposium will play a significant role, because ero ¯ s is so important in the opening sections of both dialogues.6 It is not surprising that an inquiry into self-knowledge would include a discussion of ero ¯ s, but it turns out that an account of knowledge is similarly involved with ero ¯ s. In addition to ero ¯ s, war and impending death are highlighted in both the Theaetetus and the Charmides, giving to both a political dimension whose role in knowledge and self-knowledge must be clarified.

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1. FRAMING THE QUESTION OF KNOWLEDGE IN THE THEAETETUS The Theaetetus is more than simply a straightforward inquiry concerning the definition of knowledge: In this conversation with Theaetetus and Theodorus, Socrates, admitting his own perplexity, directly asks the question of knowledge only at 145d, some three Stephanos pages into the dialogue. The “direct” conversation about knowledge is doubly framed, first (142a–143c) by a device involving Euclides, Terpsion, and a slave, which provides the dramatic setting for the reading of an “edited” version of the “original conversation,” long after Socrates’ death. The second frame, within that “edited rendition,” establishes the personal connections and “credentials” of the principals of the “original” discussion. It is important to note at the outset that many Plato scholars—for example, Cornford,7 McDowell,8 White,9 Bostock,10 Burnyeat,11 Desjardins,12 and Chappell13— barely take cognizance of the frames, or at least attribute little or no philosophical significance to them; some others—for example Ryle14 and Sedley15—give highly idiosyncratic interpretations; and others—such as Campbell,16 Friedländer,17 Benardete,18 Polansky,19 and Blondell,20 among others—find them to be an integral part of Plato’s philosophical undertaking in the Theaetetus. At the very end of the Theaetetus Socrates says, “I have to go to the porch of the king and meet the indictment of Meletus which he’s drawn up against me. But at dawn, Theodorus, let’s come back here to meet (210d).”21 This closing integrates the Theaetetus into two separate dramatic series—first with the two dialogues that follow and have characters interconnected with it, the Sophist and the Statesman: Socrates says that he will return the next day to continue the conversation and the discussion is indeed resumed at the beginning of the Sophist. But the Theaetetus is also related in the same sentence to the Euthyphro. Socrates interrupts the discussion to go to the porch of “King Archon” to be served the indictment drawn up against him by his accusers, Meletus, Anytos, and Lycon.22 The conversation with Euthyphro at King Archon’s porch—incidental to Socrates’ indictment for impiety and Euthyphro’s prosecution of his own father for murder—begins the “biographical” series of the Euthyphro, Apology, Crito, and Phaedo, moving from Socrates’ indictment to his trial, to his chance for an escape and refusal to do that, and on to his death. This latter tetralogy is explicitly “political,” in the sense that it deals overtly with Socrates’ relation to the city of Athens and thus generally with the relation of philosophy to the political sphere. The Theaetetus, Sophist, Statesman trilogy, in fairly obvious contrast, is “nonbiographical”: Not only does Socrates seem to become marginal to the conversation as it proceeds—as questioner he is “replaced” by the Eleatic Stranger in the last

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two dialogues; in addition, “Young Socrates,” first introduced as a friend of Theaetetus and apparently a different kind of “replacement” of some sort for the “older Socrates,” becomes the principal person questioned throughout the final conversation in the Statesman. The dissimilarity between the two series is stark—one a personal story of unresolved conflict leading to Socrates’ condemnation, imprisonment, execution; the other a record of detached, seemingly disinterested analysis. The contrast between the two sets of dialogues in turn suggests a different role for “the political” in the two series, a question we will look at more specifically as we interpret the Theaetetus, and which will raise in its turn the question of the relation of knowledge to politics. The Theaetetus, after all can be seen as part of both series and Socrates reveals “secrets”— such as his being a midwife—as well as a discussion of the leisure and freedom of the philosopher in contrast to the speeches of sophistic rhetoricians given under the pressures of time.

2. THE OUTER FRAME OF THE THEAETETUS (142A–143C) The two principal interlocutors of the Theaetetus are Theaetetus and Theodorus: As mathematicians they are appropriate participants, at least superficially, in a discussion about knowledge. The actual starting point of the Theaetetus, however, is an accidental meeting between two Megarians, Terpsion, and Euclides (142a).23 At this point we see Theaetetus, now older and more mature, laid out upon a stretcher and suffering from battle wounds and dysentery. Plato in this way has us meet Theaetetus the soldier before we meet Theaetetus the mathematician. This depiction of the wounded and older Theaetetus stands in stark contrast to that of the freshly oiled young Theaetetus, who has just finished his exercises and who is accompanied by his friend “young Socrates” when the philosopher Socrates first meets him. The time that has elapsed between the two different conversations is about eight years, if we follow the generally authoritative analysis of Debra Nails, who rejects some commentators’ suggestions that the time of Theaetetus’s war wounds has to be closer to 369, given his many mathematical accomplishments.24 Theaetetus and Theodorus are both renowned mathematicians.25 Like Socrates, Theaetetus is an Athenian, indeed one who eventually died fighting for his city, whereas Theodorus comes from Cyrene in distant Libya, and Euclides and Terpsion, who also appear as auditors in the Phaedo (59c), are from Megara.26 It is a kind of “international set” involved in the defining of “knowledge,” then as now, a remove from specific political identity, which is a token of the universal aspirations of scientific knowledge. However “eternal” the truth of mathematics may be, the dia-

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logue is in fact “surrounded” by death—the dying Theaetetus in the initial frame and the coming death of Socrates alluded to in the last sentence.27 For the specific occasion of the dialogue, more precisely how it comes to pass that we readers are made privy to the conversation that took place, we have the Megarian Euclides to thank, who recorded the dialogue as it was narrated to him by Socrates. The Theaetetus is the only Platonic dialogue that explicitly identifies the “writer” of the dialogue within the dialogue itself and specifies that it is not in fact Plato. Plato apparently thought it important that the reader know that he is not the “author” of this dialogue on knowledge; and at the same time he provides a dramatic occasion for the “coincidence” that the dialogue is read aloud by a “slave” (143c). The majority of Plato’s dialogues are in “simple” or straightforward dialogue form. We are directly presented with a conversation between Socrates (in most cases) and one or more interlocutors. It is as though we the readers were present at a live performance. In another group of dialogues, however, we are at one remove from the actual talk and the entire conversation is given to us through the mouth of a narrator. In three dialogues (Charmides, Lysis, and the Republic) Socrates himself is the narrator. In the Symposium and the Parmenides there is a more complex narrative structure, in which the reporters, Apollodorus and Cephalus respectively, were not in fact present at the original conversations. And finally there is a small group of dialogues (Phaedo, Euthydemus, Protagoras, and Theaetetus) where the inner dialogue is framed by another dialogue. The Theaetetus stands out from this group in that both the frame and what is framed are presented as direct dialogues: In neither frame nor main dialogue are there passages with “I said” and “he said.”28 In the other three we have an outer dialogue that provides the occasion for one of the interlocutors to narrate the ensuing dialogue: In two cases, Euthydemus and Protagoras, the narrator is Socrates himself; whereas in the dialogue about Socrates’ death, as dramatic necessity would dictate, it is Phaedo who tells the story. The question that arises with regard to the Theaetetus is this: Inasmuch as there is no narrator to provide continuity, what is it that holds the frame dialogue and the main dialogue together? In narratives, the narrator tells all from her own perspective. It is the persistent, though often subtle, domination of this single perspective that gives the succession of events or arguments a certain kind of unity. This “making whole” is often accomplished through indirect statement, the oratio obliqua whereby x reports that y said p. Indirect statement allows the speaker to overcome the duality between himself and the other by constituting the other within his own framework—by giving voice to the other’s voice within one’s own. In contrast, Euclides cuts out (exeltho ¯ n) the bothersome

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in-between things (hai metaxu) (143c)—the bonds of “I said” and “he said,” which tie speeches to their speakers, and which thus make speeches come alive. In Socrates’ own original narration, in contrast, both the “being with” and the “talking with” were preserved, as Euclides puts it at 142c. That Plato presents a dialogue about knowledge as a “censored” narrative reveals something about the problem of knowledge itself. The Theaetetus is a written record of a conversation between Socrates and two mathematicians about knowledge. Mathematics is central to our understanding of knowledge. For the ancients, as for the moderns, mathematics served as paradigm for a certain kind of knowledge. Mathematics provides us with a prototype for that sort of knowledge where the knower seemingly has no effect on the known: Who is doing the knowing appears irrelevant to the issue of what in the end is known. Socrates offers a critique of mathematical knowledge in the Republic that includes a discussion of the allegation that mathematics is unreflective with respect to its own starting points, an argument which will be examined in chapter 5. Euclides’ version of the dialogue, unlike a narrative, imitates this kind of structure to the extent that he seduces us into thinking that what is being said is more important than who says it: In his explanation of what he has cut, in other words, Euclides makes it clear that it is his view that suppression of the narrator is of no consequence, so long as what is said is reported correctly. With this in mind we can better understand why Theaetetus, in parallel fashion, thinks that he can answer the question “What is knowledge?” without regard to the question of the standpoint and perspective of the knower: That is, after all, what mathematics has taught him. For Theaetetus himself, there seems to be no link between Theaetetus the mathematician and Theaetetus the nonmathematician and thus no need to connect the question of knowledge with the question of self-knowledge. It will be Socrates’ task to show him otherwise and to lead Theaetetus to a self-recognition. As the conclusion of the dialogue indicates, Socrates declares that particular task as mission accomplished, that is, he succeeds in leading Theaetetus to a knowledge of ignorance. The frame suggests that Euclides, despite these pretenses to a kind of “objectivity,” as it were, is not an entirely trustworthy source. Euclides claims that he “wrote” the dialogue which Socrates narrated to him and that, whenever he could not remember certain points, when he came to Athens he would question Socrates about them, and that he would make the necessary corrections when he returned to Megara (143a). Considering the length of the dialogue, it is not surprising that Euclides should have forgotten parts of it, but how did he know and remember which parts he had forgotten? How does he know what he does not know? It would seem that the only way we could know that we have forgotten something is if we have a good idea of the whole and therefore know

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when certain parts or links are missing or poorly connected. Thus one possible way for Euclides to know that he had forgotten certain parts would be if he had understood the conversation when Socrates related it to him—assuming that the whole made sense and thus that he knew that he had forgotten something whenever he came to a point where his dialogue did not make sense. There are other possibilities, to be sure, but if this is a likely scenario, we might well assume that Euclides’ modus operandi in writing the colloquy must have been something like the following: In transcribing the dialogue, Euclides thought that he remembered correctly whatever made sense to him and that he must have forgotten or misremembered something whenever he found a part confusing. Thus the dialogue in the form we have it seems very much to depend on Euclides’ recollections and interpretations. In his conversation with Terpsion, Euclides betrays additional reasons for suspecting the reliability of his recording of the narration of the earlier dialogue, exposing the fact that his memory is not his greatest strength. After commenting to Terpsion about his chance meeting with Theaetetus on his trip to the harbor, and then explaining that this reminded him of Socrates’ prediction of Theaetetus’s greatness, he says: “My impression is that Socrates met him shortly before his death when Theaetetus was a lad” (142c).29 Why is he so tentative in assigning the time of the conversation? The dialogue itself provides a very specific time frame, the day Socrates went to King Archon’s Court to inquire about the indictments filed against him? Furthermore, when Terpsion asks whether Euclides could relate the conversation, he answers: “No, by Zeus, not at any rate straight off from memory” (142d).30 If Euclides wrote down the dialogue from memory, then why can he not repeat it from memory? Euclides’ memory seems to be less than trustworthy—a fact which can be related to the issue of writing and the question of its reliability.31 Before turning to the specific question of memory and writing, there is need for a general observation about the role of memory in the Theaetetus. It is noteworthy that the problem of memory is not directly addressed in the discussion of knowledge in the main dialogue, whereas it plays a central role in the frame. Memory does appear on the periphery of the discussion about perception, a crucial point in Socrates’ analysis of false opinion. However, Socrates never establishes a direct link between memory and knowledge. Why does Plato treat memory in this way? We venture the following: Just as the frame is the necessary condition for the ensuing dialogue, but does not guarantee the veracity of the report; so memory is a precondition for the possibility of knowledge, but does not guarantee any knowledge. It is, in fact and perhaps surprisingly, in connection with false opinion that memory comes to play a role in the main dialogue.

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The role of memory diminishes with writing. We can reduce the risk of forgetting something important by writing it down at the time that we remember it; but writing also diminishes our ability to remember because it decreases the opportunities for exercise. Euclides exemplifies all the negative aspects of writing discussed in the Phaedrus—both the deadness of the written speech and the failure of memory that follows upon writing.32 It is as though Euclides “emptied” his memory by recording what he remembered. The writing down of the dialogue by Euclides has “objectified” the conversation in the sense that Euclides has removed himself from the argument and the argument has been removed from Euclides. To that extent the argument is now “reified,” it has an existence independent of its author, narrator, and the original discussants. In one sense that independence is now “real”—the “document” can now be presented as something that stands for itself; in another sense it is merely an alleged independence—the “document” is a result of editing, perspective, informed, and uninformed choices. If Plato had not included the frame dialogue, it would have been impossible for readers to “deduce who the author of the dialogue actually is,” or, to put the point another way, to distinguish the respective points of view of the frame dialogue, the original conversation, and the resulting edited version of the whole. We are confronted with this rather peculiar situation: In the frame of the Theaetetus Plato disavows the Theaetetus as any “child” of his own, while simultaneously pointing to himself as the author of the frame dialogue. The significance of this comes to light when we consider that the Theaetetus is the only dialogue that presents itself as written.33 Plato, like Euclides, disassociates and removes himself from the dialogue. Euclides even goes so far as to have someone else read the dialogue to Terpsion and himself. It is as though there is no bond or connection between the written work and the author. By introducing writing as a kind of “recording,” Euclides takes the “making” out of this poie¯sis and, indeed, offers a speech that is, as it were, dead. He presents us with a product that he himself did not make and his detachment from it is evident from his silence about whether he agrees or disagrees with any of the points under discussion: His “neutrality” extends that far. In addition the fact that he has a boy read the dialogue indicates a further distancing of himself from his “product.” Although Socrates is often silent with regard to his own opinions, it is virtually inconceivable that Socrates could have been equally reticent about the truth of the assertions put forward and the validity of the arguments made, if he were the narrator instead of Euclides, or if he were both narrator and participant. Commentators who want to get to the “meat” of the dialogue and consider the so-called setting as nothing other than the “trimmings,” make the same mistake that Theodorus and Theaetetus made: They ignore “the

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political,” broadly understood. Both mathematicians think of themselves as nothing other than mathematicians; they forget or suppress that which makes it possible for them to be mathematicians in the first place, namely, being human generally, and being situated in a particular city more specifically. The frame reveals what the dialogue proper conceals, namely, that the mathematician is a man, a human being.34 Euclides explains that he had been away from the city because he had encountered Theaetetus, who was suffering both from war wounds and from dysentery, and who was near death. We again breathe the air of ambient mortality: Mathematical truths may or may not be eternal, but the mathematician’s body is not deathless. A two-fold doubling becomes evident here. On the one hand, body and soul are two, or at least seem to be so in some superficial sense; on the other hand, Theaetetus the citizen, who fought courageously for his city, stands opposed to Theaetetus the mathematician, who seems to have no concern for his or any other city. Yet Theaetetus the courageous citizen might be said to have fought “body and soul” for the freedom and safety of his native Athens. Can Theaetetus the mathematician in any sense strive “body and soul” for knowledge? The issue of the unity of body and soul is raised here, but that will not be properly addressed until the Phaedo.35 It is the other split, that between political man and mathematician, that will play a major role in the understanding of the problem of knowledge, as will become especially evident in the ascent and descent passage of the Republic. What then of these two “Theaetetuses”? In the frame there is a display of Theaetetus’s body, while within the dialogue Socrates asks him to display his soul for investigation. The condition of Theaetetus’s body can only be explained by referring to political conditions, that is, a city at war. In the dialogue proper, Theaetetus strenuously avoids bringing up any political matters, but Socrates raises the level of the discussion to include political issues in a digression with Theodorus (172a–183c). Mathematicians, as the examples of Theodorus and Theaetetus make clear, believe that what they are investigating puts them outside the political and temporal realm, perhaps even beyond it. Both Theaetetus and Theodorus display something close to pride in their ignorance of the political. Socrates mentions the example of Thales, ridiculed by a Thracian maiden because he fell into a well while looking at the stars: “In his eagerness to know the things in heaven he was unaware of the things in front of him and at his feet” (174a). “The same jest,” says Socrates, “suffices for all those who engage in philosophy. For someone of this sort has truly become unaware of his neighbor next-door, . . . almost to the point of not knowing whether he is a human being or some different nursling” (174a–b). The philosophermathematician is in some deep sense apolitical.

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This innocence of the political also points to Theaetetus and Theodorus’s belief that they are somehow, as mathematicians, emancipated from the realm of doxa. There is, for example, the implication that the body plays no role in the solution of mathematical puzzles; and similarly, as we shall discuss further, Theaetetus’s account of the problem of surds (147c–148b) suppresses the role that Theaetetus as a human being plays in looking at the problem and offering the names which enable him to arrive at a solution. It does not strike Theaetetus as peculiar that he can see and address by name something that Theodorus apparently was unable either to see or to name. Theaetetus quite innocently talks about dynamis (power, 147d)—innocent to the extent that he seems not to “know” the political meaning of that term. So, on the one hand, dynamis as arithmetic power drives Theaetetus the mathematician; but on the other hand, dynamis as political power kills Theaetetus the man. It is precisely the split between body and soul, between man and mathematician, that gives us a glimpse of the difficulty involved in formulating an answer to the question of knowledge. Socrates states in the Phaedrus that before he can demythologize nature, he must first come to know himself. And that is why he is reluctant to leave the city.36 The mathematician, on the other hand, is reluctant to enter the city, convinced that his kind of knowledge is independent of who he is and where he came from, and not noticing that the very language he is using, even to say that, is laden with political meaning.37 It is as though the mathematician believes in what we in modern times would generally call “objectivity” and “objects”—the possibility, at least theoretically, of bracketing the subject or observer in the attempt to know objects in themselves and independently of the observer’s standpoint. And so in his own way does Euclides. Euclides does not recognize that the elimination of Socrates as narrator is not an innocent move, but rather is a kind of “killing,” or at least a kind of emasculation, of the logos. A logos in its completeness includes both the speaker and the speech. But Euclides eliminates the speaker. Finally, the revelations as to the recording, editing, and preservation of the dialogue, and then the reading of it by a slave, are, according to the script, all chance occurrences. By chance Euclides runs into Theaetetus, who is being transported from Corinth to Athens, and it is this chance occurrence that disrupts the orderly world of Terpsion, who expected to find Euclides as usual in the marketplace. Terpsion’s seeking and wondering (eze¯ toun te kai ethaumazon) (142a) are not philosophical in nature, for he seeks out the expected, provided by order, and wonders at the unexpected, chance.38 Philosophical wonder, on the other hand, is precisely the ability to question what is clear, to darken the light. While most people are aroused to wonder when confronted with chance, the philosopher wonders at order. It is this kind of wonder that gives rise to the question

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“What is it? (tí esti;) and initiates the search for the “being of what it was” (to tí ¯e n einai),39 and from this wonder proceeds the seeking not of the expected and known, but for the unknown. What is known “pre-philosophically” becomes an object of wonder. Chance is crucial for any investigation of knowledge: In order to hypothesize about the world, to make rational assumptions and deductions, we have to presuppose order. If everything were due to chance, then science would be impossible—at least on most accounts of it. But techne¯ would be equally inconceivable in a universe of pure chance. Both scientific knowledge and technical control would be forever undermined if all were chance occurrence. At the same time, however, chance, to the extent that it is out of the ordinary, can only be discerned if there is order in the first place; it is parasitical on order, as Aristotle argues in the Physics.40 It is only after we have understood the orderliness of things that we can take and give account of what it is that is out of order. Chaos theory can only be developed after establishment of models for orderly linear progressions and the like. Yet it is precisely this extraordinariness of chance that continually calls our knowledge into question and at the same time affirms the otherness of that which is to be known. The phenomenon of chance has as a consequence that paradigms will have an uncertain and enigmatic character, and to that extent that the nature of knowledge will remain puzzling. The issues of chance, memory, and writing, the problematic relation of body and soul, of man the citizen and man the knower, and so many other concerns in the Theaetetus, come to light only when we consider the dialogue in its entirety. If we take the frame to be nothing more than poetic decoration or dramatic device, vaguely pleasing to some aimless audience and incidental to serious philosophical intent, then Plato must have been a writer who paid great regard to logical argument and little to the order of a logos, who somehow bungled his way by chance into unexpected necessities. But if there are serious questions about questions and frames about dialogues, then the task left to us is to wonder at both the orderly and the extraordinary in this dialogue. To proceed in order we must now turn our attention to the inner frame dialogue, which also precedes what is popularly taken to be the starting point of the “serious” discussion, the definition of knowledge as perception.

3. THE INNER FRAME OF THE THEAETETUS (143D–146C) The Theaetetus has two frames prior to the introduction of the question “What is knowledge.” We have discussed the outer frame and turn our attention now to the inner frame. In the inner frame, which is part of Euclides’ report, Socrates is in search of a suitable “successor.”41

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The Euclides report begins very abruptly with a question almost insulting to the Cyrenean of whom it is asked: If I were to care, Theodorus, more for those in Cyrene, I would be asking you about the state of affairs there and whether any of the young there make geometry or something else of philosophy their concern. But as it is I don’t, for I’m less a friend to those there than to these here, and I’m more desirous of knowing who of our young are expected to prove good and able (143d).42

We can surmise from the urgency of the questions he asks that it is Socrates who has sought out Theodorus. Socrates is in search of a young man who can carry on what he is about to give up. He had asked similar questions some thirty years earlier after he returned from his duty in Potidaea: In the Charmides he wanted to know who among the young had in his absence “become distinguished for wisdom or beauty or both” (153d).43 Here in the Theaetetus he asks Theodorus “who of our young are expected to prove good and able.” The question is preceded by the strange contrafactual in which Socrates explains that, if he were to care for all youth, specifically those in Cyrene, he would ask his question more generally, but, as it is, he only wants to know about the young of Athens. It sounds in fact as though he would not be interested in any young men from Cyrene. Why is it that Socrates limits his search to Athens in the Theaetetus? Surely it has in part to do with the time frame within which he is operating. He is, after all, on his way to the Porch of King Archon and the Euthyphro and his own trial and death. So in part his urgency involves finding a replacement and examining the transmissibility of philosophy. The urgency of the search can be seen by comparing the parallel statement in the Charmides with the one here. He has significantly trimmed down his requests, requiring only the bare essentials. Wisdom and beauty are replaced by goodness and ability. If we are to take literally Theodorus’s response to Socrates’ request we are then presented with a young man who is extremely able and ugly.44 Furthermore, Socrates’ interest in an Athenian youth indicates that Socrates is city-bound. But does this indicate that philosophy too is polis-bound? And if so, how is that related to the matter of friendship specifically mentioned at the outset? Theodorus replies with a description of Theaetetus which is strange in many ways. [I]t’s certainly worth it for me to tell and for you to hear about the sort of lad of your fellow citizens I met. And if he were beautiful, I’d be afraid to speak of him with intensity, should anyone in fact get the impression that I’m desirous of him. But as it is—please don’t get annoyed with me—he is not beautiful (ouk esti kalos), but he resembles you in the snubness of his nose and the bulging of his eyes, but he has them less than you do. I’m speaking fearlessly (143e).

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Theodorus prefaces his introduction with the assertion that Theaetetus is in fact not beautiful at all and he displays his frankness by likening the ugly Theaetetus to Socrates. He says that he is being courageous in so speaking. It is evidently important to Theodorus that he can openly praise Theaetetus without running the risk of appearing to be in love with him, he is clearly squeamish about pederasty. It is as if ugliness is a precondition for impartiality, that is, if Theaetetus is ugly, then Theodorus is not in love with him and thus his account is not based on “subjective” passion, but can present itself as dispassionate truth. In fact, however, the judgment that Theaetetus is ugly is itself partial, so, in Theodorus’s construction, it turns out, “objectivity,” so to speak, is based on “subjectivity.” In contrast with this presentation of Theaetetus, the introduction of Charmides emphasized his beauty and the fact that every one, including the children, were in love with him.45 The clumsiness of Theodorus—and the actual cause of that must presumably lie in the fact that he is in love with Theaetetus after all—continues unabated as he tries to describe the youth’s intelligence and nature. I’m aware of no one yet whose nature is so wonderfully (thaumasto ¯ s) good. For to be as good a learner (eumathe¯ ) as he is, in a way that’s hard for anyone else to match, and yet to be exceptionally gentle (pra¯ on), and on top of this to be manly (andreı¯ on) beyond anyone whatsoever, I would have suspected that it doesn’t occur and I don’t see it occurring, for those as sharp as he is, quick witted, and with good memories are for the most part also quickly inclined to bursts of anger, and in darting about they’re swept along like unballasted ships, and they grow up rather more manic than more manly, whereas those in turn who are more grave face up to their lessons somewhat sluggishly and are full of forgetfulness. But he goes so smoothly, so unfalteringly, and so effectively to his lessons and investigations, and all with so much gentleness, just as a stream of olive-oil flows without a sound, as for it to be a cause of wonder (thaumasai) that someone of his age behaves in this way (144a–b).

This near-comic string of associated assertions and mixed metaphors— hardly the appropriate language of rigorous discourse usually credited to mathematicians—culminates in Theodorus’s likening of Theaetetus to a stream of olive oil. As it turns out, Theaetetus makes his appearance, along with some of his friends, and it is evident that he comes fresh from oiling himself. The characteristics Theodorus attributes to Theaetetus identify him as a top candidate for becoming a philosopher-king,46 especially in the light of his combining what appear to be opposite qualities such as gentleness and manliness.47 Theodorus thinks that by replacing beauty with wonder he protects himself from any charge of being in love with Theaetetus; but would not most lovers see in their beloved an object of wonder? It will be Socrates’ job to examine whether Theaetetus is also

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endowed with the appropriate ero¯s, whether he has a passion for wisdom. The fact that Socrates is about to examine his look-alike also points to the theme of self-knowledge, since Socrates is looking in a kind of mirror.48 Socrates inquires whose son Theaetetus is and Theodorus responds in a manner not unlike the archetypical “true philosopher” of the digression, who does not know his neighbor’s name.49 Later in the dialogue, Socrates draws a caricature of the “top” philosopher in which he mentions that knowing family and the ability to trace one’s generations is of no concern to the philosopher (174e–175a). Once Socrates recognizes Theaetetus and identifies him as the son of Euphronius, it is clear that Socrates does in fact busy himself with such mundane matters as who is whose son. In fact, in the Charmides Socrates goes on and on listing the noble ancestors of Charmides.50 So, while Theodorus knows Theaetetus through his association with him, Socrates knows Theaetetus by being able to link an image with a name. More precisely, he links the face of Theaetetus with the name of his father (144c). Not only does he know the name of Theaetetus’s father, but he is also knowledgeable about the financial affairs of the family. In these early comments personal and social aspects of Socrates are underlined. Theodorus has Theaetetus sit near to Socrates, at the latter’s request.51 Socrates wants Theaetetus close under the pretense of wanting to examine his face, since Theodorus had judged the two faces to be similar (144d–e). Clearly Theodorus’s judgment could not have been entirely dependable or unquestionable, if Socrates felt the need to take a closer look: Apparently Theaetetus did not resemble him from afar, and it is unlikely that would change on closer scrutiny. Socrates examines Theodorus’s competence with respect to faces by questioning Theaetetus as to whether Theodorus would be able to judge the likeness between two similarly tuned lyres. He proposes that a draftsman or painter would be a better judge of faces than Theodorus, and Theaetetus, allowing that Theodorus is not a painter, concurs. Theodorus is then introduced as someone who is competent in geometry, astronomy, harmonics, and other relevant subjects that are parts of the education that Theaetetus is receiving from him (144e–145b). This brief discussion is, at least on the surface, meant to show that Theodorus might not be competent to judge faces, but he surely knows his souls. It certainly seems surprising that someone who knows shapes and figures is incompetent to evaluate faces. What is the difference between a geometrical presentation of snubbedness and exophthalmicity, on the one hand, and someone’s actually having a face with a snub nose and bug eyes?52 How would a geometrical study of a face differ from an artistic one? The main difference seems to be that the one will try to capture the “living principle,” while the other one does not. Perhaps we can say that geometry is to painting as a dead thing is to a living one. Although this is clearly an exaggeration and may be misdirected, it points to an important aspect of

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mathematics that is brought out again in the example of the lyres. While Theodorus is judged competent in harmonics, no one expects him to be able to make a comparative judgment about two similarly tuned lyres. What is the difference between harmonics (the mathematical theory of pitch relations) and tunes (the actual sequence of sounds based on those relations)? In both cases we have an example that combines the physical and the nonphysical, on the one hand, and separates out the nonphysical on the other. The mathematician studies and becomes the knower of the nonphysical, but qua mathematician he is unable to recognize the nonphysical when it is combined with the physical.53 If this is correct then the mathematician qua mathematician cannot be expected to know anything about human beings, and it is once again the mathematician who is exposed in the later caricature of the “true” philosopher. Furthermore the mathematician cannot know anything about any living thing on the basis of mathematics, and thus could never be confused with a physicist or biologist. Whether or not we should take seriously anything that Theodorus says about Theaetetus depends on the possibility of distinguishing soul from body. The Phaedo instructs us that the separation of soul and body equals death,54 which confirms our initial suspicion that the mathematician is concerned with dead things. Socrates thus has good reasons to want to examine for himself the state of Theaetetus’s soul. In reflecting on the way that Socrates proceeds with his examination of Theaetetus we should be able to discern the difference between examining a living thing and a dead thing and perhaps also the difference between knowing the two. In his usual manner Socrates urges the young Theaetetus to display himself for examination, so that we may all be in a position to affirm Theodorus’s testimony. The language of the courtroom is used throughout the dialogue and is a constant reminder of Socrates’ future drama.55 Here it is Theodorus who is on trial and Theaetetus who serves as “evidence” on the basis of which Theodorus will either be indicted or released. Theaetetus displays his own discomfort with the situation by suggesting that Theodorus might have been jesting when he was praising Theaetetus’s soul. Socrates assures him that Theodorus is no jokester and that they had better get on with the show. Before turning to examine how Socrates elicits wonder from Theaetetus and proposes to cure his puzzlement through midwifery, we turn to the dramatic setting of the Charmides to find out why Socrates assumes the role of doctor there.

4. THE CHARMIDES The Charmides and Theaetetus are not commonly linked or at least not in a positive way; but in at least one instance they are mentioned in the same

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sentence. Paul Shorey, commenting on the Charmides, makes the following observation: “The dialogue involves so much metaphysical subtlety that some critics have pronounced it late, some spurious, and many feel the same distaste for it that they do for the subtler parts of the Theaetetus.”56 In this section I will try to link these “distasteful” parts and show that we can learn useful lessons about the connection between knowledge and self-knowledge when we put the two dialogues side by side. At a quick glance one would think that these two dialogues make an unlikely pair: In contrast to the Theaetetus, the Charmides is narrated by Socrates, who is recounting his experience of the night after his return from the Battle of Potidaea, when he visited the palaestra and investigated so¯phrosyne¯ with Charmides and Critias. But the very opening sentences of the two dialogues point to war (just as the Gorgias highlights war in its very opening words). While we have an extensive description of the war in Potidaea as well as an encomium on Socrates’ bravery in that war from the mouth of Alcibiades (Symposium 220e), Theaetetus’s actions during the war are not known, although Euclides mentions that he has heard some people praising Theaetetus’s conduct (142b). Both dialogues present us with detailed physical descriptions of the interlocutors before we are invited to converse with them. War and the body are in the foreground of the discussions. Charmides is said to be so beautiful that everyone—even the youngest boys—are in love with him; in contrast with Theaetetus, whom Theodorus has introduced as a nonseductive person, ugly like Socrates. In both cases it is the teacher or guardian who introduces the character to Socrates, in response to Socrates’ question which in the Charmides is: “When we had enough of such matters (i.e., talk about the war), I in my turn began to inquire about affairs at home, how philosophy was doing at present, and whether any of the rising young men had distinguished themselves for wisdom or beauty or both (e¯ sophiai ¯e kalle¯ i ¯e amphoterois 153d).” When initially inquiring of Theodorus, Socrates asks after someone who could prove “good and able” (epidoxoi genesthai epieikeis 143d). Beauty at first seems to have been dropped as a criterion in the case of Theaetetus; but, as we shall see, Socrates will repeatedly insist that Theaetetus is in fact beautiful, whereas Charmides’ beauty is stunning only at first encounter. In both dialogues Socrates is looking for someone who can do philosophy and who might be a potential successor.57 The Charmides is narrated by Socrates to an unnamed friend, someone with whom Socrates is close enough to share intimate details: He calls Chaerephon “manic” (manikos) which presumably is not a compliment, and does not shy away to tell him about his erection when glancing inside Charmides’ cloak.58 In addition, Socrates provides details of the war situation, suggesting perhaps that his auditor is not an Athenian.59 The fact

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that Socrates is narrating the dialogue makes us privy to details of his experience that are usually absent from the “straight” dialogue format. There are three other dialogues that Socrates narrates: Lysis, Republic, and Protagoras—the last includes a brief dialogue between Socrates and a friend, which provides the occasion for the narration.60 It is because Socrates is the narrator that we find out that Thrasymachus has been blushing and sweating in the Republic (350d) and in the same way we learn of Socrates’ own mock fear. Socrates includes reflections in the Protagoras that do not necessarily reflect well on him but as such make him appear completely honest to his auditor: “Protagoras got a noisy round of applause for his speech. At first I felt as if I had been hit by a good boxer. Everything went black and I was reeling from Protagoras’ oratory and the other’s clamor. Then, to tell you the truth, to stall for time to consider what the poet meant, I turned to Prodicus, calling on him”(339e).61 In a narration then the narrator is in control both of what is being said and the observations about the psychological states of others as well as his own. The first person narration, in contrast to the third person narration, provides the opportunity for self-reflection and reflexivity and provides a paradigm case for self-reflexivity: It is a logos of logos. The narration takes place the day after Socrates had returned from Potidaea and had sought out companionship and conversation at the Palaestra of Taureas. Socrates had just returned from a war that produced many casualties and, together with the battle of Corcyra, is identified by Thucydides as one of the main triggers of the Peloponnesian War. Socrates briefly refers to his military duty at Potidaea in the Apology 28e, but it is in the Symposium that Alcibiades gives a full report of his heroism there. “Socrates single-handedly saved my life! He absolutely did! He just refused to leave me behind when I was wounded, and he rescued not only me but my armor as well.” (220e).62 This particular detail is not reported in the Charmides; in fact, Socrates provides very little information about his experiences and, despite Charephon’s urging, we hear nothing other than that many died and were wounded. Socrates is more eager to find out about the state of affairs in Athens, in particular about the present and the future state of philosophy, eagerly searching for someone among the young who is outstanding in “wisdom or beauty or both.”(153d). Socrates here foregrounds beauty, in contrast to the Theaetetus which takes place at a much later dramatic date, where Socrates is searching for someone “good and able.” (143d). Beauty and wisdom are the objects of love for the philosopher but it is not entirely clear what Socrates was expecting when he inquired about wise young men but his desire for beauty is about to be fulfilled. Critias prepares Socrates for his encounter with Charmides, identifying the youth as kallistos—for the moment at least (ta ge de¯ nun). He pro-

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vides some initial genealogy to help Socrates appreciate the talent he is about to meet: Charmides is the son of Glaucon. What is most unusual about Charmides’ entry is that everyone from young to old is apparently in love with him. Socrates notes: “I noticed that none of them, not even the smallest had eyes for anything else” (154c). There is something magical about Charmides and Socrates, who considers himself no true connoisseur, because he finds all young men beautiful, is forced to take special note of Charmides and finds him wondrous, marvelous (thaumstos), just as Theodorus found Theaetetus thaumastos. But the cause of the wonder is significantly different between the two young men: Theaetetus elicits wonder on account of his good mind and gentle courage, whereas Charmides strikes wonder into the onlooker on account of his “stature and beauty” (megethos kai to kallos). The contrast between Theaetetus’s soul-qualities and Charmides’ body-qualities is further highlighted when Socrates describes the universal gazing at Charmides as if they were looking at a statue (agalma). Now statues are soulless and lifeless and as it were timeless (unless they are made by Daedelus) and whatever beauty we attribute to a statue is static and nongenerative, that is, it is doubtful that a statue would be the occasion for giving birth to virtue.63 The nonhuman quality of Charmides’ beauty is further supported by Charephon’s obscure comment following his praise of Charmides’ pretty face: “Yet if he would consent to strip, he said, you would think he had no face, he has such perfect beauty of form (eidos)” (154d). It is not the face of a statue, accordingly, that reveals its beauty and perfection, but rather the overall shape and form. Socrates is ready to submit with only minor qualifications—that his soul be goodnatured (eu pephukos) as well, an attribute that Theodorus ascribed to Theaetetus (144a). Through Critias’s contrivance, Socrates gets a close-up look in order to strip and examine Charmides’ soul and he is momentarily overwhelmed and awestruck by his body. “But here, my friend, I began to feel perplexed (e¯ poroun), and my former confidence in looking forward to a quite easy time in talking with him had been knocked out of me.” And in the midst of all the jostle because everyone wants to sit next to Charmides, Socrates peeks inside Charmides’ cloak: I saw inside his cloak and caught fire, and could possess myself no longer (ouket’ en emautou); and I thought none was so wise in love-matters as Cydias, who in speaking of a beautiful boy recommends someone to “beware of coming as a fawn before the lion, and being seized as his portion of flesh”; for I too felt I had fallen prey to some such creature (155d–e).

The fact that Socrates has such a strong physical and erotic reaction to Charmides contrasts with his strong resistance when Alcibiades tries to

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seduce him (Symposium 219b–d). It is as though Socrates is momentarily overpowered by physicality and his own immediate bodily reaction upon the sight of Charmides’ naked body. As he tells his auditor, he was experiencing aporia, which made him momentarily speechless, rather than babbling poetic nonsense, which is the other reaction to being inflamed by erotic passion.64 Why does Socrates include this part in his narration? Is it merely to demonstrate that he knows how to regain self-control through his use of reason, as some commentators have suggested?65 It is, after all, Socrates’ narration and he is in complete control of what to include and what to exclude, so why include a scene of loss of control? It points to the elusiveness and the difficulty of self-control. Self-knowledge and selfcontrol are parallel in the respect that one can be taken by surprise: Someone thinks that she has gained self-knowledge only to encounter some new circumstance that shows that there is something still to learn; or he may find that self-mastery is in fact not mastered. The previously mentioned commentators parade a certain confidence in reason which this very episode calls into question: We are not creatures whose behavior can be dictated exclusively by reason. We are embodied and we need to take account of that in our discussion of knowledge and self-knowledge. In both the Theaetetus and Charmides a “rational” dialogue is framed by body and irrationality—war, death, and eros. Plato writes dialogues dealing with the latter two but for now our primary concern is with eros, given its suppression by Theodorus in the Theaetetus and its triumph in the Charmides.

5. FRAMING THE SYMPOSIUM In the Symposium we have an example of the third mode of narrating a dialogue—a narration of a narration. The Theaetetus displays a narration of an original dialogue transformed back into dialogue through various editorial devices; the Charmides is a firsthand narration of a dialogue that took place the previous night; and the Symposium is secondhand, and in the case of Socrates’ narration of his encounter with Diotima it is thirdhand narration which takes place several years after the original conversation.66 The actual narrative is introduced through a brief dialogue between Apollodorus and an unnamed friend, which provides us with a genealogy of the story about to be told. In all three cases we are confronted with the particular difficulties involved in the issue of the transmissibility of philosophy. In contrast to the “logical” and sober-minded Euclides, who does his best to transform Socrates’ narration into a “reasonable” document, we have a fanatical and manicky Apollodorus in charge of passing on the speeches on ero¯s given by an extraordinary set of individuals on the eve of Agathon’s victory celebration.67

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The frame of the Symposium is structurally complex and involves a narrative style that is not always smooth:68 We encounter numerous instances of phrasing like the following: “He said that when he heard this he said” or “And I said he said” (174b–c). It is almost as if we are getting the justification for why Euclides decided to cut out all these bothersome “inbetween” things. We are regularly reminded that we are reading a narrative that is narrated by someone, Apollodorus, who was in turn told the story by one of the symposiasts, the uninvited guest Aristodemus. Apollodorus is narrating the story to an unnamed comrade, but before he even begins to tell the story itself, he tells his comrade about the circumstances and details of the narration a few days earlier to Glaucon, who in his turn had previously heard an account from someone who heard it from Phoenix—a most confused version, Apollodorus thinks. It is clear that we are dealing with a “hot” story, that there is more than one narrator busy passing on this tale, that not all the narrators are equally reliable. According to Apollodorus, the muddled account by Phoenix also went back to Aristodemus. Glaucon is so confused and unclear about the entire affair, that he begs Apollodorus to tell him the true story. He shows his confusion from the outset. He thinks that Apollodorus himself was present at the party, suggesting that he is young and historically uninformed: He doesn’t know about Agathon’s absence from Athens. Glaucon also shows that he is confused by expecting to hear erotic speeches rather than speeches about ero ¯ s. This would be unsurprising, if all speeches about ero¯s are erotic; but that can only be determined by hearing the narration itself. And so, in the course of just a few days, Apollodorus is called upon to narrate the Symposium twice. In addition to the narration about narration we learn something about the secondhand narrator himself. He clearly puts himself forward as someone in love with Socrates and hints that he has replaced Aristodemus as the one who loves Socrates the most. He sounds like a flatterer, who claims to love philosophy, but whose true love is Socrates, according to his companion. The companion says: You are always of a piece, Apollodorus, for you are always slandering yourself and others; and in my opinion you simply believe that—starting with yourself—everyone is miserable except Socrates. And how you ever got the nickname “Softy” (malakos), I do not know, for you are always like this in your speeches, savage against yourself and others except Socrates (173d).

This was the companion’s response to Apollodorus’s comment: As for me, whenever I make any speeches on my own about philosophy or listen to others—apart from my belief that I am benefited—how I enjoy it. But whenever the speeches are of another kind, particularly the speeches of

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the rich and of moneymakers—your kind of talk—then just as I am distressed, so do I pity you comrades, because you believe you are doing something of importance, but in fact it’s all pointless. And perhaps you, in turn, believe that I am a wretch; and I believe that you truly believe it. I, on the other hand, do not believe it about you, I know it (173c–d).

How would Apollodorus classify the speeches he is about to narrate? The reliability of Apollodorus as narrator, as well as that of Aristodemus as source, has been questioned by various commentators, including an extensive analysis by David Halperin.69 From the Phaedo (59a) we learn that Apollodorus was something of a fanatic when it came to Socrates. Both narrators apparently enjoyed imitating Socrates and in Aristodemus’s case he went so far as to dress like “the master.” Apollodorus lets us know that he did not simply take Aristodemus at his word, but checked back with Socrates to confirm the account. “Naturally, I checked part of this story with Socrates, and Socrates agreed with his account” (173b). Apollodorus must have employed a strategy similar to Euclides, who also had reason to go back and check with Socrates. But could they have used the same criteria to determine whether or not something was missing or out of place? Or was Apollodorus merely spot-checking the story told to him by Aristodemus? Presumably there is a difference between finding holes and misplaced premises in an argument about knowledge and noticing something missing in speeches praising ero¯s. When his friend begs him to finally tell the tale he replies: “All right. . . . Well, the speeches went something like this—but I’d better tell you the whole story from the very beginning (ex arche¯s), as Aristodemus told it to me.” (173e–174a). As eager as his friend is to hear the actual speeches, Apollodorus insists on delaying his pleasure for a little bit longer for the sake of completeness. Thanks to Apollodorus’ thoroughness we are introduced to a Socrates who has made himself beautiful for Agathon’s party and who invited Aristodemus to accompany him. On the way Socrates is overcome by a “thinking fit” which leads to the awkward situation that the uninvited Aristodemus arrives at Agathon’s house alone. If Socrates were narrating the dialogue would he comment about his thoughts? In the Republic (392d–395a) Socrates expresses a preference for narration over the mixed style so often found in epic poetry, because it precludes deceptive imitation. Unlike Homer, who assumes the voice of Agamemnon in the Iliad, Apollodorus speaks in his own voice and offers the entire dialogue in indirect discourse. But this is not a straightforward narration like the Charmides, which is narrated by Socrates himself. In fact Apollodorus is convinced that Socrates would not have narrated the Symposium himself: When Glaucon wonders whether Apollodorus hears

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the account from Socrates he exclaims: “Oh for god’s sake, of course not!” (173b). Nor is it like the Phaedo, which is narrated by one of the characters present at Socrates’ death. The frame of the Symposium suggests something like gossip, a secondhand report. Narration makes connections and transitions in a way that direct dialogue and transcription of a conversation cannot achieve. It can make the isolated comment seem plausible in context, give color to mood as well as an interlocutor’s cheeks, smooth out interruptions, and the like. It can make impromptu talk seem more orderly and logical than it is in “real life.” It fills in the dots with authorial connections. It makes interpretation possible, but it puts the spontaneous and chaotic under a particular interpretation. The subjective nature of narration can be seen as both a boon and a bane. The difference between Socrates’ narration and Apollodorus’ re-narration is that the former is self-consciously subjective while the latter implicitly claims a kind of objectivity. Socrates is recounting his own experience while Apollodorus was not present at the Symposium and as such cannot provide a perspective. In that sense Apollodorus is closer to Euclides who also was not present at the conversation between Socrates and the mathematicians and thus has a certain distance that he thinks allows him to present the dialogue more clearly and coherently. The frames of the three dialogues we have here discussed all point to the problematic nature of transmitting philosophy or knowledge: All three underline the possible unreliability of accounts that purport to tell “what really happened” and “what was really said.” The Charmides appears to be more reliable than the others, because it is a report of Socrates’ experience; but from our vantage point we still need to question the veracity of the account: What did Socrates omit and why is he so brief in his depiction of his war experience? On the other hand, we may wonder whether “who said what” is important in philosophical deliberations. Is what we can know a matter of who said what? When presenting Plato’s dialogues, teachers are frequently asked whether Socrates really said what Plato wrote, as if everything depended on the accuracy of the report; and many Plato scholars still busy themselves trying to separate Socrates’ voice from Plato’s. Plato writes in a way that invites these questions, but at the same time he is dismissing them as trivial. In constructing the frames for the three dialogues we have been investigating Plato shows that any account of anything can be unreliable: We cannot be sure whether Plato himself is more like a Euclides or an Apollodorus—or perhaps even some completely different kind of fanatic. Platonic frames intensify the perspectival character of the dialogues by introducing narrators whose life experiences shape their understanding of events and issues. They force readers to ponder the characters’ perspectives as well as their own. In the first place, they situate us as readers

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for our understanding of the position of Platonic characters, Socrates included, making it possible for us to see the concerns from which they take on their positions, the interests they want to defend, the possible limits of their initial and final perspectives. Second, and philosophically more important, they give us some access into the self-understanding of those interlocutors. By the nature of the case that access is never complete: We do not have a complete understanding, from the limits of our own perspective, of the limits of their perspectives. Their knowledge and self-knowledge, as well as ours, are all “framed,” limited. Euclides’ attempt to have an unframed story, a view without a standpoint, signals the desire to present an account that at least has the appearance of “objectivity.” Suppression of the bond between the narrator and that which is being narrated takes away the middle ground, the ta metaxu, which is the place that makes knowledge possible in the first place. As is clear from both the Republic and the Symposium, it is the realm that lies between knowledge and ignorance which provides the starting point for inquiry into knowledge. Ironically, the inner frame of the Theaetetus compounds the elimination of the ta metaxu by highlighting the absence of ero¯s. As we learn from Diotima, ero¯s resides between the divine and the human, furnishing humans with the desire for wisdom. Compared with the manic involvement of Apollodorus in his renarration of accounts retold to him, Euclides is an “author” who dissociates himself from his “creation.” It is as though Euclides cannot learn anything about himself from his writing, because it is not, properly speaking, his creation anyway. In contrast, Apollodorus seems to nourish his love of philosophy through the narration of the speeches of the Symposium. If knowledge were a code that could be written on some blank slate, irrespective of the hands and positions of the writers, there would be no deep problem of its transmissibility. The codes or slates, dialogues or treatises, could simply be handed from person to person, from one generation to the next, and, so long as history smiled and natural catastrophes did not interfere, there would be no particular problem understanding old or new materials written on these changing media. But if knowledge is framed, demanding that we understand ourselves and others as claimants to its truths, then Socrates and all subsequent philosophers will have to rely on people who can see through the matter into the spirit, and see the knowledge in its frames.

NOTES 1. For examples of self-reflection and methodology, see Herodotus, History, bk. 1.1 and 5, bk. 4.20, and Thucydides, History of the Peloponnesian War, bk. 1.20–22.

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2. See Francis MacDonald Cornford, Plato’s Theory of Knowledge: The Theaetetus and the Sophist of Plato Translated with a Running Commentary (New York: Liberal Arts Press, 1957 [1934]), 82–83, 98–99; see also David Sedley, The Midwife of Platonism: Text and Subtext in Plato’s Theaetetus (Oxford: Clarendon Press, 2004); and Timothy Chappell, Reading Plato’s Theaetetus (Indianapolis and Cambridge: Hackett Publishing Co., 2004). 3. Immanuel Kant, Critique of Pure Reason: Unified Edition, trans. Werner S. Pluhar (Indianapolis and Cambridge: Hackett Publishing Co., Inc., 1996), 18 [B xii]. 4. Although both Critias and Charmides are commonly referred to—even by well-established scholars of the highest rank—as members of the “Tyranny of the Thirty” after the defeat of Athens in the Peloponnesian War, in fact Critias was the leader of “the Thirty” and Charmides was in the related group of “the Ten” in the Piraeus. See Debra Nails, The People of Plato: A Prosopography of Plato and other Socratics (Indianapolis and Cambridge: Hackett Publishing Co., 2002), 92. 5. Aristotle, Nicomachean Ethics 1.1094a–b, trans. Terence Irwin (Indianapolis and Cambridge: Hackett Publishing Co., 1985), 2–3. 6. On the relation of ero¯s to the overall structure of the Symposium, see Karl Vretska, “Zu Form und Aufbau von Platons Symposion,” Innsbrucker Beiträge zur Kulturwissenschaf Serta philologica aenipontana, ed. Robert Muth (Innsbruck 1962), 143–56. 7. See Cornford, Plato’s Theory of Knowledge, 15–17. 8. See J. McDowell, Plato’s Theaetetus (Oxford: Clarendon Plato Series, 1973). 9. See Nicholas P. White, Plato on Knowledge and Reality (Indianapolis: Hackett Publishing Company, 1976), 157–59. 10. See D. Bostock, Plato’s Theaetetus (Oxford: Oxford University Press, 1988). 11. See M. F. Burnyeat, The Theaetetus of Plato (Indianapolis: Hackett, 1990). 12. See Rosemary Desjardins, The Rational Enterprise: Logos in Plato’s Theaetetus (Albany: State University of New York Press, 1990). 13. See Chappell, Reading Plato’s Theaetetus, 25, 29–30. 14. See Gilbert Ryle, Plato’s Progress (Cambridge: Cambridge University Press, 1966), 23–29. Ryle speculates that the reading by the slave in the Theaetetus and the substitution of the Eleatic Strange for Socrates as primary interlocutor in the Sophist and Statesman is a sign of Plato’s aging and loss of voice, as well as a signal of changing positions. According to Ryle the dialogues were usually recited aloud in the Academy by Plato himself and his voice was becoming a victim of aging. 15. See Sedley, The Midwife of Platonism, 6–8, 15–17. Sedley considers the Theaetetus one of the few cases in which Plato is not speaking “in his own voice” through the mouth of Socrates. Thus for Sedley it is the crucial case in which Plato is distancing himself from the words and doctrines of Socrates, and moving toward philosophical positions strictly his own, as indicated by the removal from authorship. 16. See Lewis Campbell, The Theaetetus of Plato, with a Revised Text and English Notes (Oxford: Oxford University Press, 1861), xiv–xix. According to Campbell Plato was in constant dialogue with his contemporaries, and in the case of the Theaetetus the frame indicates that the Megarians are being addressed.

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17. See Paul Friedländer, Plato, trans. Hans Meyerhoff (Princeton: Princeton University Press, 1969), 3:145–51. 18. See Seth Benardete, Plato’s Theaetetus: Part I of The Being of the Beautiful (Chicago and London: University of Chicago Press, 1986 [1984]), 85–93. 19. See Ronald M. Polansky, Philosophy and Knowledge: A Commentary on Plato’s Theaetetus (Lewisburg, Pa.: Bucknell University Press, 1992), 33–42. 20. Ruby Blondell observes that Euclides and Terpsion are the counterexamples to Socrates’ “reading” of a text: The Play of Character in Plato’s Dialogues (Cambridge: Cambridge University Press, 2002), 305–9. 21. Translations are taken directly or adapted from Seth Benardete, Plato’s Theaetetus. 22. See Euthyphro 2a, where this setting is specified. The term “King Archon” is a kind of archaism. Early in Athenian history there were three archons—King (basileus), General (polemarchos), and Eponymous. The Eponymous Archon had the most power. By the time of Socrates’ trial there were ten, selected by lot, and essentially powerless. Since the original King Archon had authority over religious matters and over the Areopagus, however, and over litigations involving religious disputes, charges of impiety were introduced through this “shadow institution.” 23. There is extant an anonymous ancient commentator on the Theaetetus, probably from the first or second century CE, who asserted that there was an alternative introductory frame (presumably also written by Plato). Anonymous Commentator, On Plato’s Theaetetus, ed. Diels and Wilhelm Schubart (Berlin 1908). 24. For further discussion see Nails, The People of Plato, 275–77. 25 Although there were many ancients named Theodorus and although Diogenes Laertius (Lives of the Philosophers, 2.86, 97–103) relates various items, in fact all we know of Theodorus comes directly from this dialogue. See Lewis Campbell, ed. The Theaetetus of Plato (Oxford, University Press, 1861; reprinted New York, Arno Press, 1973), lii–liv. In contrast, Theaetetus was more widely recognized and mentioned by Euclid for his solution to the problem of the surds and his contributions to the theory of the five solids. See Sir Thomas Heath, A History of Greek Mathematics (Oxford, Clarendon Press, 1921), 1:202–12. 26. In Diogenes Laertius (Lives of the Philosophers 2.106–12) Eucleides appears as the founder of the Megarian School. According to Aristotle (Metaphysics bk. 9, chap. 3, 1046b), the Megarians deny the existence of potentiality (dynamis). See Benardete note in part 1 of The Being of the Beautiful, 1.184. 27. Polansky (Philosophy and Knowledge, 34–35) points to the very presence of Euclides and Terpsion as a further indication of the connection between the two deaths. The telling of the Phaedo and the reading of the Theaetetus take place far away from Athens. 28. In Phaedo the frame is a dialogue between Phaedo and Echecrates, whereas the inner part is narrated by Phaedo; though the narration is interrupted by direct dialogue at 102a. In the Euthydemus the outer dialogue is between Socrates and Crito, the inner narrated by Socrates. Socrates’ narration of the main body of Protagoras is introduced by a direct dialogue between Socrates and a comrade (hetairos). In Parmenides Cephalos narrates a dialogue which was previously narrated by Antiphon, and in Symposium Apollodorus repeats to Glaucon his narration to a comrade of Aristodemus’s narration to him of events at Agathon’s party.

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29. Dokei gar moi oligon pro tou thanatou enteuchein auto¯ meirakio ¯ onti. 30. Ou ma ton Dia, oukoun outo ¯ ge apo stomatos. 31. On Socrates’ memory, Polansky (Philosophy and Knowledge, 36–37) makes the point that Euclides can only remember things by writing them down, whereas Socrates has been able to hold the same conversation in memory over a long period. 32. See Phaedrus 275a–278a. 33. Consider the odd parallel in the way Phaedrus tries to pretend that he is not holding the written speech of Lysias on the preferability of nonlovers (228e). Phaedrus wants to create the impression that the speech is spontaneously spoken as his own, whereas in fact he is only repeating somebody else’s written speech. Plato uses a dramatic device to present the Theaetetus as a dialogue not his own; and Euclides uses an editing device to make it look as though it were unedited. 34. Hume, An Enquiry Human Understanding, sec. 1: “Be a philosopher; but, amidst all your philosophy, be still a man.” 35. Note that the Phaedo stands at the conclusion of the “companion tetralogy.” 36. See Phaedrus 229c–230a. 37. See Theaetetus 143d–e and Republic 7.528b–e. 38. For a more extensive discussion of the role of chance and its connection with the Megarians, see J. C. Harrison, “Plato’s Prologue: Theaetetus 142a–143e,” Tulane Studies in Philosophy (1978), 27:103–23. 39. While ti esti, “What is [it]?” is the typical beginning of Socratic questioning, to ti ¯e n einai “the being of what it was,” is Aristotle’s formulation in the Metaphysics, bk. Z, chaps. 3–4, 1029bff. 40. See Aristotle, Physics, bk. 2, chaps. 4–6, 195b31–198a13. 41. See Diogenes of Sinope in search of an honest man with Chaerephon at Delphi in search of the wisest man in Athens (Apology 21a). See also the opening of the Charmides 153d. 42. This quotation also illustrates the difference between the political Socrates and the apolitical Theodorus. Socrates is attached to his city and cares for those within the city, whereas Theodorus is a non-Athenian in Athens, who accepts students from anywhere. See Polansky, Philosophy and Knowledge, 39–41. 43. Plato, Charmides, trans. W. R. M. Lamb. Loeb Classical Library (Cambridge, Mass.: Harvard University Press; London: William Heinemann Ltd., 1955 [1927]). 44. Compare this with Charmides, who is extremely beautiful and “unable.” 45. See Charmides 154c. 46. Construing Theaetetus as “philosopher-prince,” Blondell (The Play of Character in Plato’s Dialogues, 260–70) argues that the likeness between Theaetetus and Socrates goes beyond the physical characteristics that Theodorus notices. 47. See Republic 2.375aff; 5.473c–475e. 48. See David Roochnik, “Self-Recognition in Plato’s Theaetetus,” Ancient Philosophy (2002), 22:29–45. See also Blondell, The Play of Character in Plato’s Dialogues, 260–70. 49. Compare the “true philosopher’s” ignorance of his next-door neighbor (174b). 50. See Charmides 157e–158b. 51. See the similar, but reverse, situation in the Symposium (175c), where Agathon wants Socrates to sit on a couch next to him.

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52. Compare Aristotle’s examination of this point in Physics 2.2 (193b31–194a6): “Now the mathematician, though he too treats of these things, nevertheless does not treat of them as the limits of a physical body. . . . That is why he separates them. . . . ‘Odd’ and ‘even,’ ‘straight’ and ‘curved,’ and likewise ‘number,’ ‘line,’ and ‘figure,’ do not involve motion; not so ‘flesh’ and ‘bone’ and ‘man’—these are defined like ‘snub nose,’ not like ‘curved.’” 53. See Aristotle, Physics 2.2.194a7ff. 54. Phaedo 64c: “Is it anything else than the separation of the soul from the body? Do we believe that death is this, namely, that the body comes to be separated by itself apart from the soul, and the soul comes to be separated by itself apart from the body? Is death anything else than that?” (trans. G. M. A. Grube [Indianapolis: Hackett Publishing Co., 1981]). 55. Similar legal and judicial language is used throughout the Apology, where Socrates has no choice about employing it. 56. Paul Shorey, What Plato Said (Chicago: Chicago University Press, 1933), 103. 57. See Seth Benardete, “On Interpreting Plato’s Charmides,” The Argument of the Action: Essays on Greek Poetry and Philosophy, ed. Ronna Burger and Michael Davis (Chicago and London: University of Chicago Press, 2000), 231–56. 58. See Mary Margaret McCabe, “Looking Inside Charmides’ Cloak: Seeing Others and Oneself in Plato’s Charmides,” Maieusis: Essays on Ancient Philosophy in Honour of Myles Burnyeat, ed. Dominic Scott (Oxford: Oxford University Press, 2007), 1–19. 59. Benardete suggests (“On Interpreting Plato’s Charmides,” 231–32) that the apolitical character and erotic squeamishness of Socrates’ companion points to someone like Theodorus. Unfortunately there is no additional evidence but it is a telling suggestion nevertheless. 60. The Euthydemus is for the most part narrated by Socrates but it includes a noticeable amount of direct dialogue between Socrates and Crito, at the beginning, the middle and the end. Rival Lovers is another dialogue narrated by Socrates, but few if any Plato scholars accept it is as genuine. 61. Plato’s Protagoras, translated by Stanley Lombardo and Karen Bell in John M. Cooper, ed., Plato: Complete Works (Indianapolis and Cambridge: Hackett Publishing Co., 1997). 62. Translations of the Symposium are from Seth Benardete, in The Dialogues of Plato, ed. Erich Segal (Toronto and New York: Bantam Books, 1986). 63. See Symposium 211d ff. where Diotima contrasts the love for beautiful boys and love of beauty itself: “when he looks at Beauty in the only way that Beauty can be seen—only then will it become possible for him to give birth not to images of virtue (because he’s in touch with no images), but to true virtue (because he is in touch with true beauty).” (212a). 64. See Lysis 205b–d, where Ctesippus complaints about the bad poetry Hippothales is writing to deal with his passion for Lysis. 65. See W. Thomas Schmid, Plato’s Charmides and the Socratic Ideal of Rationality (Albany: State University of New York Press, 1998), 8–9: “The chief value of this remarkable narrative is . . . to link self-control and rational inquiry. . . .” See also Charles Kahn, Plato and the Socratic Dialogue (Cambridge: Cambridge University Press, 1996), 187: “This episode prefigures the topic of the dialogue by exhibiting

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Socrates’ subsequent success in regaining self-control. . . .” Seth Benardete, “On Interpreting Plato’s Charmides,” offers a more thought-provoking explanation arguing that Socrates’ erection is pointing forward to the Zalmoxian doctrine of how the disorder of the part indicates a disorder of the whole, which is supported by the text because the inflamed passion causes a loss of the self. 66. We do not know with certainty whether Plato invented Diotima, but on the basis of dramatic clues we may accept the dating of the encounter between Socrates and Diotima as approximately 440 BCE. Agathon’s victory celebration in 416 BCE; and the date of Apollodorus’s narration some time after 408 BCE. For further discussion of the historical evidence of the dates see Nails, The People of Plato, 8–10, 137–38. 67. See Gerhard Krüger, Einsicht und Leidenschaft: Das Wesen des platonischen Denkens (Frankfurt/Main: Klostermann, 1948): “In dieser Art Einführung des Berichts verschlingen sich zwei gegensätzliche Motive, die wieder der Spannung von Mythos und Logos entsprechen: das Gastmahl liegt lange zurück (173c), aber der aneignende Bericht davon ist völlig zuverlässig und wohlbegrüdet (79).” 68. For interpretations of the Symposium frame, see David M. Halperin, “Plato and the Erotics of Narrativity,” Oxford Studies in Ancient Philosophy, ed. Julia Annas, supplement vol. 1992, Methods of Interpreting Plato and His Dialogues, ed. James C. Klagge and Nicholas D. Smith (Oxford: Clarendon Press, 1992), 93–129; William A. Johnson, “Dramatic Frame and Philosophic Idea,” American Journal of Philosophy 119 (1998): 577–98; Stanley Rosen, Plato’s Symposium, 2nd ed. (New Haven, Conn., and London: Yale University Press, 1987 [1968]), 1–38; Leo Strauss, On Plato’s Symposium, ed. Seth Benardete (Chicago and London: Chicago University Press, 2001), 17–37. 69. Halperin, “Plato and the Erotics of Narrativity,” 93–129.

2

O Intellectual Midwifery, Intellectual Pregnancy

1. THEAETETUS AND SYMPOSIUM

M

any commentators link the Symposium with the Phaedrus and Lysis on account of their common focus on love, and many couple it with the Republic on account of their similar ascent passages, describing a journey from the world of images and appearances to the vision of Forms. But there are good reasons to associate the Symposium with the Theaetetus as well:1 The former gives an account of the intellectual pregnancy which makes possible the practice of the intellectual midwifery that Socrates professes in the latter. “Intellectual” or “spiritual” pregnancy links ero¯s and knowledge. We are intellectually pregnant either because we are so naturally—that is, we are born with some sort of innate notions—or we become pregnant through interaction and intercourse with the world— through perception and opinion. Intellectual pregnancy supplies, according to the common Greek understanding, the “seeds” for knowledge. Pregnancy and “birthing,” on the other hand, are necessary but not sufficient conditions for self-knowledge. Self-knowledge is only possible upon the encounter with an “other” in whom we see an instantiation of beauty. Self-knowledge is the analogue of self-procreation: Just as procreation requires an “other,” so too does self-knowledge.2 The fact that Socrates introduces midwifery as his techne¯ has important consequences for our understanding of knowledge and self-knowledge. What is known might originally have been within us or exterior to us, but it must be appropriated by us, made our own and “internalized.” Thus what is known must be within us and coming to know the knowable is itself an 41

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exercise toward self-knowledge: coming to know the knowable is necessarily self-reflexive, since probing the limits of what we can know is a necessary part of the question what can be known in general. Maieutike¯ also illustrates this: Midwifery guides the pregnant one in putting outside what is within, and then judging whether the product of that is something that is truly worth keeping, whether it is something knowable. If it is not knowable and worth preserving, then, even though one has not gained knowledge of anything knowable, one has come to know that one does not know. That sort of self-knowledge amounts to a knowledge of ignorance, rather than knowledge of knowledge. Socrates is famous for his admissions of ignorance, his assertions of a knowledge of ignorance, and for conversations ending in aporetic shrugs. He seldom professes any specific or definitive knowledge. Nonetheless he makes an unusual such claim in the Symposium, after Eryximachus has proposed that they each make a speech in honor of ero ¯ s, to which Socrates replied: “No one will cast a vote against you Eryximachus. For I would surely not beg off, as I claim to have “expert” knowledge (epistasthai) of nothing but erotics (ta ero¯tika, 177d).” This proclamation itself provides a curious link between ero¯s and knowledge and can only be fully understood in the light of Diotima’s teaching, which reveals that ero ¯ s is not a god at all, but a daimo¯n. Residing between wisdom and ignorance ero¯s, in contrast to a god who would be a possessor of wisdom, is rather a lover of wisdom and beauty. Exemplifying this in-between-ness, ero¯s leads both to an awareness of a lack of knowledge and it can propel us to fill in that lack. We learn from the Republic that the philosophical nature is an erotic one, whose ero¯s can be employed, if properly directed, to ascend from the visible world to the intelligible, and perhaps ultimately, to the Good. Similarly, we are told in the Phaedrus that ero¯s is responsible for the regrowth of our lost wings, that allow us to rise up to the hyperouranian beings and behold the forms of justice, self-control, and so on. As a lover of wisdom ero¯s exemplifies knowledge of ignorance: Unlike beauty, which one can love “ignorantly,” wisdom seems to require some sort of knowledge. This interpretation leads to the ironic result that when Socrates makes a positive claim about knowledge, it once again becomes an affirmation of his knowledge of ignorance. To know ero¯s is to be a philosopher and, if ero ¯ s itself means love of wisdom, then in Socrates’ case knowing ero¯s amounts to a kind of self-knowledge as well as a kind of ignorance. In fact, however, the speakers preceding Socrates in the Symposium praise love in such a way that Socrates has to modify his initial claim: And then I realized that, after all, I am to be laughed at for having agreed to eulogize Eros in turn with you, and for claiming that I was skilled in erotics; for, as it has turned out, I know nothing of the matter, nor how one is to eu-

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logize anything. For in my stupidity I believed the truth had to be told about anything that was given a eulogy, and that this was the underpinning, and that by selecting the most beautiful parts of the truth one was to arrange them in the seemliest manner possible. And I was quite filled with the proud thought that I should speak well, since I know the truth about praising anything (198d ).

Socrates proposes that he, in contrast with the others, will, in plain words, tell them the truth about ero¯s and the truth is directly tied to bluntness about the fact that ero¯s is actually not a god at all.3 Everyone urges him on. After a brief interrogation of Agathon—which implies that the other symposiasts did not know what they were talking about, for they all described ero¯s as a god—he recounts his conversation with Diotima, where he was the person questioned rather than the questioner. Socrates also makes claim to a specific skill in the Theaetetus. In this dialogue about the definition of knowledge conducted with two mathematicians, Socrates lets us in on a secret: He, like his mother, is a midwife (149a).4 The revelation is shrouded in the atmosphere and language of secrecy, not unlike the secrecy that pervades the telling of the Symposium story. Theaetetus and Theodorus, the interlocutors, listen patiently to Socrates’ elaboration on his art of midwifery, which leads Theaetetus to proceed with the investigation and to offer his own definition of knowledge as perception. The theme of pregnancy, the intellectual pregnancy that is central to Diotima’s discourse on love, invites comparison with Socrates’ claims to skill in midwifery, intellectual midwifery, in the Theaetetus. Midwifery involves pregnancy and pregnancy presupposes ero¯s of some kind. In what follows we will see how ero¯s functions in explaining both the role of intellectual pregnancy, how in the presence of beauty it leads to generating and giving birth to one’s opinion. As will become clear, birthing is not a solitary event, but always involves an other. When that other is the midwife, the process of coming to know one’s offspring can also lead to coming to know oneself.

2. EROTICS Socrates says that he learned about ero¯s from Diotima, and he “recreates” his dialogue with her instead of giving his own “original” speech. The focus of this section is to examine how Diotima’s instruction of the young Socrates can be used to explain the status and condition of Theaetetus as a pregnant young man, and the relation of ero¯s to knowledge and the search for knowledge. How is it that men can become pregnant? And

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what is the cause of such pregnancy? In her analysis of ero¯s, following upon Agathon’s speech, Diotima has Socrates define it initially as a desire for beauty; then as the desire for having good things—one’s own things; and finally as the desire for immortality. Before we can fully understand the work of ero¯s, we must explore the transition from beauty to immortality as the goal or end (telos), with beauty playing the role of assistant. When Socrates is unable to answer her question about what one has if one possesses beautiful things, Diotima allows him to substitute “the good” for “the beautiful.” She already seems to be hinting that beauty itself is not the aim of ero¯s; rather ero¯s is necessary as a vehicle toward the good. It is in the presence of beauty that the issue of the good arises and beauty shows itself forthwith as a fruitful vehicle. Socrates does not yet know why he is unable to answer the question regarding beautiful things, but by the end of his dialogue with Diotima that should be clear to him. Once he substitutes “good things,” the answer is easy: Happiness is what one has as the result of having good things. Diotima introduces the element of time into the equation by suggesting that one wants to have the good things forever. She explains the behavior of those who earnestly pursue the good: “Their deed is bringing to birth in beauty both in terms of the body and in terms of the soul” (206e). The notion that we would want to possess some things forever raises the question how a mortal being can partake of the immortal, and it is here that beauty makes a comeback— not in its previous role as the aim of love, but rather as the occasion that facilitates the possibility of immortality. Diotima explains that by beauty she means harmony and it is harmonious procreation which is divine, the only way for the mortal to partake of immortality. Mortal nature is capable of immortality only in this way, the way of generation, because it is always leaving behind another that is young to replace the old. . . . He is forever becoming young in some respects as he suffers losses in other respects: his hair, flesh, bones, blood, and his whole body. And this is not only in terms of the body but also in terms of the soul: his ways, character, opinions, desires, pleasures, pains, fears, each of these things is never present as the same for each, but they are partly coming to be and partly perishing. And what is far stranger (poly atopo ¯ teon) still is that in the case of our sciences (episte¯ mai) too not only are some coming to be while others are perishing (and we are never the same in terms of the sciences either); but each single one of the sciences is affected in the same way. (207d–e).

There is throughout this passage a surprising lack of differentiation between the body and the soul. In Diotima’s explanation of ero¯s we must assume a continuum rather than a separation or duality. The idea that somehow the soul is a separable substance and as such has access to immortality, in contrast with the perishable body, is here called into ques-

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tion. The soul, like the body, is subject to constant change. We might be tempted to think that this applies only to the so-called lower parts of the soul—that is, those parts specifically connected with the body, the passions and desires; but Diotima includes science or knowledge in her list as well. She herself calls it strange that this is so, though the peculiarity does not deter her from asserting it. What does it mean, however, to say that knowledge is coming-to-be and passing away and that the fact that we have to learn and study is evidence for this claim? The need to preserve knowledge through study is characterized as a need to make it appear that knowledge remains the same, but in fact it is not the same, because all things mortal are subject to change.5 The fact of mortality, the limit on all human possibility, is directly related to the difference between finite human knowledge and unlimited divine wisdom. Claims made by Diotima in her account of ero¯s can help clarify the connection between ero¯s and knowledge. Before tracing the parentage of ero¯s, she gets Socrates to agree that there is a realm of “in-between-ness,” in which she will locate both ero¯s and right opinion. In the strange prelude, she tries to explain that there is something between beauty and ugliness by pointing to that which lies between wisdom and ignorance: ”Don’t you know,” she said, “that to opine correctly without being able to give an account (logos) is neither to know expertly [epistasthai] (for how could expert knowledge be an unaccounted [alogon] matter?) nor lack of understanding [amathia] (for how could lack of understanding be that which has hit upon what is)? But surely correct opinion [orthe¯ doxa] is like that, somewhere between intelligence [phrone¯ sis] and lack of understanding.” (202a).

It is not immediately clear why opinion, situated between knowledge and ignorance, can be used as a foil to explain why ero¯s is neither beautiful nor ugly, but something in between the two, which strives towards the beautiful. Diotima, of course, adduces thereupon the startling consequence that ero¯s is not a god at all, but is rather a desire for divine immortality and, more importantly for our discussion, a desire for divine knowledge and wisdom. If this is a “true” analogy we need to account for the account of ero¯s itself: If the difference between correct opinion and knowledge is logos, as clearly implied by the sequence of definitions in the Theaetetus, we need to figure out what the analogue of logos is in the case of ero¯s. Both the Lysis and the Phaedrus, in addition to the Symposium, show that the experience of ero¯s gives rise to speeches and poems. It seems as though the success of seduction depends on logos, on the making of erotic speeches. Erotic speeches are conveyors, go-betweens. Socrates offers a parallel type of explanation of the difference between knowledge and opinion near the end of the Meno (97e–98a). He argues

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there that true opinion can be as good a guide to virtue as knowledge; but it suffers from instability and is in need of an account (logos). More specifically he suggests that right opinion needs to be tied down with a causal account (aitias logismo ¯ ) in order for it to become knowledge (episte¯ me¯ ).6 In fact, Socrates makes yet another claim to knowledge: Indeed, I too speak as one who does not have knowledge but is guessing. However, I certainly do not think I am guessing that right opinion is a different thing than knowledge. If I claim to know (eidenai) anything else—and I would make that claim about few things—I would put this down as one of the things I know (oida) (Meno 98b).

Is there any way to “tie down” ero¯s? Diotima does offer a causal explanation of the nature of ero ¯ s by providing a genealogy: Rather than binding or securing ero¯s, however, her account instead suggests and explains why love will always be on the move. But this in turn actually makes knowledge possible because, as Diotima later explains, knowledge is not a static and stable thing, but is always in need of replenishment through study and care, just like hunger and thirst. Ero¯s, not itself tied down, fuels the desire to “tie down,” motion in search of rest. Diotima clarifies the daimonic nature of ero¯s as a being between the mortal and the immortal: “A great daemon (daimo¯n), for everything daemonic (daimonion) is between god and mortal.” (202d–e). Eros is something within us that is less than divine but more than human, and which provides us with the constant reminder that we have a connection to the divine. In addition, the in-between nature of ero¯s accounts for its double function: It leads both to the awareness of a lack and it leads to the drive to fill up that lack. Diotima explains this duality as a result of the fact that ero¯s is the child of Poros and Penia, a mixture of resource or wealth and poverty or neediness. “And his nature is neither immortal nor mortal; but sometimes on the same day he flourishes and lives, whenever he has resources; and sometimes he dies, but gets to live again through the nature of his father” (203e). The similarities between Diotima’s depiction of ero¯s and Socrates’ selfdescription in the Apology are significant. They allow of at least two possible interpretations: Either Diotima is teaching Socrates how to “become Socrates,” or Socrates is rather inventing a disguise in order to surreptitiously praise himself. As in Apology 17a–18a, where Socrates chides the preceding speakers, his accusers, and promises to tell the truth, in a similar way he is here introducing his account with the claim: “To tell the truth on my own terms” (199b). Just as Diotima characterizes the philosophizing ero¯s as something daemonic and superhuman, so at his trial Socrates characterized himself as being in possession of something divine and dae-

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monic (theion ti kai daimonion, 31d). Finally, Socrates points to his poverty (penia) as evidence (martura) that he is not a teacher (31c) and he notes the lack of resources (aporia)7 that brought about his conviction and ultimate death. In his response to the death penalty in the last segment of the Apology Socrates expands: “And yet it is through a lack (aporia) that I have been convicted, not however a lack of words, but of impudence and shamelessness, and of willingness to say to you such things as you would have liked best to hear” (38d). Diotima successfully initiated Socrates into philosophy. The analogy Diotima makes between the preservation of the “self” from childhood through old age, on the one hand, and from parent to offspring, on the other, raises additional questions. The apparent explanation for this claim is that the work of ero ¯ s is not directed toward individual selfpreservation, but is rather focused on human beings as a whole. Just as ero¯s was initially introduced as a daimo ¯ n, which provided a link between humans and gods, so now in the development of Diotima’s teaching, we see ero¯s providing a link between human and human. By this point, the gods have disappeared from her account and she succeeds in giving an explanation for immortality without referring to them. So the actual work of ero¯s is accomplished independent of the gods, but the gods are nonetheless introduced in all the explanations for the origin and birth of ero¯s. Diotima explains how the mortal can partake of immortality without the gods. And she finally convinces Socrates: At the end of his speech (212b) he admits that he has been persuaded, that the ultimate goal of ero¯s is immortality, but not continuation of individual personal existence. She points out that even among the animals mothers are willing to die for their young, and she thus generalizes the phenomenon of ero¯s beyond human beings to other natural beings. Along with the double sense of preservation there is a double sense of pregnancy. Diotima introduces the notion that men can be pregnant in body or in terms of soul and it is this division of body and soul which introduces the ascent. Let us look closely at her formulation: Now there are those that are pregnant in terms of their bodies, she said, and they turn rather to women and are erotic in this way, furnishing for themselves through the procreation of children immortality, remembrance, and happiness (as they believe) for all future time (208e)

What are the implications of this? When they are pregnant in their bodies, men will be drawn to women for the sake of procreation. We must in this context remind ourselves of the ancient understanding of conception. According to Apollo in the Oresteia, the male seed contains all that is necessary, except the soil and nutrition, the material conditions necessary for

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the seed to unfold.8 This is in a speech made on behalf of Orestes, illustrating why killing a father is more heinous than killing a mother. The male sperm is understood to be already fertilized. The female contributes nothing other than matter, while the male provides the form.9 This conception of conception remains in place for a long time, though some later Hippocratic writers change the model, introducing female seed, and argue that both sexes contain both kinds of seed and that the sex of the child is determined by the proportion that each contributes.10 While it is clear that Plato knew of Hippocrates, it is not certain which, if any, of the surviving works in the Hippocratic corpus were actually written by Hippocrates, nor which of them Plato might have known. Although it is not entirely clear whether Plato subscribes to the “two seed” theory, he does put forward something we might call a “two pregnancy” theory. On the one hand we have the claim that men are already pregnant and that what we would consider conception is discussed as giving birth to the pregnant seed; on the other hand an additional pregnancy and birthing is needed in order for a child to be produced.11 Our word “impregnate” might be appropriate here—if taken literally, it means to implant that which is born (-[g]natus) beforehand (prae). According to Diotima the same kind of desire and process applies to the soul. But there are others who are pregnant in terms of soul—for these in fact, she said, are those who in their souls even more than in their bodies conceive those things that it is appropriate for soul to conceive and bear. And what is appropriate for soul? Prudence and the rest of virtue; it is of these things that all the poets and all the craftsmen who are said to be inventive are procreators (209a).

Thus, the cause of the desire (being pregnant) and the object of the desire (immortality) are ultimately the same for both body and soul, but the kinds of offspring generated are different. That difference is accounted for by the difference of the seed.12 Also, some have the seed and are pregnant, whereas others presumably are not, for Diotima clearly does not say that all are pregnant in body and soul. Why some are and others are not remains mysterious and unexplained in the text. Socrates makes the same point when, in explaining his skill as a midwife, he says that he is a very talented matchmaker: But sometimes, if I somehow get the impression, Theaetetus, that they’re not pregnant, in recognition of the fact that they don’t need me, I very kindly act as go-between and, with allowance made for a god’s help, guess very adequately by whose association they would be benefited. And many of them I gave in marriage to Prodicus, and many to different wise and divinely speaking men (151b).

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The suggestion that some are pregnant while others are not may seem to preclude using the theory of recollection to explain “psychic pregnancy.”13 In the Meno it is evident that Socrates introduces recollection as a universal phenomenon, applicable to all human beings, not just the special entitlement of the aristocratic privileged or the scientifically knowledgeable.14 This is apparent from the fact that he chooses as his partner one of Meno’s slaves and asserts that the only requirement is that he speak Greek. Much, however, depends on what exactly is presupposed by the theory of recollection.15 Telling a story he has heard from “wise men and wise women,” Socrates says that the soul is immortal and has seen all things and hence there is nothing it cannot learn (81c). He gives the name “recollection” to the process of learning by accessing what the soul already knows. But the theory of recollection does not necessarily entail that the soul contains all knowledge, but rather that it has the potential to learn all things. In fact, it is clear that Socrates does not believe that the soul has any kind of episte¯ me¯ prior to recollection; rather it can through recollection achieve episte¯me¯ . This can be seen most clearly in the concluding comment of Socrates’ demonstration, when he is explaining to Meno what has been accomplished: “So if in both of these periods—when he was and was not a human being—he has had true opinions in him which have only to be awakened by questioning to become knowledge, his soul must have had this cognizance throughout all time?” (86a). So the seeds for knowledge are within us but a process of fertilization is required to bring about pregnancy.16 Just as, in the physical and bodily realm, there comes a time when the already pregnant sperm are ready to exit, because they are ripe, so within the soul there are ideas or seeds of knowledge which are ready, through dialogue, to germinate on the outside.17 Just as “physical seed” pregnancy is not sufficient for producing a child, so the “intellectual seed” pregnancy needs further assistance. Both require an “other” to “welcome” and nourish the seed. Diotima’s story about the birthing of ideas concludes with the promise that anyone who ascends the steps up the ladder will, upon beholding the vast sea of beauty, “give birth—in ungrudging philosophy (en philosophia aphthono ¯ )—to many beautiful and magnificent speeches and thoughts” (210d) and “in seeing in the way the beautiful is seeable, will he get to engender not phantom images of virtue—because he does not lay hold of a phantom—but true, because he lays hold of the true; and once he has given birth to and cherished true virtue, it lies within him to become dear to god and, if it is possible for any human being, to become immortal as well” (212a). The ability to discriminate between the phantom and the real thing is not part of the midwife’s traditional chores, so that the philosophical midwives need additional skills for their ministrations to pregnant young men.

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3. MAIEUTICS The image of midwifery (maieutike¯ ) that Socrates uses to help Theaetetus confront his puzzlement is seductive and difficult. If the dialogues which ensue in the dramatic sequence—the Sophist and the Statesman—introduce us to possible “appearances” of “the philosopher,”18 then what are we to make of the appearance of the midwife here?19 While the philosopher might appear to others as a sophist or statesman, he appears to himself as a midwife.20 There is a fundamental difference among these three images of the philosopher, in that two of them seem unobjectionable, even reputable, pursuits, whereas midwifery would be viewed as a bizarre undertaking for young men. By choosing the likeness of the midwife to describe himself and his techne¯ Socrates seems to confirm the suspicion many people harbor that philosophy is not to be taken seriously. Many thinkers after Socrates have worked to change that picture of philosophy, hoping to achieve for it the same status and respect that most people willingly grant to mathematics and science, or even to sophistry and politics. But what if the analogy to midwifery is the true image of philosophy? What can we glean from it about the nature of philosophy? Socrates introduces his techne¯ of midwifery in response to Theaetetus’s exhibition of his mathematical techne¯, which had allowed him to solve the problem of the surds. When Socrates asks him to apply the same skill to the question of knowledge, Theaetetus makes the following confession: But know well, Socrates, it’s often that I tried to make an examination of it, in hearing the questions that are reported as coming from you. But for all that, I am myself incapable of either persuading myself that I say anything adequately or hearing someone else speaking in just the way you urge, and I’m incapable as well of getting rid of my concern with it (148e).

In response to this stunning revelation, that Theaetetus has been practicing at “being Socrates,”21 Socrates diagnoses Theaetetus as being pregnant and suffering labor pains. To this Theaetetus responds: “I don’t know, Socrates, but I’m telling you what I have experienced” (148e).22 It is in response to this frank but very curious statement at 148e that Socrates decides to tell Theaetetus his “secret” regarding the source and nature of his peculiar techne¯. The passage from 149a through 151d is fraught with difficulties of interpretation, especially if we assume that Socrates is supposed to be a moderate and modest, rather than hybristic, human being. He explains that he resembles midwives and in fact accomplishes more than they do: In addition to inducing or calming labor pains, aborting or assisting at a birth, it is his job to examine the newborn and, along with the interlocutor, determine whether it is a wind egg to be abandoned or a fruitful offspring to be nurtured.23 The most important aspect of his techne¯,

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Socrates emphasizes, is his ability to distinguish whether the offspring is “an image and a lie” (eido ¯ lon kai pseudos) or “something fruitful and true” (gonimon te kai ale¯thes, 150c). Socrates ascribes the “parentage” of his art to his mother, Phainarete: He does for the souls of young men what the midwife does for the bodies of pregnant women.24 And what exactly was the task of the midwife during the time of Socrates?25 Socrates assigns to midwives the following tasks: Recognizing those who are pregnant and those who are not; arousing labor pains through drugs and incantations; helping to abort; cutting the umbilical cord; and “they are all wise when it comes to getting to know what sort of woman must be with what sort of man to give birth to the best possible child” (149d). These tasks can be performed by women who themselves have given birth in the past, but who are now past menopause. Thus Socrates links the techne¯ of the midwife with first-hand experience: The midwife herself knows what it is like to be pregnant and to give birth. During Socrates’ time, however, the midwife was often replaced by the doctor, presumably male, whose administration to the pregnant woman was based on something other than personal experience. Yet in this dialogue Socrates identifies himself and his techne¯ with the midwife rather than the doctor. Elsewhere Socrates does not hesitate to use illustrations from medicine and to draw analogies between the philosopher and the doctor.26 Here in the Theaetetus, however, it is not a cure that is needed, but assistance in helping a “natural” process unfold. There is no need for a “professional” doctor. It turns out that Socrates resembles the goddess Artemis as well as his own mother. Phainarete, his mother, remains within the human realm to the extent that she herself experienced childbirth before becoming a midwife.27 Socrates, in contrast, professes that he is a virgin with respect to wisdom; yet he asserts that he is capable of assisting others in giving birth to wisdom. This is a startling claim, given Socrates’ contention that “human nature is too weak to grasp an art of whatever it is inexperienced” (he¯ anthropine¯ physis asthenestera e¯ labein techne¯n ¯on an e¯ i apeiros, 149c). This, he claims, is the reason that Artemis will not allow barren women to become midwives. In contrast to human beings, the gods do not depend on experience and thus it is the virgin Artemis who is the goddess of childbirth. Artemis is summoned by the cries of laboring women; however, she is associated not only with the comforting of women and the easing of their pain, but with striking some women dead during childbirth as well. The identification of Socrates with Artemis can be associated with the fact that it was her twin brother, Apollo, who defined Socrates’ mission. The “parentage” through Artemis makes Socrates midwife to individuals, whereas the “parentage” through Apollo makes him gadfly to the entire city of Athens. Apollo’s proclamation through the oracle at Delphi that no

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one was wiser than Socrates, was used by Socrates as grounds for recognition of his sterility with respect to wisdom. In the Apology Socrates says: “What is probable, gentlemen, is that in fact the god is wise and that his oracular response meant that human wisdom is worth little or nothing, and that when he says ‘this man, Socrates,’ he is using my name as an example, as if he said: ‘This man among you, mortals, is wisest who, like Socrates, understands that his wisdom is worthless’” (23a–b).28 And in the Theaetetus he says, “I am sterile of wisdom . . . because I don’t have anything wise. . . . The god compels me to midwife and prevented me from generating”29 (agonos eimi sophias . . . dia to me¯ den echein sophon . . . maieuesthai me ho theos anakazei, gennan de apeko¯lusen, 150c).30 And so, pleasing one god, Apollo, and imitating his twin sister Artemis, the fruitless Socrates goes about administering to young men fruitfully.31 Just as Artemis is unwed (alochos), so Socrates is sterile (agonos), if not indeed speechless and witless (alogos) with regard to wisdom. After allowing Theaetetus to assent to the identity of episte¯ me¯ and sophia (145e), Socrates expresses the aporia about the nature of knowledge, which in fact fuels the entire dialogue. In contrast, it is wisdom which is central to the maieutike¯ passage. The dialogue as a whole is thus concerned with episte¯ me¯, whereas Socrates’ self-revealing soliloquy focuses on wisdom, or, more precisely, on the absence of wisdom.32 To make sense of this, we return to the point where Socrates says that his techne¯ enables him to distinguish between “an image and a lie” on the one hand and “something fruitful and true” on the other (150c). The link between the fruitful and the true may give us an inkling about the difference between Socrates’ barrenness respecting wisdom and Theaetetus’s fruitful endeavors in mathematics and episte¯ me¯. In contrast to the image, the true is properly considered fruitful and it is precisely this fecundity that distinguishes an image from that of which it is an image: Images within this framework are asexual and cannot reproduce. But that which is fruitful is also in motion and change, which seems to call into question our speaking of “the true.” This is in fact the problem and the task of episte¯ me¯ —to reveal what is true about change, to find that which underlies change but is itself unchanging. How is it that midwifery led to conceding that none of Theaetetus’s “brain children” were “fruitful and true,” that all were “images and false”? What enables Socrates to distinguish between the fertile thoughts and sterile “wind eggs” (anemiaia, 151e, 210b)? The test that Socrates uses is best characterized as an application of the elenchos. Socrates shows that the definitions of knowledge in terms of perception, in terms of opinion, and in terms of true opinion plus an account (logos) either lead to contradiction or they are circular—and they thus end in aporia. It is, so to speak, the exercising of the child’s dialectical muscle that determines its fate. But

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it remains a question why an aporetic conclusion should be required for such a complex and involved dialogue. A variety of definitions of knowledge are drawn upon here—if only in outline—yet Theaetetus and Socrates look forward to another day, to see if they can do better next time. There are at least two ways to explain the failure. One possible explanation would lay out the ways in which Theaetetus’s answers were either fruitful but not true, or true but not fruitful, or neither fruitful nor true. The other explanation relates to the initial equation of knowledge and wisdom. We will return to this point in the final chapter. The barrenness of Socrates in his philosophical maieutics has further implications for the nature of philosophy in general. It contributes both to the sense of the worthlessness of philosophy that so many people seem to experience upon their first confrontation and to the demarcation of philosophy from all other disciplines. The image of the sterile and barren Socrates underlines that philosophy calls nothing its own and that it thus permits the greatest amount of liberty to its pursuer. At 151c Socrates indicates that we are often attached to our opinions in the way many parents are attached to their children, who leave no room for critical evaluation and only permit praise for their own. Insofar as Socrates never treats an idea or opinion as a possession, he is free to dispose of those notions that prove to be false or inconsistent, instead of having to defend the indefensible. An emptiness that grants liberty surely is not a worthless nothing, but it is fruitful in its own peculiar way. It is Socrates’ explication of midwifery that explains why philosophy is dialectical and must be in the form of dialogue. Philosophy, insofar as it is empty, is in need of an “other” to provide it with nourishment. Socrates is explicit about his need for the city and he rejects the notion that philosophy can be a solitary walk through nature.33 In both the Phaedrus and the Republic, Socrates reiterates his need for other human beings. At Phaedrus 230d, responding to Phaedrus’s question of why it is that he has never set foot outside the walls of the city, he says, “You must forgive me, dear friend; I’m a lover of learning, and trees and open country won’t teach me anything, whereas men in town do.” And in the Republic (519–521b), the escaped prisoner is not permitted to dwell in contemplation, but must return down into the cave, even at the risk of death. The philosopher is not allowed to break free from the political, for, according to the argument of the Republic, he is the product of the political and must pay his dues.34 What is it then that the philosopher has to offer? In relation to the whole of the city Socrates offers his services as a gadfly, to “bug” the sluggish city and persuade each and everyone to care for virtue.35 It is when we look to the interaction with the individual that we can appreciate Socrates’ maieutike¯. A telling explanation of the Delphic injunction to self-knowledge comes in Alcibiades I, when Socrates is trying to convince Alcibiades that he

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is the only true lover Alcibiades has ever had, for he alone is concerned with Alcibiades himself rather than his belongings. Socrates is not interested in Alcibiades’ body or wealth, but rather in his soul. In this context (132cff) Socrates tells Alcibiades that the only worthy illustration of “Know Thyself” is “See Thyself” and this he interprets to mean the following: “Would it not be, that the eye should look at something in looking at which it would see itself?” (132d). It turns out that the pupil of the eye provides such an experience, for it reflects the looker. Socrates, the midwife, is the pupil that allows others to see themselves. It is his ability to reflect that makes Socrates’ emptiness such a fruitful one. It is only possible for someone to serve as a mirror if she does not darken the surface with her own distortions. In contrast to the techniques of the sophists, who are full of themselves and leave no room for reflection, Socrates’ techne¯ provides the occasion for self-examination. The sophist assumes that the pupil is empty and inscribes his teachings on the student. If successful, the sophist can enjoy watching images of himself. Socrates, on the other hand, approaches young men that appear to be full and pregnant and relieves them by letting them examine their opinions and thus find out whether the positions they hold are their own and worthy or whether they should be abandoned. The philosopher is the only one who does not need to play at a contest between opinions, who is not measuring “your” opinion against his own, but is entirely committed to letting you “see for yourself.” Thus Socrates, when Theaetetus is unsure whether he is “speaking [his] very own opinion” or “testing me,” says: You don’t remember, my dear, that it’s I who neither know nor adopt (produce) anything of the sort as mine, for I am incapable of generating them. . . .” (157c). The fact that the Theaetetus leaves the question of knowledge open, in aporetic fashion, should not exclude recognition of the positive accomplishments of maieutics. An aporia induced by the midwife’s skills is not merely a failure or an impasse. The Euthyphro, a dialogue which follows the Theaetetus in dramatic sequence, concerns the definition of piety and also ends in circularity; but something has been accomplished. Euthyphro arrived at the courthouse ready to prosecute his father for murder with a case questionable at best, but which he defends in the name of piety. The accomplishment of that dialogue is that Euthyphro leaves the conversation and, given the setting, we can conclude that he left the courthouse and at least for the time being is not prosecuting his father. It is possible, of course, that he was hiding behind some Doric column, waiting for Socrates to conclude his business and then returned, but that seems improbable. He left when Socrates proposed that they should begin the investigation of piety once again from the beginning. In the Theaetetus Socrates concludes with the following remarks, indicating clearly, that he does not consider the dialogue a failure:

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Well, then, if you try to become pregnant, Theaetetus, with different things after this, and you do become so, you’ll be full of better things on account of the present review. And if you’re empty, you’ll be less hard on your associates and tamer, believing in a moderate way that you don’t know what you don’t know. My art is capable of so much and no more, and I don’t know anything at all which everyone else does, all those who are and have been great and amazing men. But my mother and I have obtained from a god as our lot this midwifery, she of women, and I of the young and noble and all the beautiful. Now, however, I have to go to the porch of the king and meet the indictment of Meletus which he’s drawn up against me. But at dawn, Theodorus, let’s come back here to meet (210c–d).

Theaetetus knows that he does not know the answer to the question “What is knowledge?” He also knows that what he thought to be the answer is not the final answer. Theaetetus is on his way to self-knowledge.

4. IS THEAETETUS BEAUTIFUL? Of the many and varied references to beauty in the Theaetetus perhaps the most extraordinary is Socrates’ exclamation at 185e: “Why, you are beautiful, Theaetetus, and not as Theodorus said, ugly; for he who speaks beautifully is beautiful and good (kalos te kai agathos).”36 When in the outer frame of the dialogue Euclides runs into his fellow Megarian Terpsion, he explains that he has just seen Theaetetus being carried out of town on a stretcher, suffering from war wounds and dysentery. Terpsion questions him as to the kind of person he is speaking about, and Euclides answers that it is of someone kalon te kai agathon, that Theaetetus is both beautiful and good. Euclides arrives at this assessment on the basis of Theaetetus’s courage in war as well as Socrates’ prediction that Theaetetus would become ellogimon, a notable person. This evaluation refers to Theaetetus’s beautiful soul and character, not to his dying, decaying body, nor to the youthful body that Theodorus found unsightly. Thus Theaetetus is identified as kalok’agathos before he is even presented to us as a “live” character. Why then is it necessary for Socrates to repeat this affirmation that Theaetetus is beautiful? In the inner frame, when Socrates asks Theodorus if he knows of any young Athenians who “devote themselves to geometry and other forms of philosophy . . . who are expected to prove good and able (epidoxoi genesthai epieikeis)” Theodorus replies: Indeed, Socrates, it is well worth while for me to talk and for you to hear about a splendid young fellow, one of your fellow citizens, whom I have met. Now if he were kalos, I should be very much afraid, lest someone should think I was in love (epithumia) with him. But the fact is—now don’t be angry

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Theodorus not only says that Theaetetus is ugly, but this introduction itself seems to underline the absence of eros in this situation. As such this opening contrasts clearly and strongly with the Charmides, where Socrates, back from Potidaea, seeks out young men “distinguished for wisdom or beauty or both” (153d) and then has an explicitly erotic reaction to the sight of Charmides. Whereas Charmides is a “philosopher and a poet” (154e), however, and Plato’s relative, Theaetetus is a mathematician and, it turns out, Socrates’ look-alike. Just as Euclides, in his editing of Socrates’ relation of the original conversation, cut out all the things in between (ta metaxu), so Theodorus suppresses ero¯s by insisting on an absence of beauty. Theodorus thus implies that he himself is free from desire (epithumia), by virtue of the fact that he judges that Theaetetus is not beautiful. Having purged any aura of the erotic, Theodorus proceeds to praise Theaetetus, ascribing to him all the qualities delineated in the Republic as characteristics of a philosopherking: a quick intelligence, gentleness, and courage. He concludes his description with an awkward analogy: “But this boy advances toward learning and investigation smoothly and surely and successfully, with perfect gentleness, like a stream of oil that flows without a sound, so that one wonders (thaumasei) how he accomplishes all this at his age” (144b). Theaetetus is thaumastos instead of kalos, according to Theodorus, and it is curious that he should think that his being awe-struck by Theaetetus would leave him free from desire. Of course, this description of Theaetetus as such a wondrous fellow is confirmed by both Theaetetus himself and by Socrates, when Theaetetus expresses his sense of wonder and when Socrates delineates the three principles that identify those things that do not change: THEAETETUS: By the gods, Socrates, I’m overwhelmed by wonder (thaumazo¯) when I think about these things and when looking at them I get dizzy. SOCRATES: Theodorus seems to be a pretty guesser about your nature. For this feeling of wonder (thaumazein) shows that you are a philosopher, since wonder is the only beginning of philosophy and he who said that Iris was the child of Thaumas made a good genealogy (155c–d).

So Theodorus was correct in his assessment of Theaetetus’s soul But is wonder (thaumastos) then a quality of soul that can substitute for beauty with respect to philosophy? To answer this question we must refer to the genealogy of Iris, the child of Thaumas, as presented in Hesiod’s Theogony

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[775] And there [in Hades] dwells the goddess loathed by the deathless gods, terrible Styx, eldest daughter of back-flowing Ocean. She lives apart from the gods in her glorious house vaulted over with great rocks and propped up to heaven all round with silver pillars. [780] Rarely does the daughter of Thaumas, swift-footed Iris, come to her with a message over the sea’s wide back. But when strife and quarrel (eris kai neikos) arise among the deathless gods, and when any one of them who live in the house of Olympus lies, then Zeus sends Iris to bring in a golden jug the great oath of the gods [785] from far away, the famous cold water which trickles down from a high and beetling rock.37

So Iris is a messenger-god—she appears as such over three dozen times in the Iliad—and to that extent she closely resembles Hermes. We can add to this the fact that Iris is also the rainbow, which connects the sky and the earth, and in that respect she resembles Hermes even more closely: like him she is the link between the human and the divine. It looks as though Socrates is secretly reintroducing ero¯s into the dialogue after Theodorus had worked so hard to eliminate it—ero ¯ s, the go-between messenger daimo ¯ n of the Symposium. And Socrates will also work on reintroducing the kalos, initially by calling Theaetetus’s logos beautiful and finally by linking beautiful speeches to a beautiful soul. The first time that Socrates praises one of Theaetetus’s answers is at 148a, in response to Theaetetus’s explanation as to how he and young Socrates arrived at a solution to a problem which Theodorus could only partially solve. Theaetetus describes how they watched Theodorus drawing geometrical figures in the sand to examine incommensurables and to represent surds, but that they observed him get stuck at the number seventeen. Theaetetus and Young Socrates were able to devise a way to collect all the numbers and represent one set as “square” numbers, the numbers whose roots are rational, and all the others as “oblong or rectangular” numbers, whose sides represented irrational numbers or surds. In response, Socrates proclaims “Kallista,” most beautiful! (148a), as well as “Arista,” the best! (148d). In the Republic, book 7, when Socrates outlines the stages of advanced education, including extensive mathematical training, there is a particular task the students must be able to perform before they can be considered ready for dialectics: And after that, that is to say, from the age of twenty, those who are chosen will also receive more honors than the others. Moreover, the subjects they learn in no particular order as children they must now bring together too from a unified vision of their kinship both with one another and with the nature of that which is. . . . It is also the greatest test of who is naturally dialectical and who isn’t, for anyone who can achieve a unified vision is dialectical, and anyone who can’t isn’t (537b–c).

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One interpretation of Theaetetus’s mathematical accomplishment would be to say that, unlike Theodorus, he was able to create a unified vision of surds, whereas Theodorus proceeded case by case. If so, we can understand why Socrates excitedly proclaimed “Kallista” and “Arista,” because he has found a soul ready to begin training in dialectics, the final step of education for the philosopher-king according to the Republic.38 At 159b Socrates again praises Theaetetus, saying, “You’ve got it most beautifully” (kallista hupelabes).39 The preceding discussion was concerned with testing Theaetetus’s definition of knowledge as perception and whether he is committed to accept that everything is always in a state of becoming. Socrates introduces the problem whether something which is different in every other way cannot still share qualities with something else, illustrating this by the interaction between the two elements of perception, the passive and the active, and maintaining that the active in fact transforms the passive and makes it other. Socrates uses himself as an example: SOCRATES: Well, then, let us take me, or you, or anything else at hand, and apply the same principle—say Socrates in health and Socrates in illness. Shall we say that the one is like the other, or unlike? THEAETETUS: When you say “Socrates in illness” do you mean to compare that Socrates as a whole (holon) with Socrates in health as a whole? SOCRATES: You grasp this most beautifully.

Here the introduction of holon earns Socrates’ praise, for if he can indeed conceive of the whole, he has already refuted the thesis that everything is becoming. And he has taken another step toward showing himself to be the philosopher. By identifying the sick Socrates and the healthy Socrates,40 each as a whole and each as completely other than the other, Theaetetus demonstrates that we do not have one becoming two, but rather two different ones. It is in his grasping of being over becoming which elicits a “most beautiful!” from Socrates. The most serious praise poured upon Theaetetus is at 185e, where Socrates observes: “It’s because you are beautiful (kalos), Theaetetus, and not, as Theodorus was saying, ugly. For whoever speaks beautifully is beautiful and good.” This occurs toward the end of the final refutation of the first definition of knowledge as perception. After Socrates has concluded his discussion with Theodorus, refusing to discuss Parmenides and Being, he returns to Theaetetus as interlocutor. In explaining his shame and fear before Parmenides, Socrates quotes half a line from Homer’s Iliad “as awesome to me as [they are] uncanny,” words spoken by Helen to Priam. Benardete comments: “The ugliest of men, whom the gods had made barren of wisdom, compares himself with the most beau-

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tiful of women, whom the gods punished with barrenness for her crime. Now that he has done with Theodorus, he repudiates Theodorus’s competence to judge his looks.”41 Socrates declares that he himself is beautiful, before he acknowledges the beauty of his look-alike. Socrates asks Theaetetus whether we perceive with or through the eyes and ears? When, after some prodding and insistence on precision by Socrates, Theaetetus replies that it is through the eyes and ears, Socrates replies: That’s because it’s surely dreadful, my boy, if many kinds of perceptions sit in us as if in wooden horses, but all these do not strain together toward some single look (idea), regardless of whether it’s soul or whatever one must call it, by which we perceive through (dia) these as if they are tools of all the perceived and perceptible things (184d).

The introduction of the preposition dia brings with it the need for an agent who uses the tools to collect sense-data. The instrumental dative is indifferent whether it’s the eye seeing or something seeing with the eye.42 The examination focuses on the limitations each sense-organ had, that is, the eye can see but it cannot see sound, and the ear hears but it cannot hear color. And if one wanted to determine whether what is seen is salty or sweet, neither the eye nor the ear would be of any help. In addition to the limitation in terms of function, Socrates also stresses that there needs to be some tool which can unite all the different perceptions into a single whole, and judge them severally as individuals, and compare them all with one another. It is in response to this questioning that Theaetetus states: THEAETETUS: You mean being and to be not and similarity and dissimilarity and “the same” and other and, further, one and the rest of number about them. It’s plain that you’re asking about both even and odd as well, and everything else that follows them, though which of the things of the body do we perceive them by means of the soul. SOCRATES: You’re following exceedingly well, Theaetetus, and these are the very things I’m asking about. THEAETETUS: But, by Zeus, Socrates, I for one could not say except that I’m just of the opinion, that there is no private (peculiar) tool of that sort at all for these things as there is for those, but that soul itself through itself (aute¯ di’ haute¯s), it appears to me, examines the common things about all of them. (185c–e)

Theaetetus’s assertion that it is soul itself through itself examining being and not-being, same and other, as well as number, is what causes Socrates to proclaim Theaetetus’s beauty. Socrates’ introduction of ero ¯ s and beauty into the Theaetetus is best understood as supplying charms and assistance to the pregnant young Theaetetus,

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who is said to undergo birthing. Diotima teaches that we can only give birth in beauty: “And he goes round in search, I believe, in which he might generate; for he will never generate in the ugly. . . . So in touching the one who is beautiful, I suspect, and in association with hem, he engenders and gives birth to offspring with which he was long pregnant” (209b–c). Theodorus thought that both Socrates and Theaetetus were ugly; thus it is important for Socrates to counter that claim, if birthing is to be possible. Even though Socrates insists that he is barren and sterile with respect to wisdom, Theaetetus’s beauty moves Socrates to generate such lively issues as the investigations of Protagoreanism, Heraclitean ontology, opinion, and logos. Although Socrates disavows all these speeches, claiming they are not his own, just as Plato abnegates responsibility for the dialogue by identifying Euclides as its author, the upshot of the dialogue is that it offers a comprehensive and detailed examination of the possible definitions of knowledge.

5. CONCLUSION When we weave together passages from the Theaetetus and the Symposium, along with relevant themes from other dialogues, we come to a better understanding of the fabric of philosophy and gain insight into the difficulties involved in defining knowledge in isolation. If philosophy is understood in terms of the skills Socrates claims for himself, erotics and midwifery, then it has an inherent need for an “other”—we might call this its “parasitic” nature. It does not so such matter whether it be the poet, the politician, or the craftsman—each can contribute to the philosopher’s selfunderstanding. In his defense speech Socrates declares that he is wiser than they are: At least he knows that he does not know. But that sort of knowledge can only be had from encounters with these “others.” Diotima’s teaching shows Socrates that ero ¯ s, as desire for the beautiful and for immortality, points to the consciousness of incompleteness, the awareness of a lack within us. Similarly, in his insistence on his own sterility and barrenness in his discussion of midwifery, Socrates underlines the essential emptiness of philosophy. Philosophy, as depicted in these two dialogues, is not self-sufficient. It needs to discover content through an “other” in order to approximate its goal, sophia. To that extent the question of the nature of philosophy is parallel to the problem of self-knowledge as discussed in the Phaedrus, where Socrates explains his need for the city and his lack of interest in demythologizing nature.43 And again, later in the Phaedrus, after Socrates himself mythologizes the soul in order to give a proper account of ero¯s, Socrates concludes his elaborate story of the journey of the soul, as it regains its wings, by asserting that the “other” in the relationship becomes as a mirror to the beloved.44

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The juxtaposition of the Symposium and the Theaetetus helps to clarify the aporetic conclusion of the attempt to define knowledge in the Theaetetus. Diotima’s insistence that knowledge, like desire and physical processes, is ever changing and that its preservation requires study and care, points toward the necessary presence and involvement of the knower. The “who” is as important as the “what”; knowledge demands a personal connection. There is a difference between mathematical and philosophical knowledge and the way that each is communicated. It may not be necessary to give an account of the knower in defining every type of knowledge; but the knowledge which aspires to wisdom requires such an account. Given this peculiar nature of philosophy, it is unsurprising that its transmissibility is problematic. The respective frames of the Theaetetus and Symposium throw light on different attempts to preserve Socratic philosophizing and transmit it to future generations. On the one hand, we see Euclides’ detached, edited, “objective” account of what had been narrated to him by Socrates. On the other, stands the impassioned disciple who renarrates the speeches on love told to him by a lover of Socrates—a highly “subjective” version. Each in its way demonstrates why philosophy cannot be written down—the former by turning a philosophical dialogue into mathematical formula, as it were, where the connection between knower and known is severed; the latter by overemphasizing the personal connection. Both point to an unreliability that obliges the reader to become involved in the attempt to reconstitute the meaning of the original dialogue. In his Letters, Plato writes that philosophy cannot be written down;45 and the later part of the Phaedrus points to the problematic nature of writing. And yet, if philosophers desire to communicate with future readers and interlocutors, they cannot rely exclusively on oral transmission by their disciples.46 And so Plato writes dialogues that mirror the nature of philosophy, dialogues that are erotic and maieutic, seducing the reader into giving birth to ideas and testing those ideas against the claims of other interlocutors and of Socrates himself. NOTES 1. Some recent articles, noted below, connect intellectual pregnancy with recollection, and there is a long-standing debate whether or not midwifery implies or presupposes the theory of recollection; to my knowledge, however, the only article that deals with all three themes and dialogues—the Meno, Symposium, and Theaetetus—is Miles F. Burnyeat, “Socratic Midwifery, Platonic Inspiration,” Bulletin of the Institute of Classical Studies (1977), 24:7–16, reprinted in Hugh M. Benson, Essays on the Philosophy of Socrates (Oxford and New York: Oxford University Press, 1997), 53–65.

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2. See this passage from Socrates’ “Second Speech” on Love in the Phaedrus (255 c–d) “Think how a breeze or an echo bounces back from a smooth solid object to its source; that is how the stream of beauty goes back to the beautiful boy and sets him aflutter. It enters through the eyes, which are its natural route to the soul; there it waters the passages for the wings, starts the wings growing, and fills the soul of the loved one with love in return. Then the boy is in love, but has no idea what he loves . . . ; he does not realize that he is seeing himself in the lover as in a mirror. . . .” Plato, Phaedrus, trans. and ed. Alexander Nehamas and Paul Woodruff (Indianapolis and Cambridge: Hackett Publishing Co., 1995). 3. This proposition also suggests a relation between the party at Agathon’s house in the Symposium and the famous Hermocopidae, the profanation of the mysteries just prior to the Sicilian expedition. See Stanley Rosen, Plato’s Symposium, 7–8. 4. “I pursue the same techne¯ ?” (epite¯ deuo¯ te¯ n aute¯ n techne¯ n). 5. Consider Meno 97c–e in this context, where Socrates, differentiating between opinion and knowledge, compares true opinions to the statues made by Daedalus, so life-like that they are prone to run away. 6. The goal of the discussion is to determine how human beings become virtuous and whether virtue can be taught. Socrates concludes his investigation with the suggestion that virtue might be a gift from the gods. Diotima in contrast offers a more concrete answer to the question of virtue by showing that it is the end result of ero¯s which enables the one who has climbed the ladder of love to give birth to true virtue in the contemplation of true beauty. 7. Poros means both “opening” (“pore”) and “wealth” or “resources. Thus aporia can be either an “impasse” or a “lack of resources.” 8. Aeschylus, Eumenides 657ff. 9. Consider also Aristotle, On the Generation of Animals 1.20.729a. 10. “The Seed” 6: “What the woman emits is sometimes stronger, and sometimes weaker; and this applies also to what the man emits. In fact both partners alike contain both male and female sperm. . . .” Hippocratic Writings, ed. G. E. R. Lloyd, trans. J. Chadwick and W. N. Mann. (Harmondsworth, UK: Penguin Books, 1978 [1950]), 320. 11. R. G. Bury put forward the notion that “Agathon is the embodiment of that kallos which here stimulates the eraste¯ s in his search for truth: It is in Agathon’s soul (en kalo¯i) that Socrates deposits the fruits of his pregnant mind.” Cf. R. G. Bury, The Symposium of Plato, 2nd ed. (Cambridge: W. Heffer & Sons, 1932), xxxviii. 12. We should also note the comment about poets and inventive craftsmen who are mentioned as procreators of virtue. Diotima has mentioned the poets in connection with lovers (205a–d), when she discussed the phenomenon of a part of a class receiving the name of the whole. Just as there are many kinds of makings (poie¯ sis), it is only those who do their “making” in meter and rhythm who receive the designation “poet.” Similarly with lovers, honor-lovers, wisdom-lovers, and others are not designated as “lovers,” but only those “who earnestly apply themselves to a certain single kind, get the name of the whole, love, and are said to love and are called “lovers” (erastai, 205d). The analogy between lovers and poets is striking in the light of the discussion of poetry in Republic 10, where the poet as

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creator of virtue is chided for being thrice removed from the good and painters as makers of beds thrice removed from the truth. 13. See Frisbee C. C. Sheffield, “Psychic Pregnancy and Platonic Epistemology,” Oxford Studies in Ancient Philosophy, ed. David Sedley 20 (Summer 2001): 1–33. 14. Consider Meno 81c–e, where Socrates introduces the theory of recollection. 15. See Glenn Rawson, “Platonic Recollection and Mental Pregnancy,” Journal of the History of Philosophy 44, no. 2 (2006): 137–55. Rawson argues (144–48) that the mental pregnancy of the Symposium is the next step of development in Plato’s epistemology and is derived from the theory of recollection. Unlike recollection, however, the pregnancy model indicates that that which is within us is an embryo that needs to develop before it can be considered knowledge. Rawson uses the ladder of love to support this claim—that is, the initial pregnancy involves a potentiality for and toward the development of knowledge. 16. For a fuller and persuasive discussion of the connection between the theory of recollection and psychic pregnancy see Rawson, “Platonic Recollection and Mental Pregnancy.” 17. See Rawson, “Platonic Recollection and Mental Pregnancy,” 25–33. In this section of her paper examining mental pregnancy and the theory of recollection Sheffield argues that what she calls “psychic pregnancy” is an alternative to recollection. It is an improvement on that theory because, on her view, Plato succeeds in the Symposium in separating his epistemology from the belief in immortality. According to her argument, Plato here develops something much closer to what Leibniz was looking for—a notion of innate ideas that does not depend on any notion of the preexistence of the soul. 18. See Sophist 217a–b. 19. See Harold Tarrant, “Midwifery and the Clouds,” The Classical Quarterly, n.s., 38, no. 1 (1988): 116–22. Tarrant argues convincingly that Plato did not borrow this image from Aristophanes in the Clouds. Aristophanes depicts Strepsiades as miscarrying a “brain-wave.” I agree with Tarrant that an audience could only find this particular sequence funny if they first had some inkling about Socrates the midwife. And Plato certainly knew the play well. But the other crucial elements of the analogy—barrenness, examining, matchmaking—are entirely absent from Aristophanes. 20. See Julius Tomin, “Socratic Midwifery,” Classical Quarterly 37 (1987): 97–102. 21. See Ruby Blondell, The Play of Character in Plato’s Dialogues (Cambridge: Cambridge University Press, 2002), 263, who clarifies the contrast between a second-hand imitation of Socratic method and a first-hand encounter with Socrates himself. 22. My translation. 23. For the significance of “wind eggs,” or unfertilized eggs, in ancient biology and philosophy see Lesley Ann Dean-Jones, Women’s Bodies in Classical Greek Science (Oxford: Clarendon Press, 1996), 161, 206. 24. David Sedley, The Midwife of Platonism: Text and Subtext in Plato’s Theaetetus (Oxford: Clarendon Press, 2004), discussing midwifery (28–38) and recollection (29), straddles the middle ground: Socrates (“innocent of any heavy-duty metaphysical or epistemological theory”) has no theory of recollection, but Plato does. And so it is Socrates who puts forward the aviary model of knowledge, with the

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mind empty at birth, whereas Plato is hinting at recollection in the midwife passage. 25. See Nancy Demand, Birth, Death, and Motherhood in Classical Greece (Baltimore and London: Johns Hopkins University Press, 1994), 63–68, 130–34; Helen King, Hippocrates’ Woman: Reading the Female Body in Ancient Greece (London and New York: Routledge, 1998), 40–53; Dean-Jones, Women’s Bodies in Classical Greek Science, chap. 3. 26. Consider especially Gorgias 464b–465c and the subsequent references to this analogy; his pretense that he can cure headaches at Charmides 155e; interesting references at Lysis 209e–210a, Phaedrus 270c, and in numerous passages of the Republic and elsewhere. 27. Literally, the name means “the woman bringing virtue to birth” or “the woman bringing excellence to light.” 28. Translations of the Apology are based on G. M. A. Grube, trans., Plato Five Dialogues (Indianapolis: Hackett Publishing Co., 1981). 29. This starkly contradicts all those who characterize Socrates as a lover who impregnates young men. See Kenneth Dover, Greek Homosexuality (Cambridge, Mass.: Harvard University Press, 1977): Dover concedes that there is some similarity, but he maintains that there is “a profound difference too; a midwife’s role is not a progenitor’s, and in Theaetetus 150c–d Socrates denies his own fertility” (151). 30. Burnyeat speaks otherwise of the Symposium: “In the Symposium the great lover in the spiritual sense is Socrates himself, . . . [it is] he therefore who is most fruitfully pregnant, while it is not Socrates but Beauty, present in the boy, who has the midwife’s office of relieving travail (206d),” “Socratic Midwifery,” 8. 31. See Radcliffe G. Edmonds III, “Socrates the Beautiful: Role Reversal and Midwifery in Plato’s Symposium,” Transactions of the American Philological Association 130 (2000): 261–85. 32. See Ronald M. Polansky (Philosophy and Knowledge: A Commentary on Plato’s Theaetetus [Lewisburg, Pa.: Bucknell University Press, 1992], 62–65), who emphasizes that Socrates’ barrenness is with regard to wisdom, not opinions or thoughts in general. Polansky develops the notion of divine barrenness, which he relates to being barren with respect to opinion, and introduces that as the goal which Socrates has in mind when he talks about becoming as divine as possible. 33. See Cratylus 440e. 34. The Crito can be interpreted as making a similar point. 35. See Apology 29e–31c. 36. I disagree with Radcliffe G. Edmonds III (“Socrates the Beautiful”) when he argues that it is the beauty of Socrates which acts as the midwife in the Symposium. Among other things, he never clarifies what exactly Socrates’ beauty brings to birth. It is hard to see how “generating in beauty” can be identified with midwifery. Socrates’ beauty is internal rather than external, which makes it unlikely that all “eligible” interlocutors would have access to it. As is clear from Socrates’ actions as a midwife in the Theaetetus, he tries to “create” beauty in Theaetetus, as I discuss below. 37. Hesiod, Theogony, in The Homeric Hymns and Homerica, trans. Hugh G. EvelynWhite (Cambridge and London: Harvard-Heinemann, 1954), 135–37.

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38. See Republic 7.532a–535a. 39. Hupolambano—to take up from below, take up by getting under, take on one’s back—is a verb used, among other things, to describe the up- and downward motion of dolphins. The more conventional rendition would be “You grasp this most beautifully,” that is, from the inside. 40. Perhaps we are also to draw a parallel between the sick Theaetetus of the outer frame and the healthy Theaetetus of the dialogue proper. 41. Seth Benardete, Plato’s Theaetetus: Part I of The Being of the Beautiful (Chicago and London: University of Chicago Press, 1986 [1984]), 142. 42. See Benardete, Plato’s Theaetetus, 142–44. 43. Phaedrus 229e–230a: “But I have no time for such things; and the reason, my friend, is this. I am still unable, as the Delphic inscription orders, to know myself; and it really seems to me ridiculous to look into other things until I have understood that.” 44. See Phaedrus 255c–d. 45. See Epistle 7.341b, 344c. 46. Numerous ancient philosophers did precisely that: Pythagoras, Socrates, Pyrrho, and others.

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y far the longest investigation in the Theaetetus concerns the first hypothesis that the young mathematician proposes, that perception is knowledge. The discussion of perception is so lengthy and rich, because Socrates relates Theaetetus’s answer to Protagoras’s teaching that “human being is the measure” as well as Heraclitus’s pronouncements concerning motion and flux. The task at hand is to arrive at a convincing formulation of the interconnections among the three claims, and to explain how they culminate in Socrates’ account of the mechanism of perception, an account that is precise and detailed and which remains unrefuted in the dialogue, but which nevertheless he calls “the myth of twin motion” (156c). In addition we must pay particular attention to the way in which Socrates guides Theaetetus toward the discovery of soul, leading him from the realm of the visible to the invisible. This particular step can be taken as evidence that Socrates is attempting to guide Theaetetus out of the cave—which will be discussed in detail in the final chapter; but the fact that there is an ascent in the Theaetetus should be evident by the end of our analysis of perception in this chapter. Midway in the analysis whether perception is or is not a viable candidate for a definition of knowledge, Socrates seduces (or perhaps forces) Theodorus into taking part in the discussion, and in that “digression” the two discuss the nature of the “true” philosopher, which mimics an ascent. Throughout their discussion on perception Socrates calls Theaetetus and his logoi beautiful, supporting Diotima’s claim that we can only give birth in the presence of beauty. It is clear, then, that Socrates is mindful of the erotic starting point of the quest for philosophical knowledge. He once 67

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again demonstrates that he was a good student who has learned his lessons from Diotima. It is fitting that Socrates introduces beauty during the discussion of perception, because, as we saw in the previous chapter, the initial experience of ero¯s is triggered by perception. Like perception, ero¯s cannot be completely separated from the body. At the same time Socrates proves to be masterful in instilling wonder and dizziness in Theaetetus through his use of Heraclitus and Protagoras, enabling Theaetetus to move from perception and the visible realm to opinion and logos in the invisible realm. It will be the paradoxical nature of perception that calls for the introduction of opinion (doxa), making the ascent possible. Finally, we need to assess the role that the examination of perception plays in guiding Theaetetus toward self-knowledge. In the final segment of the passage on perception it becomes clear that Socrates is intent on sorting out and discovering what capacities are involved in the act of perceiving. He makes it clear that we, as human beings, never stop with sense-awareness, but proceed to form an opinion or judgment about whatever it is that we are sensing. It is on account of this added capacity that we are capable of error—or prone to error, as the case may be—and by implication it is because of perception that we are capable of hitting upon the truth. Socrates wants to clarify the contribution of the body through the sense organs and the contribution of the soul (psyche¯ )1 through its ability to identify and judge what has been reported by the senses. Socrates explains perception as a cooperative endeavor between body and soul and it is through this recognition that both body and soul are involved, that he can proceed, attempting to isolate the soul’s contributions. It turns out that it is through a kind of self-reflection that Theaetetus discovers the work of soul. In the Theaetetus Socrates accomplishes dialectically what he achieved in Republic 5–7 by using images and analogies. Rather than accepting the mathematical manner of answering the question, which Theaetetus exhibited in his first attempt by enumerating the various sciences and crafts, Socrates pushes him a step further and insists that listing the contents of knowledge is an inadequate way of answering the question. Theaetetus must try to apply to the case of knowledge what he successfully accomplished for the problem of surds, that is, he must find a way of articulating what encompasses all the “knowledges” mentioned. In addition, unlike his experience in mathematics, which enabled Theaetetus to deduce other truths, Socrates teaches him the need to examine each provisional answer (hypothesis) and he thus introduces the way of dialectics.2 In this way Socrates instantiates what he described in Republic 6, in the famous analogy of the line, where he criticized the mathematicians for accepting their hypotheses as starting points without examining them to see whether they are true starting points.3

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In the process of performing his maieutic art, Socrates offers an extraordinary analysis of perception. Once Theaetetus asserts that knowledge appears to him to be perception, more than half the dialogue is taken up in an examination of the full meaning of that claim, as well as in tests of its validity. Before the reader can gain a foothold on any particular point, Socrates presents an array of topics—measure, motion, thoughts, dreams and insanity, myths and refutations—as if, just like a wandering eye, the theme of perception displays the various and wondrous “views” that perception itself presents to each of us. But there are also organizing principles and a governing arrangement of what appears initially to be a motley collection of disconnected claims. Protagoras’s principle that “man is the measure” is the “vanishing point” around which all other points in this long passage can be located, and from which a coherent picture emerges. Socrates will first fully explore the meaning of Theaetetus’s definition, and that falls into two parts: an examination of Protagoras’s maxim, and an account of perception in the context of motion. This leads next to Socrates’ introduction of the conditions which would be necessary for perception to be knowledge—the combination of Protagoras’s principle that “man is the measure” and Heraclitus’s doctrine of flux. The application of the Protagorean maxim implies that all my perceptions are true, and that implication is true only if it is stipulated that all things are in motion. The introduction of “man the measure” satisfies the infallibility criterion of knowledge, because there is no appeal beyond the measurer, that is, the measurer and the measured (perceptions) are ultimately the same. But if it is also necessary to stipulate that all things have to be in motion, so that all things both are and are not, then that in its turn would lead to the collapse of Theaetetus’s first definition, because the criterion that knowledge must be knowledge of being could not be met under that qualification. In summary then, the discussion unfolds in the following way: Once the meaning of “perception is knowledge” is fully articulated, Socrates moves on to a critical analysis that can be divided into three parts: the refutation of Protagoras, the refutation of Heraclitus, and finally the refutation of Theaetetus’s definition proper. The critical analysis of the Protagorean standpoint is comprised of several refutations, which are prompted by the fact that Socrates himself comes to the defense of Protagoras. Before concluding the refutation of Protagoras and tackling Heraclitus, Socrates persuades Theodorus to become his interlocutor and the two engage in a conversation about orators and philosophers, which Socrates refers to as a “digression.” Thereafter he turns to an analysis of motion and his refutation of Heraclitus. The final section introduces a new set of considerations and proves definitively why perception is not to be identified with knowledge.

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1. PERCEPTION IS KNOWLEDGE AS UNDERWRITTEN BY PROTAGORAS AND HERACLITUS After Socrates discloses his “midwifely nature” and urges Theaetetus to “be a man” and “answer the question of knowledge once again,” Theaetetus avers that knowledge is nothing other than perception: “My opinion is then that whoever knows something perceives that which he knows, and as it now appears, knowledge is nothing other than perception” (151e). What is surprising about this response is that a mathematician, of all people, should identify perception as knowledge. If we think of mathematics as the paradigm for episte¯ me¯ or scientific knowledge, where does perception fit into that? Geometry might be viewed as the science of perception and Theodorus, who for some reason could not transcend the “drawing stage” in his search for the solution to the problem of the surds,4 would have been a better candidate for identifying knowledge and perception. Theaetetus’s answer nevertheless reflects his own experience, because both he and young Socrates “visualized” their solution to the surds by creatively using the images of oblong and square figures to represent the numbers. And in that regard one can say that they perceived what 5 they knew. Socrates begins his investigation of Theaetetus’s newborn by examining the nature of appearances, rather than by investigating perception (aisthe¯ sis) directly. It is as though Socrates focused solely on the middle, almost parenthetical, part of Theaetetus’s answer—“and as it now appears” (kai ho ¯ s ge nuni phainetai) rather than on the identification of episte¯ me¯ with aisthe¯ sis. This move, made in this way, will see Theaetetus confronted with both Protagoras and Heraclitus; and, as we read through these pages of the dialogue, we confront difficult problems of physics—especially the problem of motion in relation to perception. Socrates appears to be examining Theaetetus’s soul by making him do physics. On the dialogic level, the problem of self-knowledge is hinted at when Socrates tries to make Theaetetus understand how it is that his definition “knowledge is perception” appeared to him, that is, that for perception to be knowledge both Protagoras’s claim that man is the measure, as well as Heraclitus’s principle of flux, need to hold. Rather than beginning with the stated claim, Socrates insists that they examine the “secret” doctrines or causes behind the claim. The connection between the mind and the world, between perception and motion, is made quite elegantly in the Greek by Socrates’ introduction of the word phantasía (152c), which can be translated as either “imagination” or “appearance.” There could hardly be a better term to signal the ensuing discussion of physics and knowledge. The other term that Socrates introduces in his quotation from Protagoras is metron, “mea-

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sure,” which will also serve as a middle term, a medium between subject and object. Measure forces us to consider who and what measures and what is being measured, as well as the standard of measurement itself. Socrates will further complicate the issue by suggesting that the measure itself is measured by that which it measures (154b).6 It is in this context that we will be able to examine the complexity of motion and how motion challenges us to put forth a measure in the first place.

2. PROTAGORAS: MEASURE In taking a closer look at Protagoras’s dictum we must keep in mind the question as to how it is that Socrates moves from Theaetetus’s definition to an examination of Protagoras’s assertion. The first part states that “human being (anthro ¯ pos) is the measure (metron) of all things (panto¯n chre¯ mato ¯ n).”7 Thereupon that which is being measured is characterized in the following way: “of the beings (to ¯ n onto ¯ n) which are, that/how they are (ho¯s esti) and of the nonbeings (to ¯ n de me¯ onto¯n), that/how they are not (ho ¯s ouk esti).” If we examine the first part of the sentence taken by itself, we can arrive at an interpretation that would make it easy enough to concur with Protagoras, especially if things (chre¯mata) are understood to mean human-made things. Human being is the appropriate measure of artificial things, in that people are the makers of such things and the design and techne¯ involved in such making can serve as the measure of the product made. But what is it that we measure with regard to artificial things? If we translate chre¯ mata with its most primary meaning, “needs” or “useful thing,” as the word is typically used in the singular, then it is not too difficult to find a way of agreeing with Protagoras. We humans are the ones who determine—and to that extent “measure”—the functions and uses of things in our attempt to fulfill our needs.8 The translation of chre¯ mata with its acquired meaning of “money,” as used in the plural, further clarifies the determining function of measure. Money is indeed “the thing” that is completely dependent on human beings.9 Its existence, its value, and its meaning are entirely the result of human creation. Among the class of artificial things it stands out to the extent that there is no paradigm for it to be found in nature. If we were to follow Aristotle’s discussion in the Physics10 it would seem that those things made by techne¯ are the result of our ability to imitate nature. It is difficult to imagine a scenario that would have our creation of money explained as an imitation of anything within nature. Thus if Protagoras said that humans are the measure of money, we would expect no exclamations of surprise or protests of objection. The surprise and difficulty arises in the second half of his assertion where he replaces chre¯ mata with onta. Onta

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can designate the beings that actually exist, and it will prove to be much more difficult to understand in what sense man is the measure with regard to these beings. Nor is it entirely clear how we should translate ho¯s, which could mean either “that” or “how” in our present context. And it is even more perplexing what is meant by saying that the measure applies to “the beings that are” and the “beings that are not.” In Socrates’ interpretation of Protagoras’s assertion he discusses as an example the quality of the wind, which seems to suggest that he is understanding ho¯s as “how.” It may be helpful if we try out interpretations of “measure” for both translations. If I am the measure that a thing is, I must stand to it in a relation of receptor and acknowledger. Maybe nothing more than my taking notice of something is needed for me to be a “measurer of its existence.” Since there are no degrees of existence, it is difficult to imagine what else might be meant by this utterance, unless the second half of the second part—man is in addition the measure of things which are not that they are not—is taken seriously as well. Before we can continue to address the perplexity of measuring that which is not, however, we need to clarify what exactly it is that is doing the measuring, that is, what ability or capacity a human being employs in attempts at measurement. It is clear on the basis of Socrates’ jump from aisthe¯ sis as knowledge to “man the measure” that, unless perception is the measure, we have no connection between the two. While this makes sense, or at least can make sense, with regard to the existence of things, it is difficult to unravel the perplexity of how perception would function as a measure of the nonexistence of things that are not. How can nonbeing be measured at all? We cannot with complete assurance ascertain whether Socrates’ construction of Protagoras’s Truth is in line with Protagoras’s own intentions, but ancient authors already took Plato’s depiction of Protagoras in the Theaetetus as a guide to their own understanding of the sophist. Aristotle discusses the self-contradictory nature of Protagoras’s claim in book 11 of the Metaphysics: He [Protagoras] said that man is the measure of all things, by which he meant simply that each individual’s impressions are positively true. But if this is so, it follows that the same thing is and is not, and is bad and good, and that all the other implications of opposite statements are true; because often a given thing seems beautiful to one set of people and ugly to another, and that which seems (phainomenon) to each individual is the measure. . . . But to attach equal importance to the opinions and impressions (phantasiais) of disputing parties is foolish, because clearly one side or the other must be wrong.11

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Earlier in the Metaphysics12 Aristotle discusses how any position which calls for the same thing to be and not to be at the same time will ultimately fall into a kind of monism, because it is impossible to differentiate one thing from another. Sextus Empiricus also elaborates on his understanding of Protagoras’s doctrine of the measure: and by “measure” (metron) he means the criterion (krite¯ rion), and by “things” (chremato ¯ n) the objects (pragmato ¯ n), so that he is virtually asserting that “Man is the criterion of all objects, of those which exist that they exist, and of those which exist not that they exist not.” And consequently he posits only what appears to each individual, and thus he introduces relativity (to pros ti).13

Sextus also discusses Protagoras’s commitment to flux; but it is not clear whether Plato’s Theaetetus is his main source, because he also connects the flux of matter with embedded reasons that he uses to differentiate Protagoras from the skeptics. From these ancient interpreters we learn of two distinct ways of identifying measure: Aristotle identifies the phainomenon and Sextus the krite¯rion as the metron (measure). At first glance these two seem to be identifying the measure from different perspectives, because the former, the phenomenon, is something which appears (erscheint) and which thus points to something outside the perceiver; whereas the latter, the criterion, is connected with choosing and deciding or judging, which points to something inside of the perceiver. Is it not the case, however, that this apparent divide exemplifies human experience itself? Something acts on our sensory apparatus and we react to it and judge it to be a certain something. Socrates’ example of the wind appearing warm to one and cold to another illustrates precisely this interaction. The coming together of phainomenon and krite¯rion is similar to Socrates’ account of perception as the interaction of perceiver and perceived in the myth of twin motion. The very notion of measuring that which is not is paradoxical, unless nonexistence is a parasite feeding on existence and unless it is through the measure of beings that are that we can determine the nonexistence of beings which are not. An example from science might help to clarify this hypothesis. In 1887, in their famous experiment, Albert Michelson and Edward Morley attempted to measure the speed of light more accurately by adjusting for the factor that aether, as a medium, would play; and ultimately their measurement established the nonexistence of the medium itself—one of the most important experiments with a negative result that had crucial scientific consequences. Another possible standpoint from which to attempt a measurement of nonexistence would be desire. In the Symposium Socrates, through his in-

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terrogation of Agathon, analyzes desire as a response to the awareness of absence. “Such a man or anyone else who has a desire desires what is not at hand and not present, what he does not have, and what he is not, and that of which he is in need; for such are the objects of desire and love” (200e). In this context, philosophy would be the measure of absence and lack, and the result of that measuring is expressed by a declaration of the desire for wisdom. This also illustrates Socrates’ self-proclaimed emptiness in his discussion of midwifery. It should be clear, in any case, that we need to specify what in a human being is doing the measuring before we can fully comprehend Protagoras’s dictum. In Theaetetus 151–61 it is clear that we are to substitute perception for the measure. And that is precisely what enables us to move from Theaetetus’s definition to Protagoras. But Socrates does not restrict perception as the measure of existence per se but his talk of cold and warm winds indicates that he would restrict perception to the measure of qualities. Perception cannot answer the tí esti (what is it?) of the wind, it can only judge its appearance, it can only say what it feels like. Or as Socrates makes the point when discussing how the same wind can appear cold to one and warm to another: “Are we to say that at that time the wind itself in itself (auto eph’ heautou) is cold or not cold? Or are we to obey Protagoras that it’s cold for whoever’s cold and not for whoever’s not” (152b). This relativizing of the quality of the wind as such does not amount to naive realism (i.e., what I perceive is real and not just for me), nor to some kind of Berkeleian idealism (esse est percipi).14 Socrates is after all still referring to the “same” wind and speaking about “the wind itself in itself.” So there is room for an underlying reality which interacts with the perceiver and this interaction gives rise to perceptible qualities.15 The consequences Socrates draws from this interpretation of Protagoras is that “nothing is one alone by itself” (152d). If there were “a one” or if there were being itself by itself, then there would be no need for man as measure. The one or being would comprehend all things and it would assign functions and determine the fulfillment of these functions. The forms too are called into question in the Protagorean maxim, as is evident in many dialogues such as the Meno, where Socrates appeals to something, the form of virtue, which functions as the measure of Meno’s answers. The forms are commonly posited as standards, against which we measure our thoughts. The challenge of Protagoras, then, is to give an account of knowledge without making appeal to any “higher power”—to answer the question in terms of the knower. By making humans the measure, Protagoras negates any possibility of forms or gods, putting forward man as the standard and stabilizer. By denying being, forms, and gods, Protagoras has set everything into motion and has proclaimed human beings to be the constant who can measure motion.

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At the end of the examination of perception Socrates shows definitively that it is not perception that enables a person’s measuring capacity, but instead Theaetetus proposes that it is soul which can determine the common things (ta koina), such as being and not being by itself (185dff). It turns out that more than this is required to give a full account of knowledge but a very important step has been taken, a step made possible by starting with the radical Protagoreanism,16 which allowed for the possibility that a human being can play a measuring role with regard to beings. This particular point should have been evident to Theaetetus on the basis of his own experience, that is, the measuring ability that allowed him to solve the problem of the surds, but it takes this rather long and circuitous route before he can gain this insight into himself. Humans do not fully determine being but have a significant role to play in the revelation of being. This idea that reality or being is the result of an interactive process between knower and known will initially be illustrated in Socrates’ analysis of motion, which turns out to be a clandestine imitation of the motion of ero¯s.

3. MOTION Socrates attempts to explain motion as a creative force and marshals impressive thinkers to support the thesis that everything comes from motion. The products of motion are identified in the following sequence (153a–c): 1. 2. 3. 4.

Fire is the result of motion and it in turn provides the motion for: The birth of the genus of animals and preserves The hexis (condition, habitus) of bodies and The hexis of soul.

From these Socrates concludes that: 5. Motion is the good both with regard to soul and body.17 How Socrates arrives at “the good” here is not entirely clear, unless we identify “the good” with becoming: Motion is the cause of fire that nourishes life, and motion preserves both body and soul; and furthermore it improves the latter through learning. So motion could be understood as activity and the active is judged to be better than the passive. If the good is “beyond being” and the source of being and knowing, as it is affirmed in Republic, book 6, and here the good is defined in terms of motion with regard to body and soul, it is tempting to say that, by substitution, motion is

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the source of being and knowing. This particular emphasis on the beneficial effects of motion points also to the work of ero ¯ s: both in the Diotima’s speech in the Symposium as well as in Socrates’ proof of the immortality of the soul and the myth of the charioteer in the Phaedrus highlight the moving force of ero ¯ s. The soul as self-moved mover has, according to the Phaedrus myth, the power guided by a beloved to move toward a vision of the hyperouranian beings, the beings beyond the heavens, and thus to gain knowledge. The accounts of knowledge in the erotic dialogues are all entangled with motion. Taking this as a tenable hypothesis, all varieties of interesting conclusions would follow. It most certainly would explain why the forms don’t make an appearance in the Theaetetus. The forms are unmoving and we must wonder whether the categories of active and passive can be applied to them. In the Sophist the Stranger explains that nothing can act on the forms.18 This makes sense to this extent: If the mind or anything else would act on the forms that would imply a change. But if knowing is like perceiving and requires correlative motions, then the forms cannot be known—unless there is a way of combining motion and the forms. Again, it is possible to use ero ¯ s to explain this particular puzzle because it is through the erotic interaction with another which clearly is a motion that we come to know, that is, the practice of dialectics.19 Perhaps another model can help us to unravel what now appears to be puzzling. If motion “gives rise to” both perceiving and the perceived (aisthe¯ton), and that which we name is the result of the collision of twin motions—as will be explained below—then the phenomenon of motion calls for the question of “what it is” (tí esti). Perceiving does not halt motion, but it can be explained in terms of motion—we need to find something that can arrest motion if we want to make any claims to knowledge. Examination of the radical flux doctrine makes it clear that, if everything is in constant motion, we cannot assign any valid predicates to anything, for, as soon as we call something “purple,” it is not purple. This particular difficulty is made very clear in Hegel’s examination of sense-certainty in the first section of the Phenomenology of Spirit, where all individuals, such as “this,” “here,” and “now,” when considered from the perspective of sense-certainty alone, turn out to be nothing more than vanishing moments. If there is only flux, then there are no lasting predicates or attributes, and thus there can be no knowledge. Socrates shows that he does not think that human being can serve as the constant, by conspicuously employing the middle voice of parametroumetha20—we ourselves need to measure ourselves over against something. Protagoras’s measure itself is relativized and thus cannot be the constant we are looking for. Socrates explains this in the following: Isn’t it the case, then, if that against which we are measuring ourselves (parametroumetha) or which we are touching were great or white or hot, it would

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never, in its fall on something else, have come to be something else, if, that is, it itself does not at all alter. And if, in turn, that which is doing the measuring against or the touching were each of these things, it would not have become, if it itself were not affected in any way, different when a different thing approached it or underwent something (154b).

Lest Theaetetus attempt to escape the puzzling consequences of ever changing motion by turning to mathematics, Socrates, using the example of dice, shows him that counting and numbers are not capable of solving the dilemma. If you measure 6 over against 4 it is 11⁄2, while if you measure it over against 12 it is 1⁄2. This is a rather strange example, inviting several interpretations. In contrast to aisthe¯ sis and the aisthe¯ ton, both of which are subject to change in relation to one another, the numbers themselves do not change in relation to one another: 6 remains 6, whether it is 1⁄2 of 12 or 11⁄2 times 4. On the other hand, if we were ignorant of that (x) over against which 6 is being measured and were only cognizant of the result of measurement, namely, 6 = 1⁄2 and 6 = 11⁄2, we would steadfastly maintain that 6 has a changeable nature. Perhaps the same process occurs with our judgment about the quality of the wind. The wind is what it is by itself; but, when it is judged by one of its relata, it might be either warm or cool. The problem is, however, that we can never move beyond speculation with these matters. Just as we do not know what the wind is without making some sort of judgment about it by relating it to something else (ourselves), so the number 6 is revealed to us through its relation to other numbers. If we want to utter more than mere tautologies and penetrate the nature of something by answering the question, tí esti we are forced into nonidentity relations and incur the risk of relativity.21 Perception is the immediate relation, whereas opinion is a mediated one, and knowledge has to take notice of the relation as well as the relata. An explanation of knowledge has to include an account of the transformation of the sensible into something measurable and this is the crucial step for all empirical knowledge.22 But the question of measure is just as relevant for nonempirical knowledge and a careful analysis is needed to show whether or not the soul has the capacity to measure an intelligible reality. Confronted with these puzzles, Socrates proposes to turn inward and talks as though, in examining the nature of one’s thought, one could escape the difficulties one faces when examining the outside world. Then if you and I were dreadfully canny (deinoi) and wise (sophoi), having scrutinized all the things of our mind (panta ta to¯n phreno¯n), we would then for the future be testing one another out of a superabundant store and, engaged in sophistic fashion in a battle of this sort, we would proceed to strike and ring the speeches of one against the speeches of the other. But as it is, because we’re laymen (idio¯tai), we’ll want to observe them in relation to

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Socrates’ speech indicates that he will now turn to something other than experience and show that, in contrast to perceiving the world and encountering the problem of relativity, it is in fact possible to isolate the things of the mind without falling into the traps of the problem of measure. The turn inward results in the articulation of three logical—or what some might also see as metaphysical—principles (155a–b): 1. Nothing becomes greater or less, either in bulk or number, as long as it is equal to itself, 2. To whatever there should be neither addition nor subtraction, this never either increases or decreases but is always equal. 3. Whatever was not before, this is incapable of being later without having come to be. We should refer to these as logical principles, because none of them are derived from experience, but rather all three of them are the work of thought. In contrast to perception, thought can consider something in isolation and thus escape the relativism to which perception appears to be inextricably tied. It is the dissonance between thought and perception that gives rise to the philosophical wonder that Theaetetus experiences (155d)—the dichotomy between the discrete unit, that is, a thing in itself, and that which is the result of relatedness, the percipiendum. Socrates speaks as though it were possible for thought to consider something as a unit and contemplate it in its concreteness. According to the first and second principles, this “one thing” is stable and equal unto itself until change is brought about by some manipulation such as addition and subtraction. It is not clear, however, what it is that is being changed. The unveiling of Protagoras’s truth in the myth of twin motions is the result of reason’s inability to combine being and motion without generating becoming. The result is that nothing is by itself, but everything is becoming. We can’t hold to the two ones as units when we put them in the process of addition or subtraction. We can think of a thing as a unit and by itself or as the product of a relation but cannot do both at the same time. If we can imagine a line defined as a point in motion, we understand that it is not possible to address the point as point and line simultaneously. Theaetetus betrays the difficulties involved in giving an account of motion by expressing once again a sense of wonder and an experience of dizziness when contemplating becoming and change. Socrates commends

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Theaetetus’s experience as a sign of his philosophical nature: “for this experience is very much a philosopher’s, that of wondering. For nothing else is the beginning of philosophy than this, and, seemingly, whoever’s genealogy it was, that Iris was the offspring of Thaumas (Wonder), it’s not a bad one” (155d). If we trace the genealogy given in Hesiod’s Theogony it turns out, as we saw earlier, that Iris was the child of Thaumas, daughter of Pontus, and Electra, child of Oceanus and Tethys. This brings us back to 152e, where Socrates introduced Homer as one of the champions of motion: “Homer with the line ‘Oceanus and mother Tethys, the becoming (genesis) of gods’ has said that everything is the offspring of flowing and motion.” Socrates introduces this genealogy to explain in terms of traditional Greek myth the beginning of philosophy. Removed from the context of mythology, the point is that motion is the beginning of philosophy. It is thus not surprising that Socrates is now prepared to reveal Protagoras’s secret teaching about motion. After ensuring that none of the repulsive materialists is anywhere nearby (155e), Socrates turns his attention to giving an account of motion. Curiously, he refers to his exegesis on motion and becoming as a mythos (156c).

4. THE MYTH OF TWIN MOTION Socrates’ “wonderful” analysis of motion is the culmination of his critique of Protagoras and Heraclitus, the putting together of a relativistic epistemology and a mobile ontology. It is the ultimate articulation of the notion that “knowledge is perception” and falls into two parts: what the myth says (156a–c) and what it wants to say—that is, what it means (156c–157c). The principle that underlies both parts is that everything is motion and nothing else. This in itself suggests that we must find some way to reveal motion; for surely we cannot begin directly with it, because addressing motion, whether through language or number, is equivalent to “making an arrest,” arresting motion. Socrates is quite correct, then, in calling his account a “myth.” He will talk initially about things such as eyes and stones even though he knows that the hypothesis under investigation does not allow for stable objects. But he will move beyond sticks and stones to the revelation that there is to be nothing that is one itself by itself, but always to become for something, and “be” must be removed from everywhere—not that we’ve not been often compelled even now by habituation and lack of knowledge to use it . . . : to be is neither a something nor of something nor of me nor this nor that nor any different name that makes for stoppage, but one must make utterances in accordance with nature—becomings and makings and perishings

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Chapter 3 and alterings—since if one stops something in one’s speech, whoever does it is easily refutable. One must also speak in this way piecemeal and about many things collected together: it’s to this aggregate that they lay down for themselves the names human being and stone and each animal and species (157b).

How does Socrates get here? In the first part of the story (156a–c) Socrates introduces the infinite motions of activity and passivity whose interactions generate infinite twin offspring which we identify as percipiendum (aisthe¯ ton) and the cogenerated perception (aisthe¯ sis). These are the phenomena that we name colors and sounds and so on, and sight and hearing and so on respectively. Socrates points out that there are indefinitely many such in both groups that have no names. He reiterates the twinness of the motions by pointing out that the aisthe¯ton is a congener (homogonon) of the aisthe¯sis. The puzzling notion of passive motion can best be understood if we think of it as reaction. Reaction conveys what is clear in Socrates’ account, namely, that the distinction between the active and the passive is not to be understood as the creation of two stable classes, one of which comprises the passive motions while the other consists of active ones. Rather, passive motion can become active motion and vice versa. So it might be appropriate, though it is anachronistic, to translate Socrates’ first principle as “every action has a reaction.” So much for what the myth says. We must now turn to what Socrates extrapolates as the meaning of the myth. In an attempt to clarify the meaning of the story of motion Socrates introduces the concept of speed and explains that we can distinguish between swift and slow motions. The measure of speed is not discussed as such by Socrates, and it is clear that we arrive at the distinction by measuring the speed of each against the other. So in fact speed is a concept that relies on the corelativity of motion. Slow motions generate faster ones and the distinguishing difference between the two is that the former move in place while the latter move “locally.” In order to make sense of this we need to discuss the example that Socrates uses to illustrate his point. He describes the motions involved of an eye seeing something white. Both the eye and that which is correlative to it—let us say a white rock—are what Socrates would describe as slow motions. The “seeing white” and the “being white” are the result of the cogenerated faster motions, whiteness and the concomitant perception that can be understood as moving between the eye and the white rock. Perception and percipiendum are but momentary motions, reactions that transform their respective sources into their motions. Thus the eye is not a “thing,” but a seeing; and the rock is not whiteness, but being white. To put it in another way: When something visible comes under the purview of the eye it makes the eye react in accordance with its nature, namely see, and this seeing in turn makes the

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object exhibit its visible nature, that is, its being of a particular color. It is the conjunction of all these motions that constitutes a momentary experience, and the next moment a different experience is in the making. This is precisely all there is—motions on the make. What we call “eye” is nothing more than a collection of slow motions and the same applies to the socalled seen objects. Indeed as Socrates states the conclusion of the discussion: “Nothing is itself by itself” (157a); everything is always becoming. There are both “positive” and “negative” interpretations of this explanation of the process of perception. One can read the myth of twin motion as an illustration of how a strictly atomistic account of experience undermines both subject and object permanence. In Socrates’ account of perceiving a white stone neither the quality whiteness nor the capacity of perception can be isolated or “arrested” and what is “being white” the moment “I am seeing” it, is “not being white” and “I am not seeing” it the next moment. There is neither a subject nor an object but rather perceiving is the process of constant interactive motions. At the level of a preliminary analysis this correctly reflects the initial steps of perception, that is, if we examine perception on the basis of sense organs alone as a strictly physical process. It is very difficult however to understand where measure can fit in if everything is in flux. The very idea of measure implies some constant, but in this account the measure changes from moment to moment. On the other hand, it is clear that the perceiver plays a constructive role which, when aided by opinion and logos, leads to a measured judgment such as “this appears white to me.” Yet another reading of the myth of twin motion betrays its similarity to the account of ero ¯ s offered in both the Symposium and the Phaedrus, where ero ¯ s sets humans into motions leading them to give birth to offspring. “And out of the association (homilias) and rubbing (tripseo ¯ s) of these against one another, there come to be offspring (egkona), infinite in multitude”(156a). It is curious that Socrates would choose the term homilia to characterize the process of perception, since it can mean both “discourse” and “intercourse,” neither of which seems particularly apt as a description of perception. These rubbings and associations also play a role in the ascent of the lovers and it is in our experience of ero ¯ s that we can understand the particular reciprocal active and passive motions. In the Phaedrus 250d–255e Socrates provides an account that explains the journey of the soul from beauty to self-knowledge. The first step is to recognize that there are no images of wisdom and that beauty is a mediator which will seduce us to undertake the journey: “Vision, of course, is the sharpest of our bodily senses, although it does not see wisdom. It would awaken a terribly powerful love if an image of wisdom came through sight as clearly as beauty does, and the same goes for other objects of inspired love. But now beauty alone has this privilege, to be the most clearly visible and the most

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loved” (250d). Socrates then details how the interaction with a beautiful other stimulates the growth of wings, which—at least metaphorically— will enable the lovers to undertake a flight leading to mutual selfrecognition and culminating in philosophical discourse the closest expression of the love for wisdom. In some cases at least, the journey goes from intercourse to discourse. After some prompting Socrates gets Theaetetus to adopt this theory of homilia as a likely account of perception. Acting within the context of the hypothesis, Socrates asks Theaetetus how the theory feels to him, whether he finds it “tasty” (geuoio). Given the form in which Socrates asks the question, it may not be surprising that Theaetetus answers: “I don’t know . . . ” On the other hand, this seems to be a favorite response for Theaetetus, for he answered similarly earlier (148e). What is different about this assertion of ignorance from the previous one, however, is the fact that Theaetetus links it to his not knowing whether Socrates believes any of these arguments. Socrates, in response, admonishes Theaetetus to remember the principles of maieutike¯. Socrates re-asks Theaetetus the question but once again in a somewhat puzzling manner: “Well, say once more whether it satisfies you that there not be anything, but good and beautiful and everything we were just now going through (be) always becoming?” (157d). Socrates does not offer any explanation why he switches to the beautiful and the good, when up until that point the discussion was really about sensory qualities such as white, warm, and bitter. But if we consult Socrates’ extensive list of examples of named perceptions in his account of twin motion we find that he does include desire: “Now the perceptions have for us the following sorts of names: sights and hearings and smellings and freezings and burnings and, yes, pleasures certainly and pains and desires and fears (are) their designations and different ones as well, the nameless of which (are) without limit, and the named very many.” (156b) He continues and explains that in each case there is also a cogenerated percipiendum, which for the case of desire includes beauty and the good, as we have learned from the Symposium. It should be clear that Socrates is pushing Protagoras’s dictum to an extreme limit by making everything a matter of generation: “Then I believe the only thing left is for us to be for one another if we are, or if we become, to become for one another, since necessity binds our being together and it binds it to nothing else of all the rest, not even to ourselves, so it’s only left that it has become bound with one another” (160b). And a little later he delivers the puzzling statement: “My perception is after all true for me—for it is of my being on every occasion—and I am the judge according to Protagoras of the things which are for me that (how) they are, and of the things which are not that (how) they are not” (160c).

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There are translation issues regarding the above passage, that lead to significant differences of interpretation, particularly with regard to the phrase “for it is of my being (ousia).” Bostock inserts the word “part,” and interprets the text as asserting that perception is of part of my being.23 Bostock interprets the segment as a Platonic anticipation of Hume’s “bundle of perceptions” theory of the self. As evidence he cites Socrates’ talk about aggregates at 157b–c, where Socrates is concerned with the potential inadequacies of language. The aggregates which Socrates mentions, however, are abstract, or better yet, universal terms, like “human being,” “stone,” “animal,” and other species. In order for this interpretation to stand up, Bostock and his followers would need to show how these terms apply to individuals—which is, after all, what underlies Hume’s discussion about his unsuccessful search for the self in contradistinction from the evident particular perceptions which might be bundled together into a self.24 Pace Bostock, the text here suggests that class names are aggregates of particular perceived qualities, not that we are aggregates of our perceptions. John McDowell interprets the sentence to say that perception in each case is for my being.25 McDowell reads this passage as a reiteration of 160a–b, where Socrates says: Yes, and it’s just as much a necessity that I become of something (perceiving something) whenever I become perceiving—for it’s impossible to become perceiving and perceiving nothing—as for that to become for someone whenever it becomes sweet or bitter or anything of the sort. For it is impossible to become sweet and sweet for no one (160a–b).

McDowell’s interpretation is at least consistent with the discussion, but it is not clear why Socrates would make the same point again only a few sentences later and why he would then be less clear about it to boot. The Greek te¯ s gar eme¯ s ousias aei estin contains neither “for” nor “part,” but literally says that “for it (perception) is always of my being.” What new angle is Socrates adding to the preceding discussion with this particular formulation? To fully explore the meaning of this passage, we need to put together three points: (1) necessity binds our being together; (2) my perceptions are true for me, because they are of my being; and (3) Protagoras’s maxim. With the introduction of motion, Socrates has eliminated all possibility of stable objects: Everything is in an unhalting process. In his examination of perception, he has made it clear that both perceiver and percipiendum are in motion, which leaves only the relation between the two as the locus where anything can be or become something. The connection between perceiver and perceived is necessary in order for either one to be. I cannot see a white rock in the absence of both my seeing and the rock’s being seen. It is in this sense that necessity binds the two of us together. If this is the

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case, then it is impossible for my perception to be false, because that would require something other than perceiver and percipiendum to which we could appeal in evaluating perception. But, given the principle of motion, this is impossible. Since my perception is in part generated by me and the act of seeing establishes what I see, I am the measure of what I see and this will inevitably be true for me. The point we need to recognize here is that Socrates, in his interpretation of Protagoras, establishes that what comes from me is true for me. In perception there is no need, indeed Socrates would maintain there is no possible way, to turn to something other than the process of perception itself for verification of what I see. My perceptions are incorrigible.26 Perception is of my being, inasmuch as the act of perceiving constitutes the act of being. Insofar as I perceive, I must be. The investigation of perception requires discussion about the nature of the perceptibles, as well as the perceiver, but we should not go as far as Kenneth Sayre does in arguing that the primary purpose of the discussion is to clarify the ontological status of sensible objects.27 If anything, the passage about perception and motion seems to suggest that one cannot understand a relation by investigating just one side of the relation. The question of knowledge is, after all, a question that involves both the knower and the known. Socrates emphasizes the interconnection of these in his summary of the discussion that he offers to Theaetetus for acceptance and which will set the stage for the examination of the “child”: So after all, it has been said very beautifully that knowledge is not anything else than perception, and there has been a coincidence to the same point of the assertion, according to Homer and Heraclitus and the entire tribe of this sort, that all things are in motion like streams; of the assertion, according to Protagoras the most wise, that (a) human being is the measure of all things; and of the assertion, according to Theaetetus, that since these things are so, knowledge comes to be (gignesthai) perception (160d–e).

This passage challenges us once again to explain why there is a link between Protagoras and Heraclitus, and how the linking of the two supports Theaetetus’s definition of knowledge as perception. Historically there is a straightforward explanation of why Socrates links Protagoras and Heraclitus and why Theaetetus assents to it so readily. Both Aristotle and Porphyry make the same connection and they explain it on the basis of Protagoras’s opposition to Parmenides.28 Plato is not quite straightforward about the role of Parmenides and he hints at it negatively by exempting Parmenides from becoming a topic of discussion. The clearest indication of Protagoras’s objection to Parmenides occurs at the end of his dictum where he uses ouk estin, speaking of things that are not and indicating that a human being is a measure of that as well. This stands in stark contrast to Parmenides’ poem, where he has the goddess proclaim: “It is

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necessary both to say and to think that being is, because to be is possible but not being is not (ouk estin).”29 In the course of the poem Parmenides asserts that motion and change are impossible. This stands, of course, in stark contrast with Heraclitus’s river fragments and the one quoted in the Theaetetus that all is flowing and in motion. Traditionally, Heraclitus’s fragments are interpreted to refer to the sensible world, whereas Parmenides speaks about the intelligible realm. For Parmenides it would then seem to follow that there can be no inquiry and knowledge of the sensible world; all that is possible in that arena of sense perception is the “way of opinion.” In contrast to this, Protagoras suggests that all that is needed to know the sensible, which is in motion, is a frame of reference that will allow the sensible to become measurable and he offers the human being as that frame of reference: man is the measure.30 Socrates is ready to move on after this lengthy and difficult exegesis of the first definition of knowledge. He is ready to examine the newborn and determine its “status of being”—or, as he puts it, to run it around in a circle” (160e).31 If Theaetetus truly believes that “perception is knowledge,” and if in addition he believes that Protagoras is correct—and Theaetetus says that he does indeed believe that Protagoras is correct—then there should be no need to test its correctness and viability. That should be the end of the discussion. In addition, if the view that “knowledge is perception” is Theaetetus’s own brainchild, he might well be sensitive about the possibility of having it tested: “A mother loves her own child best, it is said, and Theaetetus would want to protect “his own.” But, even though Theaetetus thinks that his definition is good and correct, he nevertheless entertains the notion that he may be in error, which shows that Socrates’ measure of maieutike¯ has defeated Protagoras’s principle. Interestingly enough, it is Theodorus who agrees on behalf of Theaetetus and urges Theaetetus to submit to further examination. No wonder Socrates remains so eager to engage in a dialogue with Theodorus. We, in fact, never discover whether or not Theaetetus was truly persuaded by Protagoras.

5. MEASURING PROTAGORAS The testing of the hypothesis that man is the measure is complex and different parts are examined at different stages. Protagoras’s maxim is refuted three different times: The first inspection considers animals and majority opinion.32 The second refutation is the so-called self-refutation of the homo mensura claim. The third attack involves the consideration of judging future states of affairs: Here the notion of the wise man as expert is introduced, the wise man as the one who is the measure of future judgments.33 The refutation of Protagoras surrounds the passage (172a–177c),

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which Socrates himself calls a “digression,” in which he and Theodorus examine the philosopher and the orator and consider political matters. The importance of this passage will come to light at the end of our examination of the dialogue, for the interpretation of this passage has important implications for the dialogue as a whole. Cornford and others, for example, have argued that it is the digression that proves their reading of the Theaetetus as a dialogue that shows that knowledge is impossible without the theory of the forms.34 After the refutations of Protagoras, Socrates constructs a separate argument about motion to refute the Heracliteans (179c–183c). We will need to examine how Socrates’ discussion of the two motions, local-spatial motion and alteration, differs from the myth of the twin motions (166a). All these attacks are undertaken by Socrates with the assistance of Theodorus, rather than Theaetetus, because Protagoras had demanded a level of seriousness which required adults rather than children (166a). The last part of the refutation (183c–187a) concerns Theaetetus’s own formulation that knowledge is perception and Theaetetus himself will be the participant in this examination. All of these very “serious” discussions, however, are preceded by a playful ad (Protagoram) hominem attack, a scolding by Protagoras, three debater (antilogikos) points, and a lengthy apologia, a speech in his own defense by Protagoras. Theaetetus’s “newborn” is attacked vigorously by Socrates, who makes the charge that, given the identity of perception and measure in Protagoras, any sentient creature, whether it be pig or dog-faced baboon (161c), could equally well be considered the measure of the things that are. To make matters still worse, Socrates introduces the gods—which is a stab at Protagoras, who specifically excluded the gods from discussion, claiming that nothing can be known about their existence or nonexistence or their form.35 So if pigs and gods, as well as Joe Schmo, are all possible measures,36 then why should we admire and pay great wages to “the wise Protagoras”? Within this ad hominem attack Socrates makes an important transition from perception to opinion, which seems to nullify the very attack he just made. Socrates asks Theodorus how it is that we would consider Protagoras wise, if it will be true to each whatever each opines (doxaze) through perception, and if neither someone else will discriminate the experience of someone else better nor will another be more competent to examine (diakrinei [discern]) the opinion of an other whether it’s correct or false, but as it has been said many times, each one alone by himself will opine (doxasei) his own things, and all these are correct (ortha) and true (alethe¯ ) . . . since each of us is the measure for himself of his own wisdom (161d–e).

We have here then the claim that what is true is not the perception as such, but rather the opinions formed on the basis of perceptions. Opinions

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are not as easily attributable to all sentient beings and it will turn out that the serious refutation of Protagoras as well as his own apologia will have opinion, not perception, as the main target. Once this transition is made from perception to opinion, it is also clear, as Socrates himself points out, that his very own activity of maieutike¯, as well as Theodorus’s expertise are called into question—or at the least considered laughable. When Socrates impresses these points upon Theaetetus, the mathematician is baffled and considers his own position and in fact the entire doctrine as being refuted. It is indeed shocking how quickly Theaetetus is willing to give up his “newborn” and Socrates’ rebuke in the voice of Protagoras admonishes him to take the discussion more seriously. Thus far, the “Socratic Protagoras” claims, the discussion has been based on “plausibility and likelihoods” (pithanalogia te kai eikosi) and matters as important as these demand the same kind of examination that geometrical problems would, that is, instead of basing the argument on probability, they should proceed in accordance with necessity (ananke) (162e–163a). The procession that follows is based on what Socrates later describes as verbal disputes, as though quarreling about the meaning of names and demanding linguistic precision could somehow fulfill the demand for “the necessary.” Socrates and Theaetetus engage in three brief skirmishes, each leaving Theaetetus a bit more baffled and the more ready to abandon his original hypothesis. The first (163b–c) concerns the identity of perception and knowledge, and Socrates suggests that it is possible to either see or hear something without knowing it, using as an example the letters and phonemes of a foreign language. Theaetetus deals with this objection by pointing out that while we don’t know the meanings of the letters and sounds of a foreign language, we do know the letters and sounds as letters and sounds through perception. After quick praise, Socrates brings up the next objection (163d–164b), which concerns memory and more specifically whether a remembered perception would count as knowledge. He construes the problem, with the help of sight, claiming to show that after seeing something I can shut my eye, and while I’m literally not seeing, I can remember what I saw. So either remembering a perception or experience does not count as knowledge or else knowledge is not identical to perception. The last skirmish, and what appears to be the most sophomoric objection, is introduced immediately after Socrates steps back and condemns the previous discussion as contentious and agonistic: We seem in the contentious way of contradiction to have gained an agreement in light of agreements about words (names) and to be satisfied with our prevailing over the speech by something of the sort. And though we say we’re not competitors but philosophers, we are, without our being aware of it, doing the same things as those dreadful men (163c–d).

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To underline the shortcomings of the “competitors,” Socrates shows how they would argue against the proposition that knowledge is perception by applying the law of noncontradiction and pointing to the violation of that law, showing that it is possible both to see and not to see at the same time—when you shut one eye and keep the other one open. Applying the adjectives and adverbs of perception to knowledge might be the next argument and Socrates points out that it is high time that we hear from Protagoras himself to see how he would deal with these contentious speeches. Since Theodorus has refused to speak on behalf of Protagoras, Socrates himself will take on this task.

6. THE SEDUCTION OF THEODORUS, OR APOLOGIA PROTAGOROU Protagoras—with Socrates taking on his role—begins his defense speech with a sort of ad hominem as well: He accuses Socrates of doing nothing more than frightening children with his verbal displays. He continues to advise Socrates on the proper operation of the dialectical method and later on provides a recipe for turning people into students of philosophy rather than students who loathe him. This latter part is particularly relevant, if we consider that Socrates is about to face charges against him brought by people who loathe him. Protagoras insists that Socrates’ method of questioning and examination can only refute him if the interlocutor responds, answers, and reacts exactly the way he, Protagoras, would; in all other cases his arguments would still be valid. This is a very strange assertion from the man who holds that every man is the measure of the truth. If Theaetetus is the measure and he proclaims Protagoras refuted, then would it not follow from Protagoras’s own dictum that Protagoras must be refuted? Socrates will bring up a similar point when he responds to Protagoras’s defense (170a–171c) and he will claim that the opinion of the majority refutes Protagoras’s claim. From the various objections discussed by Socrates and Theaetetus, Protagoras speaks out the argument concerned with memory and perception to show how it misses his point. He points out that everyone would agree that there is a difference between the memory of an experience and the experience itself. He doesn’t quite tell how he would characterize the difference, but surely something like the difference in the degree of vividness would serve him quite well. This somewhat “Humean” interpolation is appropriate, especially if we consider what follows. Protagoras reminds Socrates of the discussion about difference and otherness and argues that there is no way to compare the differences between experience and a remembered experience, because there is no underlying subject of these ex-

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periences, but rather a succession of individual experiences. This principle also calls into question the applicability of the law of noncontradiction, for there seems to be no way to construe “he knows and he doesn’t know” on this interpretation. So Protagoras, self-satisfied, reiterates his maxim, having made it clear that perceptions are completely private, with some reformulation: “each of us is the measure of the things which are and are not, and another differs from an other in thousands of things by this very fact, that to one different things are and appear, and to one different” (166d). The last counterargument contained in Protagoras’s defense speech refers back to Socrates’ ad hominem attack and concerns the topic of wisdom. This is a serious challenge issued here. Socrates, at the beginning of his conversation with Theaetetus, identified wisdom and knowledge, calling them “the same thing” (145e). Protagoras, on the other hand, distinguishes knowledge from wisdom in the following way: Knowledge is concerned with truth and is indeed covered by the principle of measure, but wisdom has to do with the good and the conditions necessary for attaining the good. Protagoras describes the wise man as one who “by inducing a change makes appear and be good things for anyone of us to whom they appear and are bad” (166d). He compares himself to physicians and farmers who can bring about changes in their subjects’ condition that effect a change in their perceptions. (Yes, Protagoras does indeed believe that plants have perceptions.) And just as a doctor can bring a change about that makes the bitter wine taste sweet by using drugs, so by means of speeches the sophist and orator can effect a change in the city that makes good rather than bad things appear or seem just.37 Protagoras does not explain what the farmer does to bring about a change in plants, but it is not that difficult to fill in this lacuna. These constructions are not exactly parallel but there are many important points to be garnered from the comparison of the sophist and the physician. First, we need to recognize that after this speech it should be clear that Protagoras cannot be characterized as a “mere” perceptual relativist, for here he includes “political predicates,” such as justice, as well. This is not so surprising, since there have been several times where the discussion shifted from perception to opinion. In the political context, then, it is the city that is the measure of the things that are just or beautiful for it. What is not entirely clear is whether or not Protagoras is promoting “moral relativism” for he says: But it’s wise and good public speakers who make cities be of the opinion that the good things in place of the poor things are just. Since no matter what sort of things these are that are just and beautiful in the opinion of each city, these also are for it as long as it holds them to be so, but the wise makes good

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Who is the measure of the good? Protagoras nowhere explains on the basis of what the sophist or orator determines the good, all he says is that their wisdom is concerned with the good. If we examine the analogy with the physician we can come up with some clues but how the sophist arrives at the good remains unanswered. If the city’s need of a sophist is like the body’s need for a doctor, then the city must be sick. So the city is in need of a sophist who can remedy its sickness through speeches only when it is unjust.38 Just as the goal of the physician is health, so the goal of the sophist is justice. The physician accomplishes health through his knowledge of medicine, but what is the knowledge that enables the sophist or orator to heal the feverish city? These characteristics ascribed to the sophist are applicable to Socrates himself and in the Apology he describes his concern with the city in a language similar to the one employed by Protagoras. The question about the good remains and we can only wonder whether we are to consider this a refutation of moral relativism or an incomplete argument. 7. THE REFUTATION OF PROTAGORAS Socrates responds to Protagoras’s challenge as follows: You will truly examine what we’re saying, in declaring that all things are in motion, and which is the opinion of each, this also is for a private person or a city. And on this basis, you’ll go on to examine whether knowledge and perception are the same or may be different . . . (168b).

After some coaxing he finally persuades the reluctant Theodorus to become an interlocutor who will assist him in examining the Protagorean and Heraclitean doctrine. As his starting point Socrates puts forth a “counter-truth” which claims that all human beings distinguish between ignorance and wisdom and, when asked, manifest this opinion by claiming themselves to be wiser in some areas than others and others to be wiser than themselves in other areas. Socrates believes that the everyday behavior of people verifies this claim, in times of sickness, people consider the doctor wiser than themselves, in times of war they listen to the generals. This apparently universal claim becomes truly threatening to Protagoras when we find out the definitions of wisdom and ignorance: “They are convinced that wisdom is true thought and folly false opinion” (170b). Here, in his refutation of Protagoras, Socrates once again assumes the identity of wisdom and knowledge. And furthermore, their behavior

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demonstrates that they do not consider themselves to be the measure of all the things that are. Socrates proceeds to a further weakening of Protagoras’s claim when he applies the general principle established above to the Protagorean dictum itself. He attempts to catch Protagoras in a self-contradiction by showing that his “truth” refutes itself. Within this argument Socrates appeals to the majority: Even if Protagoras’s principle is correct, if the majority would assert that Protagoras’s measure principle is false, then by this very principle they would be asserting a truth and thus the principle would be false. This is the so-called self-refutation argument. It is in this context that the shift to opinion plays such a crucial role because judging Protagoras’s doctrine to be true or false is surely outside of perception and would best be considered the expression of an opinion. Protagoras before his defense speech may have been able to rescue his doctrine by limiting it to perception. But in his own apologia he extended it to include political matters, which surely cannot be explained on the level of perception. Some commentators try to defend Protagoras’s claim by noting that the qualifier “for him” has been dropped from the argument and once reintroduced can resolve the self-refutation. Burnyeat counters that even if we were to supply the missing qualifiers that would appropriately “relativize” each opinion, the doctrine would still remain paradoxical, in that it would relativize everything but itself. As Burnyeat puts it: The relativist may reply “All truth is relative” is not asserted as an absolute truth, which would indeed be self-refuting, but only as a relative one: it is true for me that all truth is relative. This is no help. This second proposition is less interesting (because it is no longer clear that the objectivity of our beliefs is jeopardized if relativism is true only for the relativist), but it is still an assertion. “It is true for me that all truth is relative” is put forward as itself true without qualification. A commitment to truth absolute is bound up with the very act of assertion.”39 Burnyeat’s underlying assumption is that relativism as such is selfrefuting because it is like saying “Never say never.” This entire line of argument is of course immaterial, if Protagoras is not an “absolute” relativist; and his point about the distinction between knowledge and wisdom seems to confirm that there is at least one area, the realm of the expert, in which he would limit the relevance of the doctrine of measure. Like Burnyeat, Socrates too is guilty of constructing an interpretation of “man the measure” that would allow the self-refutation argument. Bostock, I think, puts forth a valid point when he claims that: “As it stands, Protagoras has the defense that he can distinguish between ‘it is true for me that it is false for others that P’ and ‘it is false for me that P’; and this defense is not adequately rebutted.”40 Bostock claims that Protagoras may very well argue that the measure principle does not apply to itself, that is, that a human

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being is indeed a measure for what is the case for her but she is not the measure of the measure. We might add that the principle itself is the utterance of a wise man and thus it cannot be refuted by the ignorant. The last point of attack that Socrates offers Theodorus, whom he occasionally addresses as “Protagoras,” is that his measure principle does not apply to what will be, the future. If we are concerned about the arrival of a fever, whether the wine will taste bitter or sweet, we consult experts in such matters rather than relying on ourselves as measures. This attack picks up from the previously introduced principle that all human beings consider others wiser than themselves in certain circumstances. The circumstance here is the future and I would venture that few of us would feel comfortable predicting future outcomes when it comes to sickness, battles and other events of that sort. Socrates tightens the stranglehold by pointing out that it is precisely with regard to the future outcome of a court case and the general well being of a city that Protagoras would proclaim himself and other sophists to be the measure. Socrates demands the following agreement from Theodorus on behalf of Protagoras: So it will be stated by us in a measured way (metrio ¯ s) before your teacher that it’s a necessity for him to agree that someone is wiser than someone else, and that whoever is of that sort is the measure, and there is no necessity whatsoever for me the non-knower to become the measure (metron), as the speech on his behalf was just now compelling to be of that sort, whether I was wanting to or not (179b).

In this statement Socrates continues to identify wisdom with knowledge—despite Protagoras’s attempt to distinguish them—and he involves himself in an indirect contradiction by identifying himself as non-knower and at the same time claiming to speak in a measured way. Surely this is a hint from Plato that this argument is not to be considered a total refutation. Nevertheless, Bostock who argued very persuasively against the notion that Protagoras’s position is self-refuting, thinks that the introduction of experts and judgments about the future—both of which are directly relevant to Protagoras’s acknowledged profession of sophistry—finally accomplishes a successful refutation, for if the homo mensura is correct, then no one should pay attention to him. So, the doctrine becomes fruitless. Burnyeat also makes the interesting claim: “The very notion of the future makes us submit to objectivity. So, then, does action. That is to say, life itself.”41 Obviously Burnyeat agrees wholeheartedly with Theodorus that the problematic of future judgments cannot be handled by Protagoras and he is thus thoroughly refuted. Also, the future cannot be predicted unless one is omniscient—whether or not we follow Hume’s analysis in which he questions the assumption about the future resembling the past or the general uniformity of nature.

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There is, however, a way to question what it is that Socrates has done. First of all, he relies heavily on time to make his point about experts and we may wonder whether the expert is actually wiser than the rest of us simply because he knows the truth for a longer time. When Socrates and Theaetetus were discussing dreams, both of them rejected the notion that length of time should determine truth. What is at stake in this discussion of the future is whether or not Protagoras’s homo mensura can have any predictive power. If the entire measure principle is restricted to perception, then there cannot be future predictions, because we do not perceive the future. If, however, it is the case that experts can make predictions about the future, then they must be relying on something more than just perception. Has Protagoras really been refuted, and if not, what is the point of all these attempts at refutation? We should notice that the refutation rests entirely on the “opinions of the many.” It is the distinction between wisdom and ignorance on the part of the many that Socrates appeals to when he begins his refutation. Furthermore, it is the consultation of experts by the many that brings up the issue of future judgments for Socrates. The one thing that Socrates establishes with his constant appeal to the many is that they make a distinction between knowledge and opinion, which is in fact most clearly exemplified by their consultation of experts. Socrates, we can surely say, is practicing philosophy “in the marketplace” here. But what is it that he tries to accomplish with his counter-speech against Protagoras? Socrates’ refutation seems to be pointed at the claim that every human being is the measure of everything. What we have seen in the discussion about perception is that such a claim holds true for perception, and Socrates wants to limit it to that. He never denies that man is the measure, but what he does emphasize in his refutation is that some human beings are the measure of some things and other people of other things. That surely is the basis on which there can be a distinction between experts and nonexperts, as well as the distinction between knowledge and opinion. There is no expertise in perception, but there are experts in other areas. In fact, the interlocutors in this dialogue are all of them experts. Socrates has begun an examination, which he will continue throughout the rest of the dialogue, where he will address directly that which here is merely suggested, namely the distinction between knowledge and opinion. A further question raised by Protagoras’s homo mensura is the extent to which we are capable of measuring ourselves: Even if we grant that perception provides us with the starting point of knowledge of the external world and can thus be constructed as a kind of measure, it is surely not the case that we can perceive and know ourselves in the same way. Whereas we can offer a possible explanation on the basis of the myth of twin motion of the birthing of particular percepts that are born moment

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to moment through the interaction between perceiver and the percipiendum, the same process can be applied to self-knowledge. As we have shown, however, if we understand the myth of twin motion in terms of ero¯s, the erotic interaction between two lovers can be a path toward selfknowledge. Similarly, the model of perception when applied to the dialectical interchanges between Socrates and Theaetetus which causes Theaetetus to give birth to certain ideas can potentially lead to selfknowledge. It is the measure of the midwife which will ultimately disclose both the measure of knowledge and self-knowledge.

8. REFUTATION OF HERACLITUS Following Protagoras’s instructions, Socrates next turns to an examination of the Heracliteans. Theodorus is passionate in his intense dislike of these “despicable characters.” Socrates identifies their position at this point as somewhere between the “motion people” and the “being people.” He proposes that they first examine the “motion people” or “streamers” and later if unpersuaded, investigate Parmenides and his group. The entire passage employs images taken from warfare, and it is all but irresistible to “root” for the hero caught in the war between motion and being. It is surprising that being is not dealt with in a dialogue on knowledge: Even though it is briefly mentioned here, Socrates and Theodorus refuse to examine it. Being appears, however briefly, in the refutation of Theaetetus’s thesis, but it is not until the Sophist that it is subjected to thorough philosophical scrutiny. In contrast to the myth of motion, which offered a physiological analysis of motion, this treatment is better described as a logical analysis of motion. Socrates characterizes the problem they are about to confront in the following way: from the ancients who were concealing it from the many with poetry, it was that the becoming (genesis) of everything else happens to be streams, Oceanus and Tethys, and nothing is at rest, and from those later who, because they were wiser, were revealing it openly, in order that even the shoemakers, once they heard it, may understand their wisdom and stop believing in their foolishness that some of the things which are at rest and some in motion, but once they understand that everything is in motion they may honor them? (180e).

There is a noticeable difference between the ancients and the moderns, as here understood: The former account for becoming (genesis), while the latter address themselves to motion proper without giving an account of genesis. It is in the context of discussing motion, without using motion to

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explain the becoming of anything, that both experience and language become tied into contradictions and are deemed impossible. The premises of the argument are quite simple. Socrates distinguishes between alteration and locomotion (181d), neither of which can be identified exclusively with the passive or active motion of the earlier discussion but which can be applied to both. He then insists that, if the Heracliteans want to avoid contradiction, they must agree that everything is in motion in both ways. Now, if seeing something white is the result of spatial motion as it was described in the myth of twin motion, then how are we to superimpose the motion of alteration? The alteration of seeing would be not seeing and similarly white would be nonwhite. This extreme version of Heracliteanism would make it impossible to say “I see white” for as soon as I utter the sentence I could have uttered “I do not see white” and “I see nonwhite,” contradicting both the verb and the predicate. In contrast to the earlier account of motion and becoming where “I see white” referred to the coincidence of the motions “seeing eye” and “being white,” this account of motion makes reference impossible.42 The refutations of Protagoras and Heraclitus concludes Theodorus’s active involvement in the dialogue and this particular exhibition of Theodorus’s prowess and of his likes and dislikes must have provided Theaetetus with a new angle on his teacher. At the beginning of the refutation section it appeared that Theaetetus was not quite ready for a full and serious examination of his offspring and Socrates chose to draw or force Theodorus into the discussion. This particular segment of the dialogue is reminiscent of the exhibitions sophists put on in an attempt to attract students. Since Theaetetus is already Theodorus’s student and an able mathematician, the exhibition of intellectual power can best be understood from Socrates’ point of view as an attempt to draw Theaetetus away from mathematics to philosophy. But before this can happen he needs to ascertain whether Theaetetus is a candidate for philosophy. And for Socrates the ultimate test is whether the undertaking will lead to selfknowledge. In the final section of the discussion about perception Theaetetus shows himself to be well on his way because he recognizes the role of soul in examining the different percepts and formulating opinions about them.

9. TROJAN BEING The final stage of the refutation of the definition of knowledge as perception concerns Theaetetus’s definition itself and returns Theaetetus to his role as the primary interlocutor. Socrates insists on a precision of language that gets Theaetetus to distinguish between perceiving through the eyes

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and ears or with the eyes and ears. The difference between the instrumental dative and the construction of the genitive with the preposition dia (through) is the difference between having a being that can collect the perception into a whole, versus, having a bunch of individual perceptions. Referring to the deception perpetrated by the Greeks with the “Trojan horse,” Socrates describes the difference in the following way: That’s because it’s surely dreadful, my boy, if many kinds of perceptions sit in us as if in wooden horses, but all these do not strain together toward some single look (idea), regardless of whether it’s soul or whatever one must call it, by which we perceive through these as if they’re tools, all the perceived and perceptible things (184d).

Socrates is differentiating between the sense organs themselves perceiving and something underlying the sense organs perceiving through them. Socrates underscores the limitations of the senses by showing that each of them is function-specific, that is, each sense can only fulfill its particular function. Thus, the eyes can only see and the ear can only hear, neither one of them can assume the task of the other. So, if we have the perception of a color and a sound, something other than perception is needed for us to think about them in conjunction. Socrates remarks that the mere fact that we can count them, consider them a pair, or think of them individually, suggests that there must be a faculty other than perception whose function it is to consider these matters. Socrates, using a contrafactual construction, forces Theaetetus to look at something other than perception to consider the following: If it should be possible to conduct an examination as to whether both of the pair are salty or not, you know you’ll be able to say by what you’ll examine, and this appears as neither sight nor hearing but something else (185b–c).

Add to that the question concerning being and not being and Theaetetus cannot help but arrive at the following conclusion: That “the soul itself through itself, it appears to me, examines the common things about all of them” (185e). This is a remarkable conclusion indeed. The response once again underscores how well Theaetetus is following and anticipating the argument. As I pointed out above, it is in response to this identification that Socrates declares that Theaetetus is beautiful. And Socrates adds: “And besides being beautiful you did me a favor and freed me from a very long speech, if it appears to you that the soul itself through itself examines some things, and some things through the power of the body” (185e). If we consider the dialogues where Socrates establishes the functions and makeup of the soul—the Republic and the Phaedrus, for example—we can

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appreciate Theaetetus’s discovery of soul by himself as a major accomplishment indeed. The passage in question explores perceiving, examining, and thinking. Socrates and Theaetetus arrive at the conclusion that, insofar as we have a concept of common things (ta koina), it is necessary to suppose the existence of soul (psyche¯ ). Soul, as it is here discussed, is capable of attaining being “through itself.” The discovery of soul was made possible through the slow and detailed examination of perception. Experiences “stretch to the soul through the body” (186c) and the soul examines and inspects them and considers their being.43 The word that Plato uses here (eporegetai) is the same word (minus the prefix) that Aristotle uses in his famous formulation of the first sentence of the Metaphysics, “All human beings by nature desire (oregontai) to know.”44 Socrates insists that it is the “hitting” upon being that should be equated with truth and this task can only be accomplished by the extra-perceptual activity of the soul. How precisely this can be accomplished is something that Socrates does not say. Is it that he does not need to state it explicitly, because he is “showing” it? The “action” of the dialogue shows how Theaetetus and Socrates, through the logos they are having, are aiming at the being of knowledge.45

O What is remarkable about the development of the discussion on perception is that it is only when we come to this very brief passage that Socrates actually refutes Theaetetus’s initial definition of knowledge as perception. If there are things that cannot be accessed by perception, but things about which we nevertheless pronounce judgments, then there must be something involved in knowledge that is other than or in addition to perception. Presumably, Socrates could have made the distinction between sense organs and their functions as over against the soul and its function early on. Instead, however, he took Theaetetus on a circuitous journey through Protagoras and Heraclitus. He apparently found it necessary to deal with the issues of measure and motion and present a thorough analysis of perception. Part of the explanation of this is related to his midwifery: He is more concerned with getting Theaetetus himself to examine his answer, with all its implications, than with showing Theaetetus that he is wrong.46 Theaetetus must himself come to know what it is that he is saying before he can move on to the next level on his journey to knowledge. Socrates not only has shown that perception is not identified with knowledge; he has also revealed to Theaetetus that it did not in fact appear to Theaetetus to be so, despite what Theaetetus initially said “appeared.” The results of the examination of Theaetetus’s initial definition of knowledge are not entirely negative. Important lessons are learned about

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the difficulties of measure: We are, on the one hand, made to recognize the need for measure; but it is not at all clear which of the human capacities should properly be considered the measurer, and what the limitations of our ability to measure are. Given our sensory apparatus, we may be well equipped to measure sense qualities; but what is it that allows the soul to measure the “common things” (ta koina)? At this point we do not know. Socrates has introduced himself, through his expertise in maieutike¯, as the measurer of what is fruitful and true and what is false and a lie; but he has not specified what capacity within his soul makes that possible. Protagoras’s rival measure doctrine is similarly vague: It specifies what is being measured, but it does not specify the means of measurement. With the move “upward” from the perceptible sense-qualities to the thinkable ta koina, a new measure will be introduced, which Theaetetus initially identifies as “opinion” (doxa). More importantly for the investigation at hand, Theaetetus has discovered the role of soul and identified soul as that which “strives” toward being. The significance of this recognition cannot be overemphasized: On the one hand, it is clear that Theaetetus could only have come to this observation through introspection, which can be considered an elementary form of self-knowledge or a movement toward that; but, on the other hand, he has identified the proper “object” to which knowledge is related, namely being—in any case as that theme is developed in the Republic. The identification of the relation between knower and being in terms of striving combines all the elements of desire (ero¯s), knowledge, and selfknowledge. Theaetetus has come a long way; but we still need to find out if he truly is the “philosopher-prince.” Theaetetus is on the way toward knowledge, but only on the way.

NOTES 1. For consistency I will translate psyche¯ as “soul” throughout, even though in some contexts “mind” might be the more obvious modern translation. 2. See Ronald M. Polansky, Philosophy and Knowledge: A Commentary on Plato’s Theaetetus (Lewisburg, Pa.: Bucknell University Press, 1992), 12. 3. For a fuller discussion of this point, see the last chapter. 4. On Theaetetus’s solution to the problem of the surds, see Miles F. Burnyeat, “The Philosophical Sense of Theaetetus’ Mathematics,” Isis 69 (1978): 172–95; Rosemary Desjardins, The Rational Enterprise: Logos in Plato’s Theaetetus (Albany: State University of New York Press, 1990), 171–80; and Sir Thomas Heath, A History of Greek Mathematics (Oxford: Clarendon Press, 1921), 1:202–13. 5. As Theaetetus describes the process of arriving at the solution, he looked at Theodorus’s drawings, which illustrated the incommensurability of the numbers 2, 5, 7, 10, 11, 12, 13, 14, 15, and 17, where Theodorus was apparently stuck at 17.

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On the basis of looking at these, “Young Socrates” and Theaetetus were able to come up with a universal formulation that would be applicable to all irrational numbers by naming them “oblong.” The very process of solving this problem is interesting in the way it combines number and image. The role of images in mathematics is discussed and critiqued by Socrates in Republic 6 in his differentiation between the third and the fourth segment of the line. 6. This is, of course, very suggestive in terms of modern quantum physics where this particular problem of measure is clearly addressed in Heisenberg’s formulation of the Uncertainty Principle. 7. “ho anthro¯pos” can be taken to stand for an individual human being or for the species. McDowell (Plato’s Theaetetus [Oxford: Clarendon Plato Series, 1973], 118) claims that “it is clear that the formula applies, at least as Plato understands it, to any member of the human race.” To the contrary, Laszlo Versenyi, in “Protagoras’ man-measure fragment,” American Journal of Philology 83, no. 2 (1962): 178–84, argues that we need to understand anthro ¯ pos as species. The strongest version of Protagoreanism, I believe, could endorse both, thus creating an individual “subjective” standard whereby one’s perceptions are just what they appear to be and thereby seem to create a universal (“objective”) standard, which has to be true for everyone. This reading could explain how Protagoras, later on in the discussion in the Theaetetus, can differentiate between the expert and the nonexpert— even though a purely individualist version of his maxim would allow no such distinction. 8. St. Thomas Aquinas discusses the idea that human beings measure humanmade things but are in turn measured by natural things. “The divine intellect is, as the first measure, not measured; a natural thing both measures and is measured; but our intellect is measured, and measures only artifacts, not natural things” (De Veritate, Q1, A2). 9. In important ways, this point is fitting for Protagoras. In the first place, Protagoras is among the professionally expert, paid sophists. In the second place, it fits the “utilitarian” approach that Protagoras takes with respect to the useful and the not useful in Plato’s dialogue Protagoras. 10. See Physics 194a20ff. 11. Aristotle, Metaphysics 11.6.1062b13 translated in Rosamond Kent Sprague, ed., The Older Sophists: A Complete Translation by Several Hands of the Fragments in Die Fragmente der Vorsokratiker (Columbia: University of South Carolina Press, 1972), 80 A. 19, 13. 12. See Aristotle, Metaphysics 4.4.1007b18. 13. Sextus Empiricus, Outline of Pyrrhonism 1.216. See Sprague, The Older Sophists, 11. 14. For a useful discussion of the similarities and differences between Berkleiean Idealism and the present discussion see Myles Burnyeat, “Idealism and Greek Philosophy: What Descartes Saw and Berkeley Missed,” Philosophical Review 90 (1982): 3–40. Burnyeat points out that an important difference between Socrates’ account and Berkeley’s idealism is that, for Berkeley, ideas depend on minds; whereas Socrates’ myth of twin motion creates a symmetry between the perceiver and the perceived. As to similarities, note the lack of common “public objects,” and that what is perceived is as it appears. (See p. 16.)

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15. The fact that Socrates refers to the same underlying wind goes beyond anything that could be attributable to Protagoras. Francis MacDonald Cornford, Plato’s Theory of Knowledge: The Theaetetus and the Sophist of Plato Translated with a Running Commentary (New York: Liberal Arts Press, 1957 [1934]), 33–34, assumes that the wind itself is both hot and cold, leading Protagoras into a contradiction. But it is not at all clear why we need to make this assumption. In fact, I am inclined to agree with McDowell, who argues: “It seems obvious that Protagoras refuses to make sense of questions about what the wind is like in itself, as distinct from questions about what it is like for one person or another” (Plato’s Theaetetus, 119). A third alternative reading is offered by A. E. Taylor, who suggests that “reality itself is individual in the sense that I live in a private world known only to me, you in another private world known only to you” (Plato: The Man and his Work [New York, Meridian Books, 1955 (1936)], 326). 16. The relationship between perception and being—that is, that perception (aisthe¯sis) is the first step in the disclosure of being—is the guiding thread in Heidegger’s discussion of the Theaetetus. See Martin Heidegger, The Essence of Truth: On Plato’s Cave Allegory and Theaetetus, trans. Ted Sadler (London and New York: Contiuum, 2002), 118ff. 17. Socrates makes a similar argument about the “goodness” of motion in the Charmides when he examines with Charmides whether his answer moderation (sophrosune) of quietness is acceptable. See Charmides 159d–160b. 18. See Sophist 248a–249c. 19. Both McDowell (Plato’s Theaetetus, 130) and Burnyeat (The Theaetetus of Plato, 13) suggest that Socrates (Plato) is joking at 152e–153d. Although that may always be a possibility, for my own part, I don’t see how that is very helpful in interpreting this passage. 20. The middle voice in Greek—in contrast with the active and the passive—is used when the subject is understood as acting upon itself and for many colloquial derivative sense of that. 21. Gail Fine uses the example of dice to support her reading of Protagoras as a representative of infallibilism, which for her entails that “whenever objects appear different, they genuinely change.” “Conflicting Appearances,” Form and Argument in Late Plato, ed. Christopher Gill and Mary Margaret McCabe (Oxford: Clarendon Press, 1996), 127. 22. Desjardins (The Rational Enterprise, 181–92) tries to make the case that it is precisely the dice example which gets Theaetetus to think about the causes of mathematical propositions. She supports the reading by highlighting Theaetetus’s expression of wonder at 155c–d. 23. David Bostock, Plato’s Theaetetus (Oxford: Oxford University Press, 1988), especially p. 82. 24. See David Hume, A Treatise on Human Nature: Being an Attempt to Introduce the Experimental Method of Reasoning into Moral Subjects, ed. L. A. Selby-Bigge (Oxford: Clarendon Press, 1958 [1888]), bk. 1, pt. 1, sec. 6, p. 15–17. 25. McDowell, Plato’s Theaetetus. 26. See J. L. Austin, Sense and Sensibilia, ed. G. J. Warnock (Oxford: Clarendon Press, 1962), 104–31. In more recent discussion of this point there is some dispute whether Protagoras’ dictum should be understood as limited to perception, which

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is called “Narrow Protagoreanism,” or whether it extends to opinion and judgment as well “Broad Protagoreanism.” Protagoras as a narrow, perceptual relativist is discussed by M. F. Burnyeat in “Conflicting Appearances,” Proceedings of the British Academy 65 (1979): 68–111. David Sedley in The Midwife of Platonism argues for a the broader understanding and Gail Fine (“Conflicting Appearances) suggests that the best way to understand Protagoras’ argument as it is portrayed by Socrates is as an “infallibilist.” 27. See Kenneth M. Sayre, Plato’s Late Ontology: A Riddle Resolved (Princeton, N.J.: Princeton University Press, 1983), 206–18. 28. See Aristotle, Metaphysics 11.6.1062b; see Hermann Diels and Walther Kranz, Fragmente der Vorsokratiker: Griechisch und Deutsch (Zürich and Berlin: Weidmannsche Verlagsbuchhandlung, 1964), 11th ed., 80[74] B.2. See Edward Schiappa, Protagoras and Logos: A Study in Greek Philosophy and Rhetoric (Columbia: University of South Carolina Press, 1991), 121ff. 29. Parmenides, frag. 6. See Kathleen Freeman, Ancilla to the Pre-Socratic Philosophers: A Complete Translation of the Fragments in Diels, Fragmente der Vorsokratiker (Cambridge, Mass.: Harvard University Press, 1957), 28.6.43. See Diels and Kranz Fragmente der Vorsokratiker, 28 [18], B.6, 1:232–33. 30. Edward Schiappa, in book Protagoras and Logos, suggests that we too often overlook the great accomplishment of Protagoras, namely, that Protagoras is the first one to formulate the concept of relativity, pp. 117–33. 31. The reference is to a ritual called amphidromia. McDowell (Plato’s Theaetetus, 158) writes: “The allusion is to a ceremony which took place shortly after birth. . . . The child was carried around the hearth, named, and given gifts. The ceremony probably marked acceptance into the family; hence the remark about deciding whether to bring up Theaetetus’s offspring. The name of the ceremony means literally ‘running around,’ and Plato plays on this.” 32. Edward N. Lee finds this passage particularly comical. “The basic structural device of this segment of the critique is the turning of the tables on Protagoras, a reversal that here takes the form of the classic encounter between eiro¯n and alazo ¯ n: the boaster is first ‘built up,’ but only so that he can have the highest fall. . . . I have no wish to minimize the arguments that Plato gives here, but his aim is not restricted to advancing those: he is not aiming merely to refute Protagoras . . . , so much as to expose him up for what he really comes to.” (“Hoist by his own Petard: Ironic and Comic Elements in Plato’s Critique of Protagoras,” Exegesis and Argument: Festschrift for Gregory Vlastos, ed. Edward N. Lee, Richard Rorty, and Alexander Mourelatos, Phronesis Supplement (Assem: Van Gorcum, 1973), 225–26. 33. Kenneth Sayre also thinks of the objections as “frivolous.” See Plato’s Analytic Method (Chicago: University of Chicago Press, 1969), 80. 34. See Cornford, Plato’s Theory of Knowledge, 82–83, 98–99. 35. “About the gods, I am not able to know whether they exist or do not exist, nor what they are like in form; for the factors preventing knowledge are many: the obscurity of the subject, and the shortness of human life,” in Freeman, Ancilla to the Pre-Socratic Philosophers, 80.4.126; see Diels and Kranz, Fragmente der Vorsokratiker, 80 [74], B.4, 2:265. 36. See Xenophanes, frag. 15: “But if oxen (and horses) and lions had hands or could draw with hands and create works of art like those made by men, horses

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would draw pictures of gods like horses, and oxen of gods like oxen, and they would make the bodies (of their gods) in accordance with the form that each species itself possesses.” See Freeman, Ancilla to the Pre-Socratic Philosophers, 21.15.22; see Diels and Kranz, Fragmente der Vorsokratiker, 21[11] B15, 1:132–33. 37. Within this passage there is a shift from perception (aisthe¯ sis) to opinion (doxa), which Maguire describes in the following: “The progress is from phaietai (of perceptions and sensations, 166d4, 7–8, 34) through doxazei (of opining about perceptions, 167a2, 6, 7, 8, e9) to dokei (of opining about “the right” and “the laudable,” 167c4, 5), from simple perceptions to judgments about perceptions to value judgments, all being elicited from the initial phainetai by way of doxazei, as if there were no difference among them” (118–19). See Joseph P. Maguire, “Protagoras— or Plato?” Phronesis 18 (1973): 115–38. 38. For a fully developed analogy between medicine/health and sophistry/justice, see Gorgias 464ff, where Socrates critiques sophistry as not fulfilling the craft of justice but rather as a knack, which aims at flattery. 39. Burnyeat, The Theaetetus of Plato, 30. See also Gail Fine, “Knowledge and Logos in the Theaetetus,” Philosophical Review, 88 (July 1979), and David Sedley, The Midwife of Platonism. 40. Bostock, Plato’s Theaetetus, 92. 41. Burnyeat, The Theaetetus of Plato, 42. 42. See Cratylus 402ff, 440d–e. 43. Prior to the soul’s stretching is the all-important depiction of the soul’s “striving” toward being (186a). As Theaetetus states it in response to Socrates’ question as to where he locates being: “Well, I place it [being] in those things which the soul by itself aims at (desires, eponta, 186a). Eporegetai is a rare word, which Plato uses only two other times, in the Republic. 44. Metaphysics 1.1.980a22. 45. See Sophist 248a: “And we, you say, share in becoming through perception by means of body, but theory and calculation (logismou) by means of soul in being in its being, which is always, you assert, in the same state in the same respect, but becoming (is) at different times in different states.” trans. Seth Benardete, The Being of the Beautiful, pt. 2 (Chicago and London: University of Chicago Press, 1984 [1986]), 2.41. 46. Polansky, Philosophy and Knowledge, argues that Protagoras and Heraclitus are the parents of Theaetetus’s offspring. Thus one way of understanding this exercise is to force Theaetetus to know the cause of his “opinion.” 47. See Blondell, The Play of Character in Plato’s Dialogues, 252–60.

4

O Doxa-Logy

A

fter successfully refuting the hypothesis that knowledge is the same as perception, and after having brought soul and its capacities to the fore, Socrates and Theaetetus turn to opinion (doxa) as the new candidate for a definition of knowledge. Opinion had already made an appearance in Protagoras’s defense speech: Protagoras moves to questions of the city and it would hardly have made sense to speak of perception by a city.1 Protagoras’s homo mensura encompasses both perception and opinion; but, as we shall see, the incorrigibility of perception cannot be transferred to opinion. In fact the greatest part of the examination of opinion is concerned with puzzling through false opinion, working out its very possibility by imagining soul as a block of wax and as an aviary. Finally, Theaetetus offers logos as the criterion that will make true opinion into knowledge; and Socrates in turn offers three definitions of logos that recapitulate the three definitions of knowledge. The final formulation that knowledge is “right opinion with knowledge of difference” (210a) appears circular, but both Socrates and Theaetetus nevertheless express satisfaction in having accomplished what they set out to do: Theaetetus is free from labor pains after having delivered his opinions about knowledge. In addition, Socrates has accomplished the all-important task of differentiating opinion from knowledge. In the Meno Socrates discusses the distinction between knowledge and opinion in two different contexts. The first discussion concerns the difference between having a true opinion about the solution to a mathematical problem, on the one hand, and knowing the answer precisely (akribo¯s), on the other. The second part differentiates having a correct opinion on the 103

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basis of hearsay from having knowledge on the basis of direct experience or immediate perception. It is never spelled out in the Meno precisely how we are to distinguish knowledge from opinion, but Socrates is vehement in his assertion that there is such a distinction to be made. He explains to Meno that much of their discussion about the teachability of virtue has been based on guesswork and conjecture, and continues: However I certainly do not think I am guessing that right opinion (orthe¯ doxa) is a different thing from knowledge (episte¯ me¯ ). If I claim to know (eidenai) anything else—and I would make this claim about few things—I would put this down as one of the things I know (oida).2

This is a very strong assertion by Socrates, one of his very rare claims to direct knowledge of any specific thing.3 He speaks as though the very endeavor of philosophy depended on the distinction between knowledge and opinion; and, as will become clear, to a certain extent it does. To be able to distinguish and recognize the difference between true opinion and knowledge is the task of philosophy. Opinion is ubiquitous and is always accompanied by the possibility of error. The most dangerous error is, of course, to mistake opinion for knowledge and thereby to preclude an examination of one’s opinion. Only a thorough dialectical work over of one’s “opinions” can establish that this kind of error has occurred.4 We by ourselves are not the measure of opinion and in fact depend on dialogue with an other to establish the falsehood or veracity of opinion. As will become clear in the next section, thinking leads to opinion through a silent dialogue with oneself. And yet, one’s private thoughts surely are not as such equivalent to knowledge. In order to establish successfully the difference between knowledge and opinion we must work through opinion—not abandon or skip over it.5

1. THINKING Socrates characterizes opinion in a new and curious way when he is defining “thinking”: Soul thinking looks to me as nothing else than conversing (dialegesthai), itself asking and answering itself, and affirming and denying. But whenever it has come to a determination, regardless of whether its sally was on the slow or keen side, and then asserts the same thing and does not stand apart in doubt, we set this down as opinion. Consequently, I for one call opining speaking (legein), and opinion a stated speech (logon eire¯ menon); it’s not, however, before someone else any more than it’s with sound, but in silence before oneself (189e–190a).

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The silent dialogue the soul conducts with itself leads to the formulation of an opinion whenever it can reach a conclusion about whatever it is thinking about. When the soul thinks its way to a definite answer, it is convinced by its own conclusion and does not see any reason to doubt itself—at least not at that time. The danger is that the soul might persuade itself that it is now in the possession of true opinion or knowledge and thus that further examination is no longer necessary. But, it is clear from Socrates’ description that self-examination by itself can only lead to opinion, and that something in addition to “thinking” is needed in order to move from opinion to knowledge. At the same time we must notice here that opinion is a necessary step toward knowledge: In the conversation of the Theaetetus it is the thinking about perception that gives rise to the theme of soul and its capacity to think about ta koina such as being; Theaetetus then names that capacity doxazein, to opine. The move from opinion to knowledge is facilitated by the recognition that opinions can be either true or false; Socrates and Theaetetus will puzzle through the phenomenon of false opinion before examining whether true opinion is the same as knowledge. The process of thinking can also lead to an aporia, a state of perplexity, in which case the help of someone outside oneself is needed to examine whether or not the aporia is due to an intrinsic limitation in human knowledge or a mistake in thinking. It is precisely this experience of aporia that compels Socrates to examine false opinion with Theaetetus: It’s [opining false things] something that in a sense disquiets me now and often at different times has done so, so as to have got me into a lot of perplexity before myself and before everyone else, when I’m not able to say whatever is this experience we have and in what manner it comes to be in us (187d).

The ensuing discussion will introduce different scenarios examining the possibility and the process of false opinion. The first part concerns the impossibility of mistakes when dealing with identity statements: if I know triangle (x) and I know square (y) I will not mistake x for y or vice versa. And all the other possibilities of knowing and not knowing x and y lead to the same conclusion, that is, it is impossible to misidentify either what I know or what I don’t know with something else that I know or don’t know.6 Furthermore, if knowledge like perception is always of something that is, it is impossible for me to mistake what is for what is not. Socrates, in fact, joins Parmenides and declares that it is impossible for us to opine that not being is not: “So it’s not possible to opine that which is not, either about the things which are or [to opine that which is not about] itself by itself” (189b). If to opine not being is not to opine at all, and if it is impossible to opine that not being is not, then Protagoras’s homo mensura is at

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least half refuted because Protagoras claims that humans are not just the measure of things that are but also of things that are not, which is impossible according to Socrates’ argument. Furthermore, Socrates demonstrates that in the cases of “knowing” and “being,” false opinion is not possible, and thus demarcates knowledge from opinion, because if false opinion is not possible, then by implication true opinion is not possible as well. Allodoxia represents Socrates’ last attempt at solving the puzzle of false opinion before he resorts to images and brings the soul into play. Combining the findings of the two previous attempts, Socrates puts together knowing and being and coins a new word, allodoxia, else-opining, which he defines as “whenever someone makes an exchange in his thought of some one of the things which are for something else of the things which are and says it is that” (189c). Theaetetus, in his keenness, offers an illustration of the definition, which introduces more difficulties rather than solving any. He suggests that someone who opines that the beautiful is ugly, or the ugly beautiful, would be guilty of “else-opining,” or as he puts it, “would truly opine falsely.” Socrates rightfully scolds him for engaging in such blatant contradictions and takes this illogical thinking to be a sign that Theaetetus does not respect him (189c). Socrates proceeds to examine the possibility of thinking that some existing thing is another existing thing as an explanation for false opinion. On the dialogical level Theaetetus’s controversial illustration is not as shocking, for with it he expresses his own experience. In likening him to Socrates, Theodorus identifies Theaetetus as ugly, whereas Socrates explicitly contradicts Theodorus’s opinion by proclaiming Theaetetus to be beautiful. If Theaetetus is in fact thinking that his own case provides an example of Socrates’ definition, then he is missing the point of elseopining. The difficulty lies not in explaining how two different people can assign contradictory predicates to the same one thing, but rather how two contradictory things can be identified as the same thing. “Theaetetus ugly” and “Theaetetus beautiful” reminds us of the discussion of “Socrates sick” and “Socrates healthy,” where Theaetetus and Socrates agreed that each is wholly other from the other. The only way one can arrive at the opinion that the “beautiful is ugly” from the premises “Theaetetus is ugly” and “Theaetetus is beautiful” is by forming an invalid syllogism (AAA-3) that commits the fallacy of the illicit minor. There is in fact no thinking other than fallacious thinking that would lead to this conclusion. If all false opinions are reducible to logical fallacies, then the solution to the problem of false opinion should be fairly straightforward. But it is not. Socrates concludes this section and builds a transition to the next one by insisting that they cannot leave the problem in a state of such perplexity that opens up such a sea of absurdities. To prevent the experience of sea-

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sickness, Socrates suggests that they reexamine what had previously been agreed upon to be impossible: “to opine what one does not know to be what one knows” (191a). What was considered as impossibility from a logical point of view will become possible with the introduction of memory.

2. WAX: MATCH ME IF YOU CAN Socrates responds to the logical conundrum of the impossibility of false opinion by developing two memorable images: that of wax and that of an aviary. Each is designed to explore the connection between false opinion and memory. The first example asks us to imagine that the soul is waxlike, capable of receiving impressions both of the perceived and of the thought. The problem of false opinion can then be cast as a mismatch between an imprint previously received and a new perception or some new thought. Socrates is eager to reconsider a previously rejected case, to opine, namely, that that which one does not know is what one does know. Theaetetus is once again quick to offer an illustration in which someone who is familiar with Socrates sees a man in the distance whom he identifies as Socrates, but who turns out to be someone he does not in fact know. So it is the complexity of matching a perception with something that is already present to us—that is, something with which we are already acquainted or familiar—which becomes the key factor in an explanation of false opinion. Theaetetus’s example introduces distance, or more generally space, as a variable that leads to mistakes. Socrates then adds time as yet another consideration in the treatment of false opinion, and it is time that opens the door to the problem of memory. The wax image then really becomes an image for memory. In explaining the role that memory plays in the construction of false opinion, Socrates is led to tell the following story: the wax which takes on different shapes and consistencies in different individuals is a gift from Mnemosyne (Memory), mother of the Muses. The wax is capable of receiving impressions (smeia) of both our perceptions and thoughts (aisthe¯ sis and ennoia) and we can be said both to remember and to know as long as there remains an image of the received impression. Socrates adds the following puzzling comment: “but whatever is wiped off or cannot get impressed, that we forget and we do not know.” (191e) Surely, we must wonder what lies outside the capability of memory and furthermore we must question whether that which is not impressible can also give rise to false opinion and whether the later discussion of the aviary is meant to cover these “non-memory” cases. Are we to infer from Socrates’ description of the wax that memory is the storehouse of images and any thought which cannot be translated into an image cannot be remembered?7

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Socrates proceeds with the discussion by displaying his agility at thinking. He rattles off a list in which he enumerates all cases where a mismatching between “memory knowledge” and perception is impossible. We might note that the entire list is concerned with a type of knowledge that is very close to Russell’s “knowledge by acquaintance” and the term used for “knowing” is oida, which is closely related to seeing. So Socrates is not investigating episte¯ me¯ as such here, but rather the kind of knowledge that is based on perception. The rapid specification of the impossible cases—the “impossible possibilities,” as it were—is very confusing on first reading. Like Theaetetus, the reader is initially at a loss to understand what Socrates is saying. There are fourteen possibilities that Socrates enumerates.8 Socrates presents his list as an exhaustive set following from his thinking through of all the cases “from the beginning” (ex arche¯ s). It is up to us to infer the principles that he relies upon, which enable him to present all cases in such a rapid fashion. After the display of Theaetetus’s dumbfoundedness, Socrates gives us some hints that enable us to deduce the principles. One principle which underlies the discussion is that anything known (in the sense of “memory knowledge”) can either be perceived or not perceived and the same is true for that which is not known, with the qualification that it is possible that “the not known” may only be perceived. This last addendum confirms once again that perception is not knowledge. On this basis Socrates reintroduces the logical principles that provided him with the starting points for the discussion of false opinion: (1) it is impossible to mistake something one knows for something else one knows or for something one does not know; and (2) whatever one does not know cannot be mistaken for something else one knows or does not know. These same principles can also be applied to perception. What one knows can either be perceived or not be perceived, and consequently there are three cases where one both knows and perceives something, and it is impossible for there to be mistakes regarding something else which one either knows or perceives or both knows and perceives. Socrates then constructs three parallel cases for the negative state of not knowing where whatever is neither known nor perceived cannot be mistaken for something else which is not known or not perceived or neither known nor perceived. The last impossible misidentification is concerned with the case where something that is known and not perceived is mistaken for something else that is known and not perceived. As the negative cases illustrate, we need some kind of an impression in our wax in order for the mismatching of it with something else to occur. That is, in order to mistake something for something else, there has to be something “there” for the “taking” in the first place. Since Socrates has ex-

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hausted the possible combinations of knowing and perceiving and since what one does not know is either not perceived or only perceived, the cases for false opinion are all concerned with knowing something (i.e., having an imprint in memory) and mismatching it with either the perception alone or with the perception combined with knowledge of something else. He finally does provide a case where other-opining is a case of false opinion: when both x and y are known and both are perceived at a distance and mismatched such that the perception of y is combined with the knowledge of x and the perception of x with the knowledge of y. Socrates summarizes the discovery in the following passage: “But about what we know and are perceiving, it’s in these very cases that opinion whirls and twists about and becomes true and false—true if it brings together its own impressions and (fresh) impresses straightforwardly and in a direct line, but false if it’s crosswise and crooked” (194b). Socrates clearly indicates that the false opinions that arise from mismatching knowledge and perception are avoidable. The case of putting one’s shoes on the wrong feet or mistaking left for right when looking in a mirror (193c) are like those cases of false opinion which can be avoided or corrected through care and attention. Nevertheless false opinions abound. Socrates addresses the reasons for this in a strange account about the various conditions of the wax-soul. To explain the cause of false opinion, Socrates turns his attention to things that “they say.” It is not clear whether “they” here refers to “the poets,”9 or to common opinion, or whether Socrates is merely distancing himself from the story he is about to tell. Nevertheless, the unidentified “they” seems to locate the cause of false opinion in the condition of soul. The issue of the beautiful is woven into the description of the wax, where a measured kneading creates beautiful wax, wax whose beauty is evident in that [the owners] first of all learn easily, and secondly have good memories, and so it’s not they who interchange the seals of their perceptions but they opine what is true. For inasmuch as their seals are plain and have plenty of room, they distribute them quickly to their own several casts, and it’s these casts which get called the things which are and it’s these people who get called wise (194d).

This passage can plausibly be interpreted as a foreshadowing of the Kantian (or, more precisely, neo-Kantian) picture of the “working” of the mind (Arbeit des Geistes).10 It is a strange turn of events to see Socrates—who clearly introduced the image as an image, to enable us to take the next step in our examination of false opinion—turn around and treat the image literally. At the same time, Socrates distances himself from that description by introducing it with “they say.”

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We can fairly well guess what the “ugly wax” is like, but the question that Socrates leaves unanswered is who is responsible for the condition of the wax—unless, of course, we are to assume that Mnemosyne endows us, not just with wax, but with different qualities of wax. Can education, paideia, for instance, alter the condition of the wax? Socrates concludes the discussion of the beautiful and ugly wax by pointing out that “after all, false opinions are in us. . . . And true [ones] too” (195b). So he suggests that we are a mixture of the two extreme cases and that each case provides us with a schema for explaining both true and false opinion. True opinions come about whenever we are in possession of a good and clear impression, which is derived either from a perception or a thought, and we are able to match a future perception or thought with that impression. False opinion, on the other hand, occurs when we mismatch a fuzzy or indistinct impression with a future perception or thought.11 And so Socrates has achieved what he set out to do: he has arrived at an explanation for the possibility of false opinion. The example of the wax provides an explanation of false opinion that is the twin of Socrates’ discussion of true opinion in the Meno. Having a true opinion about the road to Larissa depends on the accuracy of the instructions that were heard. In order to transform true opinion into knowledge it would be necessary to confirm or verify the instructions through one’s own immediate experience. As soon as we venture an opinion, we run the risk of falsehood, for opinion is mediated and, unlike perception, it is not immediate experience. The fickleness of opinion, which Socrates discusses in the Meno, is precisely related to the need for constant verification in the realm of empirical knowledge. The difficulties of misidentifying the man at the distance as Socrates cannot be explained as a problem of perception but rather shows how venturesome opinion is in arriving at a conclusion in the light of inconclusive evidence. So it is the loss of immediacy that opens up the possibility of false opinion. And it is the two-fold character of opinion that explains the details of false opinion with regard to our making determinations about sense-perception. Opinion about perception can misfire because it involves both a perception and a memory. Furthermore, the entire account of matching or mismatching minimizes the role of the knower because the determination that “x is Theaetetus” occurs instantaneously without any reflection or deliberation.12 Although Socrates claims that his listing of impossible mismatches between perceptions and “knowledges” is exhaustive, he does not claim that his list of possible false opinions is complete. To point toward this incompleteness and to motivate further discussion, Socrates questions whether mistaking is possible on the level of thought alone. His discussion of the possible mistaking of 11 for 12 in response to the question

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“what is 7 + 5?” leads us to suppose that another image is necessary. Consequently Socrates will engage in another round with false opinion, trying to “catch” it one more time, when he turns to investigate false opinion in the realm of pure thought.

3. THE AVIARY: CATCH ME IF YOU CAN Socrates prepares for the construction of the aviary by offering the common definition (“they say”) of knowing as “having knowledge” (episte¯me¯s hexin, 197b). He elaborates on this definition by differentiating “possessing” (kte¯sis) from “having” (hexis), maintaining that one can possess something (for example, owning a cloak) without really having it (for example, wearing the cloak). Socrates is setting up a distinction that will allow him to differentiate between virtual and actual knowledge, anticipating Aristotle’s distinction between possessing knowledge and exercising it.13 To clarify how someone might mistake 11 for 12, Socrates asks us to imagine an aviary which contains “number birds” flitting about—and in order to have rather than merely possess 12, we need to hunt down the bird. To evaluate Socrates’ new image of the aviary, we need to understand why it is that the wax model could not provide any answer to challenges of this sort. This will turn out to be equivalent to ascertaining the requisite conditions for explaining false opinion at the level of pure thought. Socrates maintains that if we think of 11 and 12 in connection with touching and seeing, then indeed it may be possible to mistake one for the other when replying to a question concerning the sum of 7 and 5; but if we were to consider the numbers by themselves, such mistaking would be impossible, at least if we were to remain with the image of the soul as a wax-block (195e–196a). To flesh out this claim, let us imagine that someone is asked to determine the number of people who are standing in line at a popular souvlaki stand in ancient Athens. Upon counting those in the queue, this individual, wanting to set up shop as a second souvlaki salesman, arrives at the result that there are eleven people, when in fact it turn outs that there are twelve. In such a case the person is mismatching a perception with an already present memorial—and that under the assumption that numbers are already present in his memory. In order to perform the function of counting, we have no alternative but to assume that numbers are already in some way present for us. The would-be shopkeeper is not really mistaking the number eleven for the number twelve; rather he is misdescribing a group of people by wrongly assigning the number eleven to that group. The counter is mistaking twelve “things” for eleven “things”—which could be likened to the mistake of misidentifying one individual as another individual, except that here the process of counting

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replaces the process of perceiving. When dealing with the task of summing 7 and 5, we can arrive at a similar explanation in the context of seeing or touching numbers. Imagine now a third souvlaki seller, who joins the two others on a sidewalk of the agora, selling his goods for half the price of the other two. He is looking at the five customers of the first vendor and the seven of the second, and he tries to figure out his potential profit, should all of them come to his stand. He miscalculates his anticipated income, since he thinks that he will have eleven customers rather than twelve. All this type of mistaking could be explained in terms of the wax mold, for all of it occurs on the level of experience. In fact, Elfriede Tielsch suggests that the transition that Plato makes in going from this problem to the next one is the transition from empirical mathematics to pure mathematics.14 What occurs as a mistake in this so-called empirical mathematics of addition and subtraction can easily be explained as a recurrence of the previous miscounting of 11 for 12. As such there is no operation of addition involved here, but rather the same process of counting that led to the previous error. What prompts Socrates to launch a new investigation of false opinion is that this explanation does not apply when we are dealing with numbers by themselves. Instead, he argues that we are confronted with the same impossibilities that confronted us when we were dealing with the issue of mistaking Socrates for Theaetetus. The underlying principle—which enabled Socrates to show that in the cases of either knowing or not knowing, one or the other or both, it was impossible to mistake one for the other—can now be put more straight-forwardly as the impossibility of thinking that two is one. The reason why numbers themselves, on the example of the wax block, cannot be mistaken for each other, rests on the same principle, that is, if we inspect the wax and find the two imprints of 11 and 12, it is impossible for us to think that they are identical, for if they were there would be one imprint rather than two. With this in mind Socrates virtually predicts their forthcoming failure to explain false opinion at the level of pure thought, when he suggests that they must first get hold of what knowledge is before they can give a satisfactory account of false opinion. Socrates proceeds then to define knowledge as minimally, the “having of knowledge,” whose actuality depends on the “possession of knowledge.” This distinction has been usefully discussed by Frank A. Lewis, who prefers to rename the two as “dispositional” and “actual” knowledge.15 Unfortunately, however, he proceeds to confuse the issue by introducing the further distinction between actual and virtual belief, in an attempt to explain the possibility of believing that 11 is 12. The problem with this latter distinction is that he assumes that what is a distinction with regard to knowledge can just as well be applied to belief (doxa).

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Equipped with this he can easily construct a scenario whereby one can have the virtual belief that 11 is 12 and thus misidentify one number for another. But there is no evidence in the text to indicate that this is where Socrates is heading. In fact, the text shows that Socrates finds himself in a quandary and is unable to solve the puzzle of false opinion at the level of pure thought, fulfilling his own prediction that in the absence of a discovery of what knowledge is, false opinion will have to remain a puzzle. In response to the antilogikos (the imagined contradictor-interlocutor, 197a) Socrates develops the new image of the aviary, which is intended to represent the level of thought unmixed with perception. By choosing to describe the difference between the possession of knowledge (kte¯ sthai) and the having of knowledge (echo ¯ n) as the difference between capturing birds and putting them into a cage in the first case and then recapturing them to “having them” and “holding them” in the second case, Socrates is giving us some hints as to the way in which pure thought differs from experience. The image of living birds suggests activity; even after their capture the birds are said to fly around in the cage and they need to be hunted down once again. Socrates intensifies the power of this image by suggesting that actively knowing something is having that which is to be known under one’s thumb and thus putting an end to the incessant birdlike motion. We must wonder to what degree this controlling also changes the nature of the bird. If it is the nature of something that we want to know, and if we need to hunt it down and “domesticate” it, then what we finally have is not precisely the same as that which we set out to discover. Some significant change must indeed occur if it is possible to transmit the sort of knowledge that Socrates describes as involving both teaching and learning. The entire discussion is reminiscent of the Meno and it seems to contradict virtually everything that Socrates tries to demonstrate there with the example of the slave and the adumbration of the theory of recollection. In contrast to the Meno, where Socrates argues that we already know all there is to know and all that is necessary is for the soul to recollect that which it already has within it, here Socrates supposes that the soul, represented as a cage, is, at the time of birth, empty: it is filled with different “knowledges” (birds) through the activities of teaching and learning. There is, however, an important similarity as well, in that both discussions explain knowledge in terms of a process that involves two kinds of knowledge: one that is residing “passively” within the soul and the other that activates what is already there. It is clear in both cases that knowledge requires a process that can “proceed” from some kind of “foundation.” Socrates defines learning in the following way: “And whatever knowledge one acquires and confines in the enclosure, one has to say that he has learned or found the matter of which this was the knowledge, and

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this is to know” (197e). Throughout this passage, in contrast to the discussion of the image of the wax, the knowledge and knowing under consideration are all different grammatical forms of the root word for episte¯ me¯. We are apparently no longer concerned with memory, as we were earlier when the term oida was used. Equipped with this strange image, Socrates is ready to tackle the problem of numbers themselves and he offers the different senses of the term “knowledge” as a solution to the initial contradiction involved in the apparent state of both knowing and not knowing the same thing at the same time. Through learning and transmission we, as arithmeticians, possess the numbers 11 and 12, but we still need to access them in order to have them. It is in this re-acquisition that false opinion is said to occur: whenever in hunting on some occasion some knowledge somewhere, while they’re flying about, one misses and seizes another instead of an other [sic!], it’s just at that time that one comes to believe the eleven is twelve—when one seizes the knowledge of the eleven in oneself instead of the knowledge of the twelve, as if it were a ring-dove instead of a dove (199b).

The language of this passage is reminiscent of the earlier discussion of allodoxia, and indeed the issue is whether that which could be worked out, at the level of perception and thought, of mistaking the other for the other is here once again raised at the level of thought by itself. It is not surprising then that Socrates follows this proposed solution with objections, such as the impossibility of mistaking one knowledge for another. We are after all not hunting down two numbers but the “knowledges” of these numbers. If it is possible to mistake one’s knowledge of 11 for one’s knowledge of 12 then the matter seems to be hopeless, for it is difficult to imagine what could possibly be the remedy for such mistaking. Socrates’ follow-up comment on this issue, however, may suggest a possible solution to these dreadful false opinions. He claims: “On the basis of this speech, nothing stands in the way of the presence of ignorance making one know something and blindness making one see, if knowledge in fact will ever make one ignorant” (199d). The two examples he uses remind us, of course, of Socratic wisdom and of Oedipus’s insightfulness and wisdom after blinding himself—the wisdom that always comes too late.16 Is it not precisely the practice of Socratic maieutike¯ and dialectics that can reveal the false opinions of thought? The question whether Socrates’ method can be as successful with the mathematician as it had been with the likes of Euthyphro remains as yet unanswered. On some level we know from the Meno that Socrates is able to assist some people at least in detecting their false opinions in the mathematical realm and in remedying them. The slave’s experience of the journey from ignorance— in the sense of not knowing—to false opinion to the knowledge of igno-

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rance to true opinion displays precisely a progression that successfully arrives at true opinion but does not constitute knowledge. Instead of directly addressing the problem that Socrates describes, Theaetetus attempts to find a way around it by suggesting that the cages contain items of non-knowledges as well as items of “knowledges.” He thus proposes that one could describe false opinion in terms of a seizing of some non-knowledge instead of “a knowledge,” whereas a successful hunt would lead to “a knowledge” or true opinion. This suggestion is by no means self-explanatory and needs some elaboration before it can make very much sense. Non-knowledge cannot function in the same way as ignorance, because no one would set out to hunt ignorance. Furthermore, we must assume that these non-knowledges share some resemblance to knowledge, since we would otherwise be unable to explain how anyone could mistake non-knowledge for knowledge. If nonknowledge cannot be ignorance and must appear to be like knowledge to the hunter, then it would seem that opinion is the ideal candidate for Theaetetus’s non-knowledge. Now, it is not so easy to imagine how we can apply this case to the mistaking of numbers, or how one is to characterize opinion within the field of mathematics. One way of approaching an understanding of this difficulty would be to consider under what circumstances a person might wrongly assert that 11 is the sum of 5 and 7, and how that constitutes opining.17 Furthermore, if the same person were to assert that 12 is the answer, would that still be a matter of opining? It must be granted that the arithmetician when thinking about the numbers themselves, would not be capable of arriving at 11 as an answer to the stated problem. One reason for that is that, instead of merely counting, the arithmetician is by definition someone who knows odd and even and thus knows that when adding two odd numbers the answer must be even. There are too many things that would have to go wrong for a mathematician to mistake 11 for 12. If we contrast that with the non-arithmetician, we can see how that person may operate on the level of opinion and thus be capable of committing such a glaring error. Rather than knowing anything about numbers, that person may be someone who is merely repeating from memory something he has heard. And thus the case of false opinion has to be constructed along the lines of mis-remembering. In that case he is not really mistaking his knowledge of 11 for his knowledge of 12, but rather his opinions about 11 and 12, which were acquired on the basis of hearsay. Socrates, however, is not interested in exploring Theaetetus’s suggestion. Instead, he praises him indirectly and refutes the idea of non-knowledges by resorting to a “skilled refuter” (elenktikos), who reduces the imagined cage of knowledge and non-knowledge to a shambles of absurdities. The refuter brings up once again the initial paradoxes of both knowing and

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not knowing the same thing. The new aspect of the refutation is that Theaetetus’s suggestion is shown to lead to an infinite regress as well: Or will you tell me once more that there are in turn knowledges of the knowledges and non-knowledges, which their possessor confined in some ridiculous dovecotes or wax molds, and knows as long as he possesses them, even if he does not have them ready at hand in his soul? If it’s in this way, won’t you all be compelled to run around to the same point thousands of times and get nowhere? (200c).

What is striking about this passage is that Theaetetus considers himself completely refuted. There is of course a way to bring such a process of infinite regress to a conclusion, and we would expect the mathematician to be able to answer this challenge. It is surprising that Theaetetus fails to mention “first principles” or “axioms” when he is answering to the antilogikos. He was, after all, able to put a stop to the tortuous labor of Theodorus in undertaking to prove the problem of the surds one by one; he introduced a principle that enabled him to address all cases. The introduction of first principles would have allowed the discussion to proceed and to go on to an examination of the difference between the kind of false opinion that is a mismatch between a perception and a thought and the kind of false opinion that arises from a mistake in counting or deduction. But, as has been the case throughout the dialogue, Theaetetus is somehow reluctant to use his own experience in discussing the question of knowledge. The question of first principles will be hinted at later on in the examination of Socrates’ dream. Perhaps the reason why first principles are not introduced here in the discussion of the aviary is that they cannot be “birds.” Unlike the knowledge that is deduced from first principles and which clearly involves a process, axioms or first principles cannot, by definition, themselves be deduced. Socrates, in contrast, must be reminded of his practice of dialectics and the conversation he once had with Critias, where self-knowledge was turned into the very same formulation—the knowledge of knowledges and non-knowledges.18 Yes indeed, there may be different orders of “knowledges”; but an argument that assumes that true opinion is the same as knowledge cannot enter into that discussion. Socrates, the midwife, prepares instead to aid Theaetetus in aborting this, his second-born. He prepares the way by once again asserting that it is impossible to give an account of false opinion without first arriving at an understanding of what knowledge is. And so finally they go back to Theaetetus’s definition of knowledge as “true opinion” and Socrates quickly disposes of it with the example of a jury trial (200d). If, on the basis of eyewitness accounts, a jury is persuaded about the guilt or innocence of someone accused of robbery, then,

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if the eyewitnesses are indeed reporting what they saw, then the jurors will arrive at a true opinion about what occurred. But their opinion needs to be distinguished from the knowledge of those who were actually present at the events. This entire example and its reasoning run parallel to the account of the “road to Larissa” in the Meno, except that Socrates adds persuasion as a factor in the account here.19 But what exactly does persuasion accomplish? How does it differ from teaching? Is persuasion primarily concerned with the character of the witness or with the occurrence of the events? Surely they are linked. If I desire to persuade you that my words are believable, ultimately I am asking you to trust me as well as my words—even if I introduce “independent” evidence, for I am then asking you to trust that.20 It is also noteworthy that Socrates here reintroduces perception, and that it is perception that ties down opinion. The examination of opinion has demonstrated that Theaetetus’s identification of opinion as that capacity which touches on being has proven to be very troublesome, because it has opened the door to false opinion. While the analysis of perception introduced the notion of infallibility, to that extent making perception appear to be knowledge, perception failed as a definition of knowledge, because it did not address being. Here, opinion is introduced, and according to Theaetetus opinion does touch on being but opinion cannot meet the infallibility criterion. It is clear from Socrates’ analysis of false opinion that the reason for this fallibility is that opinion apprehends being mediately or discursively. As long as we were dealing with only one kind of knowing or only with being, false opinion did not arise; but once we had two, as in the case of perception and memory and virtual and actual knowledge, the possibilities for false opinion became evident. The road that has brought us here should have provided sufficient grounds to anticipate what the next step needs to entail. Socrates and Theaetetus must do one of two things: either they must find an account of knowledge that provides for the direct apprehension of being, thus meeting both the criteria of infallibility and being, or they must find some way to ensure the truth of opinion. Theaetetus will opt for the latter, working on the assumption that it must yet be possible to convert true opinion into knowledge by adding logos to it.

4. “KNOWLEDGE OF KNOWLEDGE” IN THE CHARMIDES Before going on to the third definition of knowledge in the Theaetetus as “opinion together with logos,” this is a good place to explore the parallels between the proposed accounts in the Theaetetus and the sequence of definitions in the Charmides. In a curious way Socrates’ instructions to Charmides mirror the development of the three definitions of knowledge

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in the Theaetetus. After having introduced himself as a curer of headaches, trained by the Thracian Zalmoxis, Socrates explains that the patient needs to have so ¯ phrosyne¯ in order for the charm to work. And although Critias assures Socrates that Charmides is most moderate, Socrates insists that he needs to examine the patient himself to find out what the state of his soul really is. He provides Charmides with the following instructions: Now it is clear if so ¯ phrosyne¯ is present in you, you should be able to opine (doxazein) about it. For it is necessary, I suppose, if being within you, if indeed it is within, it should afford you some perception (aisthe¯ sis) from which you can form some opinion (doxa) about it, both what so¯phrosyne¯ is and what kind of thing it is; or don’t you think so? I do, he said. Well then, I said, what you think, since you know how to speak Greek, you should be able to say how it appears to you. Perhaps, he said. Then in order for us to decide whether or not it is within you, speak and say what so¯phrosyne¯ is according to your opinion (159a).

Remarkably, these few sentences repeat the steps on the path to a definition of knowledge that Socrates and Theaetetus took—the path from perception to opinion and from opinion to opinion accompanied by a logos. Socrates clearly indicates that both self-examination and examination by the midwife are required to determine whether or not someone is virtuous. The notion that one’s inner state is perceivable is puzzling, unless we can understand Socrates’ instruction as a kind of invitation to something like Leibniz’s version of “apperception,” an inducement to become selfconscious. Socrates’ formulation suggests that we do have access to ourselves and should be capable of coming to know ourselves. As we saw, Socrates defines thinking in the Theaetetus as: Soul thinking looks to me as nothing else than conversing (dialegesthai), itself asking and answering itself, and affirming and denying. But whenever it has come to a determination, regardless of whether its sally was on the slow or keen side, and then asserts the same thing and does not stand apart in doubt, we set this down as opinion. Consequently, I for one call opining speaking (legein), and opinion a stated speech (logon eiro¯menon); it’s not, however, before someone else any more than it’s with sound, but in silence before oneself (189e–190a).

So opinion is the result of a form of self-examination that leads to a determination. Charmides exhibits this kind of process and Socrates describes his efforts in response to Socrates’ urging in the following way: “He paused for a little and after quite a manly effort of self-examination (andriko ¯ s pros heauton diaskepsamenos): Well, it appears to me (dokei toinun moi), he said, that sound-mindedness (so¯phrosyne¯) is the same as modesty or shame” (160e). Socrates easily refutes this answer, just as he had rebutted

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Charmides’ previous opinion that sound-mindedness was the same as quietness. If we consider that Charmides is still quite young, then it should not be surprising that his self-examination revealed the commonly held— that is, pre-philosophical—conception of sound-mindedness and that Socrates would demonstrate that both definitions were partial and incomplete. But it is possible that Charmides accurately reflected what he found within himself, and what he found was the opinion of the city. It turns out that Charmides is not sufficiently sound-minded (so ¯ phro ¯ n hikano ¯ s 158b) and he implicitly recognizes that by offering someone else’s opinion when Socrates questions him once again about sound-mindedness: “I, just now, remembered that I once heard someone saying that sound-mindedness is ‘doing (prattein) one’s own thing’ [or ‘minding one’s own business’]” (161b). It is in response to this definition that Critias becomes the main interlocutor and the focus of the discussion shifts to various formulations of self-knowledge. Critias is a much more contentious interlocutor21 and Socrates needs to remind him that it is not about who refutes whom, but rather for the sake of truth that they are having this investigation. The transformations of “doing one’s own things” into “doing good things” (163e) into “knowingly doing good things” (164a) are all triggered by Socrates and lead to Critias’s exclamation that sound-mindedness is identical to selfknowledge (gigno¯skein auton heauton) (165b). Critias is willing to abandon all his previous claims, but wants to insist on this one and is challenging Socrates to agree with him about self-knowledge. To this Socrates responds: “Why, Critias, I said, you treat me as though I professed to know (eidenai) the things on which I ask questions, and needed only the will to agree with you. But the fact of the matter is rather that I seek with you each time something is put forward because I myself do not know. Therefore, I want to examine before I say whether I agree or not. Now, give me a moment to examine (myself).” (165b) Socrates does to himself what he asked Charmides to do, that is, look inside and find out what exactly he is thinking. This particular break in the action is, of course, reminiscent of other times when Socrates is found to be in a fit of thinking.22 After a brief pause Socrates raises the possibility that the knowledge (gigno ¯ skein) part of self-knowledge is a kind of science (episte¯ me¯) and wonders what the content of that science would be (165c)—to which Critias responds with the surprising answer that sound-mindedness as a science “is a science of the other sciences and of its own self (aute¯ heaute¯s). Socrates adds non-science to the equation and offers the following reformulation of Critias’ claim: Then only the sound-minded person will know himself, and will be able to discern what he knows and does not know, and he will be able to examine

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other people and (judge) what someone knows and thinks, if he knows and in turn if he does not know what he thinks or knows and no one else will be able to do this. (167a).

If this is indeed the definition of the sound-minded person’s ability with regard to self-knowledge, we can confidently identify Socrates as soundminded because he self-describes his own knowledge of ignorance in the Apology and his craft of maieutics in the Theaetetus as encompassing precisely the ability to discern his own ignorance and that of others. Nevertheless, here in conversation with Critias he professes to be perplexed (167b), particularly about the self-reflexive nature of the knowledge Critias had identified as sound-mindedness. Socrates’ argument against the possibility of self-reflexive knowledge has recourse to the inability of perception to be self-reflexive: sight cannot see seeing, but has a specific object—color and light—which it is in tune with; ears cannot hear hearing, and so on. There are a few examples that are not as convincing, however: fear and opinion. In modern psychology it seems commonplace to think of fear without a specific object as anxiety and, given the model Socrates is working with, we might think of anxiety as a fear of fear. The same may be the case with desire, the love of love. More importantly, the argument breaks down with the example of opinion: Socrates is discounting the possibility of there being “an opinion which is an opinion of opinions and of itself, but without opining about the thing which other opinions opine” (168a). The fact that Socrates was able to specify the object linked with the various capacities (167c ff)— whether it be in the case of desire, wish, love or fear—but does not do the same for opinion, implies that the object of opinion cannot be specified in the same way The case of opinion is more like knowledge to the extent that we can have opinion about beauty (the object specified for ero¯s) or the good (the object specified for willing, boule¯sis) and that, unlike all the other capacities mentioned, opinion can have an opinion about opinion. In fact, the problem that Socrates encounters again and again in his examination of interlocutors is that they opine that opinion is knowledge. But it would be knowledge to discover that opinion is non-knowledge. The Charmides clarifies that the knowledge of knowledge and nonknowledge can be understood as a form of self-knowledge, so long as we keep in mind Socrates’ own formulation of what he knows and does not know. Unlike Theaetetus, who is baffled by his own idea of introducing into the aviary birds representing non-knowledges, Socrates embraces the knowledge of non-knowledge as a form of moderation. At the end of the dialogue, Socrates claims that Theaetetus has become more moderate and this is a result of his knowing his non-knowing of knowledge—again making a link between non-knowledge and moderation. Socrates never

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disclaims the possibility of a knowledge of knowledge and nonknowledge in the Charmides; rather he questions its usefulness, absent the knowledge of good and evil. Socrates consistently illustrates the former in many dialogues and regularly professes the difficulty of the latter. In Republic 506b–e, for example, Socrates says explicitly that he cannot speak about the good directly, but can only portray his opinion about it through images depicting its offspring. In his discussion with Theodorus about the “true” philosophers, Socrates claims that mortal nature always partakes of evil and Socrates associates the good with the divine: “But it’s not possible for the evils either to perish, Theodorus—it’s a necessity that there always be something contrary to the good” (176a). It is necessary, therefore, that knowledge of the good cannot be part of the strictly human realm; it requires an ascent. But it is precisely the knowledge of nonknowledge that stirs up the desire for the ascent. 5. INTERPRETATIONS OF A DREAM The third and final definition of knowledge discussed in the Theaetetus, that “knowledge is true opinion accompanied by logos,” falls into two parts: the first part (201d–206b) examines the possibility of knowing any complex thing, along with the elements of which that compound is constituted. This section is generally referred to as “Socrates’ dream.” The second part (206c–210b) analyzes the different definitions of logos in order to determine whether there is any one of them that can provide sufficient conditions under which true opinion could be considered knowledge. The two parts actually capture, upon reflection and analysis, the essence of episte¯ me¯: the discursus on dreams and letters stands in analogy to the dual character of knowledge, the otherness of knowledge as over against that which is to be known; the second part discusses three senses of logos which, when they are taken together, present the evolution of logos from the pre-philosophical voicing of opinion to the philosophical analysis of difference, which successfully completes the process of intellectual movement from whole to parts to synthetic unity. Instead of reaching such a conclusion, however, Socrates and Theaetetus conclude their discussion in an acknowledged aporia. But the impasse comes together with Socrates’ articulation of the benefits which have come to Theaetetus by virtue of his having undergone this painful process of “birthing” his opinions (210b–d). Socrates has barely concluded his refutation of the definition of knowledge as “true opinion,” when Theaetetus digs up from some vaguely identified other source his final answer to the question about knowledge, repeating the words he has heard “from somewhere.”23

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He said true opinion with speech (logos) was knowledge, but true opinion without speech was outside of knowledge, and of whatever there is not speech, these things are not knowable—that’s just the word he used—and whatever admit of speech are knowable (episte¯ ta, 201d).

This definition not only provides the criterion for knowledge—namely, logos accompanying true opinion—but it also includes the distinguishing mark which differentiates knowledge from non-knowledge.24 Socrates takes up the latter part of the definition, zeroing in on that criterion and asking what it is that distinguishes knowledge from non-knowledge. But Theaetetus is not up to the task. Socrates continues to assist Theaetetus by offering a dream in exchange for a dream. Theaetetus never objects to having his definition named a “dream,” and in fact he concurs with Socrates’ telling of the “true content” of the dream. Before considering in the abstract the reasons for classifying the ensuing account as a dream, let us work through the elements that constitute it. The first part of the dream may be divided as follows: 1. The first things are just like elements, out of which everything else is composed, and they themselves do not admit of any logos. 2. One can do no more than name any thing taken alone by itself, that is, the elements are only nameable. 3. One can neither apply being nor nonbeing or anything else to those first things. “It,” “that,” “each,” “alone,” “this,” cannot be applied, for each one of these is used in a way that qualifies them as universals rather than singular terms.25 If we think of the fact that each of them can be applied to a myriad of things—virtually all things, in fact—we can easily enough understand what Socrates is getting at. Insofar as every one of them can be used to pick out an indefinite number of things, each one of them fails to name any one thing uniquely. 4. If it were possible to use any of the terms discussed in (3), then it would be possible to construct a logos of the first things. 5. But it is not possible to use universally applicable names to pick out anything simple and unique. Therefore, 6. We can only “name” the elements and naming is not a sufficient condition for knowing. Within the first part of the dream an important distinction is drawn between the elements, on the one hand, and the complexes that are composed of elements, on the other. The significance of the unspeakable (alogon) nature of the elements becomes clear when we consider that logos is introduced as that which, when added to true opinion, would be a satis-

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factory explanation of knowledge. If the third definition is supposed to provide the sufficient condition for knowledge, the dream suggests that there can be no knowledge of the building blocks of what there is. The conditions laid out in one to six suggest that the limitation of the first things is that we cannot predicate anything of them and without predication knowledge is impossible.26 It is only when I can ascribe something to some other thing that I can think of myself as being on the way to knowledge. The ability to name something is not sufficient for knowledge. Socrates addresses this difficulty in the second part of the dream when he discusses the relation between names and logos. That which is composed of the elements provides the model for logos in that logos is composed of names. Just as the plaiting together of elements brings about a compound, so the plaiting together of names becomes a logos, “for the plaiting of names is the being of speech” (202b). Socrates proceeds with this analogy by pointing to perception as the “middle term”—that is, the elements are perceivable and thus nameable, but in contrast to the compounds they do not admit of an account (logos). “Compounds are knowable, speakable and opinable by true opinion” (202b). Perception is accountable for our acquaintance with what there is, but it is incapable of asking and answering the question “what it is.” Perception enables us to name things, but it cannot give an account of what it is that it has named.27 Socrates does not offer any details as to how it is that we can perceive and name the simples nor of how we proceed from that to the knowing of the compounds, though he does assign a significant role to logos. But the conclusion of the dream makes clear that, although logos is a necessary condition for knowledge, it is not a sufficient condition. It too is conditioned and it is that which conditions logos that remains mysterious. Socrates concludes the dream with the following words: And that, in short, whenever anyone gets the true opinion of anything without speech, his soul tells the truth about it but does not know, for whoever is incapable of giving and receiving an account (speech) is without knowledge of this very fact. But if he gets in addition a speech, he becomes capable in all these respects and is in a perfect condition relative to knowledge (kai teleios pros episte¯ me¯n echein) (202c).

But what is it that activates or actualizes this “perfect” condition? Logos as such is not a new theme in the dialogue, for in his definition of thinking and opining Socrates already introduced logos as a crucial part in the discussion of knowledge. What he adds here, however, is essential. Instead of the silent speech of opinion, episte¯ me¯ demands externalization and the first step of getting out the word is characterized by Socrates as

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“giving and receiving” logos. Surely it is dialectics that is at stake here. Episte¯ me¯ , defined as true opinion and logos, requires dialogue. It is as if Socrates suggests that thinking as an internal dialogue is incapable of selfexamination, and some form of examination is requisite for the attainment of knowledge. The only way we can be sure that we are in the possession of knowledge is if we can give an account supporting our claims. And since there is always the possibility of madness it is not sufficient to convince ourselves but rather the safe route is for us to convince someone else. Presently Socrates will suggest another level of externalization, when he examines the relation between the simple and the compound, as well as the part and the whole, by using the examples of letters and syllables.28 The first point to be noticed is that Socrates uses examples from written and not merely from the spoken language. The written word gives us the illusion of being an “all,” which is the result of the composition from something like primary elements (letters): We imagine, anyway, that we learn individual letters and then put them together to make syllables and words. In that sense, the written word is, or seems to be, an example of a complex composed of simples, where the enumeration of the simples might deceive us into thinking that we know the complex. Socrates then turns around and talks about the word as in fact being a whole, and in that sense it is a simple and thus, according to the dream theory, it would be unknowable. What needs to be underscored, however, is this: That which makes the word into a whole is a principle of combination prior to and different from the written word itself. Not all letters or sounds can be combined with all others in any way; rather there is a principle of combination that guides and determines which letters can and should be added to which others. Socrates asserts in response to Theaetetus’s definition that he thinks it is likely that they have hit upon the correct definition “for what would knowledge still in fact be apart from logos and correct opinion?” (202d). And it is the “doubleness” of the definition—involving opinion but explicitly mentioning logos—that gives an indication as to what is involved in episte¯ me¯. The definition suggests that it is doxa that gives us the whole, and it is only thereafter that we can move on to the task of analysis that is accomplished through logos.29 Logos as analysis is only possible when meaning is already given. Complexity as an issue arises out of analysis and analysis needs some whole for it to work on. The further difficulty of reconstituting wholes, synthesizing elements, is pointed out by Socrates in his insistence that this work requires an identity between the all and the whole. This process of analysis and synthesis is possible on the level of logos but presumably, the end-product of logos—episte¯ me¯ —differs significantly from the original.30 Socratic dialectical method proceeds to the whole, whereas division proceeds from the whole. Plato has chosen to connect

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Socrates with the method of dialectic and the Eleatic Stranger with the method of division. In the context of our discussion, it seems that it is Socrates’ task to lead the interlocutor “upward” to the whole,31 while it is the task of the Eleatic Stranger to lead Theaetetus “downward” in the analysis of the whole. The two of them together represent “the whole” of philosophical knowledge or wisdom. On the next day of the dramatic trilogy, Theaetetus will be introduced to the method of division (diaire¯ sis), by the Eleatic Stranger, rather than by Socrates. Plato seems to be indicating awareness that we can always get from the whole to the part, but that there is no clear or reliable method of proceeding from part to whole, because the first cut destroys the principle of unity, without which all we can have is a myriad of minute parts.32 To judge from the Apology, which in dramatic timing follows shortly after the Theaetetus, Socrates prefers knowledge of ignorance, that is, the knowledge that he does not know the whole, to partial knowledge or knowledge of a part. This systematic making of wholes may be an appropriate program for scientific knowledge, but will not satisfy Socrates’ desire for wisdom. After recounting the dream, Socrates proposes that they should “torture” it, using logos, not forms, as paradigms.33 Socrates suspects that the author of the dream had written speech in mind and thus, to test the dream theory, they turn to an examination of syllables and letters.34 In fact, it appears that the entire examination is backward: instead of examining the different meanings of logos first, they turn to examine the application of logos. Socrates invites Theaetetus and the rest of us to an “autobiographical” self-examination of how it is that we learned to write. Even though he does not clarify the point, it is clear that the ensuing analysis can only pertain to written speech, since the conclusion suggests that we do indeed learn the simple elements first, and no one would maintain that we learn language by learning the letters first and then putting them together in syllables and words and only then finally into sentences. One of the things that this examination accomplishes is to persuade Theaetetus, who initially wants to distinguish the all from the whole (204b), to conclude that they are the same (205a).35 In addition, Socrates brings it about that their initial assumption that the simples are unknowable because they are unsayable (alogon), garnered from the dream, will be turned upside down when applied to written speech. To turn Theaetetus “upside down,” to overturn his assumption that there is a difference between the whole (to holon) and the all (to pan), Socrates introduces a third term, “all things” (ta panta), which serves as a “middle term,” bringing about an equivalence between the whole and the all. Using the example of the syllable to stand for the complex, Socrates presents the following choice to Theaetetus: “Do we mean by the syllable both elements,

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or if there are more than two, all of them (ta panta), or some single look (mian tina idean) that has come to be when they are put together” (203c). Theaetetus chooses the former option and is quickly thrown into a state of confusion when Socrates questions him as to how the addition of two unknowables, the elements, can be conjoined into something knowable. It is as though one were claiming that (e & f) is knowable, but that is somehow derived from the fact that e and f are not knowable separately. An absurdity indeed! Naturally, Theaetetus wants to explore the other option, namely, that the syllable is a whole, but that too proves to be unacceptable, for as a whole it is like the elements and thus unknowable. To explain to Theaetetus that there is no distinction to be made between the all and the whole, Socrates resorts to mathematical examples showing that there is no difference between the all (to pan) and all things (ta panta). He uses four examples, each of which relies on numbers: There is no difference between 1, 2, 3, 4, 5, 6; 2 3 3, 1 1 2 1 3, 4 1 2 (ta panta) and 6 (to pan); no difference between the number of the plethron (ta panta) and the plethron (to pan); no difference between the number of the stade (600 feet) and the stade; and no difference between the number of the army and the army. The conclusion Socrates draws on the basis of these examples is that the numbers represent the parts of the all, and in that sense the all is identical to the number of its parts. The last example introduced by Socrates raises a question about the identity of the whole and the all. The army, in contrast with a stade or a plethron, is presumably “more” than the number of its constituents: there is a principle of organization and unity that combines the number of individuals into a complex whole which, like the syllable of the dream, constitutes one look (mia idea) (203c). So there is a sense of “whole” which differs from “the all,” as aggregate, that Socrates is not mentioning here. Theaetetus, too, seems to suspect that Socrates’ account is not exhaustive, but he nonetheless gives in to Socrates very quickly. Theaetetus could still defend his distinction by insisting that in contrast to the all, the whole does not have parts. But Socrates is prepared for this kind of objection and he puts forth the following argument: “But won’t a whole be this same thing, from whatever nothing in any way stands apart? But from whatever there is a standing apart, it is neither a whole nor an all, and that is the same result for both of them at once out of the same?” (205a). This finally convinces Theaetetus that the whole and the all are the same and Socrates concurs that the whole that has parts is identical to the all. Part of the motivation behind Socrates’ proof derives from the fact that any discipline that relies on addition and division cannot successfully make a distinction between the all and the whole. The very act of counting which Theaetetus presented as his first attempt to answer the question of knowledge defies the idea of the whole. It is this notion of

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“whole” that Socrates is trying to “teach” Theaetetus. Hence the initial refusal to accept the distinction between the all and the whole. Now that Theaetetus has given up the distinction, Socrates introduces him to the idea of a whole without parts. It is as though Socrates is inviting the mathematician to consider more deeply the concept of the One. It is the unknowability of the one that is indicated and imagined in the dream through the unknowability and unsayability of the elements. In contrast to the dream, where the compounds are knowable and the simples merely perceivable and nameable, Socrates shows that in written speech it is precisely the simple letter rather than the syllable that we know most vividly and clearly. The prime example that guides these reflections is the first syllable of Socrates’ own name. SV (SO) has a logos, insofar as it is voiceable, and thus amounts to some form of speech; and it is furthermore divisible into its elements, S (sigma) and V (omega). Thus an account can be given of it to the extent that one can enumerate its elements. To show the first part of the dilemma, that is, that the complex is knowable but the simple is not, Socrates and Theaetetus agree that it is impossible to say what the “S” is. The most one can say is that it can’t be voiced, that it is at most a hissing sound. Maybe most of what we claim to know would actually, upon examination, look very much like the “S,” but that presumably is not the point here. Some commentators insist that this is precisely the point at which the dream can be refuted. Gail Fine, for example, argues that the division of the simples into those which have voice and those which do not, is in fact a way of giving an account of the simple.36 Consequently Socrates is able to meet the minimum requirements for a definition of knowledge—being able to give an account. The argument that division amounts to knowledge, which the Eleatic Stranger will introduce in the Sophist, “the next day,” is not at all evident in the Theaetetus. The Stranger appears, so to speak, before his time. Instead of going down Fine’s path “proclaiming” knowledge in such an odd way, Socrates chooses to travel in the direction of paradox: If the compound itself is only knowable in terms of its elements, but the elements themselves are unknowable, then how can knowledge be possible? The paradox becomes doubly paradoxical when we consider that the syllable is a whole and qua whole is a simple, and thus unknowable. It would be a fantastic claim to assert that the syllable as an “all” is knowable, because it is compound, and that all we need to do to assert knowledge is to name its elements, but on the other hand to insist that the syllable is an unknowable “whole,” claiming that it mimics the simple elements.37 Julia Annas, comparing the Theaetetus with the Cratylus, argues that the refutation of the dream theory shows us that we are committed to the principle that knowledge must be based on knowledge.38

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In his famous 1952 lecture to the Oxford Philological Society, “Logical Atomism in Plato’s Theaetetus,” Gilbert Ryle interprets Socrates’ dream as a prescient formulation of logical atomism, and an analysis of the problems it entails.39 He likens both Russell’s and Frege’s analysis of sentences as complex names to Socrates’ discussion of the syllable “SV” [SO—sigma omega]. Just as the complex syllable can be dissected into its simple elements, “S” and “O,” each of which is unknowable but perceivable, so a sentence can be broken down into its simple names, which by themselves can neither be known nor be asserted, but with which there can be an acquaintance and which can be mentioned.40 He concludes: Socrates’ Dream was a first rate precognitive dream. Philosophers have, in this half-century, held views about the import of propositions, which have tallied not merely in general pattern, but often in actual phraseology with the doctrine that Socrates expounded and criticized. This doctrine did generate just those consequences which Socrates foresaw. The notions of true and false, assertion and denial, belief and knowledge (savoir) are not accommodated but exiled by the doctrine that sentences are names of either molecules or congeries of atomic nameables. Answering questions is not an affair of calling things names.41

Persuasive though this may be, Ryle here assumes his own reading of the paradigm of letters and syllables, rather than arguing for it. It is not clear why Ryle denies that the passage could be a critique either of physical atomism or of mathematical knowledge, though these are possible interpretations42 Glenn R. Morrow reminds us that stoicheia (elements) is a term used in geometry to refer to the basic premises long before Euclid wrote his work of that title.43 Morrow’s overall conclusion is that the dream can be generalized to all forms of analysis whether physical, lexical, or mathematical. For those who, like Cornford, think that Plato composed the Theaetetus to show the necessity of the forms, Ryle’s most devastating assertion is that the simples can be understood to represent the forms themselves and that Plato is subjecting his own theory of forms to further damaging critique—a critique which he first undertook in the Parmenides and whose very success is demonstrated by the introduction of a new method of inquiry in the Sophist.44 Thus Ryle also supports his own view of the Theaetetus as one of Plato’s self-critical dialogues.

6. THE LOGOS OF LOGOS The examination of logos appears abruptly: Socrates provides neither a segue nor any reason why he abandons the dream and turns to logos. The examination of logos itself could bring with it some difficulties, such as

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the kind of circularity that arises when logos is examining logos. Under what circumstances can we give a speech about speech? Is this problem similar to the problem of knowing knowledge? If the former is possible, then it might provide a model for the latter. Socrates begins by discussing logos as the voicing of one’s thought, and from there he proceeds to a discussion of its capability of performing an analysis of wholes, and finally he moves on to the discriminating ability of logos, which enables us, as possessors of logos, to distinguish one thing from another. If logos does provide a model for knowledge, then it should be possible to show how each stage in the definition of logos “mirrors” the respective definitions of knowledge. Such an approach to the examination of logos would also contribute to our understanding of a comment that Socrates makes in the Phaedo about his chosen method of investigation: [I] feared that my soul would be altogether blinded if I looked at things with my eyes and tried to grasp them with each of my senses. So I thought I must take refuge in discussion and investigate the truth of things by means of words. However, perhaps this analogy is inadequate, for I certainly do not admit that one who investigates things by means of words (en tois logois) is dealing with images any more than one who looks at deeds (tois ergois) (99e–100a).

Socrates here identifies his method as one that is based on logos. He denies that logos is a mere image of things, but he is not entirely clear in stating what exactly the relation is between logos and things. This relation becomes clearer in the analysis of logos in the Theaetetus. Another question we must ask ourselves, as we proceed through the three definitions of logos, is how we should understand the relationship between the different definitions. Is it the case that each one is refuted and replaced by another? Or is there an increasing level of complexity, in which each one is subsumed by the subsequent one? Finally, we need to establish some connection between the dream theory and the definitions of logos. The refutation of the “dream theory” brings Socrates and Theaetetus to the last stage of their examination of the definition of knowledge, a speech about logos itself. The refutation of the “dream theory” established that we can know the elements on the basis of experience and, if we reflect on our learning of letters or musical notes, we can conclude that we do know these elements more vividly (enargesteron) and more authoritatively (kurio¯teron) than the complexes. If it is indeed possible, that our perception or experience of the simple can count as knowledge, then logos would not be the decision criterion for knowledge, because Socrates has already established that a proper account cannot be given with respect to the elements; they are merely nameable. Socrates and Theaetetus do not prove that anyone can actually give a logos of the elements, but rather make the

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case that they are knowable. Thus Socrates and Theaetetus have in fact severed the connection between knowledge and logos. The dialogue does not end here, however, because Socrates devises the conditions for a type of knowledge that cannot be achieved by experience—namely, the “most perfect and complete knowledge” (teleo ¯ taton episte¯ me¯ n, 206c4). The criterion of completeness, which is presumably characteristic of the whole, is now laid at the feet of logos. With this view of the whole and its relation to logos in mind, Socrates steers the discussion to an examination of the different meanings (se¯ mainein, 206c7) of logos to see if any one of them could fulfill the requirements of complete knowledge. Socrates sets out to examine three different “significations” of logos in an ascending level of complexity. He does not address the issue of whether this enumeration is a complete listing, nor question which kind of logos enables him to put forth the argument about logos.45 The first definition of logos rings of the poetic, as “that which makes one’s own thought evident through sounds with words and phrases, just as if it were into a mirror or water one was striking off one’s opinion into the stream through one’s mouth” (206d). The beauty and allure of the image is a temptation to simply leave it alone, but some demythologizing is necessary to garner a full understanding of logos as the “image maker” of one’s thought. How should logos as an image be distinguished from the thoughts themselves? To talk about language as an image of thought has a paradoxical ring to it, because many people would think about thought itself as an image. My thought about a tree, for example, differs from the actual tree and my voicing my thought “through words and phrases” seems to be at a still further remove. Add to this “motion or streams” and it is difficult indeed to determine what it is that is being said here. If logos is the making of images as in the context of a Heraclitean flux then it is unclear how the image would hold.46 Furthermore, if we consider the nature of images, we need to clarify what it is that logos does to thought to convert thought into an image, that is, what is the distortion that occurs when someone voices his or her thoughts? If thought is a process and logos is static, then converting the former into the latter would be the distortion that arises when one attempts to “arrest” that which moves. The language that Socrates uses here, and the attendant problem of interpretation, point back to Theaetetus’s first definition of knowledge and it looks as though the first definition of logos mirrors the problems of perception. As in perception, so here the possibility of flux presents a significant difficulty. Socrates already established the impossibility of nouns and demonstratives when he discussed perception, for when everything is in flux, there are no referents for nouns and demonstratives. In fact, even “one” cannot be meaningfully uttered.

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Nevertheless, Socrates continues with his discussion as though the meaningfulness of logos were not the real problem, but rather the fact that this definition of logos would apply equally well to all those who are capable of hearing and speaking, as a way for indicating “their opinion of which each thing is” and thus cannot provide the grounds for any distinction between opinion and knowledge. If we consider the criteria of perfection and completeness it is clear as well that logos as the voicing of one’s opinions cannot meet either one of them. The very notion of an image implies incompleteness and imperfection, for an image can only be understood in relation to something else, that of which it is an image. Indeed, if the parallel between perception and the first definition of logos is adequate, we can explain its failure in terms of the same shortcomings as they can be detected in the definition of knowledge as perception. The final refutation of “knowledge is perception” pointed to the inability of perception to touch upon being and the same problem arises when we speak of logos in terms of voice and nothing else. And just as perception can be understood as providing the basis for further development, so too can this first definition be looked upon as propaedeutic. The next two definitions follow necessarily, but the voicing of one’s opinion cannot itself provide the ground for knowledge. Language is a necessary condition for knowledge, but it is not sufficient for the attainment of “complete and perfect knowledge.” The next definition of logos explicated by Socrates is cast with mathematical overtones, claiming that the enumeration of elements might be identical to knowledge. Logos is “the capacity, when asked what each thing (is), to give the answer back to the questioner through the elements” (207a). Here is the first indication of logos as dialectical, which adds a new dimension to the first definition of logos, where the focus was the individual and the movement from the inner to the outer, that is, the externalization of one’s thoughts through voice. Here the emphasis is on the communication of one’s thoughts to another thinker in the form of questioning and answering. Knowledge, then, would be understood as the ability to answer questions, but Socrates adds an important qualification, which restricts this kind of logos to the expert. As he himself discusses with an example from Hesiod, the expert will be able to say what a wagon is by listing all its one hundred parts while he, Socrates, could merely name five parts or so. He wonders whether the ability to say that a wagon is “wheels, axle, carriage-body, rails” is as adequate an answer as the one provided by the expert. Is it the case, Socrates asks, that my logos of “Theaetetus” in terms of syllables is just as good as the one given by somebody else who specifies each letter? Socrates here wants to establish the difference between common sense and expertise. The scientist can name each element, whereas the layperson can only name either the most evident or functional parts. Theaetetus

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then agrees to the following proposition: “Tell me whether it’s [your impression], comrade, and whether you accept the procedure through elements to be speech about each thing, while the procedure which is syllable by syllable or is in terms of something greater still is not-speech (alogia), in order that we may go on to examine it” (207c). This procedure, if accepted, can be used to distinguish knowledge from opinion. The knower is capable of elemental analysis while the opiner can only offer a “partial” account. Socrates voices his opinion about the essential part of a wagon when asked what it is, while Hesiod would be able to enumerate each element. Whoever has the capacity to explicate its [the wagon’s] being (ousia) through those hundred things of it, by his addition of this, has added speech to his true opinion, and has become, instead of an opiner, artfully competent (technikon te kai episte¯ mona) and a knower of a wagon’s being, because he has gone through the whole through its elements from end to end (207c).

So, following the criteria of completeness and perfection, this definition of logos does fulfill the criterion of completeness: If I can give an account of all the elements of a particular thing, I have exhausted all the parts. The ability to list all the elements presupposes an understanding of the arrangement and system—that is, some form of analysis is needed to explicate the “being” of something through the elements. Expertise is not merely in the listing of the parts, but also in the explanation and understanding of how those parts constitute a whole. This of course depends on our accepting the identity between the all and the whole, which Theaetetus accepted in the discussion of the “dream theory.” Socrates then turns to the refutation of this second particular definition, which in part reveals what it is that enables the knower to enumerate all the elements. And it turns out that it is the criterion of perfection that cannot be met by this second definition of logos. The example Socrates uses is drawn once again from the ability to spell a name. He wonders whether we would consider someone knowledgeable concerning Theaetetus’s name if he could spell the first syllable correctly and so on for the rest, but failed to see the sameness of the first syllable of that to Theodorus’s name, and instead insisted on spelling that “tau-epsilon,” instead of “theta-epsilon.” This complex example runs deeper than it at first seems, because it involves the issue of writing and conventionality. In an oral culture or in the absence of writing, the person who can pronounce both names would not make any mistake in thinking the first syllable of one to be different from the first syllable of the other name. Part of the mistaking that occurs in this example depends on an accepted convention, which arises only in the context of writing. If it were the case that, due to regional accent or dialect,

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someone actually pronounced the first syllables of “Theaetetus” and “Theodorus” differently—imagine an Englishman pronouncing the first name and an Irishman pronouncing the second—then to say that the two differ would not in fact be a mistake. It is the development of written language and its applicability independent of local dialects that brings about the risk of being mistaken in such a concrete fashion. It is the art of writing then that should provide us with some clue about the relevance of the second definition of logos. In order to state the elements of something, it is necessary to have available some kind of system that allows one to create a standard of universality such that the similar cases are subsumed under the same rule. In the case of the “spelling bee” that Socrates discusses, it is precisely someone’s inability to apply the rule to other cases that exhibits a lack of knowledge. So the second definition, like the dream, points to the possible limitations of analysis. What would be required to avoid misspellings entirely and reliably would be a general rule about spelling and the ability to apply such a rule appropriately in all cases. Even though the only reason why I can spell out Theaetetus’s name letter by letter depends on the development of a system, I might be able to succeed in employing the system without knowing it. It is that point that Socrates illustrates by the example of the mistaking of “The” for “Te.” Socrates concludes his refutation with the claim that it is after all possible to have right opinion with speech, but nevertheless still be without knowledge (208b). It is by virtue of the possibility of making mistakes—either in not recognizing similarity and thus arriving at a general rule or, when in possession of a rule, misapplying that rule—that this kind of mistaking comes about. This second definition of logos mirrors, then, the second definition of knowledge in that both of them raise the issue of error. The second definition of knowledge involves a lengthy investigation of the possibility of false opinion, and here the second definition of logos fails because of the possibility of mistakes. The second definition of logos also shares the problem of the “common things” with the second definition of knowledge. The occasion for introducing opinion as the definition of knowledge was perception’s failure to touch on the “common things.” Here, as is clear in the example of the two names of “Theaetetus” and “Theodorus,” a principle of sameness is needed, establishing Q (theta) as the common element, in order to spell the first syllable of both names correctly. If there is indeed a recapitulation of the dialogue taking place, then the third definition of logos should prove to be the most interesting of all for it would involve a double reflexivity. Socrates makes this transition to the final definition of logos: Then, it seems, we grew rich just on a dream, in our belief that we had the truest speech of knowledge. Or are we not yet to issue an accusation? For

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perhaps one will not define it as this, but as the remaining species of the three, just one of which, we said, he will set down as speech, whoever defines knowledge to be right opinion with speech (208c).

As the first sentence indicates, the third definition of logos—having “some sign to say by means of which that which is asked about differs from all things” (208c)—is an attempt to give a true speech about knowledge. To emphasize that this is the production of a speech of knowledge in the form of speech is surely an attempt to move the reader toward reflection on reflexivity, so to speak. The complexity of this problem can be more fully appreciated if we also notice that the different definitions of logos build upon one another, that Plato constructs an ascent, in which definitions incorporate and subsume the previous definitions. The successive definitions of knowledge subsume one another, and at the same time there is a mirroring of the previous definitions of knowledge in the discussion of each of the definitions of logos.47 In the light of the dream and its discussion of the distinction between the all and the whole, we must also wonder whether Plato here gives us an example in which we are given the parts of logos—maybe even all the parts of logos—and yet we are unable to arrive at the whole of logos. It is not entirely clear whether it would be possible to determine whether the three definitions presented are exhaustive, without having the whole of logos to begin with. If it is possible to arrive at the whole through the part, then knowledge must be additive. A “mid-term” addition at this point would amount to saying that logos is dialogue, that is, the voicing of one’s opinion plus the analysis of such on the basis of a question. This, however, does not add up to knowledge, according to Socrates, because it is possible to arrive at the correct answer to a question on the basis of right opinion anyway. How then does “knowledge with speech” differ from “right opinion with speech”? The clue is provided in the refutation, where Socrates exposes “false opinion with speech” as resulting from someone’s not being able to judge the difference between the same and the other. Out of this revelation grows “naturally” a third definition of logos, that will take difference into account. The final definition of logos reflects the opinion of the many who think that those people are knowledgeable who are able on the basis of “some sign to say by means of which that which is asked about differs from all things” (208c). Socrates, at Theaetetus’s request, offers an illustration: The sun “is the most brilliant of the things that go around the earth across the sky” (208d). If one were to identify the sun as a bright body in the sky, one would be merely expressing a right opinion, but not knowledge, because this logos could be nothing more than the voicing of an opinion on the basis of perception. As such one can make the same judgment about the

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moon and a host of planets and stars, and unless one can say how the sun differs from all the other referents of “bright body” one cannot be said to have knowledge. The characteristic that Socrates points to as the distinguishing difference is that it is “the brightest,” offering a superlative that can only be met by one thing, the sun. How then does this differ from right opinion? Could not the same account that is given to explain the judgment “the sun is a bright body” also be applied to “the sun is the brightest body”? What is it that is added to perception and opinion when a comparison is made? Minimally we need a measure for the degrees of brightness in order to make the judgment that one body is brighter than another. But, in addition, there has to be some principle which determines which bright bodies can be measured in relation to each other and which ones it would be inappropriate to include. It is measure—or, in this case, the “frame of reference” or “system” in which such measure is applied—that allows us to arrive at the judgment of a superlative. The third definition of logos points then to the requirement of measure and system. How else could we tell how one thing is different from all others?48 Here too we note a similarity between logos and episte¯ me¯. Just as the third definition of logos requires a principle of difference, so the third definition of knowledge adds logos to true opinion to differentiate it from false opinion. If I can give an account of the truth of my opinion, then I know how it differs from my other opinions, which lack any account of their truth. What I know about this particular opinion is that I know it is true. In that sense, we also see the double reflexivity that arises from the third definition, namely, that just knowing something is not sufficient for knowing, but I must in addition know that I know and that requires a logos. Socrates is perplexed by his own discovery. After establishing that anyone who, in addition to right opinion, can establish difference through logos has transformed himself from an opiner into a knower, Socrates says: “Now all of a sudden, Theaetetus, I don’t understand anything at all, not even a little, since I’ve got too near to what is being said, just as if it were a shadow painting. For as long as I stood way off from it, it appeared to me that something was being said” (208e). Socrates’ confusion is the result of his inability to make sense out of the claim that one opines that which is common (ta koina) in the individual and in that sense has an opinion of the individual, but one knows how this individual differs from all others and in that sense has knowledge of the individual.49 If one has an opinion of the individual through the common things, then one isn’t really opining the individual, for one thing because the common characteristics are precisely those shared by many others. But the definition of knowledge leads through right opinion and the addition of logos to knowledge. So either I do opine the individual and thus opine difference,

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or else the addition of logos to opinion cannot properly add up to a knowledge of the individual.

7. CONCLUSION If right opinion already establishes difference, then how, finally, are we to distinguish right opinion from knowledge? Socrates shows that answering this question is a matter of finding oneself in a circle: “If to take a speech in addition, my boy, urges us to come to know but not just to opine the difference, what a pleasantry the most beautiful speech of all about knowledge would be! For to come to know (gno¯nai) is surely to take (labein) knowledge (episte¯ me¯ ), isn’t it?” (209e–210a). In this way knowledge is defined as right opinion plus the knowledge of difference. This may indeed be circular, but it is not necessarily a vicious circle. At the beginning of their meeting Socrates invited them to investigate knowledge with the following comment: Well, this is the very point about which I’m perplexed, and I’m incapable of grasping (labein) it adequately by myself (par emauto¯), whatever knowledge is. Can we really say it? What do you all say? Who would be the first of us to speak? The one who makes a mistake, and whoever at any time makes a mistake, will, as children playing ball say, take his seat an ass; but whoever prevails without a mistake, he’ll be our king and enjoin us to answer whatever he wants (145e–146a).

At the end of the dialogue Socrates no longer expresses perplexity about the issue of knowledge, so something good must have happened along the way. In fact, Socrates concludes that the entire endeavor has been a success, since Theaetetus is no longer pregnant and has attained a modicum of self-knowledge, which Socrates describes as “believing in a moderate way that you don’t know what you don’t know.” (210c) Identity and difference played a pivotal role throughout the discussion of false opinion: The wax tablet was concerned with mistaking one of the interlocutors for one of the other interlocutors. The same self-referential game was played when discussing the dream and logos, that is, all the examples referred to spelling or misspelling the names of the present interlocutors. In addition Socrates’ definition of thinking specifically referred to the self-dialoguing with itself. Throughout the discussion of opinion self-referential games are at play. At the same time it is clear that when discussing opinion, impasses are met every which way. The puzzles surrounding false opinion and the circle of logos point to considerable difficulties, but not to the same kind of aporia Socrates encountered when trying to “think through” knowledge by himself. Socrates can confirm that

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the puzzle of knowledge is tied up with the task of self-knowledge. Neither knowledge nor self-knowledge are endeavors to be undertaken on one’s own. In addition, Socrates had Theaetetus wondering about his own experience and had guided him part way out of the cave. In the next chapter we will examine the limitations of mathematics and Theaetetus’s ascent by situating him squarely in the Republic’s cave.

NOTES 1. Doxa is generally translated as “opinion,” but also as “belief” or “judgment.” In Plato it is regularly contrasted with knowledge and inferior to it, and it is thus strange as a definiens for knowledge. In the verb form it can be either intransitive or transitive. Some commentators, notably Bostock, try to limit it to propositions, but in our text that is clearly not the case. In this section we will encounter, for example, “opining Theaetetus,” in which Theaetetus is misidentified as Socrates. 2. Meno 98b. 3. See Symposium 177d; Gorgias 509a; Apology 20d. 4. See Euthyphro and Euthyphro’s presumption of knowledge at the beginning of that dialogue, as opposed to the uncertainties about his opinions raised by the dialogue. 5. Socrates would presumably not be persuaded by the Cartesian faith in method, which allowed Descartes to “discover” the starting point of knowledge through thinking by himself after discarding all opinion. 6. The discussion on false opinion in this passage has elicited numerous responses that attempt to cast the problem under discussion as an issue regarding the logical structure of identity statements. Examples can be found in David Bostock, Plato’s Theaetetus (Oxford: Clarendon Press, 1988), 169–90, where he explains the problem of “other-judging” and the mistaking of 11 for 12 as the result of a misapplication of Leibniz’s Law, and further attributes the lack of any resolution to Plato’s failure to distinguish between de dicto and de re reports of beliefs. See also John Ackrill, “Plato on False Belief: Theaetetus 187–200,” Monist 50 (1966): 383–402. For a Quinean reading of Theaetetus, see C. J. F. Williams, “Referential Opacity and False Belief in the Theaetetus,” Philosophical Quarterly 22, no. 89 (October 1972): 289–301. Williams applauds Plato’s analysis of false belief as reflecting “the views of a man who has read Quine’s ‘Reference and Modality,’ but has not yet got round to Word and Object.” Plato, on this view, has failed to distinguish between transparent and opaque interpretations of belief constructions. Burnyeat also tries to be “generous” by examining the passage in the light of Frege, wondering whether Plato has found a way to replace sense and reference—what Burnyeat considers a linguistic solution to the problem of connecting mind and world— with two or perhaps even more epistemic routes. For a consideration whether or not Socrates is subscribing here to Russell’s distinction between knowledge by acquaintance and knowledge by description see Gail Fine, “False Belief in the Theaetetus,” Phronesis (1979): 70–80, and David Barton, “The Theaetetus on How We Think,” Phronesis (1999): 163–80.

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7. We might distinguish between memory and recollection in such a way that the theory of recollection can be understood as encompassing all nonexperiential and nonimagable thoughts. However, beauty would present a peculiar case. Diotima says that “only here in seeing in the way the beautiful is seeable, will he get to engender not phantom images of virtue . . . , but true virtue” (212a). This seems to suggest the image of beauty is not really an image. 8. For a full list and examination of the fourteen possibilities see Ronald M. Polansky, Philosophy and Knowledge: A Commentary on Plato’s Theaetetus (Lewisburg, Pa.: Bucknell University Press, 1992), 188–91. In addition to outlining the various combinations Polansky also explains how Socrates arriving at this particular number is in part due to his imitating Theaetetus’ method of arriving at the solution to the surds. 9. See Meno 81a–d. 10. M. F. Burnyeat, on his own reading, instead invites us to employ Locke’s discussion of wax and error as a guide see The Theaetetus of Plato, 99–101. 11. Raphael Woolf in “A Shaggy Soul Story: How Not to Read the Wax Tablet Model in Plato’s Theaetetus,” Philosophy and Phenomenological Research 69 (2004): 573–604, argues convincingly that the discussion of the quality of wax needs to be questioned and that Socrates discusses the issue of the quality of wax after he has concluded his explanation of false opinion. Thus the wax as such does not play an explanatory role and serves to illustrate how not to construct the problem. 12. Woolf interprets the instantaneous nature of the identification of percept and impression to be evidence that true opinion cannot be knowledge because opinion formation in this case is not under the control of the subject (“A Shaggy Soul Story,” 601–3). 13. Aristotle De Anima 2.5. 14. Elfriede Tielsch, Die Platonischen Versionen der griechischen Doxalehre: Ein philosophisches Lexikon mit Kommentar, Monographien zur philosophischen Forschung, est. Georgi Schischkoff (Meisenheim am Glan: Verlag Anton Hain, 1970), 58:151–63. 15. Frank A. Lewis, “Foul Play in Plato’s Aviary: Theaetetus 195bff,” Exegesis and Argument: Studies in Greek Philosophy Presented to Gregory Vlastos, ed. E. N. Lee, A. P. D. Mourelatos, and R. M. Rorty, in Phronesis: A Journal for Ancient Philosophy, Supplementary Volume 1 (1973) (Assen, Neth.: Van Gorcum & Co, 1973), 285–305. See F. A. Lewis, “Two Paradoxes in the Theaetetus,” Patterns in Plato’s Thought: Papers Arising out of the 1971 West Coast Greek Philosophy Conference, ed. J. M. E. Moravcsik (Dordrecht, Neth., and Boston: D. Reidel Publ. Co., 1973), 123–49. 16. See Sophocles Oedipus Rex 1328–91; Antigone 1347–53. 17. Cornford’s solution to this puzzle is not warranted and was long since refuted by Lee. Cornford introduces a whole new set of creatures, such as a bird representing the knowledge of “7 plus 5” that is distinct from either 7 or 5 and which is then mistaken with 11. When Socrates sets up the aviary, however, he explains it in terms of an arithmetician’s knowledge and clearly identifies the birds as knowledges of numbers, more specifically a knowledge of the odd and the even. See Francis MacDonald Cornford, Plato’s Theory of Knowledge: The Theaetetus and the Sophist of Plato (New York: Liberal Arts Press, 1957), 137; see H. D. P. Lee, “The Aviary Simile in the Theaetetus,” Classical Quarterly 33 (1939): 208–11, a refutation of Cornford referred to regularly in the literature.

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18. See Charmides 166e. 19. At Meno 97a–c, Socrates discusses how someone who has been given directions for the road to Larissa can have a true opinion, but would have to accept the word of someone else; and this is different from someone who has actually traveled the road. 20. See Gorgias 450e–457b; see Republic 2.368b. 21. See Charmides 166c–d. 22. See Symposium 174d, 220d. 23. See M. F. Burnyeat, “The Material and Sources of Plato’s Dream,” Phronesis 15 (1970): 101–22. Burnyeat attempts to trace the possible sources of the dream, including Aeschines, but ultimately argues that the dream is of Plato’s own making and that its source is irrelevant. 24. A good discussion of the different translations of “logos” in the context of the dream, and the need to understand logos as both proposition and definition, can be found in W. B. Bondeson, “The ‘Dream’ of Socrates and the Conclusion of the Theaetetus,” Apeiron 3, no. 2 (1969): 1–13. Bondeson makes two important points: (1) Just as one cannot make entities such as statements through an additive process of cumulative non-stateables, so a definition cannot rest on cumulative indefinables; (2) True opinion is the genus of knowledge, but Plato has not clearly stated what its differentiae are. 25. This is reminiscent of the fate of language, given the Heraclitean flux (182a–183c), though the point here is not that the terms are inapplicable because of flux but because they can’t capture the singular. Hegel offers a similar analysis but to a very different purpose in the Phenomenology of Spirit when he explains terms that appear to name the singular like “here,” “now,” and “this” are actually universals. 26. Note that the primary metaphor for “knowing” was “holding” and “grasping” in the previous section on the aviary, whereas here predication is the process that ultimately leads to knowledge claims. 27. Although this may sound like an anticipation of Russell’s “knowledge by acquaintance” and “knowledge by description,” but Socrates is unwilling to ascribe knowledge to perception. 28. On the discussion of parts and wholes, see Plato Parmenides 145b–e and 157b–158d. 29. See Mitchell Miller’s remarks: “Right judgment [doxa] . . . and logos do indeed disclose the self-same object in distinctive ways, the one bringing it to mind in its simplicity, the other explicating it by laying out a plurality of parts.” “Unity and Logos: A Reading of Theaetetus 201c–210a,” Ancient Philosophy 12 (1992): 103. 30. See Plato Phaedo 96–100 and discussion of that passage in chapter 5 following. 31. Socratic dialectic leads to the whole to the extent that Socrates consistently attempts to introduce and reach toward the Good. 32. See Plato Phaedrus 264aff on the matter of “natural” and “unnatural cuts.” 33. Throughout the discussion of the third definition idea (203e, 204a, 205c, 205d) and eidos (203e, 205d) are used. But in this passage these terms are not meant to refer to the forms of the Republic, but rather they are here seen as characteristics referring to the wholeness of things. 34. The significance of turning to written language is connected with the fact that, unlike spoken language, the written is more easily broken down into its elements.

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35. Note that Socrates is choosing composite wholes. One might ask whether he would make the same claim about Being—that there is no difference between Being and the total number of beings. 36. Gail Fine, “Knowledge and Logos in the Theaetetus,” Philosophical Review 88 (July 1979): 366–97. Fine’s point is that Socrates is systematic in the division of vowels and consonants and is thus being systematic generally, which reveals that he does know the simples after all. 37. For a good discussion of the reasons why this is not an insoluble dilemma, see Rosemary Desjardins, “The Horns of Dilemma: Dreaming and Waking Vision in the Theaetetus,” Ancient Philosophy 1, no. 2 (Spring 1981): 109–26. 38. Julia Annas, “Knowledge and Language: The Theaetetus and the Cratylus,” Language and Logos: Studies in Ancient Greek Philosophy Presented to G. E. L. Owen, ed. Malcolm Schofield and Martha Craven Nussbaum (Cambridge: Cambridge University Press, 1982), 95–114. Annas writes: “The refutation of the dream theory shows us that we are committed to the principle that knowledge must be based on knowledge. Plato’s examination of the dream theory now has a clear point: it brings out how two assumptions about knowledge (it requires logos, it has a hierarchical structure) force us to recognize a third important point about it: it cannot be based on unknowables” (105). But this refutation is itself based on experience. Annas’s point that there must be distinctions among different ways of knowing is not necessarily at odds with the Theaetetus passage (113). 39. Gilbert Ryle, “Logical Atomism in Plato’s Theaetetus,” Phronesis 35 (1990): 21–46. 40. Analyzing the work of G. E. Moore and Alexius Meinong, he shows that the same point holds whether we talk about simple and complex names or concepts. He compares Wittgenstein’s critique of the shortcomings of logical atomism in the Tractatus to Socrates’ refutation of the dream theory. 41. Ryle, “Logical Atomism in Plato’s Theaetetus,” 46. 42. To Ryle, the only issue that Socrates’ discussion addresses is the problem raised by logical atomism. The simples of the dream might be taken to represent the first principles of mathematics, which are self-evidently true and which do not themselves allow of demonstration, but which make a demonstration of the complex possible. We intuitively apprehend axioms and we do “name” them, and it is because of these starting principles that we can derive conclusions. 43. Glenn Morrow, “Plato and the Mathematicians,” Philosophical Review 79 (July 1970): 309–33. Morrow concludes: “The dream then would naturally be taken as expounding the basic character of geometrical procedure; that is, all demonstration is a texture of propositions composed eventually of simple premises which, being simple and ultimate, cannot be demonstrated and therefore cannot be known to be true (327).” 44. See Ryle, “Logical Atomism in Plato’s Theaetetus,” 44–45. 45. Presumably the answer would be “dialectic.” 46. See Cratylus 431c–432c, where there is discussion of the paradoxes of mimesis in general and in relation to the flux in particular. 47. See Polansky, Philosophy and Knowledge, 223–40. 48. See Mitchell Miller, “Unity and Logos: A Reading of Theaetetus 201c–210a,” Ancient Philosophy 12 (1992): 87–11. 49. See Theaetetus 185aff.

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aving examined the three main definitions of “knowledge” in the Theaetetus, we must venture some resolution of the apparent aporia of the dialogue as a whole. As readers we enter the dialogue with the expectation that Socrates and the two mathematicians will be able to arrive at a satisfactory definition of knowledge. If they can’t do so—who can? It is the complexity of the arguments, together with the failure to reach a final definition of knowledge, that has seduced various Plato scholars into coming up with explanatory, sometimes fanciful, hypotheses. Cornford argues that the dialogue demonstrates negatively the need for the theory of forms in order for knowledge to be possible.1 Ryle offers a reading of the Theaetetus that credits Plato with anticipating the shortcomings of logical atomism and generally thinks of the dialogue as evidence that Plato entered a self-critical period where he abandoned the theory of forms.2 More recently, Sedley arrived at the thesis that the dialogue is Plato’s tribute to Socrates and an exhibition showing which Socratic ideas were crucial to the development of Plato’s own philosophy, and most importantly to the development of metaphysics.3 Timothy Chappell offers a revised Cornfordean position, claiming that it was Plato’s intention in the Theaetetus to give a critique of empiricism.4 My own hypothesis is that the purpose of the dialogue is to explore the mathematician’s understanding of knowledge and to consider whether it is a possible paradigm for philosophical knowledge and that the aporetic conclusion of the dialogue is an indication that philosophy is not reducible to mathematics. Early on in the dialogue Socrates equates episte¯ me¯ and sophia, which I will take to be a confirmation of the claim that it is philosophical knowledge that Socrates 141

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is interested in. What the Theaetetus reveals is that the mathematician who does excel at solving problems systematically (e.g., Theaetetus’s solution to the problem of the surds) cannot do the same when it comes to answering philosophical questions. To do so—to become a friend to sophia— requires self-awareness and self-reflection, a search for self-knowledge. Socrates is pleased with his accomplishments at the end of the dialogue, for he has pointed Theaetetus in that direction by letting him come to know what he does not know. To fully examine the difference between the mathematician and the philosopher and the different conception each has of knowledge, we turn to the Republic and investigate the critique of mathematical knowing in book 6. Furthermore the discussion of the philosopher in the “digression” of the Theaetetus very much invites comparison with the investigation into the nature of the philosopher in the Republic, so as to determine whether there are really two different conceptions at work. It is in this context that we will be able to assess Theaetetus’s nature with respect to its philosophical potential. Finally, I will offer a final assessment of the outcome of the Theaetetus and show that at least philosophical knowledge needs to be framed by self-knowledge.

1. PARERGA: DIGRESSION Roughly midway in the Theaetetus (172c–177c), Socrates, after much coaxing, engages Theodorus in the full examination as to whether or not Protagoras’s doctrine of the measure is in fact defensible. And it is in the midst of discussing whether the analogy between an individual’s perception regarding sense qualities and the city’s opinions regarding moral qualities is tenable that Socrates briefly digresses to put forward two very different lives, comparing the life of the orator with that of the philosopher, the former enslaved to the opinion of the many, the latter free and at leisure. Socrates proceeds to depict the philosopher as someone who is unconcerned with worldly matters, who doesn’t know his neighbor, does not distinguish the king from the shepherd, does not concern himself with any other political matters (174d–175a), but is entirely absorbed in his study of humanity itself and of justice itself and captivated by other matters above the earth and below the sky. Thales is introduced as the prototype for the philosopher, and we all laugh along with the servant girl who watches him fall into a well, as he is intent on his observations of the heavens. He, like the “top” philosopher, cannot see what it in front of him.5 This caricature of the philosopher delights Theodorus, who more than anyone else in the dialogue fits this description.

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If it is indeed the case that the “top” philosopher knows “human being,” but cannot recognize his neighbor, then such a phenomenon would represent the reverse problem of the present dialogue: the philosopher in “flight” (173e) knows the whole, but he cannot apply it to anything. He, too, lacks self-knowledge or, as Socrates puts it, commenting on the aloofness from political matters: And he doesn’t even know that he does not know all these things, for he’s not abstaining from them for the sake of good repute, but in truth his body alone is situated in the city and resides there, but his thought, convinced that all these things are small and nothing, dishonors them in every way and flies, as Pindar puts it, “deep down under the earth” and geometricizes the planes, “and above heaven” star gazing, and exploring everywhere every nature of each whole of the things which are and letting itself down to not one of the things nearby (173e–174a).

This is the image that the orators will paint of the philosopher, and, as we know from the Apology, a portrait that the Athenians, with the help of Aristophanes, have to a great extent accepted. Surely, nobody is naive enough to believe that this caricature of the digression is intended to refer to Socrates, the gadfly of the Athenian agora, who not only recognized his neighbors, their families, and their demes, but who can relate to Theodorus the specific parentage of Theaetetus. The entire image of the “top” philosopher is problematic, because embedded within it is the tension between this “ideal” philosopher who appears to be apolitical, but who is supposedly concerned with human being itself and justice itself:6 For someone of this sort has truly become unaware of his neighbor next-door, not only to what he is doing but almost to the point of not knowing whether he is a human being or some different nursling. But what (a) human being is and in what respect it’s suitable for a nature of that sort to act or be acted on that’s different from all the rest—he seeks that, and all his trouble is in exploring it (174b).

On what basis, one must wonder, could the philosopher come to know human being, given that he does not know his neighbor? In addition, he does not know that he does not know, and thus lacks an element of selfknowledge—which makes it questionable whether he can use himself as a springboard to any paradigm human being. The difficulty is reminiscent of Oedipus who was able to solve the riddle of the sphinx because he knows human being, but as it turns out in Sophocles’ account, Oedipus lacked the knowledge of the particular, namely who he was and where he came from. He lacked the basics of self-knowledge: Even though Oedipus could solve the riddle of the Sphinx, the question about man in general,

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he literally did not know who he was, who his parents were, where he actually came from. All the things that are missing from Oedipus’s knowledge are proudly denigrated in the description of the “top” philosopher (see 175a–b). Some commentators, such as Cornford, liken the discussion of the “top” philosopher to the philosopher king of the Republic and see many links between it and the Theaetetus. They interpret the Theaetetus as a testament to the need for the Forms in any account of knowledge, and who generally subscribe to a two-world ontology, find their reading confirmed in the digression. To provide just one example, Cornford is most clearly associated with that particular type of reading: “The allusions to the allegory of the Cave, the passage about the true meaning of kingship, happiness, and justice, are intended to recall the whole argument of the Republic, with its doctrine of the divine intelligible region of Forms, the true objects of knowledge. This is no mere digression. . . .”7 The “two-world version” of the Platonic explanation of knowledge seems to be confirmed in various ascent passages in the Republic and elsewhere. For example, in book 6, discussing the ways in which philosophical natures can be distorted and corrupted, and shortly before turning his attention to the question of “the good,” Socrates says: For, presumably, Adeimantus, a man who has his understanding truly turned toward the things that are has no leisure to look down toward the affairs of human beings and to be filled with envy and ill will as a result of fighting with them. But, rather, because he sees and contemplates things that are set in a regular arrangement and are always in the same condition— things that neither do injustice to one another nor suffer it at one another’s hands, but remain all in order according to reason—he imitates them and, as much as possible, makes himself like them (500b–c).

This would seem to be akin to a “true philosopher” who turns away from the world and does not know his neighbor. Yet the notion of ascent does not require a world of separation or separable forms. Socrates uses a particular phrase to describe the advantage the philosopher would have over the orator “whenever he himself gets to drag someone up” (175b) and discusses justice, happiness and kingship. The orator who has lived a life catering to the desires of the many would be at a loss and unable to speak. Dragging someone up is clearly linked to the ascent described in the cave but the ensuing discussion about the “top” philosopher’s flight from the mortal region to the divine in order to fashion himself after the divine and avoid evil and injustice is more difficult to reconcile with the discussion in the Republic. There is a tension, a disconnect, between the slow and arduous ascent versus the flight to the otherworldly. The flight to the divine suggest more of a solitary non-dialogical endeavor

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which is contraposed to Plato’s depiction of philosophy as dialectics. Furthermore, as we will see when we turn to the Republic there is a duty for the philosopher to return to the cave and to benefit the city as a whole. Here in the Theaetetus Socrates describes the philosopher’s journey as a flight that he defines in the following: “Flight (is) assimilation to a god as far as possible, and assimilation is to become just and holy with intelligence (phrone¯seo ¯ s).” (176b). It is not the case that Socrates falls short of the mentioned virtues but rather that he does concern himself with the particular in front of or next to him. Throughout the dialogues we can marvel at Socrates’ ability to recite chapter and verse for his aristocratic interlocutor’s genealogies while the “top” philosopher looking at everything sub specie aeternitatis finds such counting and reckoning as laughable (175b). In addition, I should note that there is no character in the Platonic dialogues who could be viewed as closer to the divine than Socrates: In the Apology he tells us about his mission from Apollo; about his divine sign, the daimonion which restrains him from doing harmful acts; his initiation into the secrets of ero¯s by the mantic prophetess Diotima; and here in the Theaetetus his practice of midwifery is also divinely sanctioned because it is not at all tied to experience. Yet this very same Socrates tells us about his wisdom at the end of his life that it is worth little or nothing because it is not divine but human wisdom which culminates in the knowledge of ignorance. For Socrates becoming as divine as possible—or as it described in the Theaetetus following the divine paradigm (176e)—is tantamount to ridding oneself of false opinion.8 And since he is on a mission, he seeks to rid others of their false opinions as well, which he does openly in his practice of maieutics on Theaetetus’s behalf. To fully understand the relationship between Socrates’ way of living and the divine, we need to consider the role that the divine plays in the digression. Socrates attempts to overturn Protagoras’s homo mensura in the digression by introducing a god who is “in no way unjust in any respect, but he’s the most just that it’s possible to be” (176c), and by suggesting that the divine should be taken as a paradigm after which we should fashion our lives. Clearly, Socrates advanced such a just god as a measure of what is just and good in contradiction to Protagoras’s utility and expediency as the (human) measure of the just. In contrast, Theodorus, who very much wants to associate himself with the “true philosopher” when it comes to political matters, also aligns himself with Protagoras, saying: “but the speeches are as it were our domestics, and each of them waits around to be completed whenever we decide” (173c).9 Paul Friedländer makes the thought-provoking comment: If previously mathematics was the hidden constant, if being was divined once and God as the measure alluded to once, only to disappear again, now

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there is revealed the sphere of the divine and (strictly corresponding to it) the knowledge and life, in short the existence, of the philosopher.10

It is in the digression that the philosopher comes to light. Rather than taking human being to be the measure, the philosopher asks, “What is human being? How should one live one’s life? What is justice really?” (174b). The discussion in the Republic which mirrors that of the digression occurs in a lengthy consideration of philosophical natures and the difficult path that needs to be taken to ensure that the person who has such a nature should be nurtured appropriately. The two main obstacles to the realization of philosopher-kingship are the people’s desire to engage in political rule themselves, because of the apparent benefits of political power, and, on the other hand, the attempt to enslave the philosophical nature and make it serve the desires of the many, turning the philosopher either into a tyrant or a sophist or some combination of those two. Socrates illustrates the first point with the image of the ship (5.488a–489e), aboard which every untrained sailor wants to steer, while the true pilot is regarded by the many as a “useless stargazer.” And in the same way the city embarks upon dangerous waters without a helmsman or clear bearings, with no course that would be good for the city. Instead the ship is moving aimlessly, heading north or south, east or west, depending on who won the contest among the sailors. Some may even steer the city into the storm or into war, rather than away from it, hoping to display their skillfulness, a storm that may ultimately sink the ship. If the ship sinks, the stargazer will die along with everyone else, though he might have been able to save the city. The stargazer, then, resembles both the “top” philosopher and Thales in the Theaetetus. The corruption of people of a philosophic nature is identified by Socrates as the greatest crime perpetrated by the city, since the city indeed recognizes the beauty of the young philosopher. The city claims him and seduces him to serve her every whim and desire, deforming and twisting him into a tyrannical being. As we read through Socrates’ account, we think of young Alcibiades, whose relationship with Athens, described by Thucydides, illustrates what Socrates depicts.11 Socrates concludes that it is rare for those who possess a philosophical nature to escape the clutches of the city and he says that he can only think of two who have successfully done so: Theages and himself (496b–c). Theages, because of his sickly constitution was most likely deemed useless by the city—and he may perhaps represent the stargazer—and thus escaped corruption. Socrates, on the other hand, is immune to the city’s blandishments, since he is protected by his daimonion. Socrates cannot himself be identified with the stargazer, however, for we know that he did not quietly stand by, but challenged the sailors who wanted to steer the ship, forcing them to

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display their ignorance of piloting for all to see. Thus Socrates alone represents a different relationship between the philosopher and the city, one where the city considers the philosophic nature a danger to itself and does its best to eliminate the peril.12 The difference between the sophist and the philosopher is characterized by Socrates as the difference between someone who serves the many by identifying their likes and dislikes, calling the former good and the latter bad, letting the many enjoy their own desires, on the one hand, and someone who investigates the good independently of the demands of the many. Socrates suggests that the real cause for the corruption of philosophical natures is not the sophists as such, but rather the voracious appetites of the many. He characterizes them as “a beast,” something like a tyranny of the mob. Socrates next examines the final distortion of philosophy, brought about when those who do not have a philosophical nature turn toward philosophy. He describes them as those who are subtlest in their art. Their journey from their particular art to philosophy is characterized as going from prison to the temple (495d). In contrast with these imposters, the philosophic nature patterns itself after the divine and becomes orderly and in this way resembles the “top” philosopher of the digression. While I cannot fully concur with Cornford’s arguments about the status of the forms and the theory of forms in Plato’s philosophy, I do want to join with him in drawing connections between the Theaetetus and the Republic, reading Socrates’ education of Theaetetus as illustrating the ascent out of the cave. It is only in the Sophist when Socrates no longer is actively participating that there will be an examination of Theaetetus’s flying. Here Socrates leads Theaetetus step by to the self-recognition of knowledge of ignorance. Before we can fully elaborate this claim we need to examine the discussion of the limitation of mathematics and the characterization of philosophic in the Republic to determine what kind of work is needed to turn the mathematician into a philosopher. 2. MATHEMATICS AND SELF-KNOWLEDGE The fact that Socrates would investigate the question of episte¯ me¯ with two mathematicians, Theaetetus and Theodorus, should not strike us moderns as unusual, since mathematics has long been considered the paradigm for universal and necessary knowledge. The Pythagoreans and Plato himself were already well on the way to that view, sometimes stated less directly. And in the period when Plato was writing, mathematics was on the verge of “systematization” and “formalization” as a science, and Euclid’s Elements stands as evidence of that accomplishment. We know

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that mathematics played a central role in Plato’s Academy13 and there is ample evidence in the dialogues and in secondary reports that Plato was intensely interested in the study of mathematics. For greater clarity on this matter and its importance in Plato’s philosophy generally, I turn to the discussion of mathematics in the Republic, where it is both valued as a training tool, helping us to think about invisible things, and criticized because it remains tied to the visible world and because it is based on unexamined starting points, axioms, and hypotheses. For Plato, it is clear, philosophy is in no way reducible to mathematics. In a sense one might say that the implied question ultimately answered in the Theaetetus is this: What would be required to take the step from mathematical thinking to philosophy. Kurt von Fritz offers a provocative examination of the link between mathematics and episte¯ me¯ in Plato’s philosophy in his Platon, Theaetet und die antike Mathematik. In a close analysis of Republic 6, von Fritz argues that the mathematician and the dialectician are concerned with the same objects of knowledge, but that the corresponding capacities, dianoia and noe¯ sis, yield different outcomes. The crux of the difference is the role of hypotheses: mathematicians, according to Socrates, begin with hypotheses and reason “downward” to conclusions, relying on visible images to illustrate the material they are reasoning about; the dialectician, on the other hand, begins with hypotheses and reasons upward, never making use of the visible. The deficiency on the mathematicians’ side is that they mistake hypotheses for archai, rather than using them as starting points to get to the source or origin of everything. Von Fritz explains: Arche¯ and hypothesis are, according to the meanings of the terms, both relational concepts and in a certain sense they both denote a foundation, a beginning, a point of departure. It is connected with that we can make hypotheses into archai, as the mathematicians do, according to Plato. Nonetheless, they must denote beginning and point of departure, in a different sense, since the true arche¯ is precisely unhypothetical.14

Hypotheses, for von Fritz, are “subjective” starting points for the process of coming to know, whereas he thinks of archai as “objective” ontological starting points. As we shall see, it is the blurring of these two that enables mathematics to become a science, though an incomplete science, according to Plato. This incompleteness of mathematical episte¯ me¯ from a philosophical perspective is exhibited in the Theaetetus. Curiously, what Plato finds problematic in mathematics is later celebrated by Kant and taken as a paradigm for all knowledge, that is, the becoming objective of the subjective. In the “Preface” to the second edition of the Critique of Pure Reason Kant writes:

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When the isosceles triangle was first demonstrated, something dawned on the man who did so. . . . He found that what he needed to do was not to investigate what he saw in the figure, nor—for that matter—to investigate the mere concept of the figure, and to let them inform him, as it were, of the figure’s properties. He found, rather, that he must bring out (by constructing the figure) the properties that the figure had by virtue of what he himself was, according to concepts, thinking into it a priori and exhibiting. And he found that in order for him to know anything a priori and with certainty about the figure, he must attribute to this thing nothing but what follows necessarily from what he himself put into it in accordance with his concept.15

If we substitute “hypothesis” for “concept” in this passage from “Preface B,” we can see in what way Plato might object to Kant’s acceptance of mathematics as the model for all possible knowledge. Plato would agree with Kant’s characterization of the subjective becoming objective, but he would disagree with the legitimacy of that move. It is important to note that Kant himself here points to the interplay of knowledge and selfknowledge in the development of mathematics as a science. It is the recognition of the thinker’s own contribution to the construction of mathematical figures that provides the certainty and necessity that characterize mathematics as a science. To clarify the consequences of “hypothetical” reasoning it is necessary to examine more closely book 6 of the Republic, contrasting the critique offered there with Socrates’ explanation of his own reliance on hypothesis in his intellectual autobiography in the middle of the Phaedo. The crucial difference will hinge on whether or not Socrates views the hypothesis of the forms as a self-evident starting point, or whether he is open to reconsider and further examine the forms. Finally, it must be shown how the critique of mathematical hypotheses in the Republic relates to the discussion of knowledge by mathematicians in the Theaetetus.

3. THE LINE Urged by Glaucon to expand on his discussion of the sun and the good, Socrates, cautioning that he will have to leave out quite a bit, reminds us what he has established up to this point: The form (eidos) of the visible and the form of the intelligible. It is in the context of these two forms that Glaucon is told to construct a line of unequal segments,16 and then to duplicate this initial proportion within each of the two segments.17 An immediate issue is the decision which of the two is the larger section. If we keep that determination within the context of the two forms, it seems to have little significance: What could be the meaning of saying that the form

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of the visible is “larger” than the form of the intelligible? For the immediate purpose, however, let us stipulate that there is plurality in the visible world and unity in the intelligible, at least with respect to one another, and thus assign the larger segment to the visible realm. The lower segment of the line is in its turn divided into images and originals, and the proportion of the line as a whole is maintained, because there are “more” images possible than originals—given that any original can cast multiple shadows. The smaller line segment is then subdivided into a larger segment comprising mathematical objects, and the smallest of the segments is then reserved for the forms. Let us examine each segment carefully and attempt to assess the significance of the line as a whole. Socrates is very particular in describing the first level, specifying the images as “shadows, then appearances produced in water and in all closegrained, smooth, bright things, and everything of the sort” (509e–510a). Only the shadows and reflections of physical objects are included here, and the first segment of the visible realm can thus best be called “natural” images. Contrived images, such as paintings and sculptures belong on the second level, which includes all physical objects, both natural and manmade. This is all that Socrates has to say about the visible realm and, given Glaucon’s easy assent and understanding, it seems that we are to take this part as straightforward and uncontroversial. The two segments of the visible realm, clearly, are under the dominion of the sun, for both shadows and reflections depend on light and are in fact “caused” by the play of light. Similarly, it is clear that animals (zõa) and all growing things require the sun. And the case of artifacts, though not as directly evident, can be brought back to the sun as well, since the materials used for artifacts ultimately come from natural products. Socrates begins with the presentation of effects (images) and then proceeds to their causes (originals); and the principle that determines the particular order of the specification of the line segments is said to be their relative “clarity and obscurity” (saphe¯ neia kai asapheia, 509d). This criterion of clarity puts the burden of segmentation on the shoulders of the perceiver or knower. While it is “clear” that my reflection in a puddle is murky and obscure, it is also “clearly” the case that, without some such a reflection, I could not see myself at all. As Socrates observes when he is inquiring into self-knowledge with Alcibiades, we see ourselves through others, as we see our image in the pupil of the eye of someone else.18 Before he proceeds to the third line segment, Socrates draws a curious proportion: “And would you also be willing to say with respect to truth or lack of it, as the opinable is distinguished from the knowable, so the likeness is distinguished from that of which it is the likeness” (510a). Glaucon readily agrees. Socrates points back to the previous discussion about the sun and the good, linking the line with what has gone before.

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At the same time, he seems to contradict what he and Glaucon discussed at the end of book 5, where they differentiated opinion and knowledge as two separate capacities concerned with two distinct sorts of objects. If the two segments of the visible realm on the line are intended to be proportional to the relationship between opinion and knowledge, then opinion is closely connected with knowledge, rather than completely separate from it. An image presents us with a partial view of the original and it is precisely the recognition of something as an image that makes us hunt for the original—the ti esti, the “what it is.” It will be clear from the cave story as well that our starting point is always the image or shadow, and it is because of the connection between image and original that it turns out to be a fruitful starting point. Similarly, we find that we must begin with opinion and through it work our way to knowledge. The difference between the image and opinion is that opinion requires an additional step to get to the original, to knowledge, because opinion often disguises itself as knowledge. In any case, according to Socrates’ point here, for opinion to be like knowledge it cannot be completely other. Whatever it is that is shared by opinion and knowledge is also that which allows for the possibility that knowledge can be derived from opinion. When Socrates now characterizes the intelligible realm, he introduces soul and describes the first work of soul: In one part of it a soul, using as images the things that were previously imitated, is compelled to investigate on the basis of hypotheses and makes its way not to a beginning but to an end; while in the other part it makes its way to a beginning that is free from hypotheses, starting out from hypothesis and without the images used in the other part, by means of forms themselves it makes its inquiry through them (510b).

This is Socrates’ initial formulation of what he then identifies as the mathematical procedure and which he will elaborate to help Glaucon understand. Before turning to that elaboration, however, let us see what we can glean from the particular formulation. What brings it about that we look at the originals from the visible realm as images? Indeed, what is the source of the compulsion (anagkazetai) that forces us to proceed by means of hypotheses? Jacob Klein’s discussion of mathematics and more specifically of number (arithmos) provides important clues for deciphering the upper segment of the line, and specifically toward understanding what Socrates means when he tells Glaucon that on the segment of dianoia we are forced to work with and from hypotheses.19 The best way to understand this claim is to recognize the need for a supposition when working from countable things—that is, working from physical objects to that which makes counting possible in the first place. The mathematician supposes

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that there is some foundation—an intelligible object that underlies the visible physical object—and he will base his reasoning on the intelligible objects, while using the physical object as an aid. This then implies the possibility of passage from the visible or sensible (aisthe¯ ton) to the intelligible (noe¯ ton), a move which Socrates links with going from doxa to episte¯ me¯ . The first level of episte¯ me¯, therefore, is concerned with arithmetic (arithmetike¯ ) and calculation (logistike¯ ).20 The difference between practical and theoretical logistike¯ is concerned with the relations among numbers, just as geometry is concerned with the relations among things. Geometry, like arithmetic, is also concerned with the intelligible (noe¯ ton), using visible lines merely as aids to thinking about the triangle itself and the square itself. Looking toward spatial relations, geometry provides for an understanding of the structure and order of space. There remains, of course, the important issue of the ontological status of the noe¯ ton and Aristotle’s objection (Metaphysics 7 and 8) to the separability and independence of the second part of the line. The debate about the ontological status of mathematical objects has been ongoing: It is not our concern here to contribute to that debate, but to ensure clarity about Socrates’ moves here and what these maneuvers tell us about his conception of episte¯ me¯. If we understand the mathematical object as underlying the physical object and its generation from the fact of number, that is, that it is numbers that make counting possible and not the other way around, we can see that for Socrates episte¯ me¯ is concerned with causality. The fact that the countability of visible objects depends on numbers, but that numbers are independent of physical objects, implies a cause-effect relationship. This is not to say, of course, that numbers cause the being of the physical objects, in the manner of Pythagoras, but rather that numbers make it possible for us to count the objects and thus they make it possible for us to perceive the visible world in an orderly way. For Socrates the shortcoming of the mathematicians’ procedure is that it does not allow or call for an examination of the hypotheses, but rather treats them as though they were self-evident starting points. He claims that they “treat as known the odd and the even, the figures, the three forms of angles, and other things akin to these, in each kind of inquiry. These things they make hypotheses and don’t think it worthwhile to give any further account to themselves or others, as though they were clear to all (hos panei phaneron)” (510c–d). These starting points allow mathematicians to develop a system in and from which they can derive consistent conclusions. It allows them to create a system within which conclusions follow necessarily from the beginnings. Socrates, in contrast, is quick to point out the limitation of these proofs, describing the procedure as circular: “Beginning from them [hypotheses], they go ahead with their exposition of what remains and end consistently at the object toward which

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their investigation was directed” (510d). Nevertheless mathematics is an important stepping-stone, because it enables the soul to condition itself to focus on the noe¯ ta. Though there is still a connection with the visible world, the images for the mathematician, the problem of mistaking the image for the original has been eliminated. No mathematician would mistake that the square drawn in the sand for the square itself understood mathematically. It is the latter which dianoia addresses and with which is concerned. Socrates introduces the final line segment as a contrast with the mathematical, as “that which argument itself (autos ho logos) grasps with the power of dialectics, making the hypothesis not beginnings but really hypotheses—that is stepping stones and springboards (epibaseis te kai hormas)—in order to reach what is free from hypothesis at the beginning of the whole (te¯ n tou tautos arche¯ n ion, 511b). Hypotheses are to be seen as starting points for ascent, rather than the beginnings of a deductive process of descent. But is Socrates referring to the same hypotheses that he mentioned in connection with mathematics—number, figure, angles, and so on? Given the introduction of the method of hypothesis in the Meno, we can conclude that mathematical hypotheses are in part what Socrates is talking about, but that the genus of hypothesis extends further than mathematics. In his “intellectual autobiography” in the Phaedo, Socrates describes his own “ascent” up the line and characterizes his attainment of the final line segment as follows: “However, I started in this manner: taking as my hypothesis (hupothemenos) in each case the theory (logos) that seemed to me the most compelling, I would consider as true, about cause and everything else, whatever agreed with it, and as untrue whatever did not so agree (100a).” So as not to be blinded by looking at things directly, Socrates undertakes a “second sailing,” examining things through logos and by means of hypotheses. As he continues to elaborate on this point, he introduces the form of beauty as a hypothesis, which enables him to explain the cause of beautiful things. Thus the forms are what is grasped by logos itself, and they serve as springboards to the unhypothesized; but they themselves are hypothetical. Socrates goes on to explain that the fourth and final line segment does not rely on the visible or on images at all, but it rather employs the forms themselves, “going through forms to forms, it ends in forms too” (eidesin autois di’ auto ¯ n eis auta, kai teleueai eis eide¯ ) (511c). The last level selfcontained and does not stray outside itself, relying solely on the use of the dialectical method. All of this is possible, according to Socrates, because logos, using hypotheses as springboards, has grasped (hapsamenos) the unhypothesized first principle. Clearly, we need to grasp what that unhypothesized first principle is. In the context of book 6, there seems to be no other legitimate candidate than the good and the fact that Socrates here

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consistently refers to the good as an idea rather than an eidos supports the supposition that the good is not one of the eide¯ he¯ tou pantos arche¯ ? but is something epekeina, beyond being and knowing. Glaucon’s restatement of what he has learned about the line, alas, does not address the issues of the forms and of the unhypothesized first principle: He is more concerned with locating geometry and the other arts, reasoning that “thought is something between opinion and intelligence” (ho¯s metaxu ti doxe¯ s te kai nou te¯ n dianoian ousan, 511d). It is in response to this that Socrates concludes the discussion of the line by assigning terms to the various cognitive capacities corresponding to the line segments—it is only at the end that he does this—beginning with imagination (eikasia), then trust (pistis), reasoning (dianoia), and finally comprehension or understanding (noe¯ sis). It is the very concluding phrase that sheds some light on the question whether or not the idea of the good corresponds to the unhypothesized. And thus the line is arranged proportionally, “as the segments to which they correspond participate in truth, so they participate in clarity” (ho¯sper eph’ hois estin ale¯ theias metechei, houto ¯ tauta saphe¯ neias e¯ ge¯ samenos metechein, 511e). The line represents levels of clarity and truth, but not the cause of clarity and truth. Therefore, the good is not part of the line. Also, the fact that Socrates has previously characterized the good as the cause of being and knowing, but as itself unknowable except as cause, provides further evidence for the claim that the good is knowable as arche¯, but it is not knowable in itself. The analysis of the divided line leads us back to the image and discussion of the good. Additional evidence supporting the role of the good as the arche¯ of the whole can be found in the Phaedo, where Socrates explains that in order to give an explanation for any event, it is not sufficient to state the material causes or conditions, but that one must be able to connect the occurrence of the event with the good. He is discussing his own immediate situation, sitting in jail awaiting his execution, and he insists that any adequate account of this event must include his decision-making process. Talking about his bones and sinews as necessary conditions for his sitting in jail is fine, “but to say that these things are the cause of my doing what I do, and that I act with intelligence but not from the choice of what is best, would be an extremely careless way of talking” (99a–b). Socrates continues to generalize from his case and demands the same kind of explanation for natural and human events, because it is “the good which must embrace and hold together all things (to agathon kai deon zundein kai sunechein, 99c). The good is here characterized as a cosmological principle, which orders and binds the universe, clearly to be understood as an illustration of he¯ arche¯ tou pantos (the principle of the whole). The fact that the good is not contained within the mathematical image of the line, but that the line provides a springboard to it via the hypothe-

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ses, has serious implications for the limitations of mathematical knowledge. As the line makes clear, there is a certain isomorphism between the first and third segment, to the extent that both depend on physical objects. Also, the instructions provided by Socrates for the construction of the line, as well as the accompanying commentary for each section, shows that segments two and three are in some manner interchangeable, as is the middle term in 1 : 2 :: 2 : 4. But it is the move from the visible (horaton) to the intelligible (noe¯ ton) that gives the third segment a higher status in clarity. Socrates, however, is very cautious with his praise: “And it uses as images those very things of which images are made by the things below, and in comparison with which they are opined to be clear and given honor” (ho¯s enargesi dedaxasmenois te kai tetime¯ menois) (511a). The fact that some mathematicians may, so to speak, be “Kantians,” who use their own mental constructions as starting points, without searching whether there is some higher reality of which these mental constructions are images, illustrates the problem and shows why mathematics in general falls short of philosophy. The mathematician cannot step outside his own subjectivity to examine the cause of the square itself—he knows and he does not know, but he does not know that he does not know. As explained in the conclusion of the last chapter, it takes the entire discussion of the Theaetetus to enable Theaetetus to arrive at this recognition. The line is, of course, a mathematical construction, an analogy in the strictly mathematical sense of a proportion (analogia). The issue of the limits of mathematics and of mathematical knowledge can be clarified by considering what is missing from the line. Or, in another way, we might ask how Theaetetus, the mathematician, and his understanding of knowledge, fit into the line. First, and most obviously, in the passage that follows immediately upon the comparison between the Sun and the Good, the Good is missing from the line. It may animate both the different kinds of faculties and different kind of beings, but it is not something that Socrates will “put on the line.” Also, the only animate beings mentioned in the line are the objects of trust (pistis), “animals around us, and everything that grows” (510a). Human beings are missing from this scenario. We are left to “trust” that they are among the natural objects.

4. THE CAVE The cave is no doubt the best-known image of the Republic, the guaranteed residue for every undergraduate student of philosophy, but it is by no means easy to fully comprehend Socrates’ meaning. There are two extreme points, the shadows on the wall cast by the puppets and the artifacts carried by the puppeteers on the one hand, and on the other hand,

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the sun itself, once again representing the good as ultimate cause of everything. The connection between the two is established through the ascent and descent of one of the liberated prisoners. The fact that an ascent is possible suggests that there is a continuity between the inside and the outside of the cave. I will argue in this section that, in order to escape the prison of the cave and not to be merely seduced into the upper regions within the cave itself, the released prisoner must be capable of selfknowledge. The line is a representation of the potentiality for knowledge, whereas the cave represents the possibility of self-knowledge. The difficulty with this interpretation is that the ascent occurs in silence and, except for the chatter inside the cave, there seems to be no evidence of dialogue. At the same time Socrates claims at 517a–b that we should try to connect this particular image with what has been said before. If the line can be successfully connected to the ascent, then it looks as though there would have to be dialogue outside the cave, because the fourth segment of the line is characterized by dialectics. Socrates states the point of the cave story even before he gives his instructions for the construction of this particular image: “Make an image (apeison) of our nature in its education and want of education (apaideusias)” (514a). In the segmentation of the line then, the cave is at the first level of the line, making use of the imagination.21 Socrates feels the need to reintroduce the actual topic that preceded this lengthy journey into metaphysical and epistemological consideration: He assumes that we have become wrapped up and intrigued by the analogies of the sun and the line and thus may have forgotten the point of the discussion, to wit, the proper nurture whereby a philosophical nature could be educated to the point of becoming a philosopher-king. As it turns out, the future philosopher-king is born in the cave along with the other citizens and is initially subject to the same constraints: “with their legs and necks in bonds, so that they are fixed, seeing only in front of them, unable because of the bond to turn their heads all the way around (periagein)” (514a–b). From the very beginning of the story, the “turn-around” (periagoge¯ ), the goal and achievement of education is mentioned. The double bond suggests that neither physical nor mental motion is possible, and a prisoner’s entire energy would be focused on the shadows cast upon the wall by the puppets and the other artifacts paraded in front of the fire by puppeteers and ventriloquists. But what then is the significance of the different sets of chains? We can presume that the chained legs prevent the “cavemen” from leaving the city, whereas the chained neck forestalls any questioning within the city. Both a philosopher like Xenophanes, the traveling poet, and Socrates, the critical questioner, would be excluded from this particular cave city. The city can be criticized in one of two ways: (1) by traveling to other cities, which encourages comparisons and critique, or (2) by

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questioning fellow citizens—the poets, politicians, and craftsmen—all of whom play a pivotal role in the production of this particular shadowplay—and exhibiting their lack of knowledge about the good. There is to be no questioning, but a blind acceptance of what takes place on the canvas in front. But what sort of puppet show are the prisoners viewing? Socrates specifies that the puppets are “all sorts of artifacts and statues of men (andriantas) and other animals wrought from stone, wood, and every kind of material; as is to be expected, some of the carriers utter sounds while others are silent” (514e–515a). We can easily agree with Glaucon that Socrates is speaking about some strange kind of place (atopos). The cave appears to be entirely under human control—even nature is presented as fashioned by craftsmen. We meet human demiourgoi and must wonder whether they too looked to particular patterns to fashion their wares, as the divine demiourgos does in the Timaeus. The puppeteers presumably left the cave at some earlier point and, in contrast to the philosophers who would prefer dwelling outside the cave, desired to return to the cave to control those inside. Socrates connects the cave with the light outside, speaking of its long entrance, but suggesting that those released from their chains could easily find their way out. If the puppeteers are replicating the outside word and the puppets are crafted in imitation of natural objects, then the shadows on the wall represent images of images, the “third remove” from the truth and from the good. In book 10 of the Republic Socrates differentiates three couches—the form of the couch, the couch produced by a craftsman, and the image of a couch in a painting. In addition to providing the topography of this atopical place, Socrates says of the enchained prisoners: “They are like us. For in the first place, do you suppose such men would have seen anything of themselves and one another than the shadows cast by the fire on the side of the cave facing them?” (515a). The inability to see one another keeps them from achieving what is identified by Socrates in both the Alcibiades and the Phaedrus as a necessary stepping-stone toward self-knowledge, the ability to see oneself in an other. He likens the prisoners to the puppets and to the other things carried (512b). The prisoners’ problem is that they themselves are like puppets. Socrates points to the absence of dialogue, an additional hurdle to selfknowledge: “If they were able to discuss things with one another (ei oun dialoegesthai hoioi t’ eien pros alle¯ lous), don’t you believe they would hold that they are naming these things going by before them that they see (ou tauta e¯ ge¯ i an ta onta autous nomizein haper ore¯ ien)” (515b 4–5). This does not involve an absence of language as such apparently, because the prisoners are able to associate shadows and sounds, due to the echoing effect of speaking in an enclosed space. And later Socrates speaks about them as

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receiving prizes and honors for engaging in “cave science” (516c), remembering which shadow follows upon which other shadow and predicting the future course of the mobile images. The point instead is that the language among prisoners in the cave includes no conversation, no examination of each other’s opinions. The enchained prisoners do not experience aporia or wonder which makes it clear that philosophy is not possible within the cave, absent some turning around. The conditions of the cave reduce truth, which was previously seen as light, to shadows—and not all shadows, but only the shadows of artificial things. “Now consider what their release and healing from bonds and folly (aphrosune¯ ) would be like if something of the sort were by nature (phusei) to happen to them” (515c). Socrates specifies aphrosune¯, a term that serves as the opposite of both moderation and wisdom; but given the depiction of life in the cave, we can with some confidence say that it is meant as the opposite of wisdom here: The journey from cave to sun is the journey from mistaking the shadows of artifacts for the truth to recognizing the cause of everything visible, the sun. There are two identifiable stages to this ascent from the cave: (1) the first where the prisoner is compelled and coaxed (515c–516a); and (2) when the liberated prisoner becomes free and autonomous (516a–516c). It is not entirely clear who the agent is in the first stage, but the prisoner clearly is the patient or “recipient of the action.” Socrates asks us to imagine that the release occurs as if by nature— strange, surely, given that this release ultimately signifies paideia. The prisoner is released and “suddenly compelled to stand up, to turn his neck around, to walk and look up toward the light (anagkazoito exaiphue¯s anistasthai te kai periagein tou auchena kai badizein kai pros to pho ¯ s anablepein)” (515c 6–8). There are no Parmenidean horses, but there is some compelling force leading to the turn from darkness to light. Since the prisoner, prior to release, thinks himself to be in the possession of the truth, the “reality” he has grown up with as his daily life, something as powerful as Socrates’ “ti esti” is needed to force the ascent. For this to be effective, some form of conversation is needed and Socrates, as if by magic, introduces a speaker who compels the man to answer questions (auto ¯ anagkazoi ero ¯ to ¯ n apokrinesthai hoti estin) (515d 5). What is most important for our discussion is the fact that it is only when dialectics makes an appearance in the form of a guide, that the prisoner begins to experience wonder and aporia: It is not self-evidently clear that when he is looking at the artifacts he is looking at something more “real” than the previously viewed shadows. “Don’t you suppose he’d be at a loss (aporein) and believe what was seen before is truer than what he is now shown?” (515d). The entire process of ascent is described as very painful and the released prisoner needs to become accustomed to the light before he can see clearly. This process of habituation raises some prob-

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lems, however, because it looks as if we eventually accept as true whatever we get used to, whatever we are comfortable with. The criterion of clarity which accompanies truth is willy-nilly subjective and, as the story of ascent and descent illustrates, clarity and blindness accompany both journeys. Since the prisoners in the cave do not know that they are looking at shadows, they think that what they see is in fact clear. The advantage that the released prisoner has is that he understands what causes the shadows on the wall and, if we are to believe Socrates, he can trace everything back to the sun as the ultimate cause (516b9–c2). But will the fact that he knows the causes of the shadows influence cave science? Apparently, the patterns arrived at through hypothesis and continuous observation, which are the foundation of cave science, are explanatory, although the cave scientists do not know the cause of the pattern—just as the mathematician can construct theorems and proofs without knowing the cause of number. What the knowledge of cause provides is knowledge of perspective. The enchained prisoner sees his whole world of shadows from a single perspective. When turned around within the cave, he changes perspective, but he could simply replace one perspective and one world for the other. The ascent leads the liberated prisoner to see the multiplicity of perspectives and thus gives him a perspective on perspective.

5. CONCLUSION Already in the opening scene of the Theaetetus, Theodorus describes Theaetetus in a manner that invites us to suspect, along with Socrates, that we are looking at a potential philosopher, a “philosopher-prince.” What is missing from Theodorus’s depiction is the erotic element, an essential ingredient in the makeup of the philosopher, as Socrates characterizes philosophical natures, and explains in what sense they are lovers, in Republic 6.474d–475c. In the Theaetetus Socrates introduces the erotic element in two ways: first, with his talk of intellectual pregnancy and midwifery and, second, through his calling Theaetetus “beautiful,” in apparent contradiction of Theodorus’s initial identification of the young man as “not beautiful.” Socrates brings out Theaetetus’s beauty by asking him about knowledge and Theaetetus’s beauty shines forth brilliantly when he discovers that soul by itself strives toward being by itself (186a). In addition to meeting the “wonderful” Theaetetus at the opening of the dialogue, we are also made privy to Theodorus’s judgment that Theaetetus is Socrates’ look-alike, implying that Socrates is “not beautiful” as well. It is a requirement for the achievement of self-knowledge that someone have the opportunity to examine himself or herself in an “other.” This is made explicit in Socrates’ discussion in the Alcibiades I, 132d–133c, where

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Socrates speaks figuratively and generally about seeing oneself in the pupil of the interlocutor’s eyes as an image of self-knowledge, whereas here in the Theaetetus Socrates has the opportunity to see himself face to face. This dramatic set-up invites readers to link the question of knowledge under discussion with the Socratic desire for self-knowledge. The ascent of the emergent philosopher described in the cave, and that detailed in the segments of the divided line, in addition to linking up with the digression of the Theaetetus, present by means of images what Socrates accomplishes dialectically in his discussion with Theaetetus. The details of the cave, the manipulation of the prisoners to believe in a human-made world as though its two-dimensional moving figures were some ultimate and steadfast reality, are an exquisite illustration of the issues involved in Protagoras’s “human being is the measure of all things.” There is no reason as such measuring cannot be practiced in the cave. In fact, the enchained prisoners pursue a kind of “cave science,” measuring the shadows and their motions, and thereby, they seem to think, measuring their own intelligence and sophistication. In the cave, perception plays an integral part and some sort of “naïve realism” seems to be the order of the day within the cave. Turning away from the world of perception requires something like Theaetetus’s discovery of soul, that is, the discovery of something that cannot be explained by perception. It is the recognition that perception cannot get hold of being or of the common things which allows Theaetetus to move on to his own ascent and consider opinion as a possible candidate for knowledge. At the same time it is important to note that the first step in the ascent is perception, that perception plays an integral role in the discovery of soul and being. When interlocutors come to Socrates expressing their unexamined views, he does not dismiss or disrespect them. Here in the Theaetetus perception is not “abandoned”; rather they work through it, incorporate it and move on. The painful process of the ascent is mirrored in the Theaetetus by Socrates’ description of the labor pains that accompany the birthing of ideas. Theaetetus shares the experience of aporia with the released prisoner as well, the prisoner confused and temporarily blinded by the changing light, and understands that wonder is the beginning of philosophy. Socrates, like the guide in the cave, coaxes Theaetetus along, forbidding him to be satisfied with the habitual answers to the question about knowledge. The challenge for Theaetetus throughout the dialogue is to figure out what it is that he really believes: When confronted with the Protagorean version of his first definition of knowledge as perception, he initially believes that humans are the measure. But as Socrates reveals other layers of assumption beneath Protagoras’s dictum, Theaetetus no longer agrees. Socrates is habituating Theaetetus to the life of philosophical inquiry.

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Theaetetus already knew that he could not solve Socrates’ questions the same way that he solved the mathematical questions posed to him by Theodorus (148e). This fact indicates an early awareness about the difference between mathematics and philosophy. Rather than looking at Theodorus’s demonstrations and arriving at a solution to the problem of irrational numbers by formulating a hypothesis which comprehends all irrational numbers, dividing them into square and oblong numbers, Socrates is asking Theaetetus to examine his own activity, not just practice it, when he is asking him to answer the question about knowledge. Theaetetus complies and answers that perception appears (phainetai) to be the same as knowledge—beginning what turns out to be a thorough investigation of Protagoras’s homo mensura and Heraclitus’s doctrine of flux. Socrates refutes both—at least to Theaetetus’s satisfaction—and thus shows Theaetetus the way to soul and being. It is noteworthy that it is in the digression with Theodorus that Socrates introduces an alternative to human being as the measure, namely the divine, but he lets Theaetetus discover soul by himself. Through an examination of false opinion and the “logos of logos” the interlocutors arrive at a conclusion that appears to have brought them to an impasse. Even though Theaetetus agrees to let go of all three of his definitional offspring, Socrates seems satisfied with what they have accomplished. As a midwife Socrates has delivered Theaetetus of his ideas about knowledge and tested their viability. He concludes that Theaetetus is a better person as result: He will either conceive better ideas in the future or stay empty and be gentle with his companions, believing in a moderate way (so ¯ phrono¯s) that you don’t know what you don’t know” (210c). By trying to answer the question, “What is knowledge?” Theaetetus has gained a modicum of self-knowledge. At the end of the dialogue Socrates pronounces Theaetetus “moderate,” the only quality not ascribed to him in Theodorus’s opening praise (143e–144b). Rather than characterize Theaetetus as “moderate,” Theodorus calls him “gentle” or “mild” (praion), which is not quite the same as Socrates’ criterion of knowing what you know and do not know. “Gentle” and “mild” are two adjectives that would not befit either Socrates himself or the philosopher-king of the Republic. Thus, if Socrates’ assessment is correct, then Theaetetus, by virtue of gaining some degree of self-knowledge, is one step closer toward qualifying as philosopherprince after all.

NOTES 1. See Francis MacDonald Cornford, Plato’s Theory of Knowledge: The Theaetetus and the Sophist of Plato (New York: Liberal Arts Press, 1957).

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2. See Gilbert Ryle, Plato’s Progress (Cambridge: Cambridge University Press, 1966). 3. See D. N. Sedley, The Midwife of Platonism: Text and Subtext in Plato’s Theaetetus (Oxford: Clarendon Press, 2004). 4. See Timothy Chappell, Reading Plato’s Theaetetus (Indianapolis and Cambridge: Hackett Publishing Co., 2004). 5. Socrates refers to the philosopher as koruphaio ¯ n (173a), referring to leaders or those on the top—a somewhat suprising expression and one that contrasts with the description of the “true” philosopher in the Republic and the Phaedo. 6. Rachel Rue in “The Philosopher in Flight,” Oxford Studies in Ancient Philosophy 11 (1993): 71–100, suggests that Socrates presents himself as a mean between two extremes in his discussion of the “top” philosopher and the orator. Julia Annas in Platonic Ethics, Old and New (Ithaca, N.Y.: Cornell University Press, 1999), 52–71, argues that the depiction of the philosopher presents an ideal and is not real like the discussion of the philosopher in the Republic. More recently, Timothy Mahoney in “Is Assimilation to God in the Theaetetus Purely Otherworldly,” Ancient Philosophy 24 (2004), 321–37, has taken on both of these interpretations and suggest that the otherworldly nature of the philosopher which makes him appear unreal is balanced by the emphasis on the virtues of holiness, courage and most importantly justice the latter of which by definition provides a connection with the earthly realm. 7. Cornford, Plato’s Theory of Knowledge, 89. 8. See Polansky, Philosophy and Knowledge, 63: “Stated differently, the gods, as all-wise, are barren of opinion.” 9. See Ronald M. Polansky, Philosophy and Knowledge: A Commentary on Plato’s Theaetetus (Lewisburg, Pa.: Bucknell University Press, 1992), 137. 10. Paul Friedländer, Plato, trans. Hans Meyerhoff (Princeton, N.J.: Princeton University Press, 1969), 3:172. 11. To put the matter briefly, Alcibiades (450–404 BCE), “adopted son” of Pericles, playboy, powerful rhetorician, played many duplicitous roles. He doublecrossed Spartan ambassadors, so as to undermine the “Peace of Nicias,” the truce in the Peloponnesian War from 421 BCE to 415 BCE. He then urged upon the Athenian Assembly an expedition against Syracuse, but was recalled as one of its commanders because of a scandalous desecration back in Athens. Thereupon he defected to the Spartans and revealed Athenian military secrets. After a sojourn in Persia, Alcibiades helped the Athenians against the Spartans and ultimately returned to Athens and was reinstated as commander. But he was dismissed in 407 BCE, fled, and was ultimately murdered. See Thucydides History of the Peloponnesian War 5.45ff; 6.15ff, 88ff; 8.11ff, 46ff; Xenophon Hellenica 2.1.25–26. 12. See Apology 32a–33b. 13. The legendary motto written over the entrance to the Academy was “Nonmathematicians need not enter.” More important, numerous members of the Academy—including—Eudoxus, Speussipus, and Heracleides—were important mathematical innovators and theorists. See David Fowler, The Mathematics of Plato’s Academy: A New Reconstruction, 2nd ed. (Oxford: Clarendon Press, 1999). 14. “Arche¯ und hypothesis sind ihrer Wortbedeutung nach beide Relationsbegriffe und bedeuten beide im gewissen Sinn eine Grundlage, einen Anfang, einen

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Ausgangspunkt. Damit hängt es zusammen, dass man die hypotheseis zu archai machen kann, wie es nach Platon die Mathematiker tun. Dennoch müssen sie in verschiedenem Sinn Anfang, Ausgangspunkt bedeuten, da die wahre arche gerade anypothetos ist.” Kurt von Fritz, Platon, Theaetet und die antike Mathematik (Darmstadt: Wissenschaftliche Buchgesellschaft,1969 [1932]), 53. 15. Immanuel Kant, Critique of Pure Reason: Unified Edition, trans. Werner S. Pluhar (Indianapolis and Cambridge: Hackett Publishing Co., 1996), 18 [B xi–xii]. 16. Although a few commentators have argued that it should involve equal segments—reading anisa as an[a] isa—there would be no proportion if all the parts were equal, and there would be no possibility of an argument from analogy. 17. Rosemary Desjardins suggests that the proportions of the divided line are parallel to Theaetetus’s proposed solution to the surds. That is the instructions that Socrates gives for drawing the line in book 6 would parallel the steps Theaetetus would following in arriving at his solution. See Desjardins, “Epilogue: The Mathematical Paradigm (147d3–148b2), The Rational Enterprise, 171–80. 18. See Alcibiades I 132d–133c. 19. Jacob Klein, A Commentary of Plato’s Meno (Chicago: University of Chicago Press, 1965), 115–25. 20. Compare the definitions in Gorgias 450d and Charmides 165e. 21. The three levels of the line are illustrated by the three images Socrates uses in books 6–7: He begins with the physical object (sun) and moves to mathematical (line) and to clarify everything he goes to that which he identified as the least clear, the image (the cave). The cave is not just an image, however; it is also a natural object. It thus represents both levels 1 and 2 of the line. The fourth level of the line would then be the conversation itself or the critical abstract discussion at the end of book 5, where Socrates uses dialectics rather than images to establish definitions of knowledge, opinion, and ignorance.

6

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he notion that knowledge needs to be grounded in self-knowledge is no novel thesis in our post-Kantian age; but Plato’s unique way of tackling this problem has something to offer, even to those who consider themselves to have moved beyond Kant. Contemporary philosophers are still divided on whether or not mathematics and its offspring in “modern science” should be seen as paradigmatic for philosophical inquiry or a model of philosophical knowledge. It is clear from Plato’s writings, I think, that mathematics does play an important role in shaping philosophical inquiry, but that it is not comprehensive enough to provide an account of knowledge. A close examination of the Theaetetus reveals the difficulties involved in trying to arrive at a definition of knowledge, but it also provides the main ingredients that make up our knowledge of the world: perception, opinion, and logos. The question that arises in the context of our investigation is whether those three are also the most appropriate tools in our quest to come to know ourselves. If we could perceive ourselves the way we can perceive, say, a pink flower, we would be in a much better position to make claims to knowing ourselves. There are places where Socrates suggests that such self-perception is possible—most notably in the Charmides, where he asks young Charmides to look inside his soul to see whether or not he is in possession of moderation (so¯phrosyne¯ ). As discussed at the end of chapter 4, the sequence of orders given to Charmides mirrors the sequences of the definitions of knowledge developed in the Theaetetus. It is difficult to think of this progression of moving from perception to opinion to logos as a mere accident, especially in light of the fact that the second 165

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half of the Charmides examines Critias’s formulation of self-knowledge as the knowledge of knowledge and non-knowledge. My interpretation of the Theaetetus is very much guided by following the threats and clues Plato plants so often in the dramatic and literary structure of the dialogue. By doing so I was able to uncover themes, connections, and concatenations that shed additional light on both the individual dialogues and the problem of knowledge itself. Beginning with the frame of the Theaetetus, I was struck by its peculiar set-up, featuring Plato’s explicit disavowal of authorship of this dialogue. Euclides and Terpsion provide the occasion for our coming to know about the conversation that took place between Socrates and the two mathematicians, Theaetetus and Theodorus. The fact that Euclides shares his editing techniques with Terpsion raises the suspicion that the editing out of any human perspective—hiding the fact that he is restructuring Socrates’ narration, and instead presenting it as if it were a direct dialogue—was an implicit problem about the nature of knowledge and that pointed to the question of the role of perspective. The philosophical importance of frames is further highlighted when we compare different kinds of frames in the Platonic dialogues to discover the principle of framing. I looked to both the outer and the inner frames of the Theaetetus in an effort to distill the themes that connect it with other dialogues. The most obvious issue raised by the outer frame, which takes place long after Socrates’ death and depicts the dying Theaetetus, is the question of how to preserve and transmit philosophy. Concomitantly, given the explicit topic of the dialogue, the issue of the preservation and transmission of knowledge arises as well. The “sister dialogue” which responds or corresponds to the first question is clearly the Symposium, whose complicated frame introduces the fanatical Apollodorus as narrator of speeches given a long time ago at an occasion where he himself was not present. In addition to juxtaposing the frames of those two dialogues a natural third (to complete the charioteer, so to speak) was the Charmides that, like the Theaetetus, is framed by war and introduces Socrates in search of a successor. (Given the three topics of the dialogues, it is tempting to compare them to the tripartite structure of the soul in the Republic, with ero ¯ s corresponding to epithumia, so¯phrosune¯ playing the part of thumos, and episte¯ me¯ as the counterpart to logos. But a full elaboration of that possibility would go beyond the boundaries of this book.) The inner frame, including the early section of the Theaetetus, raises a different set of issues. Most notable are the following two “dramatic events”: Theodorus’s disavowal of any ero¯s with respect to Theaetetus, given the latter’s Socrates-like ugliness; and Socrates’ introduction of himself as a midwife, who delivers ideas from the pregnant souls of young men. Again, it is only when we connect the Theaetetus with other

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dialogues that we can gain a fuller understanding of these themes. Diotima’s discussion of spiritual or mental pregnancy surely can help to make better sense of Socrates’ midwifery. Diotima insists that we can only give birth in beauty, which helps us to understand why Socrates proclaims Theaetetus beautiful throughout the dialogue. Furthermore, a fuller analysis of ero¯s helps us to grasp the idea of spiritual pregnancy, which is presupposed in the Theaetetus; but it also sheds new light on our conception of knowledge. If we draw Plato’s other dialogue on ero ¯ s into the equation—the Phaedrus, which in turn is a companion piece to the Symposium—we arrive at a conception of knowledge that is inextricably linked to self-knowledge. The Phaedrus illustrates how ero ¯ s fuels our thirst for knowledge through the recognition of ourselves in another. In addition to tracing connections between the themes of the frames and the forms and contents of other dialogues, I have also examined those works more traditionally taken to be companion dialogues and linked by the common bond of the investigation of knowledge. When we approach Plato’s writings from the point of view of the “chronologists”—those commentators who interpret dialogues by first trying to establish their place within a sequence of Platonic works and a presumed development of Platonic thought within the total corpus—it seems that the young Plato must initially have made sense of the possibility of knowledge through his theory of recollection, discussed by Socrates in the Meno, thus presumed to be an early dialogue. The more mature Plato, it is conjectured, must then have “improved” his account of knowledge in the Republic by developing a more sophisticated metaphysics, which thereby enabled him to put forward the Forms as objects of knowledge. As a consequence, Plato, using Socrates as his mouthpiece but presenting his own original ideas, draws a much sharper distinction between opinion and knowledge and moves beyond the discussion of the Meno that linked those two, by suggesting that knowledge is true opinion which has been “tied down.” The Theaetetus, identified as later than the other two, appears to ignore the Forms, offering instead a definition of knowledge as true opinion plus logos, which appears to be a refinement of the Meno rather than the Republic. Rather than approaching the dialogues from this developmental perspective, I put them in direct conversation with one another, drawing illumination whenever possible from the relation they have to each other. The “interdialogic” approach to Plato’s works invites new ways to see old problems, and in the case of the Theaetetus a new way to think about the problem of knowledge. Every definition offered in the Theaetetus can be reinterpreted in the light of the themes discovered in the frame, as well as through discussions of similar definitions in other dialogues. Thus, for example, the longest examination unfolds in response to Theaetetus’s identification of knowledge with perception, leading the

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interlocutors to consider the ontology of motion, and culminating in Socrates’ proposal of the myth of twin motion. This myth, when cast in the light of the discussion of the Phaedrus, reveals features that are reminiscent of the creative activity of ero¯s. It is in the interaction between perceiver and perceived that the visible world is born. We might like to understand this as a paradigm for knowledge and say that in the interaction between the knower and the known, the intelligible world is born. The Republic offers a discussion that seems to support this analogy, by lining up the capacities of soul with appropriate correlates; but this approach becomes problematic when we consider the nature of the Forms: the Forms are not interactive, they are not in motion, they do not care about us. One possible solution to this problem is to turn to ero¯s and determine how it is that the interaction between two lovers can bring us closer to that goal. This I take to be the work that is done by the myth of the charioteer in the Phaedrus, where lover and beloved transform themselves into reciprocally loving friends who engage in philosophical discourses. While Socrates does not claim that the exchange will give rise to knowledge, he does describe it in terms of self-knowledge. Selfknowledge, especially when understood in terms of knowing what knows and does not know, becomes the touchstone for the possibility of knowledge. The Theaetetus is a dialogue that exemplifies the way in which Socrates leads his young interlocutor to the threshold of self-knowledge. The examination of Theaetetus’s offspring simulates the ascent “imaged” in the Republic through the analogy of the line and in the myth of the cave. With each refutation of the successive definitions Theaetetus gains a better understanding of what is involved in the problem of knowledge. During the refutation of knowledge as perception, for example, Theaetetus discovers soul and being and is called “beautiful” by Socrates. One can well argue that by the end of the dialogue Socrates has exhibited to Theaetetus the shortcomings of mathematical knowledge, in the sense that the three definitions mirror the procedure Theaetetus and Young Socrates used to arrive at the solution to the problem of the surds (147d–148a): They saw, they opined, and they explained. Yet, the dialogue ends in Socrates’ declaration that they have not been able to come to any satisfactory conclusion regarding the nature of knowledge. He declares that his own work of midwifery has been successfully completed, but he leaves us the readers with an impasse about the problem of knowledge. The success and failure of the dialogue points to the success and failure of mathematics as a paradigm for philosophy. As we learn from Socrates’ discussion in the Republic, mathematics is an important stepping-stone to dialectics; but it falls short, because it does not provide for the possibility of examining its own starting points. The virtue of philosophical knowledge is that it is

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constantly examining and reexamining starting points (one more time, from the beginning). Mathematics does not need self-knowledge in order for it to be a successful endeavor, whereas philosophy does. Theodorus’s self-proclaimed apolitical and unerotic nature alerts us to this problem; and the question whether or not Socrates was able to “seduce” Theaetetus can be answered partially by referring back to the frame of the dialogue, where Theaetetus lies on a stretcher dying from disease and wounds incurred in war. The most basic traditional sense of the Delphic oracle was, “Know yourself to be mortal.” Human mortality and finitude remain the context and perspective of even the loftiest discussions.

Works Cited

PLATO Bury, R. G. The Symposium of Plato. 2nd ed. Cambridge: W. Heffer & Sons, 1932. Cornford, Francis MacDonald. Plato and Parmenides: Parmenides’ Way of Truth and Plato’s Parmenides. Library of Liberal Arts. Indianapolis and New York: BobbsMerrill Co., n.d. Plato. Charmides. Translated by W. R. M. Lamb. Loeb Classical Library. Cambridge, Mass.: Harvard University Press; London: William Heinemann Ltd., 1955 [1927]. ———. Epistles. Translated by Glenn R. Morrow. Library of Liberal Arts. Indianapolis and New York: Bobbs-Merrill, 1962. ———. Five Dialogues: Euthyphro, Apology, Crito, Meno, Phaedo. Translated by G. M. A. Grube. Indianapolis: Hackett Publishing Co., 1981. ———. Gorgias. Translated by Terence Irwin. Oxford: Clarendon Press, 1979. ———. Gorgias. Translated by Donald J. Zeyl. Indianapolis and Cambridge: Hackett Publishing Co., 1987. ———. Phaedo. Translated by G. M. A. Grube. Indianapolis: Hackett Publishing Co., 1981. ———. Phaedrus. Translated by Harold North Fowler. Introduction by W. R. M. Lamb. Loeb Classical Library. Cambridge, Mass.: Harvard University Press; London: William Heinemann Ltd., 1982 [1914]. ———. Phaedrus. Translated and edited by Alexander Nehamas and Paul Woodruff. Indianapolis and Cambridge: Hackett Publishing Co., 1995. ———. Platonis Opera. Edited by John Burnet. Oxford: Clarendon Press, 1958–1959 [1900]. ———. Republic. Translated by Allan Bloom. New York and London: Basic Books, 1968. 171

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———. Republic. Translated by G. M. A. Grube. Indianapolis: Hackett Publishing Co., 1974. ———. Republic: The Comprehensive Student Edition. Edited by Andrea Tschemplik, with a complete revision of the classic translation by John Llewelyn Davies and David James Vaughan. Lanham, Md.: Rowman & Littlefield, 2005. ———. Sophist: Part II of The Being of the Beautiful. Chicago and London: University of Chicago Press, 1986 [1984]. ———. Symposium. Translated by Seth Benardete. In The Dialogues of Plato, edited by Erich Segal. Toronto and New York: Bantam Books, 1986. Plato’s Protagoras. Translated by Stanley Lombardo and Karen Bell, in Plato: Complete Works, edited by John M. Cooper. Indianapolis and Cambridge: Hackett Publishing Co., 1997.

THEAETETUS Anonymous. On Plato’s Theaetetus. Edited by Diels and Wilhelm Schubart. Berlin 1908. Campbell, Lewis. The Theaetetus of Plato, with a Revised Text and English Notes. Oxford: Oxford University Press, 1861. Cornford, Francis MacDonald. Plato’s Theory of Knowledge: The Theaetetus and the Sophist of Plato Translated with a Running Commentary. New York: Liberal Arts Press, 1957 [1934]. Benardete, Seth. Plato’s Theaetetus: Part I of The Being of the Beautiful. Chicago and London: University of Chicago Press, 1986 [1984]. Plato. Theaetetus. Translated by Harold North Fowler. Loeb Classical Library. Cambridge, Mass.: Harvard University Press; London: William Heinemann Ltd., 1987 [1921].

OTHER PRIMARY SOURCES Aeschylus. Eumenides. Translated by Richmond Lattimore. Chicago: University of Chicago Press, 1962 [1953]. Aristotle. Metaphysics. Translated by Hugh Tredennick. 2 vols. Loeb Classical Library. Cambridge, Mass.: Harvard University Press; London: William Heinemann Ltd., 1956 [1933]. ———. Nicomachean Ethics. Translated by Terence Irwin. Indianapolis and Cambridge: Hackett Publishing Co., 1985. Diels, Hermann, and Walther Kranz. Fragmente der Vorsokratiker: Griechisch und Deutsch. 11th ed. 3 vols. Zürich and Berlin: Weidmannsche Verlagsbuchhandlung, 1964.

Translations of Greek texts, particularly Plato, have sometimes been adapted by the author.

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Index

Aeschylus, 47–48 aisthe¯sis. See perception Alcibiades, 28–30, 53–54, 146, 150, 162n11 analogy (analogia), 6, 7, 41, 45, 47, 50, 51, 56, 62, 63n19, 64n26, 68, 90, 102n38, 121, 129, 142, 155, 156, 163n16, 168 Annas, Julia, 40, 127, 140n38, 162n6 aporia, 2, 7, 10, 13, 14, 31, 42, 45, 47, 52, 53, 54, 61, 62n7, 105, 121, 136, 141, 158, 160 appearance, 25, 35, 41, 50, 74, 76, 100n21, 101n26, 150 Aristotle, 14, 23, 37n26, 38n39, 39n52, 71–73, 84, 97, 111, 152 ascent, 9, 31, 41, 47, 67, 81, 121, 134, 137, 144, 147, 153, 156, 158, 159, 160, 168 Austin, J. L., 100n26 author/authorship, 3, 6, 11, 13, 17, 20, 34, 35, 36n15, 60, 166 aviary, image of, 9, 63n24, 103, 107, 111, 113, 116, 120, 138n17, 139n26 beauty, 1, 8, 24, 25, 28, 29, 30, 39n63, 41, 42, 43, 44, 45, 49, 55, 56, 59, 60, 62n2, 62n6, 64n30, 64n36, 67, 68, 81, 82,

109, 120, 130, 138n7, 146, 153, 159, 167 Benardete, Seth, 15, 37n21, 39n59, 39n62, 40n65, 58 Berkeley, George, 74, 99n14 Blondell, Ruby, 15, 37n20, 38n46, 63n21 Bondeson, W. B., 139n24 Bostock, David, 15, 83, 91–92, 137n1, 137n6 Burnyeat, Myles F., 15, 61n1, 64n30, 91–92, 99n14, 100n19, 101n26, 137n6, 138n10, 139n23 Bury, R. G., 62n11 Campbell, Lewis, 15, 36n16 Chaerephon, 1, 3, 28, 38n41 Chappell, Timothy, 15, 141 Cornford, Francis MacDonald, 13, 15, 86, 128, 138n17, 141, 144, 147 Critias, 7, 12, 14, 28–30, 36n4, 116–20, 166 Crito, 37n28, 39n60 daim¯on, 46, 47, 145, 146 Dean-Jones, Lesley Ann, 63n23 Descartes, René, 4–5, 99, 14, 137n5 Desjardins, Rosemary, 15, 98n4, 100n22, 140n37, 163n17

179

180

Index

dialectic, 1, 5, 9, 52, 53, 57, 58, 68, 76, 88, 94, 104, 114, 116, 124, 125, 131, 139n31, 145, 148, 153, 156, 160, 163n21, 168 digression, 9, 21, 26, 67, 69, 86, 142, 144–47, 160 Diotima, 1, 6, 8, 31, 35, 39n63, 40n66, 42–62, 62n6, 62n12, 67–68, 76, 138n7, 145, 167 Dover, Kenneth J., 64n29 doxa. See opinion Edmonds, Radcliffe G., III, 64n31, 64n36 Eleatic Stranger, 15, 36n14, 125, 127 episte¯me¯, 7, 13, 42, 44-46, 49, 52, 70, 104, 108, 111, 114, 119, 121–24, 130, 135, 141, 147, 148, 152, 166 er¯os/erotic, 5, 8, 9, 30, 31, 32, 39n59, 42, 43, 45, 47, 56, 60, 61, 67, 76, 94, 159 error, 68, 85, 104, 112, 115, 133, 138n19 Euclid, 37n25, 128, 147 Euclides, 3, 6, 11–24, 28, 31–35, 37n20, 37n27, 55–56, 60–61, 166 forms, 13, 41, 42, 74, 76, 86, 125, 128, 139n33, 141, 144, 149–54, 167, 168 Fine, Gail, 100n21, 101n26, 127, 137n6, 140n36 frames, dramatic, 1, 3, 6, 8, 12–24, 31–35, 36n16, 37n23, 37n28, 55, 61, 142, 166, 167, 169 Friedländer, Paul, 15, 145 Fritz, Kurt von, 148 geometry, 3, 24, 26, 55, 57, 70, 87, 128, 140n43, 143, 152, 154 Good, 6, 14, 42, 44, 63n12, 82, 89, 90, 121, 139n31, 149, 150, 153–57 Hegel, G. W. F., 4, 6, 139n25 Heidegger, Martin, 100n16 Heraclitus, 5, 8, 60, 67–70, 79, 84–86, 90, 94–97, 102, 130, 139n25, 161 Hesiod, 56–57, 79, 131–32 Hippocrates, 48

Homer, 33, 57–58, 79, 84 homo mensura, 85, 92–93, 103, 105, 145, 161 Hume, David, 38n34, 83, 88, 92 hypothesis, 148, 149, 151, 153, 154, 159, 161 ignorance: knowledge of ignorance, 4, 7, 10, 14, 18, 35, 42, 114, 120, 125, 145, 147 immortality, 44, 45, 47–49, 60, 63n17, 76 intelligible world/visible world, 42, 77, 85, 144, 149–52, 155, 168 Iris, 56–57, 79 Kant, Immanuel, 4, 13, 109, 148–49, 155, 165 Klein, Jacob, 151 knowledge, limits of, 1–5, 7, 11, 35, 42, 45, 98, 105, 137, 147, 155 Lee, Edward N., 101n32, 138n17 Lee, H. P. D., 138n17 Lewis, Frank A., 112 logos, 11, 12, 22, 23, 29, 45–47, 97, 103, 117, 121–25, 128–36, 139n24, 153 Maguire, Joseph P., 102n37 Mahoney, Timothy, 162n6 mathematics, 3, 7, 9, 13, 18, 27, 57, 61, 68, 70, 77, 100n22, 112, 115, 128, 140n42, 140n43, 141–57, 161, 165, 166, 168, 169 McDowell, John, 15, 83, 99n7, 100n15, 100n19, 101n31 measure, 8, 67, 70–78, 80, 81, 84–94, 98, 99n6, 99n8, 104, 135, 142, 145, 146 Meletus, 15, 55 memory, 19, 20, 38n31, 87, 88, 107, 108 metaxu, 18, 35, 56, 154 method, 2, 3, 88, 114, 124, 125, 128, 129, 137, 153 Michelson-Morley Experiment, 73 midwifery, 1, 6, 8, 9, 10, 12, 16, 27, 41–43, 48–55, 60, 74, 94, 97, 116, 118, 145, 159, 161, 166–68

Index Miller, Mitchell, 139n29 moderation, 118, 120, 136, 158, 161, 168 Morrow, Glenn, 128, 140n43 motion, 8, 69, 70, 75–79, 83–85, 90, 94, 95, 168 objectivity, 7, 12, 18, 22, 25, 34, 35, 91, 92 Oedipus, 114, 143–44 opinion, 103–24, 130–37; false opinion, 105–17, 133–37, 145, 161; right opinion, 45, 46, 103, 104, 133–36; true opinion, 2, 9, 46, 49, 52, 62, 103–06, 110, 115–17, 121–24, 132, 135, 167

181

62n3, 62n11, 63n15, 63n17, 64n30, 64n36, 73, 76, 81–82, 166–67 Polansky, Roger M., 15, 37n27, 38n31, 64n32, 102n46, 138n8 pregnancy, 41–49, 61n1, 63n15, 63n17, 159, 167 Protagoras, 8, 17, 29, 37, 60, 67–98, 99n7, 99n9, 100n15, 100n21, 100–01n26, 101n30, 101n32, 102n46, 103–06, 142, 145, 160–61 Prodicus, 29, 48 Pyrrho, 65n46 Pythagoras, 65n46, 147, 152 Quine, Willard van Orman, 137n6

perception, 67–120, 107–11, 131–34, 161, 165–68 Phainarete, 51 philosophical knowledge, 3, 7, 9, 61, 67, 125, 141, 142, 165, 168 Plato: Alcibiades I, 5, 53, 157, 159; Apology, 1, 3, 15, 29, 38n41, 39n55, 46–47, 52, 90, 120, 125, 143, 145; Charmides, 1, 7–14, 17, 24–31, 33–34, 30n65, 56, 64n26, 100n17, 117–21, 165–66; Cratylus, 64n33, 102n42, 127, 140n46; Euthyphro, 15, 24, 37n22, 54, 114, 137n4; Gorgias, 2, 28, 64n26, 102n38; Letter VII, 5, 12–13, 61; Lysis, 17, 29, 39n64; Meno, 1–2, 7, 45-49, 69n1, 62n5, 63n14, 74, 103–04, 110, 113–14, 117, 139n19, 153, 167; Phaedo, 15–17, 21, 27, 33–34, 37n27, 37n28, 38n35, 129, 149, 153–54, 162n5; Phaedrus, 4, 5, 9, 12, 20, 22, 38n33, 41–42, 45, 53, 60–61, 62n2, 76, 81, 86, 157–68; Protagoras, 17, 29, 38n28, 99n9; Republic, 1–2, 4–7, 9, 14, 17–18, 21, 29, 33, 35, 41–42, 53, 56, 56–68, 62n1268, 75, 96, 99, 102n43, 121–37, 139n33, 142–61, 162n5, 162n6, 166–68; Sophist, 15, 36n14, 50, 76, 94, 127–28, 147; Statesman, 15–16, 36n14, 50; Symposium, 1, 6, 8, 11–14, 17, 28–29, 31–36, 37n28, 38n51, 39n63, 40n68, 41–49, 57, 60–61, 61n1,

Rawson, Glenn, 63nn15–17 recollection, 19, 49, 61n1, 63n15, 63n24, 113, 138n7, 167 Rosen, Stanley, 62n3 Rue, Rachel, 162n6 Russell, Bertrand, 108, 128, 137n6 Ryle, Gilbert, 15, 36n14, 128, 140n42, 141 Sayre, Kenneth, 84, 101n33 Schiappa, Edward, 101n30 Sedley, David, 15, 36n15, 63n24, 101n26, 141 Sextus Empiricus, 73 Sheffield, Frisbee C. C., 63n17 Shorey, Paul, 28 soul, 2, 4, 5, 8, 21, 22, 23, 26, 27, 30, 39n54, 44, 45, 48-60, 67, 68, 70, 75–77, 81, 95–98, 103–07, 111, 113, 118, 123, 151, 153, 160, 161, 166, 168 surds, problem of, 3, 22, 50, 57, 58, 70, 75, 116 Tarrant, Harold, 63n19 Terpsion, 3, 6, 12, 15–22, 37n20, 36n27, 55, 166 Thales, 21, 142, 146 Thaumas, 25, 36, 57, 79 Theodorus, 3, 8–9, 15–16, 20–31, 37n25, 38n42, 38n46, 39n59, 43, 55–60,

182

Index

67–70, 85–98, 106, 116, 121, 132–33, 142–47, 159, 161, 166, 169 thinking, 104–06, 118, 123, 124, 136 Thomas Aquinas, 99n8 Thucydides, 12, 29, 35n1, 146, 162n11 Tielsch, Elfriede, 112 Tyranny, 7, 14, 36n4, 146–47 Versenyi, Laszlo, 99n7 wax, image of, 107–11 White, Nicholas, 15

whole, 58, 96, 124–34 Williams, C. J. F., 137n6 wisdom, 1–3, 29, 35, 42, 45, 52, 61, 81, 82, 89–94, 125 wonder, 22, 23, 25, 27, 30, 56, 68, 78, 79, 158, 160 Woolf, Raphael, 138nn11–12 writing, 5, 6, 12, 13, 19, 20, 23, 61, 132, 133 Xenophanes, 101n36, 156

About the Author

Andrea Tschemplik is an associate professor of philosophy at American University.

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