Metaphysics and Method in Plato's Statesman

Metaphysics and Method in Plato’s Statesman At the beginning of his Metaphysics, Aristotle attributed several strange-sounding theses to Plato. Generations of Plato scholars have assumed that these could not be found in the dialogues. In heated arguments, they have debated the significance of these claims, some arguing that they constituted an “unwritten teaching” and others maintaining that Aristotle was mistaken in attributing them to Plato. In his previous book-length study on Plato’s late ontology, Kenneth M. Sayre demonstrated that, despite differences in terminology, these claims correspond to themes developed by Plato in the Parmenides and the Philebus. In this book, he shows how this correspondence can be extended to key, but previously obscure, passages in the Statesman. He also examines the interpretative consequences for other sections of that dialogue, particularly those concerned with the practice of dialectical inquiry. Kenneth M. Sayre is professor of philosophy and director of the Philosophic Institute at the University of Notre Dame. He has published sixteen previous books on a variety of philosophical topics, of which four are on Plato.

Metaphysics and Method in Plato’s Statesman

KENNETH M. SAYRE University of Notre Dame

cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, S˜ao Paulo Cambridge University Press 32 Avenue of the Americas, New York, ny 10013-2473, usa www.cambridge.org Information on this title: www.cambridge.org/9780521866088
c Kenneth M. Sayre 2006

This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2006 Printed in the United States of America A catalog record for this publication is available from the British Library. Library of Congress Cataloging in Publication Data Sayre, Kenneth M., 1928– Metaphysics and method in Plato’s statesman / Kenneth M. Sayre. p. cm. Includes bibliographical references and index. isbn-13 978-0-521-86608-8 hardback isbn-10 0-521-86608-1 hardback 1. Plato. Statesman. 2. Political science – Philosophy. 3. Dialectic. I. Title. jc71.p314s295 2007 321 .07–dc22 2006000511 isbn-13 978-0-521-86608-8 hardback isbn-10 0-521-86608-1 hardback Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party Internet Web sites referred to in this publication and does not guarantee that any content on such Web sites is, or will remain, accurate or appropriate.

To Patti and Michael once again always

Contents

Acknowledgments

page xi

Introduction

1.

2.

3.

4.

1

part i method Becoming Better Dialecticians 1.1 Topical Structure of the Dialogue 1.2 Some Initial Missteps 1.3 Emergence of the Shepherd Paradigm 1.4 Dialectical Contributions of the Myth of Cronus 1.5 The Main Purpose of the Dialogue Collection in the Phaedrus and the Sophist 2.1 Overview 2.2 Collection in the Phaedrus 2.3 Collection in the Sophist 2.4 Collection and the Identification of Necessary Features 2.5 Complications in the Philebus Division in the Phaedrus and the Sophist 3.1 Subdivisions of Mental Derangement in the Phaedrus 3.2 The Paradigmatic Definition of Angling in the Sophist 3.3 The Possibility of Alternative Definitions 3.4 Five Faulty Definitions 3.5 The Sophist of Noble Descent 3.6 The Authentic Sophist 3.7 The Final Definition Collection Yields to Illustrative Paradigms 4.1 Platonic Uses of the Term
  vii

11 11 15 21 25 28 36 36 38 43 46 48 52 52 55 58 62 65 67 70 73 73

Contents

viii 4.2 4.3 4.4 4.5

Paradigms Augmenting Collection in the Sophist A Paradigm to Illustrate the Use of Paradigms The Importance of Verbal Paradigms Paradigms and Necessary Conditions

5. The Weaver Paradigm 5.1 Antecedents to the Paradigm of Weaving 5.2 Intermingling Paradigms 5.3 How Defining Weaving Provides a Paradigm for Defining Statesmanship 5.4 The Definition of Weaving Dissected 5.5 Left-Hand Division 6. The Final Definition 6.1 Arts to Be Separated from Statesmanship 6.2 The Complete Sequence of Divisions 6.3 Nondichotomous Division 6.4 Division to the Left 6.5 The Statesman as Weaver

7.

8.

9.

10.

part ii metaphysics Excess and Deficiency in General 7.1 From Methodology to Metaphysics 7.2 Excess and Deficiency in Aristotle and His Commentators 7.3 Equivalent Expressions in These Ancient Authors The Great and the Small in Plato’s Dialogues 8.1 The Purpose of This Chapter 8.2 Three Synonymous Designations in the Philebus 8.3 The Definite, the Equal, and Their Privations 8.4 More and Less: Unlimited in Multitude 8.5 A Problematic Appearance in the Republic The Generation of Everything Good and Fair 9.1 Return to the Problems of Chapter 7 9.2 Excess and Deficiency Revisited 9.3 The Being Necessary for Generation 9.4 The First Kind of Measurement 9.5 The Second Kind of Measurement 9.6 The Interdependence of Art and Normative Measure Accuracy in the Art of Dialectic 10.1 Knowledge and Art in the Philebus 10.2 Division of Arts with Respect to Accuracy 10.3 Forms as Numbers 10.4 The Involvement of Dialectic in Numbers and Measures

74 77 81 85 92 92 96 100 103 109 113 113 120 124 126 131

139 139 149 150 154 154 156 159 162 168 171 171 173 176 179 182 188 191 191 193 197 203

Contents 11. Division According to Forms 11.1 Relevant Texts in Other Dialogues 11.2 What Gets Divided? Some Familiar Answers 11.3 Making Cuts through the Middle 11.4 Comparisons by Contraries and According to Measure 12. The Metaphysics of Division 12.1 Review of Outstanding Questions 12.2 Classes, Kinds, and Parts 12.3 Kinds Divided According to Forms 12.4 Cutting through the Middle Revisited 12.5 Cutting through the Middle and the Second Kind of Measurement 12.6 Cutting Kinds through the Middle 12.7 Increasing the Likelihood of Encountering Forms 12.8 The Accurate Use in Dialectic of Numbers and Measures

ix

206 206 209 214 219 223 223 225 228 230 232 235 238 240

Appendix: Equivalents for the Great and the Small in Aristotle and His Commentators

241

Bibliography

245

Index Locorum

249

Index of Names

261

General Index

263

Acknowledgments

Having been able to spend much of my career working with Plato’s dialogues is a privilege for which I am deeply grateful. This privilege is due in large part to the ample support provided through the years by the University of Notre Dame. It was through discussion with colleagues and friends such as Catesby Talliaferro, Frederick Crosson, and Robert Vacca that my fascination with Plato’s writings first emerged. And it was in the process of sharing insights about these writings with hundreds of Notre Dame students, both graduate and undergraduate, that Plato moved to the center of my scholarly interests. I am also grateful for the formative influence of visiting appointments at Princeton University (1966–67), Oxford University (1985), and Cambridge University (1996), which enabled frequent conversations with scholarly role models such as Gregory Vlastos, John Ackrill, and Myles Burnyeat. Lacking a distinct lineage of my own in Platonic studies, I am pleased to think of these eminent scholars as among my surrogate mentors. There are many others to thank in connection with my work on the Statesman specifically. My once casual interest in this dialogue began to take on focus during a conference on Plato’s trilogy directed by Catherine Zuckert in 1998. Although I had written previously on the methodology of the Theaetetus and the Sophist, this conference led me to realize that the Statesman has a great deal to say about Plato’s methodology as well. Shortly thereafter, I began working on the manuscript that developed into the present book. Excerpts from early versions of the manuscript were presented on various occasions over the next few years, leading to penetrating criticism xi

xii

Acknowledgments

by Ed Halper, Richard Patterson, Steven Strange, Jacob Howland, Ian Muller, ¨ and Apostolos Pierris, among others. A scholarly gift of extraordinary generosity was bestowed at this stage by Mitchell Miller, who read the then-current manuscript from start to finish and made numerous suggestions that were incorporated into the final version. Another conference on the Statesman was convened in 2004 at the University of Notre Dame, when the penultimate draft of the manuscript was nearing completion. Organized by Gretchen Reydams-Schils, this meeting brought together a number of experienced students of the dialogue including Christopher Rowe, Mary Louis Gill, Mitchell Miller, David Roochnik, and Dimitri El Murr, along with Catherine Zuckert and David O’Conner from Notre Dame’s own faculty. Sustained conversation with these experts convinced me that the manuscript as it stood required extensive reorganization. The transition into the final draft was mainly a matter of interchanging the two parts on metaphysics and method. Specific reasons for giving precedence to the chapters on method are explained in the Introduction. The final version of the manuscript was read with great care by Dimitri El Murr, whose perceptive comments led to a number of last-minute revisions. I am very grateful to Dr. El Murr for this service. I am also grateful for the helpful suggestions made by an anonymous reader for the Cambridge University Press. I wish finally to record my gratitude to Patti White Sayre and our son Michael for encouragement and support needed to put a book like this together. The artistry both exhibit in their lives has inspired me to regard writing books on Plato as an art form in itself.

Introduction

The two parts of this book require separate introductions. Although Part I (on method) comes first in order of presentation below, Part II (on metaphysics) was composed earlier and thus will be introduced first. Part II is a continuation of the inquiry into the metaphysics of Plato’s late period that resulted in the publication of Plato’s Late Ontology: A Riddle Resolved (PLO) in 1983. PLO was concerned primarily with the once strange-sounding theses attributed to Plato in Aristotle’s Physics and Metaphysics. Among them are the theses: (i) that numbers come from participation of the Great and the Small in Unity, (ii) that sensible things are constituted by Forms and the Great and Small, (iii) that Forms are composed of the Great and the Small and Unity, and (iv) that Forms are numbers. Prior to PLO, there were two radically opposed positions on the significance of Aristotle’s reports. One (represented by K. Gaiser and H. J. Kr¨amer of Tubingen, ¨ among others) held that Aristotle was reporting a set of doctrines passed on orally by Plato but never committed to writing – the so-called unwritten teachings. The other position was championed by Harold Cherniss in The Riddle of the Early Academy, to the effect that Aristotle simply did not understand Plato’s views and was reporting them erroneously. Opposed as they were in other respects, both camps maintained that the views attributed to Plato by Aristotle could not be found in Plato’s dialogues. PLO offered a third alternative. It argued that all of the theses attributed to Plato by Aristotle can be found in the Philebus. The reason they are not immediately apparent is that they are expressed in terms other than those used by Aristotle in reporting them. 1

2

Metaphysics and Method in Plato’s Statesman

The argument for this intermediate position was based on the texts of several commentators on Aristotle writing in Greek during the fourth through sixth centuries a.d. (the “Greek Commentators”). While repeating the expressions (‘the Great and the Small’ and ‘the Indefinite Dyad’) used by Aristotle in reference to Plato’s views, these writers employed several other terms in the same referential capacity (notably ‘the Unlimited’, ‘the Unlimited Nature’, and ‘the More and Less’). These terms all play prominent roles in the Philebus, appearing in passages clearly answering to Aristotle’s claims on Plato’s behalf. So at least it was argued in PLO. As far as terminological overlaps with the Greek commentators are concerned, this previous work was focused primarily on the Philebus. Whereas other dialogues figure in the argument of PLO, the Statesman is scarcely mentioned. The Statesman came into the picture with the serendipitous discovery, over a decade later, that the term (in translation) ‘Excess and Deficiency’ is yet another synonym for the expressions used both by Aristotle and his commentators in reference to the Great and the Small. A striking feature of the Statesman is the dual appearance of the expression ‘Excess and Deficiency’ at either end of a sequence occupying the exact middle of the dialogue (283C–285C). This is the section in which the Eleatic Stranger undertakes an examination of the two kinds of measurement, one of contraries with respect to each other, the second of contraries with respect to fixed measure. Recent writers on the dialogue have found this section difficult to deal with. Some have passed it by as a mere distraction, while others have taken substantial liberties in translation to lend it a semblance of intelligibility. Such difficulties have led to an underestimation of the importance of this section in the structure of the dialogue overall. The key to bringing this central passage of the Statesman into focus is the realization that it has close connections with passages in the Philebus containing other expressions designating the Great and the Small. When these connections are traced out, it can be seen that the Philebus provides a background against which the Statesman’s recalcitrant section on measurement becomes almost transparent. As indicated by the corresponding theses (i) through (iv) attributed to Plato by Aristotle, this background from the Philebus is largely metaphysical in character. The overall purpose of Part II of this study is to lay out the metaphysical underpinning of the Stranger’s examination of measurement, along with that of other key sections of the Statesman. Toward this end, Chapter 7 presents a translation and preliminary discussion of the section on the two kinds of measurement, followed by a

Introduction

3

brief survey of alternative designations for the Great and the Small found in Aristotle and his commentators. The Appendix, titled “Equivalents for the Great and Small in Aristotle and His Commentators,” provides a more extensive listing of sources from which the survey is drawn. Chapter 8 continues the discussion with a selective look at other dialogues containing terminology of the Great and Small, including the Parmenides and possibly the Republic, along with the Philebus and now the Statesman. Chapter 9 returns to the section on measurement (283C–285C) with the intention of elucidating the two kinds of measurement in light of connections with the Philebus. A pivotal point in the dialogue comes with the Stranger’s remark, at the very middle of this section, that all the arts depend for their existence on the second kind of measurement. Explicitly mentioned in this regard are the arts of statesmanship and weaving, but the context makes it clear that dialectic is included as well. The stake of dialectic in the second kind of measurement is examined in Chapter 10. This chapter is primarily concerned with the depiction of dialectic in the Philebus as the most accurate of the arts in its use of numbers and measures. Among the theses attributed to Plato by Aristotle is the thesis that Forms are numbers. As argued in PLO (and again here), what this means is that Forms are numbers in the sense of measure. The superior accuracy of dialectic lies in its ability to make divisions according to Forms in the role of measures. Chapter 11 considers various other explanations offered by recent commentators of what division according to Forms amounts to. It tests these explanations against the Stranger’s remark in an earlier passage (262B) that one is more likely to encounter Forms or Ideas by making cuts through the middle, and finds them unable to account for the meaning of that remark. Important questions raised in the course of this discussion include: “What gets severed when cuts are made through the middle?” and “What results from such cuts?” Chapter 12 concludes Part II of the study with textually based answers to these and related questions. In the course of examining the Stranger’s distinction between parts and kinds (at 263B), it argues that kinds in the Statesman (but not always elsewhere) are classes of entities all sharing in the same Form. After making a connection between cutting things through the middle and the second kind of measurement, it then argues that kinds are what dialecticians are supposed to cut through the middle and that correct cuts produce other kinds in turn. The reason cuts through the middle are likely to encounter Forms is that the relevant middle is established by Forms initially. This is the answer the Stranger

4

Metaphysics and Method in Plato’s Statesman

himself points out in his summary statement of the second kind of measurement at 284E. Immediately following the section on measurement, the Stranger discloses the main purpose of the dialogue (285D). Contrary to what might be expected, the main purpose is not to define the statesman but to make the participants in the dialogue better dialecticians. This brings us to the topic of dialectical method. As noted previously, the metaphysical part of the present work was developed before the part on method. The initial draft of the book followed this sequence, placing method after metaphysics. The order was reversed in the final draft for the following reasons. First is a matter of familiarity. To the best of my knowledge, there is no previous study of the metaphysics of Plato’s Statesman. Most recent commentaries on the dialogue nonetheless have had something to say about its method. A consequence is that students familiar with scholarly literature on the dialogue will tend to be more familiar with its methodological than with its metaphysical aspects. The sequence of method before metaphysics is dictated by the principle that a specialized book like this should begin with material familiar to its intended audience. Another reason has to do with the purpose of the dialogue. Becoming a better dialectician requires both increased competence in the techniques of correct division and increased understanding of what those techniques accomplish. The first gain is methodological (how to do it) and the second, theoretical (the significance of doing it). Beginning with the metaphysical would treat the theory in a practical vacuum. The budding dialectician must see the method in action to appreciate the questions it raises about the underlying metaphysics. Recent commentaries on the Statesman vary in the degree of attention they pay to the Stranger’s disclosure of purpose at 285D. One author allotting due consideration to this passage is Mitchell Miller, in his durable book The Philosopher in Plato’s Statesman. Frequent references are made to this work in the following discussion. Another scholar who has recognized the importance of this disclosure is Christopher Rowe, in his fine introduction to Reading the Statesman, which recently appeared under his editorship. Most commentators who approach the dialogue from a political perspective, however, give this passage short shrift or overlook it entirely. A case in point is Melissa Lane’s often brilliant Method and Metaphysics in Plato’s Statesman. Although this work contains many methodological insights, some of which figure in the discussion that follows, it neglects to mention the Stranger’s observation that the purpose of the dialogue is to produce better dialecticians.

Introduction

5

The Stranger’s disclosure of purpose serves as a point of departure for Part I of this study. Chapter 1 sets the stage with a summary description of the dialogue’s topical structure. As part of this summary, it is observed that most of the dialogue’s early divisions are flawed in an instructive manner, as is the paradigm of the kingly herdsman on which they are based. These flaws illustrate one respect in which the dialogue is set up to provide dialectical instruction. Other respects are discussed in subsequent chapters. The first chapter ends with a discussion of the text containing the disclosure of purpose itself. The Statesman is third in a sequence of dialogues employing the method of dialectical division. In both the Phaedrus and the Sophist, division is paired with a companion procedure of collection. To evaluate the absence of collection in the Statesman, it is helpful to look carefully at how it functions in these two previous dialogues. This is the purpose of Chapter 2. Also discussed in this chapter is the language of collection that appears in the Philebus, despite the absence of the corresponding methodological procedure. In similar fashion, Chapter 3 addresses the use of division in those two earlier dialogues. A notable feature of division in the Phaedrus is its use of nondichotomous distinctions, a feature which is absent in the Sophist but reappears in the Statesman. The Sophist contains eight fully developed lines of division in all, each of which is examined in the course of this chapter. Chapter 4 is concerned primarily with the paradigm for the use of paradigms introduced at 277D. As Lane notes (and as G. E. L. Owen noted previously), the Stranger’s treatment of the use of paradigms at this point ties in with his later discussion of the importance of verbal paradigms in dialectical inquiry. After a textual examination of the passages involved, the chapter ends with an explanation of the sense in which collection in the Phaedrus and the Sophist is replaced by the use of paradigms in the Statesman. Among the subtleties often missed in the Stranger’s development of his paradigm for the use of paradigms is that it actually consists of a plurality of paradigms rolled into one. The key paradigm is the use of familiar symbols as paradigms in teaching letters to children, which serves in turn as a paradigm for the use of paradigms in the advancement of knowledge. In like fashion, although weaving is introduced as a paradigm for statesmanship itself, the main dialectical lesson in this regard comes with the use of the paradigm of weaving as a paradigm for the use of paradigms in dialectical inquiry generally. After carefully distinguishing the several paradigms involved, Chapter 5 undertakes a detailed examination of the paradigm

6

Metaphysics and Method in Plato’s Statesman

of weaving in particular. As Miller has pointed out, the development of the definition of weaving closely parallels the ongoing development of the definition of statesmanship. These parallels are spelled out in detail by way of preparation for an analysis of the final definition of the kingly art. Three features of the final definition are particularly noteworthy. One, is the Stranger’s careful itemization and detailed description of the various arts that must be separated from statesmanship for the definition to be complete. Another, is his departure from the strictly dichotomous division that prevails in the Sophist and the first part of the Statesman. Third, is the fact that nondichotomous division occurs only in the leftward direction, contrary to the explicit instruction of Sophist 264E to restrict division to the right. Chapter 6 examines these three features and shows that they are intimately related. They are all part of what appears to be a new technique of definition (anticipated in the Sophist’s definition of not-Being) by way of a full specification of what the thing to be defined is not. The chapter concludes with a discussion of the sequel to the formal definition in the final pages of the dialogue (305E–311C), which describes parallels between the practical activites of the weaver and those of the statesman. Part I comes to a close with the suggestion that the formal definition relates to this final description as warp to woof and that both are needed to bring the portrait of the statesman to completion. A few disclaimers are in order regarding both the subject matter and the format of this study. Readers accustomed to approaching the Statesman as a political treatise will find relatively little in this book that responds to their interests. There is no fine-grained analysis of the Myth of Cronus, for example, nor is there much discussion of the political significance of the concluding definition of statesmanship. A consequence is that there is a considerable range of politically oriented commentary that this study does not take into account. As far as format is concerned, readers familiar with the text of the Statesman may find my frequent quotation of Greek terms somewhat disconcerting. The reason for these quotations is straightforward. As everyone involved in translation knows, one’s rendering of a given text can be strongly influenced by how one reads it. Although I have consulted other translations of the dialogue on a regular basis, the translations of the passages discussed here are my own responsibility. Frequent quotation of the Greek texts is intended mainly as an aid to readers who wish to check the accuracy of my translations. Stephanus numbering follows that presented in the electronic Thesaurus Linguae Graecae.

Introduction

7

The book has been written with readers in mind who already have experience with the methodology of Plato’s late dialogues. At the same time, it seems not unreasonable to hope that it may be of some help as well to readers who have not yet savored the delights of Plato’s methodological investigations. Another reason for including ample quotations of the Greek is to acquaint less experienced readers with the music of Plato’s language. The more scholars are attracted to a careful study of these late dialogues, the better we should come eventually to understand them.

part i METHOD

1 Becoming Better Dialecticians

1.1 Topical Structure of the Dialogue The Statesman begins with Socrates thanking Theodorus for introducing him to Theaetetus and the Stranger (  )1 from Elea. After a bantering interchange on the relative values of sophistry, statesmanship, and philosophy, and after acquiescing to the Stranger’s request that Young Socrates (YS) serve as respondent in the ensuing discussion, Socrates announces his intention to converse with his younger namesake on another occasion and takes his seat among the audience. We hear nothing more from him until the final speech of the dialogue in which he compliments the Stranger for completing an excellent portrayal of the kingly art. The Stranger begins by assuming that the statesman, like the sophist before him, is someone possessing knowledge (
   : 258B4). After securing YS’s agreement that the king, the slave master, and the household manager all share the same knowledge and exercise the same skill as the statesman (259C1–4), the Stranger identifies this knowledge

1

Translations of the Sophist (by Nicholas White) and the Statesman (by Christopher Rowe) in John Cooper (ed.) (1997) agree in rendering   ‘visitor’. I prefer the more common translation ‘stranger’, which is compatible with the person in question remaining in the city for an extended period of time – perhaps as a metic or resident alien (the term    appears to be used synonymously with   at Laws 881B6; see also Laws 866B7 and Meno 80B6). This leaves open the possibility of viewing the Stranger as a symbolic stand-in for Plato as author, who may well have thought of himself as a “stranger in his own country” at the time these two dialogues were written. [In this regard, see Konrad Gaiser (1980).] Pursuant to this interpretation, the Eleatic connection could be explained in terms of Plato’s indebtedness to Parmenides’ conception of Being in his initial theory of Forms.

11

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Metaphysics and Method in Plato’s Statesman

as theoretical ( : 259C10) rather than practical (
: 259D1). Theoretical knowledge is then divided into that responsible for making judgments and that responsible for giving directions, which latter is further divided into self-directive (
 ) and a nameless kind concerned with promulgating the directions of others. Those guided by their own directions, in turn, might be concerned with bringing either inanimate or animate products into being (  at 261B13). Inasmuch as bringing animate things into being involves providing sustenance, that kind can be subdivided into those who rear animals individually and those who rear them in herds (   : 261E8). As characterized thus far, the statesman is someone with self-directive theoretical knowledge concerned with the collective rearing of living things. But there are many other skills that fit this description, including those of the shepherd and of the cowherd. When the Stranger asks YS to divide by half (  : 262A2) the field cordoned off by this description, YS comes up with the distinction between rearing of beasts and rearing of human beings. Although this distinction seems reasonable enough at first glance, the Stranger points out that humans constitute only a small part of the class of living things and proceeds to give YS a tutorial on making cuts “through the middle” (  : 262B6). The contents of this lesson are discussed in Chapter 11. To get the definition back on track, the Stranger observes that their previous reference to rearing carries with it a distinction between wild and tame animals and that the latter could be further divided in two ways to reach the class of human beings who are the primary beneficiaries of the statesman’s nurturing activity. The shorter of the two distinguishes human beings as featherless bipeds occupying dry land. Like YS’s initial attempt, however, this shorter way involves cutting things into smaller and larger portions (bipeds constitute a relatively small subclass of creatures living on dry land). By way of avoiding this error, the longer route divides dryland animals into those with and those without feet and singles out human beings as hornless noninterbreeding animals with two feet only. This accomplished, YS assumes (267A) that the definition of statesmanship has been completed. But as the Stranger points out, there are occupations besides statesmanship concerned with the collective rearing of human beings – merchants, farmers, millers, and so forth. Ostensibly to narrow the definition yet further, he recounts an elaborate myth about an age governed by Cronus in which the course of nature ran backward, and the needs of all

Becoming Better Dialecticians

13

living creatures were met effortlessly from the time they sprang full-grown from the earth to the time they vanished in helpless infancy. An immediate lesson drawn from the myth is that the definition of the statesman as it stands applies to a divine ruler at best, but not to a mortal ruler who requires political skill to ensure that the needs of his subjects are met. To capture the skill of a mortal statesman, more must be said about the manner (
: 275A4) in which he governs. One change required in the initial definition is that the role of rearing ( ) be expanded to caretaking (
  : 275E6) generally, allowing that other occupations might be involved in providing rearing of more specific sorts. Other needed alterations involve distinguishing human from divine caretaking and specifying that the care provided by the statesman is voluntarily accepted. With these emendations in place, YS once again is confident (277A) that the definition of statesmanship has been accomplished. Once again, however, the Stranger demurs. Not only is the definition itself still lacking in clarity, but there are problems as well with the myth on which the recent emendations were based. One problem is that it contained an “astounding amount” (!" # $ : 277B4) of material, not all of which was required for the purpose at hand. Another serious shortcoming is that the myth was shaped around an unsuitable paradigm for the kingly art. Impressed by the importance of this august calling, the Stranger tells YS, they thought of it as calling for comparably exalted paradigms (
 : 277B4). This explains the paradigm of the divine shepherd. Given that the definition to which it led still lacks clarity, however, a less pretentious paradigm appears to be needed. To set their bearings straight in this regard, the Stranger draws attention to a paradigmatic case of the use of paradigms. The paradigm offered is that of using letters in familiar syllables as examples to help beginning students of writing recognize the same letters in contexts that are still unfamiliar. Ramifications of this seemingly prosaic “paradigm of paradigms” are examined in Chapter 4. The immediate upshot of this brief lesson on the use of paradigms is the Stranger’s suggestion that the paradigm of the shepherd be replaced by that of the weaver (a suitably mundane practice) in their ongoing attempt to define the statesman. There follows (at 279A–283A) an elaborately detailed definition of weaving that anticipates numerous distinctive features of the definition of statesmanship achieved later in the

14

Metaphysics and Method in Plato’s Statesman

dialogue. This paradigmatic definition of weaving is considered in length in Chapter 5. Although this shift in paradigms puts the search for the statesman back on course, the Stranger remains preoccupied with his earlier perception that the Myth of Cronus was longer than its purpose required. Even the treatment of weaving, he suggests, might seem longer than necessary. Ostensibly to adjudicate questions of this sort, he then launches into a surprisingly abstract discourse on “Excess and Deficiency in general” (the use of capitals is explained later). This discussion occupies the very center of the dialogue (283C–285C). Chapters 7, 8, and 9 are given over to an examination of its contents. Before applying the lessons of this general discussion to the particular issues that initiated it, the Stranger draws YS’s attention to the main purpose of the conversation at hand. Rather than being primarily concerned with an investigation of statesmanship as such, its overarching purpose is to make better dialecticians ( : 285D6) of its participants. Following this, there is a brief consideration of the need for verbal accounts when inquiring into important topics such as statesmanship, which brings back into view the previous question of whether their verbal definition of weaving might have been too long. Given the circuitous route taken in addressing this question, the Stranger’s answer is disarmingly simple: In the case of dialectical discussions, any length is warranted if the participants become better dialecticians ( : 287A3) as a result. At 287B, the Stranger returns to the task of defining statesmanship, which continues for almost twenty pages (to 305E). His first move here is to sanction nondichotomous division, a departure from the general practice of the Sophist and from the early definitions of the present dialogue. This provision is put to full use as the definition progresses. First, there is a division between arts directly responsible for civic caregiving and those indirectly responsible, the latter of which are shown to have multiple subclasses. Next, comes the divisions of directly responsible caregivers into those who command and those who serve, which latter again show up in various forms. Those who command are further divided into genuine and imitative (single, few, and many rulers, either lawless or constrained by law), and the former then subdivided between sovereign and subordinate (rhetoricians, generals, and judges). The authentic statesman is finally identified at 305E as sovereign among genuine commanders who are directly responsible for civic caregiving. These final divisions are examined in Chapter 6.

Becoming Better Dialecticians

15

Having finally arrived at a credible definition of statesmanship, the dialogue concludes with a discussion of the tasks involved in putting the statesman’s art into practice. The statesman’s primary task is to weave a harmonious and durable social fabric, using the courageous and moderate temperaments within the populace as warp and woof, respectively. This is to be accomplished by means such as a preliminary culling of unruly natures, marital arrangements aimed at blending opposing temperaments, and a judicious allotment of public praise and blame. Apparently pleased with these results, Socrates2 ends the conversation by complimenting the Stranger for an excellent portrayal of the kingly art. Let this suffice as a summary description of the topical structure of the dialogue. Our next concern is to look at the Stranger’s initial moves in his conversation with YS, bearing in mind the dialogue’s primary purpose of making its participants better dialecticians.

1.2 Some Initial Missteps Having secured YS’s agreement to serve as respondent at 258A, the Stranger launches immediately into a perfunctory definition of statesmanship. As noted in the previous summary, his first step is to assume (with YS’s approval) that the statesman – like the sophist previously – is among people possessing knowledge. The next step is to divide knowledge into practical and theoretical, locating statesmanship within the latter category. Subsequent divisions portray the statesman as someone possessing theoretical knowledge that is directive – more specifically, selfdirective – that is concerned with living creatures and that bears on the collective rearing of these creatures in herds. Before YS has had a chance to catch his breath, the following series of divisions has been set in place (see Figure 1.1). This abrupt beginning is in stark contrast to the initial moves in the Sophist in which almost three Stephanus pages are given over to a definition of angling by way of practicing the method to be used on the sophist. In calling for this preliminary exercise, the Stranger warns Theaetetus that the sophist is a difficult thing to look for and requires a lesser topic to serve as paradigm (
 : 218D9). As an attentive reading of this earlier dialogue makes evident, angling serves as a paradigm for sophistry not only in resembling that more prominent activity (both are acquisitive) 2

Editors disagree on whether the last speech should be assigned to the younger or the elder Socrates. I side with those who attribute it to the Socrates who began the dialogue.

16

Metaphysics and Method in Plato’s Statesman knowledge (258B4)

practical

theoretical (258E5)

critical

directive (260B4)

(nameless)

self-directive (260E5)

inanimate objects

individuals

living subjects (261C1)

herd-rearing (261E8)

figure 1.1. Division from 258B to 261E.

but also insofar as the method used in capturing the former proves useful in tracking down the latter as well. In this subsequent dialogue, however, the Stranger’s pursuit of the statesman gets underway without benefit of a practice definition or other explicit paradigm. Although YS might be expected to have learned something about the method to be employed from the morning’s conversation, it soon becomes apparent that he had not been listening very carefully. And although the Stranger eventually (at 279E) draws attention to their need for a small-scale paradigm sharing relevant features of statesmanship, the dialogue is nearly half finished before a suitable paradigm has been provided. Given such an improvident start, it is no surprise to find the early stages of the definition marred by a number of missteps. The first misstep comes with the Stranger’s assumption that the statesman, like the sophist, is someone who possesses knowledge. If YS had remembered the final moments of the morning’s conversation, he would not have agreed to that assumption. Quite apart from the statesman’s standing in that respect, it is emphasized repeatedly in the final pages of the previous dialogue that the sophist is someone lacking knowledge. At 267D, the sophist is classified as an unknowing ( % : 267D2) imitator, in contrast to others whose imitation is “accompanied by knowledge” (  & 
 : 267E1). At 267E, the Stranger first says explicitly that the sophist “is not among those who know” (    ' ( : 267E4–5) and then characterizes him as a “belief-mimic” (

  : 267E7) who thinks he knows (( : 268A1) things he only believes. To show that this crucial point has been driven home, Theaetetus explicitly acknowledges

Becoming Better Dialecticians

17

that the sophist knows nothing (  (: 268B10) at all. With YS’s unthinking agreement at 258B6 that the statesman is someone who also ()  % : 258B9) possesses knowledge, the definition accordingly gets off to a distinctly inauspicious start. A second problematic step is the assignment of statesmanship itself to the class of theoretical knowledge. As the Stranger points out, statesmanship indeed seems to have more in common with arithmetic, removed as it is from matters of practice (
 * : 258D5), than with carpentry and other handicrafts bound up with practical action (
  : 258D9). And to be sure, the power of kingship depends more on strength of mind than on manual arts and practical skills generally (+
: 259D1). The problem with this early classification of the kingly art as a form of theoretical knowledge becomes apparent only with the more reflective characterization of statesmanship achieved in the second half of the dialogue. Contrary to the initial stress on statesmanship as a theoretical skill, practical skills are emphasized in the final stages of the definition. At 284C, for example, the statesman is mentioned as someone whose “knowledge of practical subjects” (
) 
  
 : 284C2) is dependent on a certain kind of measurement. In turning to the final series of divisions at 287B, moreover, the Stranger’s first move is to separate off skills that contribute raw materials, containers, vehicles, and so forth – all practical skills – from what is subsequently described as the practical activity (
 : 289D1) associated with the art of the statesman and king. For this division to make sense, all forms of expertise involved must be practical in nature. In point of fact, as we shall see, the class within which this division takes place is that of “arts relative to all things people do” (
)
   *  : 281D8–9), carried over from the paradigmatic definition of weaving. This implies that the exercise of statesmanship is a matter of practice. Also relevant in this regard is the fact that weaving itself is a practical art. Weaving would be a poor choice as paradigm for statesmanship if the two were not arts of comparable nature. Another indication that something is amiss in this initial approach to statesmanship comes with the Stranger’s request (at 258E8–11) that YS follow him in treating the statesman, the king, the slave master, and the household manager as possessing a single kind of art. Given that a prosperous Athenian household typically included slaves, it is plausible to assume that a household manager and a slave master employ some of the same skills. And the identity of the king and the statesman is maintained

18

Metaphysics and Method in Plato’s Statesman

consistently throughout the dialogue.3 But the assumption that the king and statesman practice the same art as the householder and the slave master, which the Stranger urges YS to adopt at 258E, becomes less and less credible as the dialogue progresses. At 276E, human caring for herds is divided into enforced and voluntary, which match the tyrant and the king, respectively. There should be no doubt in anyone’s mind that this division separates the slave master from the statesman as well. At 289D–E, moreover, people who deal with slaves are described as “those who least pretend to the kingly art” (, - 
 "  ": 289E1–2). Despite the Stranger’s suggestion at 258E that the names of the statesman and of the slave master refer to the same thing, it would border on the ludicrous if the present dialogue had been titled “slave master” instead. Although his conversation with YS has barely begun, the Stranger already appears guilty of three disconcerting false steps. He has intimated that sophistry involves knowledge, in direct contradiction with the final moments of his morning’s discussion. He has suggested that statecraft is a form of theoretical knowledge, in apparent tension with the emphasis on the statesman’s practical skills in the second half of the present dialogue. And he has encouraged YS’s acceptance of the highly dubious thesis that the statesman and the slave master employ the same kind of knowledge. This naturally gives rise to the question of why these seeming missteps on the Stranger’s part were written into the dialogue. Although it is of course conceivable that Plato himself was not aware of these apparent lapses and that their insertion into the dialogue was unintentional, it seems unlikely in the extreme that the contradiction between the final page of the Sophist and the beginning pages of the Statesman was inadvertent. Another possibility is that the author intends to represent his main character in the Statesman as philosophically inept, or as committed to opposing views of statecraft at different stages of the dialogue. But it is hard to believe that Plato intended to portray the Stranger in this dialogue as a philosophic novice after depicting him in the Sophist as “very much a philosopher” (  . . .   : 216A4). A 3

This stance is not uniform throughout the corpus. While the art of kingship and that of statesmanship appear to be equated in the Euthydemus (see 291Cff.), the king and the statesman represent different levels of incarnation in the Phaedrus (248D4–5). The view that the king, the statesman, the household manager, and the slave master all practiced the same art, nonetheless, must have had some currency during Plato’s lifetime. It figures explicitly in the (probably spurious) Rival Lovers (138C); and Aristotle made a point of rejecting it at the beginning of his Politics (1252a11–12).

Becoming Better Dialecticians

19

much more satisfactory response to the previous question, surely, would reveal these lapses as part of the dialogue’s overall strategy of making its participants better dialecticians. Other commentators have noted that the initial definition of statesmanship gets off to a rocky start. Mitchell Miller, for example, has observed that the diaeresis leading up to the Myth of Cronus “yields an inadequate definition of statesmanship”4 and that the reasons for this inadequacy have to do with the method it employs. Two main faults of the initial procedure, in Miller’s view, are that it relies exclusively on dichotomous division (p. 16) – a matter we take up in Chapter 6 – and that it “is founded on a popular image – the herdsman or shepherd – which in fact misrepresents the statesman” (p. 34). On his view, the errors involved in the first definition of statesman have a distinct pedagogical purpose. Melissa Lane also traces the failure of the initial definition back to the common assumption that the statesman is a kind of herdsman dealing with human subjects.5 As she points out (pp. 45–46, 86), and as we have already noted, the definition begins without benefit of an explicit paradigm. It is instead guided by what she describes as the model “of the king as shepherd, which was common currency in the Homeric epics and in classical Greek thought” deriving from Homer (p. 45).6 The problem of this model, in her analysis, is that its tacit adoption leads to a definition in which statesmanship is distinguished from other modes of shepherding only with respect to “the kinds of herds it tends” (p. 40). A consequence is that this definition fails “to distinguish factors internal to the art of rule” (p. 44), such as the distinction in particular between the statesman and the tyrant (p. 86). As she sees it, this inadequacy cannot be addressed until shepherding is replaced by a more suitable model. Only after weaving has superseded shepherding as a paradigm for statesmanship do the methodological lessons of the false start begin to become clear (p. 61). Although neither Miller nor Lane deal with the missteps that concern us at present, we may follow their lead in viewing these lapses as having 4 5 6

Mitchell Miller (1980), p. 16. Other page numbers in this paragraph refer to this book. M. S. Lane (1998), pp. 121, passim. Other page numbers in this paragraph refer to Lane’s book. Lane observes that the traditional model of king as shepherd figures in other political dialogues by Plato as well, albeit with differing “polemical forces” (p. 45). (See, e.g., Republic 343B, Critias 109B, Laws 813D.) For a more detailed discussion of the role of the shepherd model in the Iliad and the Odyssey, see Miller (1980), pp. 40–41.

20

Metaphysics and Method in Plato’s Statesman

a pedagogical purpose. With regard to the factual error of designating sophistry as a kind of knowledge, this might be construed as a test of YS’s memory. His failure to catch this (presumably intentional) mistake may serve as an indication to the Stranger that a special effort will be required to secure his respondent’s full attention. It should also put a careful reader of the dialogue on notice that the Stranger’s interaction with YS may not go as smoothly as the interaction with Theaetetus in the morning’s conversation. But what of the two remaining missteps, which YS would not have been in a position to catch? We should now be ready to see that these two moves, problematic as they turn out to be, help the Stranger prepare the way for the disclosure of the initially implicit paradigm of herd-keeping to which Miller and Lane attach such importance. The key move in this regard is the initial depiction of statecraft as a form of theoretical knowledge. Given knowledge as the expertise to be divided, the other alternative was to classify statesmanship as practical knowledge. Although the practical aspects of statesmanship indeed are stressed later in the dialogue, however, characterizing it this way initially would have made the assimilation of statesmanship to herd-keeping counterintuitive. On the level of day-by-day practice, the activities of the statesman and of the shepherd have little in common. As Plato surely would have realized, there is little chance of encountering a shepherd going about his daily business and mistaking that person for a king or statesman. To make a mistake in the other direction, moreover, seems even less likely. As far as practical activity is concerned, it is hard to think of any occupations that are more dissimilar. Although suppressed initially, the conception of statecraft as a form of shepherding begins to surface at 261C with the specification of selfdirective knowledge concerned with living things. For this conception to play a credible role in the ongoing inquiry, it is necessary for both statecraft and shepherding to be presented in ways that abstract from the differences of their daily pursuits. This is accomplished by representing both as forms of theoretical knowledge. The Stranger thus paves the way for a very general description of the art of herding, with reference to which, as Lane noted, statesmanship may be distinguished from other forms of herd tending in terms of the kind of herd it tends. The initially puzzling claim that the statesman (and king) employ the same kind of knowledge as the slave master (and household manager), in turn, provides an illustrative example of diverse practical skills that can be accommodated under a single general description. Although the

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21

practice of statecraft and that of slave master differ radically in their daily routines, there is a very general sense in which they both involve skills of managing (“tending”) other human beings. If YS can grasp the sense in which these skills converge, the Stranger appears to be reasoning, he should be prepared to follow the series of ensuing divisions in which statecraft is treated as a form of herd-keeping.

1.3 Emergence of the Shepherd Paradigm The conception of statesmanship as a form of herd-keeping makes its first explicit appearance at 261D with the question of whether the statesman is concerned with rearing (  : 261D3) living creatures individually, like the groom or cowherd, or rather cares for them together in herds. When YS opts for the latter, the Stranger observes that “the shared rearing of many together” ( . "
      : 261E1–2) might be called “herd rearing” or “collective rearing” (   /     : 261E2) and proceeds to subdivide self-directed concern with living subjects accordingly. Two further mistakes are made in this subdivision. One mistake is corrected by the Stranger two pages later when he observes that only tame creatures can be herded and points out that concern for living creatures should have been separated by tame and wild before making a distinction between rearing separately and rearing in herds. The instructional role of this mistake becomes apparent in the Stranger’s response to a similar mistake made by YS at 262A, which we shall consider momentarily. The second mistake is more subtle. In setting up the premature division between individual rearing and rearing in herds, the Stranger first observed that living creatures can be bred and reared individually and also can be cared for (
  : 261D5) collectively in herds. The distinction that carries over from this observation, however, is between individual and collective rearing. In effect, he has shifted the reference from caring for herds at 261D5 to rearing (  ) herds at 261E2. The reason this is noteworthy is that he later tells YS that the designation ‘herd rearing’ was incorrect and recommends a designation conveying the sense of caring for herds instead. He thus returns to the terminology from which he had purposefully deviated at 261D. This about-face occurs immediately after the Myth of Cronus when the Stranger begins to criticize various steps in the line of divisions previously taken under the influence of the herdsman paradigm. As he points out in this regard (at 275D8–E1), the title ‘herd rearer’ applied in human

22

Metaphysics and Method in Plato’s Statesman

subjects is better deserved by a variety of experts, such as farmers, merchants, and doctors (from 267E), than by the statesman himself. What is needed to get the definition back on path, he says, is a more inclusive designation under which the art of statecraft can be separated from these other practices. He then mentions (275E5–6) three designations that would serve this purpose: ‘herd keeping’ (   ), ‘looking after’ (!
" ), and ‘caring for’ (
  ). This latter expression, as already noted, is none other than the one proposed at 261D5 and then rejected in favor of the ill-fated ‘herd rearing.’ When the line of division moves ahead with the category herd keeping after the Myth, we are left with the sense that much of what occupies the space between 261D and 275D would have been unnecessary if the Stranger had stuck with (the equally suitable term) ‘caring for ’ originally. Apart from the tutorial on dividing according to Forms at 262B–263B and the subsequent “trial” divisions driving the lesson home (the two routes signaled at 265A), the lion’s share of that space is taken up by the Myth itself. Given the Myth’s pivotal role, to which we return presently, the main reason for the Stranger’s legerdemain in shifting terminology at 261E may have been to provide an occasion for such a story. The next contribution to this series of instructive mistakes is made by YS. When asked by the Stranger whether he can conceive collective herd rearing as twofold in a way permitting it to be narrowed down by half, YS understands this correctly as a call for a dichotomous division. In view of the previous allusions to horse grooming and cow rearing, he naturally comes up with the distinction between rearing human beings and rearing beasts. While praising YS’s boldness in putting forward this division, the Stranger finds fault with his not having cut herd rearing “through the middle” (  : 262B6). In this respect, the Stranger points out, it is like dividing humanity into Greek and barbarians or dividing number into ten thousand and all the rest. Briefly put, the problem with not dividing “through the middle” is that it might result in cuts that are too narrow and that accordingly fail to engage Forms (262B1) or Ideas (262B7). Being able to divide in ways that correspond to Forms or Ideas, the Stranger continues, makes all the difference in the sort of inquiry they are now pursuing. The Stranger’s full response to YS’s error is discussed in Chapter 11. For the moment, it is enough to note that this error provides occasion for an important lesson in the conduct of dialectical inquiry: Correct division makes cuts according to Forms (& 0: 262D7). Stephanus pages 263E–268D test YS’s comprehension of this lesson on division. First comes the correction to the prior division noted earlier

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23

in which living creatures are divided retroactively into tame and wild, and concern for tame creatures is then divided into individual and collective. The significance of this move, which seems to pass YS by, is that the prior division (by the Stranger) of concern for living creatures directly into individual and collective rearing fails to “cut through the middle” no less than YS’s division of animals into men and beasts. A more direct test of YS’s comprehension of the lesson comes with the Stranger’s offer of two paths along which their divisions might continue. Both paths begin with a distinction between dry-land and aquatic rearing. The first then continues by setting off a smaller part against a larger, and thus is quicker, whereas the other involves “cutting through the middle” (   ' : 265A4), at the expense of being longer. When asked which path they should follow, YS should have chosen the latter at once. Instead he shows that he has not understood the lesson by suggesting that they follow both. The two paths in question are diagrammed in Figure 1.2. Without regard to relative merit, we should bear in mind that both routes are

(a) longer route (265B–266B) collective rearing (from 261E)

aquatic animals

dry-land animals (from 264D)

winged

ambulatory (from 264E)

horned

hornless (265B11)

interbreeding

noninterbreeding (265E8)

four footed

two footed (266B3)

(b) shorter route (266E) collective rearing (as above) aquatic animals

dry - land animals (as above)

four footed feathered

two footed (266E6) featherless (266E7)

figure 1.2. Alternative divisions 265B to 266E.

24

Metaphysics and Method in Plato’s Statesman

offered as possible replacements for YS’s overly hasty move from rearing of living creatures in herds to collective rearing of human beings. In effect, the two sets of divisions are being offered as alternative definitions of the human animal. It is hard to tell how seriously the Stranger (or Plato) intended these two alternatives to be taken. The shorter route is probably the source of the story in which Diogenes, reacting derisively to Plato’s definition of man as a featherless biped, plucked a chicken and presented it as a case in point. Although it is true that men have two feet and lack feathers, this characterization tells us little about the nature of human beings. By the same token, although kings deal with subjects that are bipedal and featherless, to point this out says little about the nature of kingship. Quite apart from its dialectical shortcomings, the shorter path does not appear to be a serious contender. Nonetheless, it is not clear that the longer route is more successful. The characterization of human beings as two-footed, noninterbreeding, hornless, and so forth may do a better job of “cutting through the middle,” but it says next to nothing about what it is to be a human being. A would-be Diogenes could take an unplucked chicken and present it as an example of “Plato’s man” as depicted in the longer path. Indeed, Plato may have had something like this in mind when he has the Stranger point out jokingly at 268C that, apart from the number of feet involved, the same characterization applies to pigs.7 Momentarily setting scruples of this sort aside, the Stranger cobbles together an interim definition of statesmanship (267A8–267C3) by drawing together the divisions depicted in Figures 1.1 and 1.2 (a). To counter YS’s impression that the task of their conversation has been completed, however, the Stranger immediately points out another difficulty. Statesmanship has been described as a skill dealing with the collective rearing of human herds. The problem is that there are many other ( " 1 : 268C2) skills that fit this description – those of merchants, farmers, millers, bakers, trainers, doctors, and so forth. To separate true statecraft from these many pretenders, YS is told, they must take a different 7

The Stranger’s description of the longer way ends with some contrived humor playing on “the power of two-footedness” ( "   
": 266B3), which relates to YS’s supposed interest (with Theaetetus) in irrationals. For discussion, see Miller (1980), pp. 30ff.; Stanley Rosen (1995), p. 34; and Christopher Rowe’s footnote to 266B3 in John Cooper (ed.) (1997). A less esoteric joke is the punning characterization of the four-footed pig(s) as last (2; alternatively “most piggish”) to be separated from the two-footed human among collectively reared dry-land animals.

Becoming Better Dialecticians

25

route beginning at another starting point (268D5–6). This new starting point is introduced as part of the voluminous story (  " 3! ": 268D9) about the reign of Cronus.

1.4 Dialectical Contributions of the Myth of Cronus Reflections on the content of this story and its role in the dialogue have dominated discussion of the Statesman in much the manner that analysis of the “Third Man” arguments once dominated discussion of the Parmenides. One probable reason is that commentators on the Statesman have tended to be more interested in politics than in methodology and have been attracted to the myth by its bountiful insights on political order. Another may be that the story is lively and easy to read, which make it a welcome relief from the technical and generally tedious conversation preceding it. Be this as it may, our present concern is not with the content of the myth as such but with its bearing on the continuing attempt to define the statesman.8 The avowed purpose of the myth, once again, is to distinguish the statesman from merchants, farmers, bakers, doctors, and all the rest who contribute to the rearing of humans in groups. This is accomplished in the following manner. As interpreted by the Stranger, the myth shows that the only circumstances in which a ruler actually rears or nurtures () his human subjects, in the manner that a shepherd nurtures his flock, are those typified by the age of Cronus when the universe runs contrary to the course we find familiar. What invites confusion with the nurturing skills practiced by farmers and bakers, accordingly, is the divine kingship of Cronus, not the human kingship exercised during the present age of Zeus. During the present age, kings look after the political needs of their subjects but do not nurture them like a shepherd rearing his flock. It follows that by reconfiguring our conception of kingship to conform with human practices, statesmanship can be disentangled from the nurturing arts. An initial blunder in the preceding account of statesmanship thus was its division of concern with living creatures into the rearing of individuals and the rearing of herds. A more suitable division at this point would be in terms such as ‘herd-keeping’, ‘looking after’, or ‘caring for’ (275E5–6). If the kingly art were described as one of “caring for the 8

An excellent introduction to the myth and to its political significance can be found in Miller (1980), pp. 36–53. See also Rosen (1995), pp. 40–61.

26

Metaphysics and Method in Plato’s Statesman

entire human community together” (&4
  . . .  !
  "
    : 276B7), the Stranger suggests, no other art would have a better claim to that description. The horde of contenders that challenged statesmanship in the previous account seemingly could be eliminated by replacing the category of herd rearing with that of herd-keeping. Subsequent divisions singling out features of footedness, winglessness, hornlessness, and so forth (276A4–5) should be retained.9 With the help of this revised line of division, the major error (275A1) of mistaking the divine rule of Cronus for human statesmanship apparently can be avoided by appending to the account a distinction between divine shepherd and human caretaker ( !*
   : 276D6). A lesser error in the previous account was its failure to specify the manner (
: 275A3) of kingly rule. In contrast with the tyrant, who rules by force, the king’s rule is accepted voluntarily. With a final division of human caretaking into enforced and voluntary (276E7–8), the definition of statesmanship begun at 258B is brought to an end. To augment the Stranger’s truncated summary at this point (276E10– 14), it is helpful to lay the definition out more fully in the manner shown in Figure 1.3. Although the initial line of divisions has been completed, the task of defining the authentic statesman nonetheless has not been finished. In response to YS’s expression of optimism that their search is over, the Stranger identifies several respects in which their inquiry thus far falls short of the mark. First and foremost, the king they have portrayed does not yet appear to have a complete form ( . . . 5 : 277A5–6). Just as sculptors sometimes lose time by adding more material to their work than is necessary, so progress on their definition has been retarded by relying on “large-scale paradigms” ( 
 : 277B4) to demonstrate their previous mistakes. The “astonishing mass” (!" # $ : 277B4) of material in their myth has made their demonstration longer and yet has failed to complete the story. A consequence is that their discourse, although adequate in superficial appearance, lacks requisite brightness (  : 277C3) – the kind of brightness added to paintings by mixed colors and pigments. In sum, the definition diagrammed in Figure 1.3 is incompletely shaped, lacks clarity and luster, and suffers from reliance on a paradigm too grand for the task. One thing to note in passing is that defects of this sort are not likely to be remedied by adding further details to the definition as it currently stands. From one point of view, the statesman 9

Note that 
 (winglessness) was not included in the summary of features at 267B. Its inclusion here in conjunction with
6 ' seems redundant.

Becoming Better Dialecticians

27

knowledge practical

theoretical

critical

directive

(nameless)

self-directive living subjects

inanimate objects

groups (herd keeping)

individuals aquatic

dry-land

winged

ambulatory

horned

hornless

interbreeding

noninterbreeding

four footed divine enforced

two footed human caretaker (276D6) voluntary (276E8) (= (?) statesman)

figure 1.3. Cumulative definition at 277E.

has been completely isolated by the line of divisions shown in Figure 1.3. As far as identifying a set of features that apply to statesmanship generally and to that skill alone, the definition is adequate in its present form. The problem is that statesmanship has been exhibited only in superficial appearance. The respect in which the portrayal falls short in completeness and brilliance will not be corrected by further divisions tacked on to the current series. The underlying source of the problem, as the Stranger’s next remark makes clear, is that the account thus far has been developed under the guidance of an improper paradigm. Like all important topics, the nature of statesmanship can be exhibited only through “speech and discourse” (  ) 7: 277C4) that incorporates the use of paradigms (
 : 277D1). Thus far, their attempt to define statesmanship has relied on the paradigm (
 : 275B4) of shepherding. This paradigm has shown itself inadequate by having led to a definition that

28

Metaphysics and Method in Plato’s Statesman

lacks luster and presents only surface appearances. To move beyond these shortcomings, they need to set aside this misleading paradigm in favor of another that is better suited to the task at hand. As far as the dialectical progression of the dialogue is concerned, the Stranger’s call for a new paradigm at 277D serves as a major turning point. Before this point, the Stranger’s joint inquiry with YS has been riddled by an unrelenting sequence of mistakes. Although each of these mistakes has a discernible pedagogic purpose of illustrating steps to be avoided, as we have seen, their cumulative effect has been a characterization of statesmanship that is flawed from start to finish. From this point onward, however, the Stranger leads the discussion through a series of positive lessons showing how dialectic ought to proceed, the outcome of which is deemed by the elder Socrates, at the end of the dialogue, to be an excellent (: 311C1) portrayal of statesmanship. The Stranger’s call for a new paradigm, of course, provides occasion for his treatment of the use of paradigms in learning letters as a paradigm for the use of paradigms generally (277D–278E). This is followed by a detailed development of the paradigm of weaving (279B– 283B) for use when they return to the definition of statesmanship. Next comes a succinct but far-reaching examination of the metaphysical underpinnings of dialectical division (283C–285C), leading into a discussion of criteria for evaluating the length of dialectical discussions (286B– 287B). The dialogue then returns at 287C to the task of defining the statesman, citing an alternative technique of division that will be needed for this purpose. After wrapping up what is presented as an adequate definition at 305E, the dialogue winds down with a discussion of the statesman’s practical task of weaving opposing temperaments into an integrated social fabric. Each of these topics is examined in subsequent chapters, although not always in the order of their appearance in the dialogue. Whether by way of illustrating mistakes to be avoided (before 277D) or procedures to be followed (after 277D), each major stage of the dialogue provides instruction in the practice of dialectic. This is just what we are led to expect by the Stranger’s disclosure at 285D of the dialogue’s main purpose.

1.5 The Main Purpose of the Dialogue Although various aspects of correct dialectical procedure have entered into the conversation previously (e.g., at 262B–E), neither dialectic nor

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29

its practitioners are mentioned before the following interchange. The topic mentioned at 285C4 is that of “Excess and Deficiency in general.” 285C4

285D

So after that topic, let us take up another that has to do both with the present inquiry and with the conduct of all discussions like this. What’s that? Regarding our instructional session for learning letters, what would we say if someone were to ask us about some student’s inquiry whether certain letters make up a word – that the student raises the query for the sake of that one problem in particular, or that it is raised with regard to spelling tasks in general? Obviously, with regard to the general case. What then about inquiry concerning the statesman in turn? Has it been undertaken for the sake of that topic itself, or with regard to our becoming better dialecticians on any topic? Once again, obviously with regard to the general case.

As the Stranger indicates, the new topic has to do with both the present inquiry and the conduct of similar discussions. The present inquiry, of course, is aimed at clarifying the nature of statesmanship. This is the main subject matter of the inquiry. As YS and we as readers are about to find out, however, the new topic concerns not the subject matter of the present inquiry but the conduct of the inquiry as such. The new topic has to do with the method of dialectical discussion itself of which the present discussion is an illustrative example. In broaching this new topic, the Stranger draws attention to certain instructional procedures described earlier (277E–278C) involving the use of paradigms. These procedures include the use of familiar examples in teaching the spelling of unfamiliar syllables which, as noted earlier, serves as a paradigm to help YS understand the use of paradigms in dialectic. Details of this procedure are examined in Chapter 4; but details are not necessary to get the point of the analogy. When a child is first learning to spell and asks for help in writing a particular word, the query is not just about how to spell the word on that particular occasion but is aimed at increasing his or her skill with letters generally. So at least the Stranger suggests with his rhetorical question at 285C8–D3; and YS is quick to agree.

30

Metaphysics and Method in Plato’s Statesman

But wouldn’t you say the same, the Stranger then asks, in the case of our present inquiry? Have the two of them undertaken to define the statesman just for the sake of that particular subject, or is their purpose to become better dialecticians ( : 285D6) generally?10 YS again is quick to affirm the more general alternative. It may be worth noting in passing that the Stranger’s analogy is less straightforward than YS seems to realize. The choice he was given in the case of the spelling student was between learning to spell correctly on a particular occasion and learning to spell well generally. Either way, it is clear that the learning session had to do primarily with spelling. In the case of their own conversation, however, the choice is between inquiry into a particular topic (statesmanship as distinct from sophistry, for example) and concern with the method of inquiry as such. And this latter is a choice between focusing on a particular topic and focusing on a methodological procedure, which is not a simple choice between degrees of generality. If it had been clear all along that their conversation was concerned primarily with the methodology of dialectic, then the Stranger could have offered a choice between (a) methodology in this particular inquiry and (b) dialectical methodology in general, which would have stood in direct analogy to the choice offered in the case of the spelling student. Before this point in the dialogue, however, neither YS nor the beginning reader has any particular reason to think that the conversation is supposed to be concerned primarily with dialectic. And now, halfway through the dialogue, we are instructed to begin looking at the conversation from an entirely new perspective. By maneuvering YS to go along with a deceptively simple analogy, the Stranger in effect has shifted the focus of the discussion for the remainder of the dialogue. There is another explicit mention of the goal of becoming better dialecticians at 287A, after the Stranger has returned to the topic of appropriate length for dialectical discussions. As we recall, this is the topic that provided the occasion of his examination of “Excess and Deficiency in general” (283C–285C), with particular application to the art of measurement. We shall look at 287A momentarily. At 286E, moreover, he observes that a discussion of any length is justified if it renders one

10

As observed in G. E. L. Owen (1973), the Eleatic Stranger, in comparing their inquiry into statesmanship with a “school spelling exercise,” is suggesting that the chief aim of the inquiry “is not to spell out the one thing, statecraft, but to make the group generally better at spelling – better dialecticians, that is, on any subject proposed” (p. 350).

Becoming Better Dialecticians

31

better able to make discoveries by dividing things according to Forms. Here is the passage leading up to this observation. 286B4

286C

286D

286E

Let us recall the reason why we have said all these things on these topics. What reason? Not least on account of our annoyance ("5) with a lengthy discussion of the art of weaving which was hard to accept, as well as that concerning the reversal of the universe and that concerning the being of not-Being pertaining to the sophist. Thinking they had excessive length, we reproached ourselves in each of these cases, for fear that what we were saying was superfluous and tedious at the same time. Please realize, then, that all our foregoing observations were for the sake of our not entertaining such misgivings in the future. So be it. Only say what follows. Then I say that you and I are really obligated to recall our observations just now and to assign blame or approval of shortness and length alike, no matter what we might be discussing, not by comparing lengths in relation to each other, but according to the part of the art of measurement we previously said ought to be remembered – that relating to what is fitting. Right. Yet not everything is subject to this principle. For we shall have no need at all for a length accommodating pleasure, except as a subordinate matter. Again, our principle dictates that we be content with the quickest and easiest solution to a problem posed for inquiry as a secondary but not primary consideration. Most emphatically, however, the principle assigns top value to the pursuit itself of the capacity to divide according to Forms. What is more, even though a discussion is very long but renders the hearer (#  3 ) better able to make discoveries, we should pursue that discourse eagerly and not be put off by its length; and so, conversely, if it is very short.

The ostensive reason for undertaking the examination of the art of measurement was the possibility that YS at some point might come to consider the definition of weaving unduly long (283B). Here that possibility is upgraded (somewhat disingenuously) to an annoyance with its

32

Metaphysics and Method in Plato’s Statesman

length; and the supposed annoyance is extended to the Myth of Cronus and the treatment of not-Being in the Sophist.11 Rhetorical exaggeration aside, it soon becomes clear that the Stranger’s concern in this passage is with appropriate length for dialectical discussions generally. Another remark to be taken with a grain of salt is the Stranger’s comment that this supposed annoyance was the reason for the intervening examination of “Excess and Deficiency in general.” Only a few lines earlier, he had told YS that all they had been saying then was for the sake of incorporeal things that are “best and greatest” ( . . . ) : 286A5–6), which require verbal accounts for their dialectical investigation – a concern quite different from the length of such verbal accounts themselves. Surely the Stranger is not asking YS to recall something that contradicts what he had said just a moment previously. Read without rhetorical overstatement, the sense of 286B4–5 must be that the uneasiness induced about the length of certain discussions provided the occasion for broaching the topics bound up with “Excess and Deficiency in general,” not that the latter was broached for the main purpose of relieving that uneasiness. As far as assessing the length of dialectical discourse is concerned, at any rate, the main lesson to be learned from their examination of the art of measurement is that such judgments are to be made on the basis of what is fitting (#

: 286D2) rather than on a basis of relative comparison. To be sure, there are some purposes to which discourse might be put where the principle of fit measurement does not apply. Examples are discourse aimed at inducing pleasure (like that of a rhetorician) and discourse aimed at resolving problems in a fixed amount of time (like 11

By actual count, the discussion of weaving and the Myth of Cronus occupy roughly four and six Stephanus pages, respectively. While the Stranger himself expressed misgivings about the length of the Myth on methodological grounds, there are no signs of his being annoyed by his own story; and his misgivings about the length of the definition of weaving were entirely hypothetical. If any of the three discussions mentioned were to prove hard to accept ("5.: 286B9), it would be the discourse on not-Being that took up more than half of the Sophist. In point of fact, this is the second time the discussion of not-Being has come up in the last two Stephanus pages (counting 284B6–7 and C7 as one occurrence), and in both cases a point was made about its length. This might conceivably indicate a lingering preoccupation on the part of the author about his handling of that topic. On balance, however, that seems unlikely. Philosophically engaged readers of the Sophist generally find the treatment of not-Being and associated topics the most interesting part of that dialogue. It would be strange to suppose that the author thought otherwise. These considerations reinforce the perception that the Stranger’s expression of displeasure with these discussions at 286B is not to be read as entirely genuine.

Becoming Better Dialecticians

33

that of a lawyer who speaks with an eye on the clock). In the case of dialectical discourse, such purposes are secondary at best. In the case of dialectics, rather, the principle gives precedence to developing the ability to divide according to Forms (& 0 . . . ' : 286D9). Any discussion that renders the hearer better able to make discoveries on that basis should be pursued regardless of length. It will be noted that the passage from 286B4 through 286E3 contains no direct reference to dialecticians or the art of dialectic as such. Its concern rather is with discourse aimed at enhancing the hearer’s ability to make dialectical discoveries by dividing things according to Forms – discourse exemplified by the present dialogue itself. The second explicit mention of the goal of producing better dialecticians alluded to earlier occurs immediately before the discussants return to the topic of statesmanship. Picking up the discussion again at 286E3, we find the Stranger saying: 286E3

287A

287B

Moreover, if besides this someone raises objections regarding the length of such conversations and is not content with their circuitous course, such a person ought not be let go, in all haste and without further ado, with the simple complaint that the discussion is lengthy. We should consider it necessary for him to show in addition that a shorter conversation would have resulted in the discussants becoming better dialecticians, and better able to find ways of disclosing the truth of things in words. One should pay no heed to other sorts of blame and praise of other features of the discussion, nor even appear to listen to other considerations of this sort. Now enough of these things, if this is agreeable to you also. Let us return to the statesman, and bring to bear the previously mentioned example of weaving.

This final reference to the purpose of the dialogue overall begins with the objection of an imaginary critic of conversations like the present one, on the ground that they are lengthy and convoluted.12 The Stranger’s advice is to prevent a critic of this sort from leaving the scene having said no more than just that the conversation is too long. In the case 12

The expression   37
 " at 286E5 presumably carries the same sense as
!   37 at 283B2–3, which alludes to the frequent interruptions and redirections of the inquiry up to that point. This provides closure to the section on metaphysics and methodology beginning at 283B.

34

Metaphysics and Method in Plato’s Statesman

of dialectical conversations, this by itself is not a worthy criticism. To make an objection of this sort worth listening to, what a critic must be prepared to show is that a shorter discussion would serve its purpose more adequately, the purpose being to enable its participants to become better dialecticians. This amounts to their being more capable of “disclosing the truth in words” ( . $  7 *: 287A3), a reference back to the observation at 286A5–6 that the “best and greatest” things can be explained by discursive means alone. In dealing with conversations of this sort, to say it again, their effectiveness as dialectical exercises is the only criterion of appropriate length that should be taken into account. Praise or blame on other grounds should, so to speak, pass in one ear and out the other. This said, the Stranger returns to the task of defining statesmanship. Counting 286D8–E4, we have three distinct references to the production of better dialecticians, said at 285D5–7 to be the main purpose of the present conversation. Before leaving this topic, it is interesting to note what these three passages have to say about who is supposed to benefit from such conversations. At 285D5–7, the Stranger asks Young Socrates whether their ( ' : 285D4) inquiry concerning the statesman is being pursued for the sake of that subject or for the sake of their becoming better dialecticians. The only beneficiaries mentioned here are the participants in the discussion. At 287A2–3, once again, persons concerned with the length of a dialectical discussion are advised to show that a shorter conversation would make better dialecticians of the participants ("  : 287A2). At 286D8–E4, however, the circle of beneficiaries is extended to include auditors (#  3 : 286E1) of the conversation as well. Among auditors of the present conversation are Theodorus and Theaetetus, along, of course, with the older Socrates. The implication is that all persons present are in a position to benefit, whether or not they contribute to the conversation itself. A natural extension is to think of subsequent readers of the dialogues themselves as potential beneficiaries. In a sense more than metaphorical, a fully engaged reader may be following the conversation as it develops no less intently than the auditors mentioned in the dialogue.13 So there is a sense also in which active readers are also participants in the conversation, insofar as their involvement helps determine what they find in the dialogue.14 Regardless of how the relation between reader and 13 14

Because the occasion of the dialogue was probably fictional, subsequent readers may be the only physically active participants in the conversation. This sense of participation is developed at length in Sayre (1995), ch. 1.

Becoming Better Dialecticians

35

dialogue is understood, it is clear that a serious reader stands to benefit from his or her participation in the written conversation. Let us assume that Plato wrote the dialogue between the Stranger and YS with the intent of helping his readers become better dialecticians as well.15 This assumption will figure throughout the remainder of this commentary. Before returning to the Statesman, however, we need to remind ourselves of how dialectic proceeds in the other two dialogues featuring the method of collection and division. With the intent of putting the dialectical lessons of the Statesman in proper perspective, the next two chapters discuss the dialectical method practised in the Phaedrus and the Sophist. 15

For reasons examined later, dialectic in the Statesman is primarily a matter of skilled division. An intriguing aspect of the dialogue is the extraordinarily large number of terms the Stranger uses in referring to this dialectical procedure. Although a sizeable list of terms for division can be compiled for both the Sophist and the Philebus (nine or so in each, with some overlap), no less than twenty-four terms are used for this purpose in the Statesman. This count is taken from Leonard Brandwood (1976) and the Thesaurus Linguae Graecae, backed up by LS (1883) and LSJ (1968). The count should be considered provisional, not only because of possible oversights on the part of the present author but also because of occasional uncertainty whether a particular term used for division elsewhere is being so used in a given passage of the Statesman. In order of appearance, we can find: (1)  -  (258B6), (2)  (258C4), (3)  (258E4), (4)  6 (259D7), (5) 8  (260C7), (6)  6 (260D2), (7) "   (261A8), (8)   (261B11), (9) 6 (261C5), (10) 56 (262B2), (11) 
  (262D7), (12) 
56 (262E1), (13) 
56 (262E7), (14) 56 (263A1), (15) 56 (264D5), (16)    (265A4), (17) !3 (265D6), (18)  (265E11), (19)  6 (266A2), (20) 56 (268C9), (21) 
6 (280B3), (22)   (280B7), (23)  6 (289C1), and (24) '5   (302E7). Of these twenty-four terms, six (7, 14, 15, 16, 23, and 24) occur only once in this dialogue, and three (15, 16, and 24) are found nowhere else in Plato’s corpus. As the reader may verify, fifteen of the twenty-four make their first appearance between 260C and 266A, in the middle of which comes the Stranger’s tutorial on dividing according to Forms. Although it is of course possible that Plato was unaware of using so many terms for this dialectical procedure in the dialogue, this seems unlikely for various reasons. One is that force of habit probably would have kept him to the more limited vocabulary of the Sophist unless he was aware of reaching beyond it. Another is that there seems to be no precedent in Plato’s writing for such a profusion of terminological equivalents. (Apart from the present case, the upper limit may be the ten different terms for the receptacle in the Timaeus.) Whatever other intention might lie behind this terminological display, its effect is like that of a spotlight cast on the passages dealing with dialectical division. At 363A5–8 of the Thirteenth Letter, its author describes the conversation of the Phaedo as the “dialogue on the soul.” If Plato had found occasion to cite the Statesman in similar fashion, a suitable description might have been the “dialogue on dialectical division.” This ties in nicely with the Stranger’s observation that the main purpose of the dialogue is to make its participants better dialecticians.

2 Collection in the Phaedrus and the Sophist

2.1 Overview This chapter and the next deal with antecedents present in earlier dialogues of the dialectical method exhibited in the Statesman. These antecedents are found primarily in the Phaedrus and the Sophist. A brief overview of these antecedents will indicate why this and the following chapter are needed. The Sophist and the Statesman are the second and third members of a trilogy beginning with the Theaetetus. The method followed by Socrates in the Theaetetus is an integrated version of the method of hypothesis developed in progressive stages through the Meno, the Phaedo, and the Republic.1 When Socrates cuts off his conversation with Theaetetus to go meet his indictment, he steps down as discussion leader for the remainder of the trilogy. The Sophist takes up next morning with the introduction of the Stranger from Elea, who leads Theaetetus through the steps of a substantially different dialectical process. This process is commonly characterized as the method of collection and division. Lest too much be made of the association of different methods with different discussion leaders, we should not forget that the method of collection and division first appeared in the conversation between Socrates and Phaedrus.2 In point of fact, the Phaedrus is the only dialogue in which 1 2

See Sayre (1995), Appendix, section 5. Among commentators comfortable with the assumption that Plato’s dialogues can be arranged in chronological order of composition, it is standard to locate the Phaedrus before the Sophist. As far as the trilogy itself is concerned, it would be unprecedented to arrange its constituent dialogues in other than dramatic sequence. Ordering the

36

Collection in the Phaedrus and the Sophist

37

collection and division are paired by name as companion procedures. Yet collection is the procedure featured most prominently in this earlier conversation, as we shall see in section 2.2. In the portion of the palinode extolling the benefits of a philosophic life, collection is equated with recollection (  : 249C2); at 266B7–9, it is expressly cited as a capacity typical of dialecticians. The two procedures continue to operate in tandem through most of the Sophist. After the “chance discovery” of the philosopher at 253C, both procedures are mentioned in a description of philosophic knowledge. Collection also plays a crucial role in setting up the line of division that leads to the authentic sophist at the end of the dialogue. For all this, one gets the sense by the end of the dialogue that collection no longer is the dominant procedure. This is indicated at 253D1–3, for example, where dialectical skill is characterized as the ability to divide according to Kinds, with no specific mention of collection as such. By the time of the Statesman, moreover, collection seems largely to have dropped out of view. Despite a brief mention (at 285B2–6) appended to a discussion of the importance of dividing according to Forms, collection plays no part in the Stranger’s dialectical lessons. As argued in Chapter 4, the role assigned to collection in the Phaedrus and the Sophist is given over in the Statesman to the use of paradigms instead. Skill in dialectic involves the choice of suitable paradigms by which division can be guided in fruitful directions. As far as division is concerned, in turn, it not only becomes more prominent in the Sophist and the Statesman but also gains in sophistication. In the Phaedrus, division is limited to the specific task of distinguishing divine from hubristic love, which involves some conspicuously nondichotomous subdivisions along the way. It has no broader role in this context that pertains to the search for definitions. In the Sophist, by contrast, division contributes directly to the formulation of eight distinct definitions, including the apparently successful definition of sophistry achieved by the end of the dialogue. Moreover, division in the Sophist has been standardized into a highly regular procedure. To put it in a nutshell, divisions in this dialogue are invariably dichotomous, with the understanding that a two-part division is division into halves (221B). Dichotomous division continues to be the norm in the first part of the Statesman, along with the requirement that division make cuts “through dialogues by date of composition, of course, is compatible with the possibility that Plato made alterations in a given work after it had been made publicly available.

38

Metaphysics and Method in Plato’s Statesman

the middle” (262B). As a glance at Figure 1.3 will verify, the initial definition of the statesman as a kind of herdsman results from a series of divisions that is dichotomous throughout. With the shift to the paradigm of weaving at 279B, however, a new pattern of division begins to emerge. The first sign of this new format is the (unannounced) appearance of a nondichotomous division in the definition of weaving (at 282A1–4), which is examined at length in Chapter 5. Having been explicitly sanctioned at 287C, nondichotomous division thereafter is employed extensively in arriving at the final definition of statesmanship. This leaves us with the question of whether the apparent success of this final definition depends on the shift to nondichotomous division. In one respect, of course, this manner of division is not really new, inasmuch as nondichotomous division appeared previously within the Phaedrus. But there is a considerable difference between its seemingly casual use by Socrates in this earlier dialogue and its studied use by the Stanger in defining the statesman. In order to evaluate the significance of the changes in method the Stranger represents, we need to look carefully at the methods practiced in the Phaedrus and the Sophist. This chapter deals with collection in these earlier contexts.

2.2 Collection in the Phaedrus There are three passages in the Phaedrus with distinct references to collection, each notable in its own right. The first is at 249B–C, where Socrates is discussing requirements a soul must meet to return from animal to human embodiment. These requirements stem from a need for the human person: to deliberate according to what we call Forms ("    & 9    : 249B7),3 going from many perceptions to a unity (
. (# ! ( : : 249B7–C1) brought together by reasoning.

This process of understanding, Socrates continues, amounts to a recollection (  : 249C2) of things the soul perceived at some time in the company of a god. Recollection is mentioned again in the same context at 250A1, where the requirement is repeated that a soul must be capable 3

This is the only occurrence of  & 9  (singular) in the corpus (however, see    at Sophist 253E2). Most English translators opt to read 9  here as plural (as at Phaedrus 265E1, 273E1, 277B7, Statesman 262E3, 285A4, passim). For a rationale behind an alternative translation of this phrase as “to understand according to form that which is spoken,” see Charles Griswold (1986), p. 266, n. 51.

Collection in the Phaedrus and the Sophist

39

of beholding reality in order to enter human form. Let us trace out this connection with recollection before focusing on Socrates’ depiction of collection as such. The pairing of collection with recollection in this passage should not be read as an identification of the two mental processes.4 Recollection is portrayed in the Meno and the Phaedo (the only other dialogues in which it figures explicitly) as a return of the soul to an immediate grasp of reality like it once enjoyed in a nonbodily state. Collection, on the other hand, is part of the dialectical process, aimed at discerning specific Forms with which its companion process of division might profitably begin. The point of associating collection with recollection at 249C must be rather that the two processes are similar in important respects. One respect in which they are similar is that both involve knowledge presumably gained prior to the beginning of a particular inquiry. In the Meno, for example, the slave boy’s grasp of the relation between the diagonal of a given square and another square of twice the area is taken as evidence that the boy had recollected knowledge from a prior existence. For an example of collection that is equally instructive, we may look ahead to the five faulty definitions in the first part of the Sophist.5 Despite their failure to isolate a set of features that apply to sophistry in general, each of these definitions picks out a particular branch of sophistry. The branches thus characterized serve as a set of examples among which a common property (production) is then identified that provides a beginning for the successful definition of sophistry that ensues. In order for the initial five definitions of sophistry to serve in this role, however, both Theaetetus and the Stranger must have been able to recognize the skill that each delineates as a form of sophistry. And this would require a knowledgeable grasp of sophistry antedating their joint inquiry. Without relying on the mythical account in the Meno of how this comes about, collection in subsequent dialogues requires some form of prior knowledge. Another overlap between collection and recollection appears by way of contrast with Aristotle’s brief account of perceptual induction at the end of the Posterior Analytics (100a10–100b5). According to Aristotle, the soul’s grasp of a general property is a matter of abstracting that property 4 5

In this I agree with Charles Griswold; see his thoughtful discussion of the two processes in (1986), pp. 116, 173–86. Details of the Stranger’s use of these faulty definitions for purposes of arriving at the common property of production (vs. acquisition) are examined more closely later in the chapter. For previous discussions of this matter by the present author, see Sayre (1969), pp. 54–57, and Sayre (1995), pp. 146–47.

40

Metaphysics and Method in Plato’s Statesman

from repeated perceptions of things that possess it, until the property itself occupies the soul as an abstract universal stripped of the particularities of its individual instances. This process of abstracting the general property from particular perceptions, in Aristotle’s way of thinking, is made possible by his doctrine of the literal inherence of the general property in things possessing it. In Plato’s view, on the other hand, what Aristotle calls “universals” are present neither in perceptible instances nor in the perceiving mind and hence cannot pass from one to the other by any kind of induction. When discerning a common property by collection over instances, the manner in which the shared Form becomes present to the mind cannot be a matter of abstraction. What takes place instead must be something like the process of recollection as described at Phaedo 72E–76E. In the specific example given there, just as one might be reminded of Simmias by viewing his portrait, so one might be reminded of the Form Equality by perceiving an imperfect instance that in some way resembles it. Although perfect Equality is never present to sense perception, its prior presence to the mind can be reinstated by the perception of resembling instances. In similar fashion, when one collects together several instances of a given sort in hopes of discerning some common property, one is enabled to recognize these as instances of the thing to be defined by some antecedent understanding of what things of that sort are like. Without commitment to a particular account of how that understanding arises, we see again that collection engages some kind of preexistent knowledge. The second, and most prominent, discussion of collection in the Phaedrus occurs at 265D. By way of context, we are told that there were two fortunate aspects of Socrates’ preceding speech (his “palinode,” socalled at 257A4) the nature of which it would behoove us to grasp in a methodical fashion. The first of these, Socrates says, is to bring what is multiply dispersed (
5; 
  : 265D3–4) into a single Idea (4(  . . . ( : 265D3), so that by defining each thing one can always make clear the topic about which one wishes to learn.

In the case of Socrates’ speech specifically, its topic was “made clear” by an exposition of four kinds of madness setting up a discussion of the madness (so-described at 249D5) of the lover who is reminded (<   !: 250A1) of genuine Beauty. Whether good or bad, Socrates avows, it was the resulting definition of love that allowed his speech to achieve clarity and self-consistency.

Collection in the Phaedrus and the Sophist

41

As might be anticipated, the second aspect of his speech to which Socrates next draws attention is the way it was able to partition (  : 265E1) madness “according to Forms” ( & 0: 265E1). This is tantamount to cutting a thing “according to its natural joints” ( & 1! =;
" : 265E1–2), suggestive of the way a skilled butcher deals with an animal carcass. As Socrates describes it here, this process of division is accomplished by his two speeches on the lover’s madness together, the former cutting up the sinister ( : 266A5) branch of love and the palinode responding in kind along the right-hand side.6 Having thus identified these two complementary procedures, Socrates then provides a specific label for each. Continuing the theme of the preceding speeches, he declares himself a lover of these “divisions and collections ( ) " . : 266B4), claiming them as basis for his ability to speak and think prudently (  )  ' : 266B4–5). This leads directly to the third and final description of collection in the Phaedrus. Whenever he deems a person able to see as one (( : : 266B5) what naturally extends over many (
)

"#! & . . . : 266B5–6),

he is ready to follow this person as if a god. Although this remark comes directly on the heels of a discussion of collection and division as cooperating activities, it is the former that is singled out in Socrates’ expression of admiration. This emphasis on collection in its first appearance by that name may help us appreciate the significance of its effective disappearance from the methodology employed in the Statesman by the Eleatic Stranger. When we ourselves perform a collection, as it were, over these three descriptions of collection, what we find as a common property is that each describes a movement from plurality to unity. At 249C, the process goes from many perceptions (
. ) to a unity (( : ) brought together by reasoning. At 265D, it begins with what is multiply dispersed (
5>; 
  ) and proceeds to a single Idea ((  . . . ( ). And finally at 266B, it moves from what naturally extends over many (
)
) to what can be perceived as one (( : ). The essential mark of collection, one may say accordingly, is that it enables the mind to focus on a single Form through an initial awareness of several diverse instances. 6

Reference here to division on both “left and right sides” is relevant to the similarly “counterthrusting” divisions late in the Statesman, discussed in Chapter 6.

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Metaphysics and Method in Plato’s Statesman

Before moving on to see how this process figures in the Sophist, we should be aware that something closely resembling it is invoked in the Republic where Socrates introduces the simile of the sun as an offspring of the Good. We say that there are many beautiful things (
 !: 507B2) and many good things, Socrates tells Glaucon, and that there are Beauty itself and Good itself as well. So generally, in the case of everything we count as many (?
: 507B6) we turn about and posit a single Idea ((  . . . ! : 507B6–7 to which it pertains and say that this constitutes “what it is” (@ A : 507B7) in each particular case. In Book X of the Republic, moreover, Socrates refers to this process of positing a single Form in the case of many similar instances as a “customary procedure” ((!" ! ": 596A6). As described there, the procedure is to posit (!!: 596A7) a single Form (9  . . . : : 596A6) in each case of many (B 
: 596A7) to which we give the same name. By way of illustration, says Socrates, there are many beds and tables, but only a single Idea of Bed and a single Idea of Table. So integral was this rationale for positing Forms as conceived in the middle period, apparently, that Plato saw fit to give it a prominent place in his arguments against this conception of the Forms in the first part of the Parmenides. In setting up the first of the so-called “Third Man” arguments at 132A, here is what Plato has Parmenides say: I imagine you believe there is a single Form (: . . . 9 : 132A1) in each case for some reason such as this: when some plurality (
 & 1: 132A2) of things seems to you to be large, there . . . seems to be some one character (  . . . (: 132A2–3) that is the same when you look at them all, wherefore you suppose the Large to be one thing (: #  ; 9 : 132A3).

Parmenides’ next move, of course, is to invoke the same procedure again, claiming that this Large in conjunction with the original large things calls for recognition of another Large in turn, and so forth. Although the movement from many instances to one Form in these passages seems indistinguishable from the process described in the Phaedrus, there is no use in the Republic of "  in its methodological sense. Nor is there any suggestion that the single Form reached by this process might serve as a starting point for an ensuing division. To all appearances, at least, the pairing of this process with dialectical division was an innovation first mentioned in the Phaedrus.

Collection in the Phaedrus and the Sophist

43

2.3 Collection in the Sophist Immediately following the encounter with the “free man’s knowledge”7 at Sophist 253C, the Stranger explains what he takes to be “the science of dialectic” (  . . . 
 : 253D3). This is a matter of “dividing according to Kinds”8 (   '!: 253D1), not thinking of the same Form as different or the different as the same. Someone capable of this, he goes on to say, will adequately and distinctly perceive a single Idea (  ( : 253D5) extended through many (
. : 253D5–6) [Ideas], each one lying apart [from each other], and many (
: 253D7) [Ideas] different from each other embraced from without by a single ( C: 253D7) [Idea].

This appears to be a description, from complementary perspectives, of the perception achieved through collection. First is the perspective of the one, next that of the many. As a preparation sufficient for division according to Kinds, the Stranger seems to be saying, a dialectician must be able to see clearly a single Idea manifested in a plurality of different things. Put otherwise, the dialectician must be able to view these several different things as held together by a single Idea distinct from themselves. Thus enabled, the dialectician can get on with the business of division, which amounts in turn9 to perceiving a single Kind united “into one through many wholes” (+
.  D ): 253D8), and many Kinds entirely set apart. The single Kind united into one through many wholes, presumably, is the final product of division, and the many Kinds set apart in the process are the Forms distinguished along the way from those implicated in the final definition. This particular discussion of methodology concludes with the remark that what the procedure amounts to is knowing how to discriminate, “Kind by Kind” (  : 253E2), how these several things can and cannot combine, along with the advice that only someone with a genuine love of wisdom (   % : 253E5) can be credited with this sort of dialectical skill. 7 8 9

This is an allusion to Theaetetus 172D1 where the philosopher is likened to a free man in contrast to speakers in law courts who are “enslaved” by demands of the legal process. Kinds at this point in the Sophist are equivalent to Forms, hence the capitalization. The contrasting use of   for classes in the Statesman is discussed in Chapter 12. I read E at 253D8 as an indication that the Stranger’s description of dialectical method is turning from collection to division. The many wholes at 253D8 presumably are not the many things from which collection proceeds according to 253D5–7.

44

Metaphysics and Method in Plato’s Statesman

Another reference to collection, albeit brief, occurs earlier at 234B, just before the Stranger launches into the series of divisions that yield the authentic sophist at the end of the dialogue. This reference takes the form of a remark by Theaetetus to the effect that the Stranger has just referred to a large and very diversified class (9F: 234B3), “collecting it all into a unity” (( :
  "-F : 234B3–4). Let us establish the context of this remark before considering its significance. After having worked out a fully articulated definition of angling as an illustrative example (
 : 218D9, 221C5), the Stranger spins out six distinct definitions of sophistry in rapid succession. The first five depict sophistry as an acquisitive art, by way of either conquest (sophists I and V) or exchange of “wares” for money (sophists II, III, and IV). The sixth defines the “sophist of noble descent” (so-called at 231B9), who practices an art that purifies the soul of effects brought about by the acquisitive sophists. This sixth definition is usually taken by commentators to be description of Socratic elenchus. (All six definitions are laid out in Chapter 3.) Although each of the first five definitions characterizes a form of sophistry that presumably would be recognized by the immediate audience, however, none is broad enough to apply to sophistry in all its many forms. Each characterization, that is to say, is sufficient to pick out a specific form of sophistry, but none provides a characterization that applies to sophistry in general. Inasmuch as the stated task of the dialogue (218C) is to come up with a definition that explains the nature of sophistry as such, the first five definitions as they stand are deemed inadequate. The gist of their inadequacy, as the Stranger describes it, is that they do not enable one to see clearly (' : 232A4) the generic skill (5  : 232A4) in which all these forms of sophistry converge. Looking back over the five characterizations, the Stranger then observes that all of the various forms of sophistry they represent are involved in disputation (<  # : 232B6) and that their practitioners can dispute on any topic. By way of drawing out the significance of that observation, he then proposes another illustrative paradigm (
 : 233D3). The paradigm proposed is that of someone who claims “to know how to make and do all things by a single skill” (
' ) C C7 5 ; " 
  
!
 : 233D9–10). As the Stranger soon makes clear by alluding to various particular cases of production, the skill he has in mind is that of imitation (   : 234B2). The imitator, of course, is a maker of images, which sometimes (as in the case of an artist) can be sold for a modest sum (234A5).

Collection in the Phaedrus and the Sophist

45

It is at this point that Theaetetus makes the remark cited earlier, observing that the Stranger has taken a large and diversified class of skills (those involved in producing imitations) and “collected it all into a unity” (234B3–4). Because the sophist has been included in this class as someone who engages in controversy on all topics and teaches this skill for a fee (234A8–10), the collection of all these skills under the single heading of imitation provides a single Kind under which sophistry can be further divided. As a result of working through this illustrative paradigm, the sophist emerges first and foremost as a practitioner of “the art of image making” ( (
 5  : 235B8–9). Let us look carefully at what this collection10 has accomplished. Definitions of the first five forms of sophistry all began with the acquisitive branch of art. Because their practitioners differ in manner of acquisition, none of these five definitions applies to sophistry in general. In seeking out a single skill that all five forms share, the Stranger has noticed that they all generate the impression of being knowledgeable on all topics. Being a sophist thus qualifies someone as belonging to the class of artful people who, in one way or another, are able to produce imitations of all things. It thus turns out that a single skill characteristic of sophists generally is that of image making, insofar as they are capable of creating semblances of all things in the form of words. Whereas the five kinds of sophistry were first defined as acquisitive artisans, as a result of collection they have now been displayed as artisans dealing in production as well. The Stranger thus reverts to the initial division of Art into Productive and Acquisitive and begins pursuing the sophist along that former branch instead. The dialogue ends with a definition depicting the sophist as a practitioner of productive art, with 10

One’s view of the role of collection in this dialogue can be distracted by the use of "  and its synonym "-' in reference to other sorts of activities. At 230B there is mention of gathering together ("  ) someone’s opinions as part of the process of elenchus. At 251D the Stranger considers the option of grouping together ("   ) Being, Motion, and Rest as all capable of associating with one another. And at 224C, he proposes summing up ("   ) the features attributed to sophistry of the second sort – acquisition, exchange, merchandizing, and so forth. As far as "-' is concerned, there is reference at 218C to the difficulty of grasping ("-' ) the tribe of sophists that Theaetetus and the Stranger are committed to find. At 235B–C the Stranger encourages Theaetetus to grasp ("-' ) the sophist by royal command of reason if they should happen upon him. At 250B there is the Stranger’s question whether in saying that there are both Rest and Motion one is taking them together ("-F ) as associating with Being. Once again we are led to the conclusion that Plato was not given to setting aside common terms like these as part of a technical vocabulary.

46

Metaphysics and Method in Plato’s Statesman

specific traits added that apply to that skill uniquely. Collection has paved the way for a successful line of division, leading to the final capture of “the genuine sophist” (# $    : 268D3) at the end of the dialogue. There are two other fairly distinct uses of collection elsewhere in the Sophist. One is that “bringing under one heading” ("  : 219B11) various forms of production at 219A–B, including agriculture, pottery, and the art of imitation (   at 219B1, anticipating its crucial role at 234B2). There is also mention at 267B1 of a collection (" ' ) left for someone else to do. The most distinctive use of collection in the dialogue, nonetheless, is the one we have just examined, in which skill in the production of images is discerned as a common feature of sophistry in general.

2.4 Collection and the Identification of Necessary Features As depicted in the Phaedrus, collection is a process of discerning a single Form manifested in a plurality of diverse instances. A striking illustration in the Sophist, we have noted, is where the production of images is picked out as a feature shared by all five types of sophistry that had previously been characterized as forms of acquisition. Insofar as this collection is successful, image making is essential to being a sophist. The problem with the five previous characterizations is that, although each describes a recognizable type of sophistry, no two types are acquisitive in the same respect. A consequence is that no one description applies to sophistry in general. In effect, none singles out features that are found in all cases of sophistry. None identifies features characteristic of sophists essentially. There are several respects in which an attempted collection might fail. One is that the instances from which the collection proceeds are not all genuine cases of the thing to be defined. If the “sophist of noble descent” had been factored into the collection, for instance, the Stranger would not have been able to find an identifying feature that applied equally and univocally to all (six) cases involved. As noted in section 2.2, successful collection resembles recollection (  ) in requiring prior knowledge of some sort regarding the thing to be defined. Unless Theaetetus and the Stranger had been able to recognize genuine instances of sophistry in advance, they could not have arrived at an essential feature necessary to get a dialectically sound definition of sophistry underway. Another respect in which collection can go wrong is in picking out some feature shared by all instances at hand that nonetheless is not

Collection in the Phaedrus and the Sophist

47

required for their being what they are. By way of example, all five types of sophistry distinguished initially are engaged in making money (see 223B for sophist I; 223C for II; III, and IV; and 225E for sophist V). Despite the prevalence of this practice among sophists of Plato’s acquaintance, however, turning a profit need not be essential to sophistry in general. In giving a free demonstration, Gorgias would not cease to function as a sophist; the same would be true for Protagoras if he had stopped accepting fees. A successful collection must result in a feature that is necessary to the thing being defined, as distinct from an inessential concommitant. Another possible source of failure is that the collection might rely on an inadequately comprehensive group of representative instances. For example, sophists III and IV are both involved in retailing (223D6), which is not the case with the other three types. Although retailing may be essential for sophistry of those two sorts, it is not a feature required for sophistry at large. Hence a collection based on those two sorts alone might come up with a feature that is not generally requisite. The question of sample size becomes critical when we turn in Chapter 4 to the use of illustrative paradigms in the Statesman. Despite pitfalls like these along the way, the mark of collection successfully completed is that it produces a feature that is necessary to the thing being defined. The sense of necessity here is that in which the truth of a logical consequent is necessary to the truth of the antecedent entailing it. If being a husband entails being married, then being married is necessary to being a husband. In just the same fashion, being an angler entails being acquisitive, and being a sophist entails being a producer of images. The dialectical role of collection, in brief, is to come up with a feature entailed by being an instance of the thing ultimately to be defined. Once an essential feature of this sort is identified, the process of division takes over by way of completing the definition. Whereas the feature arrived at by collection is necessary for the thing being defined, that feature does not entail being the latter thing in turn. Not all acquisitive artisans are anglers, and not all image makers are sophists. This is to say that being an angler is not necessary for being an acquisitive artisan and that being a sophist is not necessary for being an image maker. The feature produced by collection is necessary for the thing being defined, but it is not sufficient. The role of division, in due order, is to qualify the feature picked out by collection in a stagewise fashion until a characterization is arrived at that is both necessary and sufficient. This characterization constitutes the definition at which the overall dialectical process is directed. Each

48

Metaphysics and Method in Plato’s Statesman

feature articulated in the completed definition is necessary for the thing being defined. And all the features taken in combination are sufficient for being a thing of that kind. In a successfully completed definition, the set of defining features is logically equivalent to the kind of thing that has been defined. As indicated earlier, these observations on the logic of dialectical definition come into play when we turn in Chapter 4 to the use of paradigms in the Statesman. Before returning to the Statesman, however, there is another dialogue to consider in which the term "  (to collect) plays a significant role. A brief discussion of the Philebus in this regard will help us understand how collection is replaced in the Statesman by the use of paradigms.

2.5 Complications in the Philebus In both the Phaedrus and the Sophist, collection is a process by which the dialectician perceives a single Form pervading many instances. While the Form itself remains a unit, its presence is somehow revealed in many sensible things. The many thus are one, and the one thus many. It is with an “amazing statement” (!" # 5! : 14C9) to this effect that the serious business of the Philebus gets underway. Suppose that someone undertakes to posit (!!: 15A5) the one Ox, the one Beautiful, or the one Good (# ! B : 15A5–6) and then seriously sets about to divide (: 15A7) such an entity. This would give rise, says Socrates, to disputes like the following:11 First, whether we ought to suppose that unities of this sort truly exist. Then next, how each of these, being one and always the same, and admitting neither generation nor destruction, can remain altogether and unshakably one and the same in the face of our having to posit (! : 15B6) it in things that come to be and are unlimited – whether it is scattered abroad and becomes many, or whether – and this would seem the most impossible of all – it is a whole itself apart from itself, becoming one and the same in one and many things at the same time.

It is problems like these, Socrates goes on to say, that bring satisfaction if properly resolved and cause all manner of difficulties otherwise. The “godly method” of 16C–17A, of course, is the way he recommends for resolving such problems. 11

Commentators have debated the number of distinct questions posed in the following passage. See Sayre (1983), pp. 291–92, n. 4, for my own opinion against a background of alternatives. For present purposes, the number of distinct questions is not relevant.

Collection in the Phaedrus and the Sophist

49

More is said about the “godly method” in the second part of this study. The reason for not elaborating on it now is that it appears to be a method of division only. Neither the description of the method nor the passages leading up to it say anything about collection as such. Instead we hear about the positing (15A5, 15B6, 16D2) of some single Form to get things started and then about the division that follows when that Form has been laid down. In considering what to make of this, however, we must take into account the singular fact that collections are called for by name no less than six times in the discussion of the four basic kinds that follows a few Stephanus pages later. In each case, there is an acknowledged need to bring unity to some sort of multiplicity, and in each case collection (" ) is cited as the means by which this unity should be achieved. Pending the discussion in Chapter 8 of the four basic kinds in the Philebus, we may note that two of the basic kinds in question are the Unlimited and Limit. Third is the Mixture of these two, and fourth the Cause by which mixture comes about. At 23E, Socrates observes that both of the first two are scattered abroad (
  : 23E512 ) and dispersed into many (
: 23E4), and calls for a collection ("  : 23E5) of these multitudes into one ( : : 23E5). In this way, an observant person can see how each is both one and many (: )
: 23E6). Here we find something referred to as collection and described in the same terms used for describing collection in the Phaedrus and the Sophist. It is a process by which multiplicity is brought into unity. The second mention of collection in this context is at 25A. Socrates has just identified “becoming more and less” (24E7–8) as the single mark of the Unlimited kind, and this is said to comply with their agreement to collect ("  : 25A3) the scattered multitude of the Unlimited into a single unity (( : : 25A1–2). The remaining four references to collection come at 25D, in connection with the need to provide comparable collections for Limit and Mixture. Just as we collected the Unlimited into one (  % 
 " "   ( & : : 25D5–6), Socrates says, we should have collected the class of Limit but failed to do so (  %
  % " ' ,  "   : 25D6–7). But as he goes on to say, by collecting both these two (   "    : 25D8) the class of Mixture perhaps will become clear as well. The unifying feature of Limit, as identified at 25E1–2, is that it makes opposites commensurate and harmonious by the introduction of number. 12

The same term appears in the passage quoted at 15B6 and also at 25A3.

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Metaphysics and Method in Plato’s Statesman

At first glance, these several occurrences of the term "  seem to show that, despite its not being mentioned specifically as part of the “godly method,” collection still has a substantial role to play in dialectical procedure. Before resting content with that conclusion, however, we should look carefully at how the several so-called collections actually function in this particular context. Arriving at “becoming more and less” as the unifying mark of the nature of the Unlimited, for one thing, is not a matter of identifying a single Form with which an ensuing process of division can auspiciously begin. Whatever the kind or class of the Unlimited amounts to, it is not a Form subjected subsequently to dialectical division. The same may also be said of Limit. Indeed, it would have been useful to the reader if Socrates had divided Limit into proper parts – numbers, measures, Forms, whatever. This might have been of considerable help toward figuring out how Limit should be understood in this context. And whatever one makes of the classifications of pleasure that occur later in the dialogue, these are not parts of a systemic division of the class of Mixture. To put it briefly, these several so-called collections do not function as part of an integrated method of collection and division of the sort praised in the Phaedrus and applied in the Sophist. To the contrary, the unified perceptions described as collections in this context appear to have the status of finished achievements in their own right. When Socrates and Protarchus single out “becoming more or less” as the unifying feature of the Unlimited, this is the culmination of a discussion taking up an entire Stephanus page. After that unifying mark has been identified, they proceed directly to a discussion of Limit and Measure. Discerning this common feature is an end in itself. It unmistakably is not a preliminary step in the course of an ongoing dialectical procedure. The apparent upshot is that although collection of some sort plays a role in the Philebus, it no longer functions as the complement of division in a two-stage dialectical process. Instead of relying on a collection over paradigmatic instances to get division off to an auspicious start, dialectic in this dialogue begins summarily with the “positing” of some appropriate Form. As described in the “godly method,” what we are supposed to do to get division underway is “to search for a single Form to posit in each and every case” (  (
)
 # D  !  " 6' : 16D1–2), and then to look for two, three, or some other number of Forms to be treated in the same way. This description harks back to 15A, where Socrates warns about the disputes that will arise when someone undertakes to posit (!!: 15A5)

Collection in the Phaedrus and the Sophist

51

one Ox, one Beautiful, or one Good and then proceeds to divide that unified entity. One is also reminded of the recurrent theme in the Republic of positing single Forms on the basis of many similar instances (section 2.2), and of the method in the Phaedo that begins with the hypothesizing (G
!  : 100B5) a thesis one judges to be strongest.13 Whatever we do with those associations, however, the fact remains that collection as practiced in the Sophist has faded from the scene by the time of the Philebus. What happened in the interim is the topic of Chapter 4. 13

See Phaedo 99E–100A and 101D–E. My views on the method of hypothesis are laid out in Sayre (1969), Ch. 1, and Sayre (1995), Ch. 5, sec. 2.

3 Division in the Phaedrus and the Sophist

3.1 Subdivisions of Mental Derangement in the Phaedrus With regard to dialectic, the pivotal passage in the Phaedrus is 265D–266C. The passage begins with reference to a pair of procedures, identified shortly thereafter as collection and division, and concludes by assigning the name ‘dialectician’ persons able to apply them. As already noted, collection is described here as a process of bringing what is multiply dispersed “into a single Idea” (4(s  . . . ( : 265D3). Division is characterized in turn as a matter of “cleaving things according to Forms” ( & 0 . . .   : 265E1) and likened to the technique of cutting “according to natural joints” (& 1! =;
" : 265E1–2) practiced by a competent butcher. The treatment of collection in the Phaedrus has been discussed in the previous chapter, along with the relationship between collection and recollection (  ). Our present concern is with the other phase of the dialectical process in which things are partitioned according to Forms. This technique of cutting things along natural lines of cleavage, Socrates tells Phaedrus, has already been illustrated in his two speeches on love. After locating mental derangement (# . . . 1   : 265E3–4) under a single common Form (by collection), these two speeches then partitioned off the “left-handed” and the “right-handed” parts of mental derangement (termed
  at 266A2), analogously to the distinction between the left- and right-hand parts of the body. Let us examine the forms of mental derangement distinguished in these two speeches. 52

Division in the Phaedrus and the Sophist

53

Foreshadowing the contrast between the noble and the hubristic horse in the myth of the charioteer, the first speech distinguishes two principles by which human action is guided. On one hand is a natural desire for pleasure, on the other an acquired judgment that aspires to what is best. When the latter holds sway, the control it provides is called “moderation” ( 3 : 237E3). When the former prevails, however, it drags one irrationally toward pleasure; being ruled by this principle is known as “hubris” (2-: 238A2). The speech then proceeds by distinguishing various forms that hubris might take. When a person’s actions are dominated by a desire for the pleasures of food, the desire is known as gluttony, and the person involved will be named a glutton. When the dominant desire is for the pleasures of drink, the person will be known as a drunkard. And so on for other forms of overwhelming desire. Of particular interest in the first speech, however, is the overpowering desire for bodily beauty (   : 238C2). In this case, the domineering desire is known as lust (
!" . : 238C2), which Socrates describes graphically as eros in the sense related to physical force (H* : 238C3). This is the form of mental derangement characterized as “left-hand love” ( . . . A) at 266A6. Love of the “right-hand” sort is singled out in the second speech (the palinode, so-called at 243B5). Far from being hubristic, this kind of love is characterized by Socrates as a kind of madness that is divine (!' : 266A7, following 249D1). As such, it is related to other forms of divine madness distinguished in the opening passages of this speech. First to be identified among these is the skill practiced by the ancient prophets (  : 244D2). Whereas present-day diviners purport to foretell the future by exercise of their own wits, relying on birds and other omens, the practice of the older prophets relied entirely on divine inspiration. In the recapitulation of the god-given forms of madness at 265B, prophetic inspiration is attributed to Apollo specifically. Second and third in order of mention are skills dependent on inspiration by Dionysus and the Muses, respectively. Although prophetic in a way, the second skill is concerned less with foretelling the future than with remedies for the amelioration of afflictions due to guilt for ancestral sins. Avenues of healing made available by this skill involve participation in mysteries (. : 244E2) and various rites of purification. The form of divine madness induced by the Muses, in turn, is that yielding lyric and other forms of poetry. Lyric poetry is singled out specifically as a means of glorifying great deeds of the past for the edification of future generations. In the ranking of incarnate souls laid out at

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Metaphysics and Method in Plato’s Statesman

248C–E, poets and other devotees of the Muses share top rank with lovers of wisdom.1 The fourth and highest form of divine madness is disclosed at 249D, in connection with the identification of recollection as a process of understanding according to Forms. So enraptured was the soul of the philosopher in its preincarnate vision of true Beauty that when it perceives beauty among mortals it takes flight in the madness of love, and the person touched by this madness is known as a lover. It is in this manner that the palinode leads to the “right-hand” love engendered by Aphrodite and Eros specifically. Socrates sums up the results of these two sets of divisions at 266A, by way of illustrating how severing things according to Forms amounts to cutting them along their natural joints. As he puts it, the two speeches provide an initial division of the single Form of mental derangement in two distinct directions. On the left-hand side is derangement of an hubristic sort, further differentiated in the first speech into gluttony, drunkenness, and lust. This last type of hubris, rooted in an overwhelming desire for beauty, is described as the left-hand part of love at 266A6. Along the right-hand side, madness is further divided into various forms of divinely induced frenzy (   at 245A1, 245B1, passim). In order treated, these are the madness of the prophet, inspired by Apollo; that of the mystic, due to Dionysus; that of the poet, induced by the Muses; and that of the lover, enthused by Aphrodite and Eros. Although this divinely gifted form of love goes by the same name as its left-hand counterpart, it is praised in the palinode as the source of the greatest human goods. It will be helpful to lay out this multiform division of madness in diagrammatic form, as follows (Figure 3.1). Given the common assumption that the Phaedrus is earlier than the Sophist and the Statesman, this is the first fully elaborated set of divisions in the Platonic corpus. Two features of Figure 3.1 should be noted in particular for comparison with divisions found in later dialogues. One is that the process of division is pursued through both the left- and the right-hand branches of the figure. This is required by the underlying purpose of contrasting the beneficent form of 1

Socrates invoked the Muses at the beginning of his first speech, and twice describes that speech as dithyrambic (hence lyrical); but the speech was too much under the influence of the blasphemous recitation by Phaedrus to count as divinely inspired. The palinode is more successful in this regard, as signaled by the story of the cicadas (258E–259D) who bear report to the Muses of human doings, in tandem with specific mention of Calliope and Urania as having a special interest in those pursuing a life of philosophy.

Division in the Phaedrus and the Sophist

55

madness hubris

gluttony drunkenness lust

divine frenzy prophecy mysticism poetry love

figure 3.1. Forms of madness.

love in the palinode with the sinister (left-hand) form found in Socrates’ initial speech. By way of contrast, all divisions undertaken in the Sophist (with a possible exception at 223D; see Figure 3.3) proceed along the right side only. This is in accord with the Stranger’s explicit call for righthand division at 264E as he enters the final phase in the definition of the authentic sophist. The second thing to note about Figure 3.1 is that both branches end up with nondichotomous subdivisions. On the left, hubris is divided into gluttony, drunkenness, and lust, whereas divine frenzy is separated on the right into four parts including beneficent love. Within their respective narrative contexts, neither set of multiple distinctions appears unusual or out of place. In point of fact, however, this is the only instance of nondichotomous division to be encountered until roughly halfway through the Statesman. A strict pattern of dichotomous division is maintained throughout the Sophist, to which we turn in the following section.

3.2 The Paradigmatic Definition of Angling in the Sophist The stated purpose of this conversation with the Stranger is to define ( !: 217B3) the sophist – to “give a clear account of what he is” (  6  7 
& A: 218C1). This is to be accomplished by a method ( !  : 218D5) first illustrated by defining the angler, consisting of multiple stages of “dividing by Form and name” (0 ) I     : ; 220A8–9). The procedure is subsequently described as “dividing according to Kinds” (   '!: 253D1) and identified as “the science of dialectic” (  . . . 
 : 253D2–3). Following the pattern established by the definition of the angler, seven distinct attempts are made to define the sophist. Numbered in order of occurrence, these are as follows: sophist I (221D–223B), sophist II (223C–224D), sophist III (224D–E), sophist IV (224D–E), sophist V

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Metaphysics and Method in Plato’s Statesman

(225A–226A), sophist VI (“the sophist of noble descent,” 226B–231B), and sophist VII (the “authentic sophist,” 234C through the remainder of the dialogue). These are discussed in the order indicated, beginning with the definition of the angler. Anticipating that the sophist will be hard to track down, the Stranger suggests that they practice their method on something easier. They should pick out something that is familiar, but less important, and use it as a paradigm (
 : 218D9; also 221C5) for the more important topic. The Stranger proposes using an angler as the subject of their practice definition. The definition begins with their positing (!  : 219A6) that angling is a skill or art (5  : 219A5). A twofold distinction is then made between arts such as farming, bodily care, construction, and imitation (  : 219B1), summed up under the title of productive art (J  : 219B11), and arts such as learning, mental discovery, commerce, fighting, and hunting, brought together under the name of acquisitive art (: 219C7). This listing of kindred arts under their respective titles constitutes a collection of the sort discussed in the previous chapter.2 After observing that angling is an art of the acquisitive sort, the Stranger divides acquisitive art into conquest and willing exchange, conquest into hunting by stealth and open combat, and so forth. Nine divisions of this sort are made in sequence before the angler is finally isolated, yielding a definition in terms of ten distinctive features.3 These ten features are indicated in Figure 3.2, arranged in order of successive divisions. As summarized by the Stranger at 221B–C, half of art is acquisitive, half of the acquisitive part is conquest, half of conquest is by hunting, and so forth.4

2 3

4

Although occurring only infrequently in the corpus, the term " (to sum up) at 219B11 appears to provide a synonym for "  in this context. The search for a definition of a practitioner of the art of angling (
" at 218E4) ends with a definition of the art itself (
" at 221C2). What gets divided as the definition progresses are kinds of skill, not kinds of people. But the result is easily convertible into a definition of the angler as such. The term , " (half ) occurs only once in this passage (221B3), but the grammatical structure indicates that division at each stage partitions things into halves. What dividing by half amounts to is not explained in the Sophist, but it seems natural to think of it as equivalent to cutting down the middle (  ) at 229B7 and cutting through the middle (  ) at Statesman 262B6. There is an attempt in Chapter 11 to pin down the sense of these expressions. Let it suffice for now to say that it does not amount to dividing things into equally numerous subclasses.

Division in the Phaedrus and the Sophist Art (

productive

)

acquisitive (

by exchange

)

by conquest (subduing)(

(open) combat

57

)

(stealthy) hunting (

inanimate objects

)

animal hunting (

land animals

)

water animals (

fowl

)

fish (

by enclosure

nocturnal

from above

)

by striking (

)

diurnal (barbing) ( from below 5 (= Angling,

)

)

figure 3.2. Definition of angling.

The obvious intent of this series of divisions is to arrive at a unique description of the angler’s art that distinguishes it from other arts that are similar in various ways. This is accomplished by adding features to the description at each stage of division that are possessed by angling but not by the other arts in question. Although all anglers practice an art that is in some ways acquisitive, for example, there are other arts that are acquisitive as well. Angling is separated from a sizeable portion of these (“half,” according to 221B3) by the second-level distinction between exchange and conquest, and so on as the line of division progresses. At each stage of the procedure as diagrammed, of course, angling remains confined within the right-hand portion, while arts other than angling are dismissed to the left. 5

In what sense is angling supposed to deliver a blow from below? The technique is explained at Ion 538D as a matter of sinking a sharp prong to the bottom and then yanking it upward when a fish is auspiciously positioned above – a procedure normally requiring daytime vision.

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Metaphysics and Method in Plato’s Statesman

By the end of the procedure, if properly pursued, angling has been “captured” by the set of right-hand features, and all kindred arts have been eliminated. The net effect is that angling has been uniquely characterized by that combination of features. All anglers are characterized by those features in combination, and all practices with those features are cases of angling. Because all anglers are characterized by that combination of features, each is a necessary feature of angling. And because any practice with all those features is an instance of angling, possession of these features in combination is sufficient for being a practitioner of that specific art.6 It is in this way that division, successfully pursued, leads to definitions of the sort the Stranger requires. For Plato, a definition expresses the essence (
 & A: 218C1) of the thing defined. The task of the remainder of the dialogue is to find a definition expressing the essence of the sophist.

3.3 The Possibility of Alternative Definitions The requirement that a definition express the essence or proper nature ( ( . . . 3 : 264E3–265A1) of the thing defined raises the question whether successful definitions of an activity like angling (or sophistry, or statesmanship) could be reached by alternative lines of division.7 If the Stranger’s series of divisions were slightly altered to eliminate the middle two features (animal hunting and hunting water animals), for instance, the resulting definition would seem no less adequate for leaving these out. This is because each of these two features is entailed by being a 6

7

To say that a definition expresses features that are necessary and sufficient for the thing defined is not to say that a definition should be expected to express all features of either sort. To show this in the case of sufficient conditions, it is enough to point to any of the five inadequate definitions of sophistry that follow. Each of these expresses features that in combination are sufficient for being a sophist but that do not appear in the final (successful) definition of sophistry. As far as necessary conditions are concerned, we should realize that there are many features necessary for the practice of angling that do not show up in the Stranger’s definition. Assuming that all fish absorb oxygen from water, for instance, it is a necessary condition for being an angler that one hunt animals that obtain oxygen in this fashion. And given the importance of fishing by daylight, it is necessary that angling be practiced by someone with sight. Because these features are entailed by others that appear explicitly, there is no need that they be cited for the definition to be successful. Other discussants of Plato’s method of division have recognized this possibility. For examples, see J. M. E. Moravcsik (1973), pp. 165, 172; and S. Marc Cohen (1973), p. 189.

Division in the Phaedrus and the Sophist

59

hunter of fish, so that they would still figure (implicatively) within the definition.8 A more substantive departure from the Stranger’s definition of angling might come with a division involving equivalent terms but in different order. Instead of distinguishing exchange and conquest at the third stage of division, suppose we were to divide acquisition directly into open and stealthy, stealthy acquisition into exchange (e.g., replacing a valuable painting clandestinely with a worthless copy) and conquest, and then stealthy acquisition by conquest into robbery and animal hunting.9 From there on the divisions would follow the order in the dialogue, yielding a definition in terms essentially the same as the Stranger’s save that animal hunting as a form of conquest by hunting has been replaced by animal hunting as a form of stealthy conquest. As an expression of the essence or nature of angling, the resulting definition seems no less apt than the original. Both specify features of angling that 8

9

The reason these two features are included in the definition as it stands may have to do with the apparent requirement that division split things down the middle. Dividing hunting (stage 4) directly into hunting fish (stage 7) and hunting other things (non-fish) would seem to be as lopsided as separating Greeks from non-Greeks at Statesman 262D. Pending further discussion of this requirement in Chapter 11, we should assume that it applies not only to the actual process of division but to the finished product as well. As far as the finished definition is concerned, explicit mention of animal hunting and hunting of water animals is nonetheless redundant. Removal of these redundancies does not reduce the definition’s effectiveness in separating angling from related activities. It remains necessary that an angler possess these two features, even though they are not cited explicitly. The division as altered to this point may be diagrammed as follows:

art

productive

acquisitive

open

stealthy

exchange

conquest

robbery

animal hunting

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Metaphysics and Method in Plato’s Statesman

are necessary and sufficient, regardless of the order in which they are mentioned. A possible objection to this rearranged definition arises from an alltoo-common interpretation of Platonic division according to which features cited earlier in the process are somehow more comprehensive than those cited later. One way of expressing this is in terms of classes and subclasses:10 as acquisitive art is a subclass of art in general, so the art of acquiring by conquest is a subclass of acquisitive art, and so forth. Another way of putting this is in terms of generality or breadth:11 art itself is more general than the art of acquisition, which in turn is more general than the art of conquest, and so forth. Perhaps the most common way of expressing this understanding of division, however, is in terms of the Aristotelian relation of genus and species.12 Art, on this reading, is a generic feature, production and acquisition are differentiae marking off species of this genus, and angling finally is an infima species – meaning a species not subject to further division. However expressed, the point is that the features cited in a proper definition are situated within a well-ordered hierarchy. In the Stranger’s definition of angling, art stands at the top of the hierarchy, followed by acquisition, conquest, hunting, and so forth. As a genus, art is the most general feature, establishing the class within which the various species are included as subclasses. Acquisition in turn is a differentiating feature, marking off a subclass of arts that has subclasses in turn, down to the subclass of angling, which is the least general of all.13 10

Thus Moravcsik (1973), p. 172, who writes with regard to the definition of sophistry: “Our generic class will be the class of all arts. One of the significant sub-classes of this class is the class of acquisitive arts. . . . [Next we] carve out a sub-class of the acquisitive arts, namely the acquisitive arts operating by exchange. This class is, of course, also a sub-class of the original generic class. We then repeat this procedure until we reach a class with only on element; namely sophistry.”

11 12 13

See also Nicholas P. White (1976), p. 120. What Moravcsik means by a class “with only one element,” White expresses as a class that “can no longer properly be divided.” For example, Nicholas White, ibid. For example, see Cornford (1935), pp. 270–71; Henry Teloh (1981), p. 182; and Constance C. Meinwald (1991), pp. 67–68. A seemingly natural way of diagramming this hierarchical arrangement is by a nest of concentric circles representing varying degrees of inclusiveness. In the case of the angler, art would be represented by the outermost circle, acquisition by the circle next to it, and then conquest, hunting, animal hunting, and so forth, down to the innermost circle representing barbing from below.

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The objection mentioned earlier to the alternative definition stems from this conception of an hierarchy among defining terms. If acquisition by conquest contains hunting as a subclass, then stealth (which distinguishes hunting from open combat) is less general than conquest among features of acquisitive art (see Figure 3.1). When the order of division is rearranged to make conquest a subclass of stealthy acquisition, accordingly, the less general appears to include the more general art. Given the constraints imposed by hierarchical division, a rearrangement of this sort is not permissible. But this conception of division as ordered by decreasing generality finds no support in Plato’s text and in fact seems contrary to the examples he has chosen. Let us look at some reasons why. As far as the definition of angling is concerned, there is no reason to consider art more general than acquisition in the first place (there are many forms of acquisition that are not at all artful). In the field of art at large, it is not clear that conquest is less general than acquisition (there are many artful sports, like boxing, involving conquest but not acquisition). Nor is it clear that stealthy art is less general than conquest (artful thievery typically does not involve force). What these observations show is not that Plato has made mistakes in his judgments of generality, surely, but that considerations of generality are not essential to the procedure of division. Another sign that something is wrong with the hierarchical interpretation is that it confines both open and stealthy acquisition to acquisition by conquest. But there are forms of both open and stealthy acquisition that fall under acquisition by exchange as well. Buying on the open market is an example of the former, whereas buying things that are illegal is usually done stealthily. Not only are the initial stages of the Stranger’s division not ordered by generality, but the features distinguished at a given level of division are not confined to just one branch of the division preceding.14 The indication once again is that Platonic division does not fit neatly within the Aristotelian mold.15 This is not to deny, of course, that the class of acquisitive arts is less inclusive than the class of arts generally or that artful acquisition by

14 15

In Aristotelian division by genus and species, coordinate genera have different differentiating features; see Categories 1b16–24. A more detailed criticism of the tendency to read Platonic division through Aristotelian lenses may be found in Sayre (1969), ch. 3, sec. 7.

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Metaphysics and Method in Plato’s Statesman

conquest is included among the acquisitive arts. Quite apart from the context of Platonic division, for any three (non-coextensive) properties A, B, and C, class AB is less inclusive than class A alone, and things that are ABC are included among things that are AB. As far as Platonic division is concerned specifically, the point is that the inclusion of acquisitive arts within the class of art generally is no more “natural” than their inclusion within acquisitive activities (artful and otherwise). Although AB is less inclusive than A itself, by the same token it is less inclusive than B as well.16 Theaetetus accepts the definition given of angling as adequate (K .: 221C4), with the Stranger’s implicit agreement. The foregoing considerations suggest that equally adequate definitions might have been reached through alternative pathways of division. The possibility that this is true generally becomes particularly relevant when we turn in Chapter 6 to the problem of relating the initial and the final definitions of statesmanship.

3.4 Five Faulty Definitions All five definitions of sophistry articulated between 221D and 226A pertain to a branch of acquisitive arts. In this respect, each definition is reached by divisions overlapping some part of the set of divisions leading to the definition of the angler. Sophist I employs the acquisitive art of subduing animals by stealth, differing from the angler primarily in hunting land instead of water animals. Sophists II, III, and IV employ arts of acquiring by exchange, unlike the angler who acquires by conquest. And sophist V, while dealing in an art that acquires by conquest like the angler, operates openly rather than by stealth. In Figure 3.3 below, each of these five acquisitive arts is characterized in a series of divisions picking up where it deviates from the line of divisions leading to the angler. The definitions shown in (b), it will be noted, are interactive in a rather complicated way. Sophist II is a wholesaler (
: 224D1) of mental wares produced by others, sophist III 16

Instead of representing the relation among features of a Platonic definition by an arrangement of concentric circles, it would be more suitable to represent the relation in the manner of intersecting Venn diagrams. In the case of the ten features involved in the Stranger’s definition, angling would be represented by the space in which all ten features (i.e., the figures representing them) overlap. A technique for representing an indefinite number of intersecting terms is developed in Anderson, Daniel E. and Cleaver, Frank L. (1965), pp. 113–18.

Division in the Phaedrus and the Sophist open

of land animals tame

wild by violence

pugnacious

friendly

by persuasion

physical

private

public

63

for amusement

private

public

for hire

for gifts

verbal controversy

expert (eristic)

inexpert

for improvement (= sophist I)

for pleasure

(a)

for profit (= sophist V)

(c) by exchange giving

selling

own products as retailer (IV) bodily wares

others’ products

as wholesaler (II)

as retailer (III)

mental wares for show

bodily wares

for learning

aiding expertese

aiding virtue (= sophists II,III,IV)

(b)

figure 3.3. Faulty definitions of sophistry (as acquisitive art).

a retailer (
# : 224E2) of the same wares, and sophist IV a seller (
 : 224E2) of mental wares produced by himself. Although each of the three could be laid out individually, this would result in needless redundancy. Moreover, Plato himself treats III and IV together as appendages to II, devoting less than one quarter of a Stephanus page to their articulation.17 Apart from saving space, however, diagramming 17

Although Plato numbers the five sophists in the manner shown in Diagram 3.3 at 231D, he groups III and IV together at 224E. This accounts for sophist V being listed as the sophist’s fourth appearance at 225E. The reason for this discrepancy is unclear. As the

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them together in the manner of (b) shows that these three lines of division involve subdivisions in both the left- and the right-hand direction. This is the first of two departures from the pattern of right-hand division that otherwise prevails in the Sophist. It should be noted in passing that all division nonetheless remain dichotomous. After the multipartite divisions in the Phaedrus, we do not encounter such again until well into the Statesman. In his discussion of these five definitions, Cornford suggests that sophists I and V correspond to Protagoras and the Megarians, respectively, and that sophists II, III, and IV can be found among other major teachers of the fifth century (presumably including Gorgias, Hippias, and Prodicus).18 Questions of identity aside, the definitions are realistic enough that someone practicing an art characterized by any one of them could easily be recognized as a sophist. In effect, each definition specifies features that in combination are sufficient to distinguish the sophistry they characterize from similar callings. On the other hand, none of the five definitions comprehends a set of features all of which are shared by all sophists commonly. All sophists engage in acquisitive art, to be sure. But some acquire by exchange and some by conquest, some conquer openly and some by stealth, and so forth. The very fact that the five definitions distinguish different forms of sophistry guarantees that there might be sophists not sharing the entire following schema shows, however, combining III and IV still involves division in both left- and right-hand directions.

by exchange giving

selling

own products ?

others’ products

as retailer

bodily wares

mental wares

for show aiding expertese 18

as wholesaler

F. M. Cornford (1935), pp. 173–77.

bodily wares

for learning aiding virtue

Division in the Phaedrus and the Sophist

65

set of features circumscribed by any given one. A consequence is that none of the five definitions encompasses features all of which are necessary for being a sophist. This means that none succeeds in explicating the sophist’s essence or nature. In considering the role of these five definitions in the dialectical strategy of the dialogue we should not overlook the fact that all turn out to be inadequate. The positive role of these initial definitions is to serve in a collection over several representative forms of sophistry. As detailed in section 3 of Chapter 2, this collection reveals that all sophists are engaged in one specific sort of productive art. The final definition of sophistry, accordingly, reverts to the initial division of art into acquisitive and productive and follows the latter branch to a successful conclusion at the end of the dialogue.

3.5 The Sophist of Noble Descent As summarized at 231B, the art of “the sophist of noble descent” (      : 231B7–8) is a branch of education (engaged in eliminating stupidity through learning), which is a branch of teaching (removing ignorance), which in turn is an art separating better from worse by way of purifying the soul. By near consensus of commentators with a view on the matter, this is a description of the art of elenchus, and Socrates is paramount among its practitioners.19 At any rate, the art is deemed the “greatest and most important of purifications” (230D8) essential for the happiness ( : 230E3) of any soul. Let us consider the line of division by which the definition of sophist VI is generated (see Figure 3.4). It is interesting to compare this definition of sophist VI with those of the angler and of the five previous sophists. Like that of sophists III, IV, and V, this set of divisions proceeds along both the right and the left. This is the second departure from the practice of exclusively right-hand division found elsewhere in the Sophist. Particularly interesting in this regard is the complete symmetry between left and right beyond the specification of arts that separate better from 19

For reservations about the identification of Sophist VI with Socrates, see Noburu Notomi (1999), sec. 2.3. The Stranger’s diffident treatment of this definition may be due to its coinciding with (or closely approximating) a skill practiced preeminently by a member of his audience. Whatever its intended reference, the definition is disputed ( - : 231E4) but nonetheless conceded ("5 : 231E5) to be accurate.

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Metaphysics and Method in Plato’s Statesman art combinatory

separative

like from like

better from worse (purification)

bodily living

inward

nonliving

outward

mental (soul cleansing) of wickedness (discord)

of ignorance (teaching) (disproportion)

technical training

education

medicine gymnastics (heals discord) (heals disproportion)

refutation (= sophist VI)

figure 3.4. Definition of the “noble sophist.”

worse. This suggests some kind of correlation between bodily and mental purification, a matter to which we return shortly. One consequence of the parallel development of both branches of purification is that the divisions in Figure 3.4 provide definitions of medicine and gymnastics (226E–227A) as well as of the elenctic art itself. In this respect, the definition of the “noble sophist” is similar to the final definition of statesmanship in the following dialogue, which also leads to definitions of several kindred arts. Another notable aspect of this definition is that it begins with a different subdivision of the arts than the one involved in the six previous definitions. There is no immediately apparent reason why the original subdivision into acquisitive and productive could not serve in this case as well. Productive art could be divided into combinatory and separative (e.g., carding, which produces wool ready for spinning), leading by the path in Figure 3.4 to noble sophistry as an art conducive to learning. A possible explanation of the new subdivision of art with which this definition begins is that it signals the exclusion of this form of sophistry from the collection in which the other five participate. This exclusion is necessary because sophist VI removes the ignorance that the other five produce. Whatever Plato’s intentions in this regard, the fact that art is subjected to two distinct subdivisions within less than eight Stephanus pages shows that there is nothing privileged about either subdivision. Because both lead to apparently successful definitions (the angler and sophist VII for the first, the noble sophist for the second), this indicates that the dialectical requirement of dividing according to Forms does not preclude different subdivisions for different purposes.

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It is particularly interesting to note, furthermore, that this definition incorporates no “technical” name for the art of purifying souls as such. Purification in general is called !, and teaching (the removal of ignorance) is called , but the purification of souls is referred to only by definite description (227C2–3). What makes this worth noting is that there is a similar division of arts applying to the body and to the soul at Gorgias 464B–C and that in this earlier context the art of purifying souls is given a “technical” name. In both contexts, treatment of souls is divided into two parts, corresponding to medicine and gymnastics as two forms of bodily treatment. The main difference between the two contexts in this regard is that the treatment of souls in the Gorgias is labeled “statecraft” (
), which is then subdivided into justice ( 3  : 464C1), corresponding to medicine as a physical therapy, and legislation ( ! : 464B9), corresponding to gymnastics. What corresponds to medicine in the Sophist, of course, is removal of discord or vice (228B8), whereas teaching is like gymnastics in removing the ugliness of ignorance (228D4, 229A8–9). Thus, the art of statecraft in the Gorgias parallels the art of purifying souls in the Sophist, with a more specific parallel between legislation and teaching. Roundabout as this comparison may be, it seems to throw further light upon the description of Socratic refutation as “sophistry of noble descent.” The Socratic art is a further specification of a kind of purification closely akin to the care of souls identified as statesmanship in the Gorgias. And statesmanship is one of the nobler arts (  ), so described at Statesman 261C9. In brief, the Socratic art of refutation is closely akin to the noble art of statesmanship – like sophistry in some respects, but nonetheless of noble kinship. This way of thinking about Socratic elenchus is further supported by Socrates’ description of himself in conversing with Callicles. I am the only one, he says, among contemporary Athenians to take up the true art of politics (; ? !.
; L5 :; Gorgias 521D7) – the only one to practice statesmanship (
 
  : 521D7–8). When Socrates hears the Stranger describe his skill as one of noble sophistry at Sophist 231B, we can imagine him as smiling agreeably rather than taking offense.

3.6 The Authentic Sophist Approximately thirty-four Stephanus pages intervene between the disclosure of the sophist as a producer of images (234E) and the end of the dialogue. Of these, only about seven are directly concerned with the final definition of sophistry. These latter are broken up into two sections.

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Pages 234–37 reveal the sophist as someone who produces imitations in the form of false discourse, which pertains to what is not the case. In the view of Parmenides’ dictum that what is not cannot be intelligibly thought or spoken of, the Stranger finds it necessary to establish the intelligibility of the practice they are trying to define. This takes up roughly twenty-seven Stephanus pages (237A–264B), treating such philosophically crucial topics as Being and not-Being, truth and falsehood, and the nature of dialectic itself.20 Having removed the barrier imposed by Parmenides, Theaetetus and the Stranger return to the task of defining the sophist, which occupies the remaining four pages of the dialogue. Our present concern is with the divisions that generate this final definition. The sequence of divisions producing the definition of sophist VII can be schematized as follows (Figure 3.5). This sequence of divisions, it may be noted, begins with the partitioning of art into acquisitive and productive at 265A4 (repeated from 219B–C) and proceeds through six additional steps before ending at 268B3 with the division of insincere practices into public and private. All cuts in the sequence occur within 20

These topics have been extensively discussed in recent literature. For my views, see Sayre (1983), pp. 218–38.

art acquisitive

productive (265A4)

divine

human (265B6)

making originals

copy making (266A10)

likeness making

appearance making (266D9)

by tools

by imitation (267A10)

knowledgeable mimicry

semblance mimicry (267E1)

candid

insincere (268A7) public

private (268B3) (= sophist VII)

figure 3.5. (The authentic) sophist VII.

Division in the Phaedrus and the Sophist

69

these three pages in the order indicated. The entire definition of sophist VII, accordingly, is achieved within the final moments of the dialogue. This is worth noticing because it runs counter to what is probably the standard way of reading this particular definition. According to the standard reading, the definition begins with the discussion of artful imitation ensuing at 234B, is interrupted by the defense against Parmenides from 237A to 264B, and takes up again at 264C.21 If we look carefully at what happens between 234B and 237A, however, we find reason for thinking that the Stranger’s remarks leading up to Parmenides’ challenge are preliminary to, rather than part of, the final definition. One obvious consideration is that there is no distinction between divine and human production before 265B. Furthermore, although a distinction between production of originals and production of images may be implied when the Stranger starts talking about imitation at 234B, this distinction is not made explicit until 266B. The only distinction made prior to 237A that shows up in the final definition is that between the making of likenesses and the making of appearances. And even that distinction remains muddy in its initial treatment. Let us see why. The Stranger begins his discussion of sophistic deception by drawing attention to the art of imitation (   : 234B2), but almost immediately starts talking about the production of spoken copies (0   : 234C6) instead. Throughout this discussion the terms   (imitation) and (
 (copy making) are used interchangeably. At 235B, for example, the Stranger sets about to divide the art of copy making ((
 : 235B8), and ends up with what he calls two types of imitation (  : 235D1). Then, once the division has been elucidated in terms of imitation (236B1, C1), he returns to the former expression in reporting the results. Thus, he remarks at 236C6–7 that the two types of copy making ((
: 236C6) in question are likeness making and the making of appearances (( )   : 236C7). Although use of synonyms should be unobjectionable in itself, a problem arises with the fact that imitation is two levels below copy making in the final system of divisions (Figure 3.5). An associated problem is that, whereas appearance making is represented as a part of imitation at 236C, in the final divisions imitation is part of appearance making instead. There is a similar problem with the way likeness making figures into this mix. At 236C, likeness making is subordinate to imitation. In the 21

Thus, for example, Cornford (1935), p. 197.

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Metaphysics and Method in Plato’s Statesman

final set of divisions, however, likeness making is separated on the left from appearance making on the right. And because imitation falls under appearance making, it is separated from likeness making as well. The upshot of these discrepancies, as I read it, is that the several forms of image making in question are treated differently before and after the Stranger’s response to Parmenides’ challenge. This response is not an interruption of an ongoing definition as the standard reading maintains. Rather, the final definition begins once the response has been completed. The Stranger’s discussion of image making between 234 and 237 is primarily an introduction to a range of problems that must be solved before the final definition can begin. As we shall see in returning to the Statesman later, there is a similar relation between the initial definition of statesmanship terminating at 276E and the final definition beginning at 287B. The former discloses issues that must be faced before a successful definition can be initiated, whereas the final definition begins afresh once these issues have been resolved.

3.7 The Final Definition Immediately before entering into the series of divisions leading to the final definition, the Stranger describes the method ( ! ": 265A2) they are about to follow. They are to “cut the Kind they have laid down into two” (56  5; #
 !L  : 264D10–E1), “always following the right-hand part of the cut” (
3!   
)   )    %  !  : 264E1–2). In this manner, they are to hold onto characteristics in which the sophist partakes, until they have stripped off (
 : 264E3) all he has in common with other things. This will leave behind “his own proper nature” ( ( . . . 3 : 264E3– 265A1). The proper nature of the sophist is revealed in the ensuing set of divisions (Figure 3.5), as summarized in the Stranger’s final speech (268C8–D4). This description stresses two methodological guidelines that for the most part have been observed through the Sophist. One is that division should be dichotomous. As indicated by a quick review of Figures 3.2 through 3.5, division in this dialogue has been dichotomous without exception. The other guideline calls for making cuts along the right as the series of successive divisions progresses. Although this guideline is observed for the most part, two exceptions have been pointed out earlier in our discussion. One is shown in Figure 3.3(b), where division both of selling one’s own products and of selling products made by others

Division in the Phaedrus and the Sophist

71

continues in both leftward and rightward directions. The other exception is evident in Figure 3.4, where purification is further divided along both the right and the left. In the context of the Sophist, at least, it appears that the norm of dichotomous division is the more strict of the two methodological requirements. As already noted in Chapter 1, both guidelines remain in place up through 276E of the Statesman. But both are set aside in the final definition of statesmanship, as we shall see in Chapter 6. Before returning to the Statesman, however, we should consider a further indication of the relative unimportance of the right-hand requirement. The Kind said to be laid down at 264E1, of course, is that of art, which immediately thereafter is divided into productive and acquisitive. This division of art serves as the beginning of all definitions in this dialogue save that of the noble sophist. Let us combine these definitions in the following fashion (Figure 3.6).

art productive

acquisitive conquest

exchange

human

(II, III, IV) copy

appearance

selling (IV) own (III, IV)

imitation

retail

(II, III) others’

open

stealth

pugnacious

living

(II) wholesale

verbal

land

water

tame

fish

(II, III, IV) semblance

mental

private

insincere

learning

expert

private (= sophist VII)

virtue (= sophists II,III,IV)

persuasion striking

profit (= sophist V)

private

day

hire

below (= angler)

improvement (= sophist I)

figure 3.6. Overview of seven definitions.

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Metaphysics and Method in Plato’s Statesman

This diagram shows that when these several lines of division are collected together, it is arbitrary to view any one of them as proceeding exclusively in the right-hand direction. The divisions leading to the angler are rightmost in Figure 3.6 as it stands. But a mirror-image reversal would put sophist VII in that supposedly privileged position. Moreover, if the schema is reconfigured to bring sophist I to the right, all the other definitions involve leftward divisions. The same holds, mutatis mutandis, for sophists II through V. This duly observed, we should be prepared for the abandonment of the right-hand requirement when we return for a close look at division in the Statesman.

4 Collection Yields to Illustrative Paradigms

4.1 Platonic Uses of the Term
  Use of
  in the standard sense of example can be found throughout the corpus. In the Apology, Socrates suggests that the oracle’s pronouncement about none surpassing him in wisdom is a matter of singling him out as an example (
 : 23B1) to illustrate the wisdom of recognizing one’s own ignorance. In the Phaedrus, he cites his speeches on love as providing an example (
 : 262D1) of how a knowledgeable orator can mislead his audience; in the Philebus, he alludes to examples (
 : 13C8) of pleasures being at odds with one another; and so forth. While there is nothing idiosyncratic about Plato’s use of
  in the sense of example, there is another use of the term in several middle and late dialogues that is distinctly Platonic. For example, Socrates declares in the Republic that the philosophic rulers shall look upon the Form of the Good as a pattern (
 : 540A9) for the right ordering of the state. At Theaetetus 176E3, he speaks of patterns (J  ) of happiness and misery as making a stand in reality. Timaeus, in his namesake dialogue, identifies “patterns that are intelligible and always the same” (
   . . . # ) )  % $ : 48E5–6). And the youthful Socrates, at Parmenides 132D1–2, expresses confidence in Forms as patterns (
 ) fixed in nature. As each passage makes clear in its own way, the term
  in this second sense serves as an alternative designation for Forms or Ideas. But even this sense is not entirely novel. Inasmuch as Forms can be thought of as

73

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ideal exemplars, this second sense amounts to an extension of another common use of the term as pattern or model. A third and apparently novel sense of the term emerges in the Sophist and the Statesman. In neither of the more familiar senses just mentioned is the term’s meaning directly bound up with the dialectical process. Examples are employed in the procedure of collection, to be sure, but use of the term in the sense of example is not limited to that employment. And although knowledge of ideal exemplars can be understood as the aim of dialectic, the term carries the sense of pattern or model in many other contexts as well. In this third sense of
 , on the other hand, to serve as a paradigm ipso facto is to be involved in dialectical procedure. Let us label this the “dialectical sense” of the term. While the dialectical sense of
  is found only in the Sophist and the Statesman, moreover, different patterns of use prevail within the two dialogues. As detailed in section 4.2, the Sophist contains three uses in this special sense, along with three other occurrences with the common meaning either of model or of example. In the Statesman,1 by contrast, there are more than a dozen occurrences, in all of which the term carries the dialectical sense. The primary task of this chapter is to gain a clear overview of the role of paradigms in the dialectical method employed in the Statesman. One thing we shall find in the process is that the method of dialectic practiced in the Statesman differs substantially from its counterpart in the Sophist. The major difference, in a nutshell, is that the role played by collection in the earlier dialogue is taken over in the later by the use of paradigms. To prepare ourselves for an examination of this shift in procedures, we turn next to the role played by paradigms in the method of the Sophist.

4.2 Paradigms Augmenting Collection in the Sophist Having undertaken to define the nature of the sophist, the Stranger proposes trying out the method he intends to use on some lesser subject that will serve as a paradigm (
 : 218D9). In the definition of angling that ensues, as we have seen, the Stranger begins with a 1

Differences in meaning aside, the term
  appears in a majority of Plato’s dialogues. Not surprisingly, the longer dialogues tend to have more occurrences (e.g., seventeen in the Laws, fifteen in the Republic). The largest number of appearances per page, however, is scored by the Statesman, with one occurrence on the average in every four pages (the Timaeus is next, with one in six).

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distinction between productive and acquisitive arts and with a survey of specific arts within the latter class – fighting, hunting, and trading, along with learning. This survey constitutes a collection over the acquisitive arts (see section 2.3) in which angling will show up as another member. The term
  occurs a second time in this sequence at 221C5, where the Stranger suggests that they follow the paradigm of the angler, which has just been completed, and proceed by looking into the nature of the sophist himself. As the Stranger observes to his evident satisfaction, the angler and the sophist share a number of features in common. The first definition of sophistry then proceeds with the division of animals hunted by land into wild and tame and pursues the latter branch to its (ultimately unsuccessful) conclusion. There are various things to note about this choice of angling as a paradigm for sophistry. One is that it is indeed a paradigm in the dialectical sense, as distinct from an example or an ideal pattern. Although angling and sophistry are both examples of acquisitive art, angling is not an example of sophistry as such. Nor is angling in any sense an ideal which the sophist might approximate. As the Stranger makes clear, the point of adopting the angler as a paradigm is to enable a trial run of the dialectical method to be used thereafter in defining the sophist. The paradigmatic relation between angling and sophistry, in brief, is entirely dependent on the dialectical context. This ties in with another aspect of the relation between angling and sophistry that is emphasized by the Stranger in introducing the paradigm. Compared with sophistry, angling is a trivial (3 : 218D8) calling. This is enough to ensure that angling is not an example of sophistry. If it were, it would not be trivial, inasmuch as sophistry is very important ( 6  : 218E3). Being unimportant (  : 218E3) as it is, moreover, angling cannot relate to sophistry as an ideal to be approximated. One thing that goes radically wrong with the initial definition of statesmanship in the next dialogue, we recall, is that it relies implicitly on the model of a divine shepherd who nurtures his flock. The hazards of inflated models like this, we are given to understand at Statesman 278E, can be avoided by choosing paradigms that are small ( 
: 278E6) and insignificant (  : 278E8). To repeat, angling is not a paradigm for sophistry in the manner of providing an example or model. Angling is a paradigm, rather, in providing the topic of a dialectical examination illustrating how the sophist should be examined in turn. As we shall see presently, the paradigm of angling in the Sophist serves much the same role as the paradigm of weaving in

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the Statesman. Both provide dialectical guidelines for the examination of the more important topics that follow. Another thing to note about the paradigm of angling is that it functions in cooperation with the process of collection rather than in any way replacing it. As we have seen, the definition of the angler’s art itself begins with a collection over the field of acquisitive arts in general. The dialectical procedure illustrated with the help of this paradigm incorporates a collection of the sort called for in the Phaedrus. As might be expected, the same cooperative interaction between paradigm and collection is involved in getting the subsequent definition of the genuine sophist underway. Chapter 2 laid out the details of the collection leading to the successful definition of sophist VII. By way of summary, the collection consists of the Stranger’s identification of five distinct forms of acquisitive sophistry and his observation that all five engage in the production of images. Another paradigm (
 : 233D3) comes into play in the latter stage of this collection. The paradigm in this case is that of someone who professes the ability to produce all things by a single skill. As far as the paradigm itself is concerned, the relevant skill is illustrated by the painter who can reproduce anything in graphic form. Guided by the paradigm of artful imitation, the Stranger dubs the skill in question “the art of image making” ( (
 5  : 235B8–9) and proceeds to trace out the sort of image-making practiced by the sophist specifically. Here again we find a paradigm cooperating with the process of collection. In the first case, a collection over acquisitive arts initiated the paradigmatic definition of the angler. And in the present case, we have a paradigm playing an integral role in a collection over forms of sophistic image making. In light of the replacement of collection by use of paradigms in the subsequent dialogue, to which we turn presently, it is noteworthy that this development is not foreshadowed in the Sophist. There are three other occurrences of the term
  in the Sophist, none carrying a sense relating it directly to dialectic procedure. This despite the fact that one occurrence appears in the context of a collection underway. As a preliminary step in defining the “sophist of noble descent,” the Stranger lists various arts involved in separation – filtering, straining, winnowing, and so forth – leading Theaetetus to question the point of all these examples (
 : 226C1). The Stranger’s response is that all are forms of dividing, whereupon he groups them under the general label “art of discrimination” (M : 226C8).

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This marshalling of examples, of course, serves as a collection providing direction to the subsequent process of division that culminates in an apparently successful definition of Socratic elenchus. Yet although each example contributes to the collection, none serves as a paradigm in the sense that angling is a paradigm for the art of sophistry. The remaining two occurrences are at 235D8, where the Stranger refers to an artist’s model as a
 , and at 251A7, where Theaetetus asks for a
  (example) of something remaining the same although called by different names. Neither of these latter is germane to dialectical procedure as such. By way of summary, three of the six occurrences of the term
  in the Sophist refer to paradigms of a sort capable of cooperating with collection in providing guidance to dialectical division. Given the way they are used, these paradigms show no sign of being able to replace collection in its dialectical role. A fourth occurrence conveys the standard sense of example. The examples in question (filtering, winnowing, etc.) contribute to an ongoing collection, but this role is incidental to the sense of the term. The remaining two occurrences are devoid of dialectical significance.

4.3 A Paradigm to Illustrate the Use of Paradigms Chapter 1 brought us to the end of the first attempt in the Statesman to arrive at a definition of the kingly art. When YS expresses satisfaction with the result (277A1–2), the Stranger points out that the account thus far, although superficially adequate, lacks the vividness of a finished product. The underlying problem is their assumption that the kingly art called for grandiose paradigms ( 
 : 277B4), in this case that of a divine herdsman. A new paradigm is needed to direct their inquiry down a more auspicious path. In his response to YS’s request for an explanation of why the account is defective, the Stranger begins with an observation strongly reminiscent of recollection in the Meno, where the slave’s newly evoked beliefs are described as having a dreamlike (N
 $ : 85C9) quality. As the Stranger observes, when we venture as in a dream ( O $ : 277D3) to think we know everything, we wake up with the realization that we know nothing at all. This is why we cannot demonstrate such important things (as statesmanship) without use of paradigms (
 : 277D1).

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When asked by YS what he means, the Stranger responds as follows: 277D9 277E

278A

278B

278C

Paradigm itself, my worthy fellow, for my part has need of a paradigm in turn. How so? Speak on, and don’t hold back for my sake. Speak I will, since you are so ready to follow. I suppose we realize that young children, when they are just becoming acquainted with the alphabet – What’s this? That they distinguish each letter well enough in the shortest and simplest syllables, and gain skill in perceiving what is true about them. How not? On the other hand, they are doubtful about the same letters in other syllables, and both judge and speak in error about them. Entirely so. So isn’t this the easiest and best way of leading them to what they don’t yet understand? What? Take them back first to the cases in which they were judging the same letters correctly. Having done that, then put these beside the syllables they do not yet recognize, and by comparison show the same structure equally present in both combinations – until ones that are judged correctly have been displayed next to all the unknown ones. Displayed to this end, the former become paradigms, and bring it about that each and every letter in all the syllables is called both different, insofar as different from the others, and the same, insofar as always the same and identical with itself. Altogether so. So have we not grasped this point sufficiently, that a paradigm comes into play whenever the same thing [as in the original case], correctly understood in another separate case and brought together [with the original case], yields a single true judgment for each as for both together? So it seems.

As is often the case in his discussions of methodology, Plato’s language here is highly elliptical. But the sense of the passage seems fairly clear.

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The recommended procedure begins with a situation in which certain letters are easily recognizable by the student in some contexts but not in others.2 Upon encountering an instance in which the student cannot recognize a letter’s occurrence in a given syllable, the teacher finds other occurrences of the same letter in syllables the student already knows how to spell. Showing the familiar in juxtaposition with the unfamiliar, the teacher indicates to the student their identical configuration. Successfully pursued, the result of this process is that the student’s ability to recognize this configuration in familiar contexts is transferred to contexts that were previously unfamiliar. The configuration in a familiar context serves as a paradigm by which its appearance in a novel case can be illuminated. Whereas the student before was able to make true judgments about its identity in familiar cases only, he or she now is capable of identifying it in the previously unfamiliar case as well. In the language of 278C, the student is now able to identify the letter in a single true judgment covering both cases together and each case individually. Prior ability to judge correctly in the paradigmatic case has been extended to a case in which it was previously lacking. To assist the learner in this way, needless to say, the teacher must be able to come up with paradigms the student will find helpful. This means that the teacher must know enough about the student’s situation to know which letters are causing difficulty. But it also requires knowing what familiar words or syllables would be appropriate for the learning task at hand. The teacher must be able to choose examples that will serve the student effectively as paradigms. What are the requirements for an effective paradigm? In the case of learning one’s letters, the requirements are relatively straightforward. Suppose that YS, at an even younger age, is having trouble recognizing the omega in the first syllable of
 , but knows how to spell his own name P. An obvious instructional tactic would be for the teacher to point out the first syllables of the two words together, indicating the occurrence of omega in each. One thing that 2

A parallel situation is envisioned in the final pages of the Theaetetus (207D–E), where Socrates and Theaetetus discuss the case of someone just learning to read and write who spells the same syllable sometimes with one letter and sometimes with another. An example mentioned is Theaetetus as a child spelling the first syllable of his name with a theta but the first syllable of ‘Theodorus’ with a tau. The point illustrated by the example is that an account consisting of an itemization of elements in a particular isolated case is not enough to turn true judgment into knowledge.

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makes the occurrence in his own name a suitable paradigm, of course, is its familiarity to the learner. Let us call this requirement (1). Another requirement is that the paradigmatic occurrence be comparable in nature to the occurrence of the letter causing difficulty. Allowing for differences in handwriting and the like, the two occurrences may not have identically the same configuration. But the paradigmatic occurrence at least must exhibit features that are typical of the letter in question. The paradigm need not have the same slant as the troublesome letter or be inscribed in the same medium with the same breadth of line. What is required is that the paradigm share features with the original letter that are responsible for both being inscriptions of the same letter. Requirement (2), in brief, is that a suitable paradigm share with the thing being learned salient features that are essential to the latter’s nature. Looking ahead to the topic of the next chapter, we can see that both requirements are instrumental in the choice of weaving as a paradigm for statesmanship at 279B. This choice is suitable not only because weaving presumably is more familiar to the audience than statesmanship itself (requirement (1)). Its suitability also rests on the fact that it involves an intertwining of contrasting components (warp and woof ) comparable to the statesman’s intertwining of courageous and well-behaved natures. Because intertwining of this sort is an essential part of both weaving and statesmanship, the paradigm of weaving meets the second requirement as well. To highlight the point, consider the case of a king who is given to providing entertainment for his people in the form of athletic contexts and who has become known for his knack of organizing panhellenic games. Inasmuch as this particular knack is not essential to kingship, however, the practice of organizing games would not serve as a suitable paradigm. When the Stranger casts about at 279A for a paradigm that involves the same undertakings (
  : 279A8) as the statesman, we understand that he is looking for a comparable art that exhibits features substantially implicated in both.3 As it turns out, weaving not only involves an intertwining of disparate components of the sort essential to statesmanship, it exhibits other features that are essential to both arts as well. In particular, both are skills applied directly to their products, rather than contributing in some indirect fashion (see 281D11 for weaving, 287B7 for statesmanship). Other shared features are their use of 3

Sense II, 2 of
C  in “Middle Liddell” (1983) is “anything necessary or expedient” to an activity.

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contributory arts (281D10, 287B7) and their provision of services in the care of human society (passim). Another requirement, noted previously, is that the paradigm should be less significant than the primary topic of inquiry. This requirement (3) is not illustrated in the paradigm of the grammar student, but it is stressed both directly before (277B) and directly after (278E) the Stranger’s presentation of that paradigm. It was also emphasized, we recall, when dialectical paradigms were first introduced in the Sophist (218D–E); we shall encounter it again at Statesman 286B1–2.

4.4 The Importance of Verbal Paradigms There is yet a further requirement to be met by dialectical paradigms in particular. This requirement is briefly mentioned at 277C4–6 and then discussed at greater length at 285D10–286B2. Although the latter passage has attracted more attention among commentators, it is better for our purposes to begin with the former. The first passage comes immediately after the Stranger’s remark that the initial definition lacks the vividness sometimes achieved by pigments and the mixing of colors. As his next observation (277C4–6) makes clear, however, the present defect will not be remedied by means of more subtle portraiture as such. Here is that observation quoted in full: For those able to follow, it is more suitable to make every subject of depiction (6
)4 manifest by means of speech and discourse rather than by painting and manual crafts; although for others, manual crafts are more suitable.

The Stranger’s next speech contains the remark, cited at the beginning of the previous section, that the demonstration of very important things requires the use of paradigms. The speech at 277C4–6 says that discourse is the preferred way to exhibit things for those who can follow it. The subsequent speech says that it is hard to exhibit very important topics without using paradigms. Together, these passages convey the advice that verbal paradigms are required for the clarification of very important things – things with the stature of a king or statesman. This we can identify as requirement (4) for an effective paradigm. 4

The term 6
here is usually translated ‘animal’ or ‘living thing’. As indicated in LSJ (1968), however, in contexts of portraiture like painting and sculpture, the term can be synonymous with 3
, carrying the sense of figure or image generally. Thus the translation ‘subject of depiction’ at 277C4.

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Although there is nothing about dialectic as such in the paradigm of the grammar student, there are resonances in these passages that bring this philosophic enterprise to mind. First and foremost, the search for the statesman underway is a dialectical exercise, and we are told here that it requires the use of verbal paradigms. Verbal paradigms, for another thing, rely on competence in language, and the paradigm of the grammar students depicts someone in the process of gaining linguistic competence. We should not forget, moreover, that the characterization in the Sophist of the dialectician as someone capable of “dividing according to Kinds” (   '!: 253D1) was developed explicitly on the analogy of the art of grammar ( : 253A12). Inasmuch as YS was present at that earlier conversation, when the Stranger presents him with the paradigm of someone learning grammar in the current context it is not far-fetched to imagine him connecting that paradigm with his own situation as a learner of dialectic. In the longer discussion at 285D–286B, on the other hand, the connection with dialectic is explicit. In point of fact, this discussion follows immediately on the heels of the Stranger’s surprising revelation that the purpose of the dialogue is to produce better dialecticians. This passage also merits quotation in full. 285D10 But I think most people fail to notice that, on the one hand, some things are naturally provided with certain sensible 285E images that are easily understood, and not at all hard to point to when someone wants to give an easy demonstration 286A of these things to someone requiring an account that is uninvolved and free of language. For things that are greatest and most valuable, on the other hand, there is no image clearly evident to mankind, by display of which one might adequately resolve to satisfy the mind of an inquirer through means adapted to the senses. That is why we must exercise the ability to give and to receive an account ( ) of each thing. For the best and greatest things are incorporeal (* ), and can be clearly explained by discursive means (7) alone and none other. All we are saying now 286B is for their sake. In matters like this, however, it is always easier to practice with lesser than with greater things. The main distinction made in this passage is not hard to grasp. It has to do with the means available for explaining (demonstrating, setting forth; conveyed by   ! at 285E4 and  " at 286A7) certain topics,

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and in particular with the availability of sensible likeness. On one hand are topics easily illustrated by sensible images available in the normal course of events. Because images of this sort themselves are easy to grasp, they provide explanatory paradigms responsive to the needs of learners unequipped to follow complicated verbal accounts. On the other hand are topics for which sensible images are not naturally available and which hence cannot be explained “by means adapted to the senses” (
# . !*  
   : 286A3). Among such things are subjects that are “best and greatest” ( . . . ) : 286A5–6), which accordingly can be explained by discursive means alone. Because of the importance of these incorporeal subjects, the Stranger continues, we must exercise our ability both to give and to understand discursive explanations. All we are saying now – the present conversation ( %   : 286A7) – is aimed at practicing this activity. By way of afterthought, the Stranger returns to a familiar theme in remarking that practice of this sort is always easier when we chose discourse “about lesser rather than greater things” (
 C /
)  6: 286B1–2) for our verbal paradigms. Although there is nothing initially puzzling about the distinction itself, Plato has left it obscure what topics are supposed to fall under either heading. Among likely topics that can be illustrated by sensible images, one can assume, are the alphabetical symbols the student is trying to master in the instructional sessions described at 277E–278C and alluded to at 285C. The paradigms used for such purposes are sensible instances of the same symbols the student already understands in more familiar combinations. Other such topics, perhaps, will be arts such as clothes mending, carding, and spinning, involved in the definition of weaving itself. Topics that are “best and greatest” and that accordingly do not admit perceptible paradigms, on the other hand, presumably include Forms like the Good, the Beautiful, and the Just. One might plausibly consider the account of the sun at Republic 507A–509D to be a paradigm for the Good.5 There should be some sense in which Diotima’s discourse in the Symposium serves as a paradigm for the Beautiful. And one would think that the discussion of justice-in-the-state found in the Republic constitutes an illustrative paradigm for Justice itself. A case closer to hand is the topic 5

The sense in which the account of the sun might count as a paradigm for the Good is that of the Statesman, not that of the Republic itself. We should not forget that the term
  as used in the Republic generally refers to “best and greatest” things per se, rather than to paradigms useful in understanding them. For example, the Good itself is said at 540A8–9 to be a paradigm for the right ordering of the state and its citizens.

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of sophistry, explicitly said to be greater than its paradigm at 218D9 of the previous dialogue. Then, of course, there is the case of the statesman. Here is a topic explicitly said to be of greatest importance (  at 278E8, the same term as at 286A6), with the seeming result that it cannot be demonstrated by easily understandable sensible likenesses. But for someone recently confounded by the disclosure at 285D that the present conversation is not primarily about statesmanship, the status of this topic might seem to be less than crystal clear. Not only does statesmanship appear to have been upstaged by the topic of dialectic,6 but moreover the Stranger has chosen weaving to serve as its paradigm. An apparent problem in this regard is that weaving is an activity open to inspection by the senses. If statesmanship indeed is among things that are “greatest and most valuable” (285E4), then how could it have “sensible likenesses that are easily understood” (285D11–E1)? The problem, however, is only apparent. Merely having sensible likenesses does not ensure that these likenesses are useful in demonstrating the thing in question. The Stranger’s distinction in this passage is not just between things that are outstandingly important and things that have sensible likenesses. It is instead between things that have sensible images that can be pointed to by way of providing easy explanations and other things that can be explained only with the help of verbal accounts.7 Although the latter nonetheless might have sensible likenesses (the sun is said to be the 6

7

Inasmuch as dialectical skill is explicitly identified with philosophy at Sophist 253E4–5, it may also appear that philosophy has replaced statesmanship as the main topic of the dialogue. This runs counter to a common reading of the opening conversation according to which the philosopher is set aside for a subsequent conversation between older and younger Socrates (which happens never to have been written). As a careful reading of the opening will indicate, however, although the elder Socrates said he would converse with YS on another occasion, he does not say that philosophy would be the topic. Theodorus’ first speech suggests that the Stranger himself would deal with both the statesman and the philosopher, and there is no apparent reason why both might not be dealt with on equal footing within the same dialogue. In “Plato on the Undepictable” (op. cit., p. 360), Owen states that “the dichotomy of depictable-undepictable is drawn within the range of things that can be explained, that have a logos.” This seems at odds with the text. The Stranger refers at 285D9–E4 to things with sensible images that can be pointed to when someone wants an explanation (demonstration) that is free of language (5)  "), and goes on in the very next passage to contrast such things with other things that are greatest and most valuable and that can be explained only by a verbal account ( at 286A4, 7  at 286A6). The dichotomy is drawn within the range of things that can be demonstrated and comes down to a distinction between things that can be explained (through sensible images) without logos and things that can be explained only with logos.

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likeness of the Good at Republic 506E4), such things cannot be explained merely by drawing those likenesses to someone’s attention (looking at the sun does not explain the Good). Such things are likely to be both incorporeal and of utmost worth as well. Again, however, the distinction does not hinge on their incorporeality or relative worth, but on the fact that they are explainable only by discursive means. Returning to the sensible status of weaving with this in mind, we see that the visibility of the activity chosen as a paradigm for statesmanship is largely irrelevant. The dialectician could not simply point to someone engaged in weaving, without commentary or discussion, and expect much help in explaining the nature of the statesman’s art. To be sure, the activities of weaving are like those of statecraft in many relevant ways (279A7–8). This is what makes weaving a suitable paradigm for statesmanship in dialectical inquiry. But these activities must be described in a certain manner to be of any use for dialectical purposes. Strictly speaking, it is the discursive account of weaving that provides the paradigm to be followed in pursuing the definition of statesmanship, rather than the (observable) activity of weaving itself. This is why we must exercise our ability to give and to receive verbal accounts. For things that are “greatest and best” can be explained only by discursive means. It is for the sake of such things, the Stranger says, that the present dialogue is being conducted (286A7). The art of statecraft most certainly is included among these superlative things. When the Stranger and YS return to the definition of this art at 287B, their eventual success is due to the availability of a discursive account of weaving as a paradigm.

4.5 Paradigms and Necessary Conditions The Stranger’s remark at 277D, that demonstration of very important things requires the use of paradigms, is followed by an image likening a self-deceiving lack of knowledge to a dreamlike state. As he puts it, whereas we seem to know everything in a dreamlike way, when awake we seem to know nothing at all. This image in turn leads directly into the account of the grammar student that is intended to illustrate the use of paradigms. The student initially is able to recognize a given letter in familiar syllables (the paradigms) but not in others. The role of paradigms in this account is to help the student arrive at true judgment (!   : 278C6) in cases that were initially unfamiliar and eventually achieve knowledge (
 : 277D7) in that regard.

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At the beginning of section 4.3, it was suggested that the grammar student’s initial dreamlike state can be likened to the dreamlike awareness of the slave boy in the Meno following his questioning by Socrates. As a result of this questioning, the boy has been led to true judgments (!'  : 85C7) regarding the relation between the area of a given square and that of a square on its diagonal, but has not yet reached a state of knowledge. These judgments at present have a dreamlike quality (N
 $ : 85C9). But as Socrates points out, if questions like those he has been asking are put to the boy repeatedly in the future, the latter will end up knowing (
: 85D1) that topic as accurately as anyone. It is in this sense, Socrates tells Meno, that the retrieval of knowledge within oneself amounts to recollection (   !: ; 85D7). In the Statesman, the learner’s dreamlike state gives way to knowledge as a result of the effective use of paradigms. In the Meno, progression from a dreamlike state to a state of knowledge is achieved by means of recollection. Substantially different as they are in other respects, the use of paradigms and the process of recollection play roughly equivalent roles in their respective contexts.8 Both incline the student’s mind in the direction of knowledge. Recollection is linked with collection in turn within the context of Socrates’ palinode in the Phaedrus. As observed in Chapter 2, the first mention of collection comes at Phaedrus 249B7–C1, where it is described as a matter of “going from many perceptions to a unity” brought together by reasoning (section 2.2). This process of understanding, Socrates says, is a recollection (  : 249C2) of things previously perceived by the soul while in the company of a god. In a subsequent mention of collection in the Phaedrus, it is explicitly paired with division (266B4) and said to be the business of dialecticians (266C1). Socrates’ apparent identification of collection with recollection at 249C2, of course, must be understood with substantial qualification. One major difference between them is that collection is not bound up with a preexisting soul as is recollection. This and other differences aside, however, both processes situate the mind in a position conducive to the onset of knowledge. With respect to their status as methodological aids, the role played by recollection in the Meno and the Phaedrus is comparable to that played by collection in the Sophist. 8

Kato (1995), p. 167, relates these two passages by observing that the dream metaphor is used in both “in exactly the same way, i.e., to describe the acquisition of a true belief as that of knowledge in a dream.”

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In this brief review of passages discussed previously, we see distinct methodological overlaps between recollection in the Meno and the use of paradigms in the Statesman, on one hand, and between recollection in the Meno and collection in the Sophist on the other. As far as the overlap between collection and the use of paradigms is concerned, moreover, we have found both processes working cooperatively in the Sophist (section 4.2). Each in its own context, the process of recollection, the procedure of collection, and the use of paradigms play very similar roles in philosophic inquiry. Let us attempt to pin down precisely what these three methodological operations have in common. For one thing, none is capable by itself of bringing an inquiry to completion. This is clear with both collection and the use of paradigms. The collection performed by the Stranger over different varieties of sophistry reveals that all employ an art of production, but this does not constitute a definition of the authentic sophist. To bring the paradigm of weaving to bear in the Statesman, similarly, is only the beginning of a successful inquiry into the statesman’s art. A further procedure is needed to complete the inquiry in both cases, consisting of a stagewise division according to relevant Forms. The status of recollection in this regard is more ambiguous. Whereas both collection and the marshalling of paradigms are followed by a subsequent series of divisions, Plato seems not to have thought of recollection itself as part of a two-stage procedure. Strictly speaking, recollection is not a methodological technique in the first place but rather a way of explaining how inquiry (learning) can arrive at a successful conclusion. The only demonstration of recollection in the dialogues is found in the interaction between Socrates and the slave boy, and in this instance the interchange between teacher and learner appears essential. The part of the process that involves a two-stage procedure is the conduct of this interaction rather than recollection itself. As illustrated in the slave-boy sequence, the teacher’s first task is to relieve the learner’s mind of false belief, something accomplished by the process of elenchus (the business of sophist VI). This is followed by a process of calculated questioning, leading first to true opinion and eventually to knowledge.9 Recollection 9

This process of questioning itself seems to involve two stages, neither of which Plato provided with an explicit designation. First comes the series of questions leading the subject to true opinion, which is the only stage illustrated in the Meno. The next stage is that leading finally to knowledge, which involves putting questions to the subject “on the same topics” (  %: 85C10–11) repeatedly and in various ways. The translation “on the same topics” here seems preferable over the standard “the same questions,”

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is not complete, presumably, until knowledge has been achieved. According to the Meno, however, recollection is also required to reach a state of true opinion (85C). The reason recollection by itself is not capable of producing knowledge is that the deft guidance of a teacher is required to lead it through these several steps to a successful conclusion. A second feature the use of paradigms shares with recollection in the Meno and collection in the Sophist is its function of guiding the inquiry it supports to a successful conclusion. As far as recollection is concerned, an effective teacher must make sure that the recall achieved in response to the initial set of questions prepares the learner’s mind to be receptive to subsequent disclosures. With regard to collection in the Sophist, the purpose of surveying diverse types of acquisitive sophistry is to redirect the inquiry to the forms of productive art that are typical of sophistry in general. And in the case of the Statesman, to which we return presently, we have seen in Chapter 1 that a new beginning is needed in the search for the statesman’s art that has been led astray by the initial paradigm of the nurturing shepherd. For the search to be resumed in a fruitful manner, it must be brought under the guidance of a more suitable paradigm. For present purposes, however, the most instructive feature shared by these three aids to inquiry is the following. In one manner or another, each draws on an initially incoherent (dreamlike) apprehension of the subject matter at hand, which it then marshals into a form enabling the inquiry to conclude with articulate knowledge. Let us recall how this works with recollection in the Phaedrus. In the part of his palinode tying collection to recollection, Socrates observes that a person’s humanity requires an ability to grasp things according to Forms, “going from many perceptions to a unity brought together by reasoning” (249B7–C1). The perceptions mentioned here are subsequently identified as sensible likenesses (Q  : 250A6) or images (( : 250B5) of Forms the mind has perceived previously. In the case of many Forms, these likenesses are too obscure to be recognizable for what they are. One exception Socrates notes is the case of Beauty, our original vision of which was sufficiently bright that we can see it reflected in its sensible manifestations. In any case, Socrates says (250A), the soul is left to recollect the Forms on the basis of their sensible inasmuch as it is hard to see how repeating literally the same questions would have any beneficial effect. In this case, other problems involving incommensurables might qualify as included among the same topics. This seems to tie in with Socrates’ remark at 81D1–4 that all nature is akin and that when a man has recalled a single thing nothing prevents him from discovering all the rest.

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images. Recollection thus is a matter of proceeding from indistinct images in the sensible world to a renewed grasp of original Forms that is fully distinct. Collection in the Sophist begins in a similar manner with an indistinct apprehension of the relevant subject matter. To see how, consider the collection that leads into the final definition of sophistry. Having completed the practice definition of angling, the Stranger generates five separate characterizations of acquisitive sophistry. Each being different from the others, no depiction among them applies to sophistry in general. To make a start on a comprehension characterization, the Stranger helps Theaetetus see that each of these separate practices involves the production of images. At this point, the process of division takes over and leads eventually to a definition that isolates sophistry in general from other forms of image making. This final definition characterizes sophistry in terms of features that are both necessary (individually) and sufficient (collectively) for being a practitioner of the art in question. The contribution of collection to this achievement is to make explicit features that all types of sophistry have in common – features that are necessary for being a sophist. To accomplish this, the Stranger has to assemble a set of typical examples (the five acquisitive sophists) represented in verbal form. One cannot assemble a set of typical examples, however, without knowing something already about the subject being investigated. One must have some prior awareness of what a sophist is to ensure that only sophists are included in the set. The business of collection is to convert this preanalytic awareness into a form (the exhibition of necessary conditions) that can direct the inquiry toward its end of fully articulated knowledge (the final definition). What collection accomplishes, in brief, is a rendering in more explicit form of something the mind recognizes already in a less coherent manner. This is the respect in which collection is comparable to recollection in the Phaedrus. Each in its own way, both processes yield a more focused apprehension of something perceived previously in less distinct form. This brings us back to the primary concern of the present chapter. As part of our discussion of the paradigm of the language learner in section 4.3, several requirements were laid out for an effective paradigm. One is that in order to be suitable as an aid in a particular inquiry, a paradigm must exhibit features that are intrinsic to the subject being investigated. The suitability of weaving as a paradigm for statesmanship accordingly hinges on the fact that both arts involve the intertwining of contrasting elements. As the intertwining of warp and woof is essential to weaving, so

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an essential feature of statecraft is its interweaving of vigorous and gentle natures. Weaving thus exhibits an intrinsic feature that is necessary to the kingly art as well. Bringing necessary conditions to bear in this manner, the paradigm of the weaver in the Statesman plays a dialectical role very similar to that of collection in the Sophist. The main difference between the two lies in their employment of illustrative cases. This difference involves both (1) the number of cases and (2) the nature of the illustrations chosen. Collection in the Sophist begins with an assembling of (1) a plurality of instances and ends with the articulation of a feature those instances share in common. In the example we have been discussing, the instances assembled are (2) all cases of sophistry (sophists I through V), and the feature articulated (production) is essential to sophistry as such. The method of paradigm in the Statesman, on the other hand, employs (1) a single illustrative case, which is (2) an instance of something other than statesmanship itself. Although different from the topic being investigated, however, the illustrative case of weaving exhibits features that are essential to the subject of inquiry. In a sense, the use of paradigms is more “expeditious” than that of collection. What collection accomplishes with a survey of several instances, the method of paradigm accomplishes with only one. Both procedures serve as conceptual lenses, so to speak, by which the mind’s preanalytic awareness of the subject being investigated is focused into a more fully articulate form. In both procedures, moreover, the articulate grasp of the subject that results exhibits features that are essential to the thing in question. But whereas in collection this more explicit grasp involves something like what we call induction,10 in the other method it is accomplished with the choice of the paradigm itself. By way of summary, we have seen that the use of paradigms in the Statesman joins recollection and collection as aids to dialectical inquiry. Each of the three processes transforms an awareness of the subject matter that is initially obscure into a form of articulate knowledge. As collection seems to have replaced recollection in the Phaedrus, moreover, so the use of paradigms in the Statesman seems to have replaced collection in 10

Plato has no noun corresponding to our ‘induction’. The term 
 used by Aristotle in this regard carries the sense of magical inducement for Plato (e.g., Republic 364C4, Laws 933D7). Interestingly enough, the one place Plato uses the term 
 in a methodological sense is Statesman 278A5, in the Stranger’s remark that the method of paradigm he is about to introduce is the best way of leading (
 ) learners of language to knowledge.

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turn. At any rate, collection plays no explicit role after the introduction of the weaver paradigm at Statesman 279B. The last occurrence of "  as a term for collection occurs at the end of the paradigm illustrating the use of paradigms, with the Stranger’s remark that a paradigm comes into play whenever familiar and unfamiliar cases of the same thing are brought together (" 5!L : 278C5) yielding a single true judgment in either case. Our next task is to examine the role of the paradigm of weaving in the continuing investigation of the statesman’s art.

5 The Weaver Paradigm

5.1 Antecedents to the Paradigm of Weaving Having illustrated the use of paradigms with the modest example of their use in learning letters, the Stranger returns to the task of defining statesmanship. What they need to do next, he tells YS, is to bring a paradigm to bear in grasping the nature of “looking after those in the city” ( . 
 !
 : 278E9). In this way, that nature will become present to them “in a waking state instead of a dream”(2
  & I  : 278E10) – a clear allusion to the dreamlike state said at 277D1–4 to be remedied by the use of paradigms. A chronic problem with previous efforts to define statesmanship in the dialogue was an inability to distinguish it from a host of similar skills. At 268C2 there is reference to myriads of skills that lay claim to the title “rearer of the human herd,” several of which are specified at 267E7–8. According to 275B, this problem was one reason for introducing the Myth of Cronus. The reader is encouraged initially to think that the problem has been resolved, under the influence of the myth, by the replacement of herd rearing (  ) by herd keeping (  ) in the definition. Such at least appears to be the sense of the Stranger’s remark at 276B7–C2 that statesmanship has better claim than any other skill to providing civic care (
  at 276B7, approximate synonym for    according to 275E5–6). When the search for a definition takes up again at 279A, however, it turns out that the problem remains unresolved. For as the Stranger says there, we must return to the matter of myriads challenging kingship for “the role of caring for cities” (
) 
 
 : 279A2). It is precisely to separate kingship from these many contenders, the Stranger 92

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declares, that a paradigm other than herd keeping is needed. After YS’s perfunctory agreement, the Stranger poses the following questions: 279A7

279B

So what really small-scale paradigm, with the same business (
  ) as statesmanship, can be set beside it so that we might satisfactorily gain what we are looking for? By Zeus, Socrates, does this suit you – if we don’t have another ready at hand, then what if we were to choose the art of weaving?

Just as the paradigm employed in learning letters was a familiar symbol juxtaposed to an unfamiliar instance, so the Stranger is looking for a kindred art with which statesmanship in turn can be compared. In accord with the requirements laid out in the previous chapter, this kindred art must be initially more familiar than statesmanship (requirement (1)), must involve the same “business” (share essential features; requirement (2)), and must be less significant than statesmanship itself (requirement (3)). The final requirement (4) is that the paradigm be verbally expressed, as distinct from something that can be grasped entirely by sensible means. The stage now is set for the deployment of the paradigm of weaving. This seemingly casual introduction of the weaver paradigm should not be read as an inspiration of the moment of the part of the Stranger. The mild oath
# M that goes with it is reminiscent of the same expression at Sophist 253C7, where the Stranger pretends to have “stumbled unawares” on the “free man’s” (the philosopher’s) knowledge. Just as it would be incongruous to suppose that the author intended his Eleatic protagonist to be genuinely surprised by this encounter in the Sophist, so we should understand the introduction in the Statesman of the weaver paradigm as a carefully planned move in the project of defining statesmanship. In point of fact, there are reasons for thinking that the parallels between weaving and statesmanship had been on Plato’s mind for some time before writing this passage into the present dialogue. A background consideration is that weaving counts among Plato’s favorite examples of the arts and crafts, making roughly two dozen appearances before the Eleatic dialogues. Whereas in most of these earlier contexts it functions merely as an instance of a practical skill,1 however, in the 1

A possible exception is at Phaedo 87B–C, where Cebes raises an objection against one of Socrates’ arguments for immortality in which a cloak is analogous to the human body and its weaver analogous to the soul. Here the product of weaving and its use function as a key analogy in the argument and not as a mere example.

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Statesman it is elevated to a central role in the dialectical process underway. The nature of its role as illustrative paradigm should be more or less familiar, having been considered at length in the previous chapter. What may be less apparent are various subtle ways in which the art of weaving was being groomed for this role in the earlier conversation between the Stranger and Theaetetus. One of the more frequently discussed passages in the Sophist is 259E4– 6, the upshot of which is that discourse (Q  ) owes its existence to “the weaving together of Forms with one another” (  . (. "
  ). This remark clearly applies to discourse in general. A similar remark a few pages later pertains to particular instances. In preparing to address the problem of truth and falsity in speech and judgment, the Stranger observes that the simplest sentences (e.g., “man learns” at 262C8) result from a combination ("
 : 262C6) of names and verbs. This observation is repeated at 262D4, where he says that speech accomplishes its results by “weaving together verbs and names” ("
  H   ' I  ). These remarks illustrate an underlying theme of the Sophist to the effect that speech, on whatever level of generality, depends on the weaving together of appropriate constituents. In this connection, we should recall that the stated goal of that dialogue is “to bring to light in a clear statement” (  6  7: 218C1) what the sophist is. The goal of the present dialogue, of course, is to do the same for the statesman. Inasmuch as the purpose of both dialogues is to accomplish something through discourse, and inasmuch as discourse accomplishes its results by weaving together appropriate elements of speech, the ability of either dialogue to achieve its goal depends on success in this weaving process. A weaving of sorts thus is deeply implicated in the project of the Statesman before its first explicit mention at 279B2. Another notable appearance of the term "
 in the Sophist comes at 268C6, where the Stranger calls for a “plaiting together” ("
  R ) of the various features contributing to the definition of sophistry. Once these features have been woven together in a clear description, the task of the dialogue has been accomplished. Not only is the project of dialectical definition dependent on a kind of weaving for its initial feasibility, as noted previously, but a kind of weaving is also involved in bringing it to completion. Taken together, these observations suggest that when Plato was looking around for a paradigm to illustrate the kind of blending skill involved in genuine statesmanship, the art of weaving was close at hand. Weaving

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is an art that had already been put to work (metaphorically) in describing key aspects of dialectical procedure. And because the primary purpose in undertaking a dialectical definition of statesmanship was to make participants in the conversation better dialecticians (285D), nothing would be more suitable as an illustrative paradigm than an art that could be used to elucidate both statecraft and dialectic at the same time. Interestingly enough, the term G  and its derivatives, which comprise the vocabulary most often used for weaving in the Statesman, do not appear in that role in the Sophist. Expressions used for this purpose in the earlier dialogue, as indicated earlier, stem from the nearsynonym "
 instead. Terminological overlap between the dialogues is established by the not infrequent appearance of expressions based on "
 in the Statesman as well. For example, weaving is describing at 281A3 as a sort of intertwining ("
 ); and at 282D5, the term "
 is used explicitly as an equivalent of G  .2 This terminological overlap suggests that, in the author’s mind at least, (a) the combination of nouns and verbs (from the Sophist), (b) the blending of strong and mild characters (from the Statesman), and (c) the intertwining of warp and woof are different species of the same generic art. While reflecting on the sources of Plato’s main paradigm in the Statesman, we should also consider the literary precedent provided by Aristophanes’ Lysistrata. Written during the political turmoil following the disastrous defeat of the Athenean fleet at Syracuse, this play depicts an effort by the women of Athens, under the leadership of Lysistrata, to instruct certain male authorities on ways to unify the city and to arrange peace with Sparta. The women’s strategy is described in the language of wool working, calling both for cleansing the raw material (the populace) of sheep dung and burrs (political intrigues and demagogues) and for fashioning a final product serving all members of the polis. The comedy of the plot plays on a contrast between the martial skills of the men and the weaving skills of the women, as Lysistrata and her crew connive to replace the former by the latter in affairs of state. Comparison of the Statesman with the Lysistrata can be illuminating, with regard to both differences and similarities. One instructive difference is that the Statesman not only is devoid of sexual politics but

2

Other occurrences are the noun "
  used in reference to kingly weaving at 306A1 and 308E2, along with the verb "
 " at 306A2. Further, at 309E10 we find "
  referring to the weaving of courageous and moderate characters, along with "
 at 309B7.

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moreover portrays weaving in a manner that appears to be genderneutral.3 Although Plato certainly was aware of the stereotype associating women with weaving (Republic 455C), this preconception apparently was set aside in his choice of weaving as a paradigm for statecraft.4 Despite this and other differences, however, a striking similarity between the treatments of weaving by Aristophanes and Plato is the amount of attention each pays to technical detail.5 In the Lysistrata, the details in question correspond to particular steps needed to unify a shattered polis – eliminate impurities from the raw material, recognize the resources of the colonies, produce a social fabric serving all citizens (lines 574ff.), and so forth. Plato’s treatment in the Statesman, on the other hand, incorporates details corresponding to specific skills and functions implicated in governing a state. A particularly interesting aspect of Plato’s description of weaving is its incorporation of a substantial number of neologisms referring to specific technical skills. These occur mainly between 280C and 281B, in connection with the Stranger’s first definition of weaving after introducing the paradigm. We shall look at these neologisms in detail when we turn to a detailed examination of the definition of weaving in section 5.4.

5.2 Intermingling Paradigms When the Stranger observes at 277D that it is hard to demonstrate important things like statesmanship without using paradigms, YS asks what he means. The Stranger’s response is that paradigm itself stands in need of a paradigm. This leads to his account of how children are taught letters by using familiar cases as paradigms for comparison with unfamiliar cases. What stands in need of a paradigm initially is the use of paradigms in a dialectical definition of statesmanship. What responds to that need is a brief narrative about the use of paradigms in learning letters. Our present task is to pin down exactly the sense in which the use of paradigms in the narrative can serve as a paradigm for the dialectical use of paradigms. 3

4

5

Suppression of gender issues in the Statesman is consistent with the featured doctrine of the Republic that leadership roles should be open to both men and women. A useful discussion of attempts to explain the dialogue’s gender-neutrality, with regard to weaving in particular, can be found in Lane (1998), pp. 167–69. It should be noted that although the Stranger insists that a paradigm should be of lesser value than the thing it illustrates (278E, 286A–B), he nowhere intimates that weaving is inferior to statesmanship for reasons specifically involving gender. This point is noted and developed at length in El Murr (2002), pp. 61–69, 70–75.

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There is a tendency among translators to render the term
  in this context as ‘example’.6 This tendency should be resisted. Not only is the term used consistently throughout the Statesman in a specifically dialectical sense (section 4.1), which is not that of example, but moreover the generic translation ‘example’ makes a muddle of the passages we are considering. The familiar appearance of a letter in the case of the learner is not an example of its unfamiliar appearance (although both are instances and hence “examples” of the same letter). Weaving, similarly, is not an example of statesmanship. And there is no directly apparent aspect of the story of the learner that is an example of the use of paradigms in the dialectical treatment of important topics like statesmanship. To serve as an example is a matter of exemplification; and the paradigms at work in the Statesman do not exemplify things they are used to illuminate. To arrive at a clear understanding of how paradigms function in this context, it will be helpful to distinguish the various paradigms involved. We start with the more obvious. Apart from the paradigm of shepherding (so-called at 275B5 and 277B4), the first paradigm introduced as such in the dialogue is that of the letter appearing in a familiar syllable. Let us refer to this as paradigm A. Paradigm A is used by a teacher to prompt recognition of the same letter appearing in an initially unfamiliar context. Its role is not one of exemplifying that latter appearance, but rather one of rendering that appearance familiar in turn. If the teacher is successful in using the paradigm for this purpose, the student’s capacity to make correct judgments about the paradigm will be extended to the initially unfamiliar appearance of the letter as well. The second paradigm so identified in this set of passages is that of weaving, which we may refer to as paradigm B. Paradigm B serves as a prototype exhibiting features that figure prominently in the definition of statesmanship that follows. In this role, it functions as a sort of model – not in the sense of a model ship that copies (replicates) features of an actual vessel, but more in the manner that a dress rehearsal models (simulates) the circumstances of a regular performance. Paradigm B provides the subject of a practice definition, much as angling served as the subject of a practice definition in the Sophist. Let us return to the Stranger’s assertion that paradigm itself stands in need of a paradigm. As the context makes clear, the need arises from 6

For example, Jowett, Fowler, Skemp, and Benardete, among others. Waterfield uses ‘illustration’, which is similarly problematic. Rowe’s ‘model’ is preferable to these others, if read in the sense of ‘model for’ rather than ‘model of ’.

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YS’s puzzlement about what the Stranger meant in saying that it is hard to demonstrate important things without using paradigms. The observation that paradigm itself needs a paradigm is an elliptical way of saying that a paradigm is needed for the use of paradigms in the dialectical treatment of statesmanship. What exactly is the paradigm the Stranger offers in response to that need? Obviously enough, the paradigm in question is contained in the story about how children learn letters. But just as obviously, the paradigm in question is not paradigm A as such. The paradigm of a letter in a familiar syllable is not a suitable paradigm for the dialectical use of paradigms. There is an important difference, however, between paradigm A itself – the familiar letter – and the use of that paradigm for the purpose of extending the student’s competence in recognizing letters generally. In introducing the story of the learner, the Stranger is setting up a paradigm for the use of paradigms in defining the statesman. The paradigm thus provided is that of the use of paradigm A in learning letters. Let us refer to this paradigm of a paradigm in use as paradigm C. Paradigm C, in short, is the paradigm offered for the use of paradigms in defining the statesman. Paradigm B is the paradigm for statesmanship proposed by the Stranger at 279B. At the beginning of section 5.1 we noted reasons for thinking that weaving is an adequate paradigm for that purpose. We have now seen that paradigm C is the paradigm offered for the use of paradigm B in the dialectical definition of statesmanship. Let us consider the further question of whether paradigm C is adequate for this purpose in turn. Taking our requirements for a suitable paradigm in order, we observe first that whereas many children are familiar with the use of paradigms in learning letters, relatively few people ever experience the use of paradigms in dialectic. Paradigm C thus is more familiar than the use of weaving as a paradigm in defining statesmanship. The second requirement is that a suitable paradigm should exhibit features that are essential to the topic it is intended to illuminate. An essential feature of the use of paradigms in defining statesmanship is that the paradigm can be set beside (compared with,
!   at 279A8) the thing being studied, which is also an essential feature of paradigm C. A further desideratum in the choice of paradigms, stressed at 278E– 279A, is that a paradigm should be less significant than the thing it helps to demonstrate. The Stranger himself assures that this requirement has been met with his description of paradigm C as “small and partial” ( 
  : 278E6) and with his stress at 277D1–2 on the importance of

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using paradigms in dialectical demonstrations. The remaining requirement is that paradigms used in demonstrating important topics like statesmanship should be in verbal form. Insofar as paradigm C is developed as part of an on-going conversation, this requirement is met as a matter of course. Paradigms A, B, and C are all referred to by the Stranger explicitly as paradigms (at 278B4, 287B2, and 278E7, respectively). There is another paradigm importantly at work in this context, however, which is not explicitly designated as such. This is the use of weaving as a paradigm for statesmanship, which serves as a paradigm for the use of paradigms in dialectical inquiry generally. Let us refer to this as paradigm D. We need to be clear about how D differs from the other paradigms identified previously. To repeat, paradigm A is a letter in a familiar syllable, which serves as a paradigm for the same letter in an unfamiliar context. This paradigm is brought to bear in the process of teaching and learning letters. Paradigm B is the art of weaving, which serves as a paradigm for the art of statesmanship. This paradigm is brought to bear in the process of defining the latter art. Paradigm C, in turn, is the use of A in the learning process, and this serves as a paradigm for the use of weaving as a paradigm in the definition of the statesman’s art. Paradigm A is used by the teacher in helping the student recognize letters. Paradigm B is used by the Stranger as a means of identifying features essential to statesmanship. Paradigm C is also used by the Stranger, but in this case as a guide for bringing B to bear. This brings us back to paradigm D. Under the guidance of paradigm C, the Stranger employs the paradigm B of weaving in his development of the definition of statesmanship. This employment of B in the dialectical definition of statesmanship is what we have designated paradigm D. Paradigm D serves as a paradigm for the use of paradigms in dialectical inquiry generally. But who uses D in this capacity? There are two answers to this question, depending on one’s perspective on the dialogue. From an internal perspective, paradigm D is used by the Stranger to provide instruction in the dialectical use of paradigms. This ties in directly with the disclosure at 285D that the purpose of the dialogue is not merely to define the art of statesmanship, but to make its participants better dialecticians. Put otherwise, the main purpose of the dialogue is to instruct YS and others present in the procedures of dialectical inquiry, using the specific project of defining statesmanship as an illustrative paradigm (paradigm D). To the extent that YS is able

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to grasp the details of the procedures involved in the illustration, he is making progress toward becoming a better dialectician. From an external perspective, in turn, paradigm D is being used by Plato himself. As pointed out in section 1.5, there is a sense in which careful readers of the dialogue are also participants in the ongoing conversation. With this sense in view, we understand that the purpose of the dialogue is to make better dialecticians not only of YS and others present but of readers seriously engaged with the dialogue as well. From this external perspective, accordingly, paradigm D is being used by the author of the dialogue to enable his readers to become better dialecticians. In either case, the goal of making its participants better dialecticians is served only to the extent that they are able to follow the use of the weaver paradigm in step-by-step detail. The remainder of the chapter is given over to detailed examination of that paradigm.

5.3 How Defining Weaving Provides a Paradigm for Defining Statesmanship Paradigm D, once again, consists of the Stranger’s treatment of the definition of weaving as a paradigm for the subsequent definition of statesmanship. Weaving is defined in four Stephanus pages from 279C to 283B. The definition overall divides into three distinct parts: (i) a perfunctory initial definition between 279C and 280A, (ii) an account of the initial definition’s shortcomings between 280B and 281B, and (iii) an emended definition between 281D and 283B that avoids these shortcomings. The definition of statesmanship, on the other hand, occupies well over half of the dialogue. Interludes on methodology and metaphysics aside, it extends from 258B to 277A and again from 287B to 305E7 – a total of more than thirty-seven pages. The Stranger’s treatment of the paradigm of weaving is so contrived that the major stages in the cumulative definition of statesmanship are mirrored by stages in the definition of weaving.8 The purpose of this section is to trace out the general outlines of this mirroring relationship. The perfunctory definition of weaving begins with the division, according to purpose served, of everything we “make or acquire” (  " %  7 8

The last six Stephanus pages function as a coda illustrating the statesman’s task of weaving citizens with opposing character traits into a well-functioning polis. Essentially the same point is made in Miller (1980), pp. 60–64, employing the same metaphor of mirroring.

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) * !: 279C7–8). Things we make or acquire might be either for the sake of doing something (B   %
' : 279C8) or to prevent something being done. The latter category goes through nine subsequent divisions in rapid sequence (see following Figure 5.1), after which the results are presented to YS as a definition of weaving for his reaction. Young Socrates accepts the definition without further ado (280A7). This initial definition of weaving corresponds to the extended definition of statesmanship as a version of shepherding, which culminated just prior to the Stranger’s call for a paradigm of paradigms and which YS had also accepted without question at 277A. The breathless character of this initial definition seems to reflect an effort on the Stranger’s part to maneuver his interlocutor into a similar state of acceptance as quickly as possible, providing time for a more leisurely explanation of what had been overlooked in both cases. As he noted repeatedly in connection with their initial attempt to define statesmanship (268C, 275B, 276B, 279A), the portrayal of kingship as the art of caring for human herds fits many other arts of caregiving within the polis as well. A similar problem affects the initial definition of weaving, as the Stranger now proceeds to demonstrate. The Stranger begins this second stage in his treatment of weaving with the observation that some people (notably YS) might consider the initial definition adequate because it separates off many related arts, even though weaving still has not been divided from yet other arts that cooperate with it. In response to YS’s lame question of what related arts he has in mind, the Stranger undertakes a detailed itemization of a dozen or so arts in question. This itemization of related arts is noteworthy in several respects. For one, the related arts identified by the Stranger are mentioned in reverse order from that of their original appearance in the definition. The Stranger is quite deliberate about this, saying that they must go back through the account of weaving “starting at the end” (5  
# ": 280B6). Another aspect of some interest is that the Stranger employs a sizable number of neologisms in identifying these related arts. Several of these are terms found nowhere else in the extant Greek corpus. Yet another notable aspect of this sequence is that it focuses on arts that were separated off on the left side of the initial line of division. Rather than being set aside and passed by, as is the usual procedure in a sequence of standard dichotomous divisions, these features are emphasized in the Stranger’s reversal of the definition. For the moment, it is enough to note these distinctive aspects of the list of related arts spelled out between 280B and 281D. We return to

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these matters in the following section, both to fill in details and to assess their significance. The immediate relevance of this set of passages lies in its demonstration that the initial definition of weaving, like the faltering definition of statesmanship before it, fails to distinguish its subject from a variety of arts that cooperate with it. Other cooperative arts not yet distinguished from weaving include those of carding and fulling, along with those that make the weaver’s tools. We recall that the initial definition of weaving began with a distinction between things made or acquired for the sake of doing something and things made or acquired to prevent something happening to us. The art of weaving (identified with the art of clothes making at 280A3–5) has been characterized thus far with respect to its role in fabricating protective garments and has been distinguished from other preventive arts falling under the same general category. But the carder and the fuller are both concerned primarily with doing things to wool, and the tool makers in question are responsible for producing implements used in the actual process of weaving. In a word, these other arts from which weaving must now be distinguished fall under the general category of arts directed by the purpose of doing something. To distinguish weaving effectively from these other productive arts, it too must be characterized with respect to what it does. The second attempt to define weaving thus begins with a focus on things that artisans do (*  : 281D9). The first distinction made under this general category is between direct causes and contributory causes ("  : 281D11). Makers of tools used in weaving fall under the latter. Direct causes, on the other hand, are further divided between the art of the fuller and arts concerned with working the fulled wool itself. Wool working is further divided between arts of separating (by card or spindle) and arts of combining. This latter, finally, is divided between arts responsible for spinning warp and woof, and weaving itself by which warp and woof are intertwined. Weaving emerges from this final definition as the art directly responsible for working wool by the combining of warp and woof. This final definition of weaving corresponds to the final definition of statesmanship initiated at 287B and brought to a conclusion at 305E. Developed initially under the preconception of statecraft as a form of herd keeping, the attempt to define the statesman’s art began with the division of knowledge into practical (
 : 258E5) and theoretical (  : 258E5). The art of the statesman (posited at 259B–C as identical to those of the king, the slave master, and the household manager)

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was assumed to fall under the latter. Further subdivisions under this category led to the flawed definition at 276E that gave rise to the Stranger’s call for a paradigm of paradigms. The persistent problem with this line of definition, as already noted, is that it has been unable to distinguished the statesman from “myriads” of competitors. Among competitors explicitly identified at 267E are merchants, farmers, bakers, trainers, and doctors, all of whom can lay claim to the role of providing care for people living in groups. Although no note was taken of this at the time, the skills practiced by these experts as a class tend distinctly more toward the practical than the theoretical. To distinguish the weaver from the spindle maker, as already observed, a categorical shift from “preventive art” to “art of doing” is required. Similarly, to distinguish the statesman from merchants, farmers, and bakers, it appears that a shift might be required from the general category of theoretical arts, with which this line of division began, to the opposite category of practical arts. This indeed is what happens when the definition of statesmanship is resumed at 287B. As a first move in this renewed effort, the Stranger repeats the distinction between direct causes and contributory causes that inaugurated the successful definition of weaving at 281D. Whether contributory or direct, the causes concerned in either case are for the sake of doing something. In the case of the statesman, this means that they pertain to the practical rather than the theoretical arts. To drive the point home, we note that the Stranger at 287D4 begins talking about the “products of the kingly art” (- A 5 ) and that by 289D1 he is speaking of kingship and statesmanship explicitly as a practical activity (
 ). The category of practical arts (
 ), set aside to the left as a first step in defining statesmanship at 258E, has now reappeared as the key category in an ultimately successful definition. We shall return to this apparent about-face in the following chapter. In the meanwhile, we should look more carefully at certain details in the definition of weaving.

5.4 The Definition of Weaving Dissected Part (i) of the process of definition consists of a series of ten divisions, crammed into a scant seventeen lines of text (279C7–280A1). A diagram of this series of divisions is provided in Figure 5.1. It will be noted that this series of divisions does not add up to a definition of weaving as such. What is defined, in effect, is woolen clothing. The art that has charge

104

Metaphysics and Method in Plato’s Statesman things made or acquired for sake of prevention

for sake of doing

defenses

charms

protections

armaments

deflectors of cold and heat

screens shelters spread under single piece stitched from vegetable fiber felted

bodily coverings wrapped around compounded unstitched from hair bound with hair (= product of the art of weaving)

figure 5.1. Initial definition of weaving (279C7–280A6).

of such clothing is designated the art of clothes making (K  " ) at 280A3 and then identified with weaving (G  : 280A3) itself. The Stranger’s rationale for this rather implausible move is that weaving constitutes the largest part of clothes making (280A3–4). This is enough to elicit YS’s wholehearted endorsement of the foregoing as a definition of weaving. Having maneuvered his interlocutor into accepting this perfunctory definition within the span of about one-half Stephanus page, the Stranger spends three times that much space in pointing out its shortcomings. This second stage of the overall definition consists of (a) a listing in reverse order of the related arts from which weaving has been separated in the initial definition (Table 5.1 following), and (b) a further listing of arts that cooperate with weaving from which it has yet to be distinguished. Before looking at these lists in detail, we should note two respects in which list (a) reverses the order of the initial definition. One respect, to repeat, is that the arts concerned are mentioned in (roughly) opposite order from that in which they were initially separated

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from the art of weaving. This presumably is what the Stranger means in saying at 280B7 that in going back again they must “start from the end.” The second respect is less direct. Regardless of order of mention, the several arts in question have been separated from weaving in the sense of having been set aside to the left as the series of divisions producing the initial definition progressed along successive right-hand branches (see Figure 5.1). By listing arts that have been set aside in this fashion, the Stranger in effect is restating the results of that series of divisions. But whereas the initial definition specified features that are characteristic of weaving, this second listing specifies features that weaving lacks. In short, the second listing reverses the initial definition by proceeding along the left-hand of the series of divisions rather than the right. By specifying features that weaving lacks, it singles out weaving by a process of elimination. To identify weaving uniquely, however, this reverse process must eliminate all kindred arts with which it shares distinctive features. The purpose of list (b) (in Table 5.2) is to complete this process of elimination. Following (Table 5.1) is a list of arts initially separated from weaving, showing both the sequence of mention at 280B–E (to the left) and order of elimination under the category of prevention in the course of the initial divisions (in parentheses to the right). It will be noted that the sequence of this list is not the exact reversal of the initial order of mention, inasmuch as the first art listed (that of fabricating blankets) is fifth in the initial order and the second and third arts remain in their initial sequence. Possibly of more interest than the order of listing is the fact that all save one ("  ) of the terms used to designate specific arts in table 5.1. (a) Arts Initially Separated from Weaving (280A8–E4) (The art of fabricating) coverings spread under – e.g., blankets (The art of fabricating) garments from vegetable fiber – e.g., flax The art of felting [
] The art of cobbling ("  ) The art of working with single piece skins [  "]* The art of building shelters [)] The art of joining screens [ ]* The art of arms manufacture [Q

] – a branch of defense-production [
 -  "] 9. The art of magic [ "]*

1. 2. 3. 4. 5. 6. 7. 8.

(5) (8) (9) (7) (6) (4) (3) (2) (1)

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table 5.2. (b) Arts Yet to Be Separated (281A–D) 1. 2. 3. 4. 5. 6.

The art of breaking (fibers, etc.) apart ["] The art of carding [  ] The art of manufacturing () warp and woof The fuller’s art [ "] The art of clothes mending () The arts of making tools used in weaving

this sequence appear to be neologisms.9 Whereas the first two arts are identified by description only, the last seven are assigned specific names. The neologisms among these are indicated by their inclusion in brackets. In three cases, the terms in question appear to have been used only by Plato and by him only once.10 These terms are marked by asterisks in Table 5.1. We return in the final section of this chapter to assess the significance (if any) of Plato’s striking reliance on neologisms in this section of the dialogue. Regardless of what we make of it, use of neologisms continues in the Stranger’s list of cooperative arts. The problem with the initial definition is that although it separates weaving from kindred arts having to do with prevention, there are other arts involved in the production of woolen garments from which weaving has yet to be distinguished. These cooperating arts are described and given names at 281A–D. They are mentioned in the order indicated in Table 5.2. As before, the names enclosed in brackets appear to have been coined by Plato. However, none of these is used in this passage exclusively. We have observed that all these cooperative arts are pursued for the sake of doing something, as distinct from preventing things from being done. To bring these auxiliary arts into account, the Stranger begins his second (and ultimately successful) definition of weaving by distinguishing two broad categories of art exercised for the end of doing 9

10

For present purposes, a term is counted as a neologism if it appears in no author prior to Plato in the canon of Greek authors included in the Thesaurus Linguae Graecae (TLG), as indicated by a search of authors from the eighth to the fourth Centuries b.c. The present compilation of neologisms in these passages was arrived at independently of Campbell (1867) and contains three entries not found in that previous listing (made without benefit of electronics). I am indebted to Dimitri El Murr for bringing Campbell’s list to my attention. Use of a term is considered a sole occurrence (hapax legomenon) if it is used by no other author in the TLG canon and used by Plato only once. Given the nature of the technology, electronic searchs are not 100 percent reliable, and for present purposes have been cross-checked against LS (1883). Several neologisms (e.g.,  and Q

) that initially appeared in TLG to be hapax legomena have been eliminated on this basis.

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something, those of contributory cause ("  : 281D11) and (direct) cause ( : 281D11). In this application, the distinction is applied specifically to the production of woolen clothing (
)  C !: 281C9). The line of division continues as shown in Figure 5.2. The conventions introduced in Table 5.1 apply to this figure as well: neologisms are enclosed in brackets, and sole occurrences are marked with asterisks. There are several notable differences in format between Figures 5.1 and 5.2. Whereas the former is concerned with distinctions among protective devices, Figure 5.2 distinguishes specific arts with respect to what they accomplish. After the general distinction between contributing and directly responsible arts, particular arts are named specifically at each subsequent stage of division.

arts exercised in doing things contributory causes (arts making tools for other arts)

direct causes

the fuller's art [

art of clothes washing ] [

art of clothesmending [

art of furbishing clothes )

art of wool working (

art of separating ) ( art of carding ] [

"one-half of art of weaving” [ art of the shuttle

]:*

art of combining ( )

art of twisting ] [ ]* also [

art of warp spinning ] [

art of woof spinning [ ]* weaving proper ( )

figure 5.2. Final definition of weaving (281D8–283A8).

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Another salient difference between the two figures has to do with the distribution of divisions on opposite sides of the diagram. In Figure 5.1, all divisions appear on the right-hand side of the figure. In this respect, they are like most divisions in the Sophist (see Figures 3.3(b) and 3.4 for exceptions) and like all preceding divisions in the Statesman. In Figure 5.2, on the other hand, key divisions are made on both sides of the diagram. In point of fact, the overall configuration of Figure 5.2 gives the impression that most of the work in this series of divisions is done along the left-hand side. This impression is reinforced when we begin looking at details. The purported task of this sequence, stated at 281D1–4, is to distinguish weaving from the cooperating arts listed in Table 5.2. This is accomplished by a chain of division locating the arts in question along the left side of the figure. First to be set aside are the arts making tools used in weaving (number 6 in Table 5.2). Next is the fuller’s art (number 4), under which the Stranger includes the art of clothes mending (number 5). Then come the arts of breaking apart fibers and the like (number 1), and of carding (number 2), both of which are forms of separating. Last are the arts of manufacturing warp and woof (number 3), which fall under the more general art of twisting. In following through this process of elimination, one gets the sense that the distinctions made along the left are no less important than those along the right. Both sides contribute to the final definition of weaving. Another intriguing aspect of Figure 5.2 is its concentration of neologisms in the left-hand sector. Of the fourteen arts explicitly identified in this sequence as directly responsible for getting things done, eleven fall out to the left; and nine of these eleven are designated by neologisms. (No neologisms appear on the right.) Of these nine neologisms, moreover, three count as sole occurrences (by the criteria in note 10). Let us render our tally of neologisms current. There are seven neologisms listed in Table 5.1 and three more in Table 5.2, two of which latter are subsequently repeated in Figure 5.2. This leaves seven in Figure 5.2 which are not repetitions, adding up to a total of seventeen in this set of passage. Of this total, six appear to be terms found nowhere else in the extant Greek corpus. Let us recall also that all seventeen neologisms signify arts that are located in one way or another within the left-hand sectors of their respective lines of division. Table 5.1 lists arts identified in moving backward up the left side of Figure 5.1. Table 5.2 lists arts that, as of 280E, have not yet been separated from weaving in a comparable fashion. Figure 5.2 finally

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accomplishes this separation by providing a place for these arts to the left of weaving, which ultimately falls out at the lower right. In a nutshell, within the roughly two and one-half Stephanus pages from 280C to 283A, there are seventeen terms coined by Plato for the purposes at hand. One such purpose at least was to identify arts that in various ways are kindred to but distinct from weaving and to set them aside in a series of left-hand divisions. All seventeen terms in question are employed toward that end. It seems highly unlikely that this concentration of neologisms in these particular passages is coincidental.11 The task remaining for this chapter is to consider reasons why the author might have taken such extraordinary steps in the process of formulating his final definition of weaving.

5.5 Left-Hand Division After his extended analysis of not-Being in the Sophist, the Stranger calls Theaetetus back to the task of defining sophistry. The task is to be pursued by “dividing in two” (56  5: 264D10) the art of production, and thereafter “always holding to the right” (  
)   ): 264E1) in subsequent divisions. These specifications are followed in all remaining divisions in the Sophist and in all divisions prior to the definition of weaving in the Statesman. With the series of divisions laid out in Figure 5.2, however, we have a procedure that does not adhere to these specifications. Although the initial division (of artful ways of doing things) indeed is pursued only to the right, all subsequent divisions along the right have counterpart divisions in the opposite direction. In one left-hand section (the fuller’s art), moreover, there is a further division into three separate arts (the art of clothes washing, that of clothes mending, and that of furbishing clothes). This is a clear deviation from the guideline of dichotomous division. Not only do the divisions shown in Figure 5.2 depart from the guidelines in the Sophist, but they occur in a section made conspicuous by innovations of a terminological sort as well. To be sure, the terminological innovations seem to highlight the departures of method. As noted earlier, all of the neologisms between 280C and 282B occur in connection with division in the leftward direction. Whatever else might lie behind this 11

Campbell (1867) lists some eight dozen neologisms in the Statesman overall, averaging less than two per page. Between 280C and 283A, the average is about seven per page.

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concentration of neologisms, the author surely was aware that it would catch the attention of his intended audience (or readership). He must have been aware at the same time that it would also draw attention to the contents of the passages in which the new coinages occur. In evaluating the significance of this pattern of coinciding terminological and methodological innovations, we should be aware of a sense in which innovations of both sorts appear unnecessary. As a glance at Figure 5.2 should disclose, weaving could be defined simply as the art directly responsible for working wool with respect to combining (as distinct from separating). Or as the Stranger himself points out to YS (283A4–8), weaving has been set forward as that part of wool working that produces something by the combining of warp and woof. Either way of summarizing their results at this point would amount to an accurate characterization of weaving, and neither way requires extending the pattern of division in the leftward direction. A consequence is that neither calls for coinage of the sizeable number of neologisms associated with these leftward divisions. If an abbreviated definition of some such sort would suffice, both the left-hand divisions and the neologisms that go with them would be extraneous. The natural question for us is why the left-hand divisions nonetheless were included. This is equivalent in effect to the question next posed to YS by the Stranger. Why, he asks (283A10–B2), didn’t we say directly that weaving is an intertwining of warp and woof, instead of going around in a circle distinguishing a great number of things needlessly? This question whether their definition of weaving was unnecessarily lengthy, of course, provides occasion for the Stranger’s examination of “Excess and Deficiency in general,” to which we return in Chapter 7. The answer that emerges at 286D–E is that no discussion is too long if it results in making its participants better dialecticians ( ": 287A3). This comes on the heels of the disclosure at 285D that the main purpose of the dialogue overall is to make better dialecticians of those involved (see section 1.5). By implication, we are told not only that the rather lengthy definition of weaving was dialectically appropriate but also that the left-hand divisions involved have their dialectical purpose. We are left with the question of what purpose they serve. A partial answer, presumably, is that the author is providing a preview of the format of division employed in the final definition of statesmanship. In point of fact, the innovations exhibited in Figure 5.2 reappear even more prominently in these final divisions. When the Stranger returns to the statesman at 287B, as commentators often point out, one of his first remarks is that they will no longer be able to rely on strictly dichotomous

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division. And as will become evident in the next chapter, most of the divisions contributing to the final definition occur in the leftward direction. By demonstrating the same methodological peculiarities as the upcoming definition of statesmanship, the definition of weaving is merely serving its role as a useful paradigm. But this is a partial answer at best. Given that both the definition of weaving and the definition of statesmanship rely extensively on left-hand division, the question of its dialectical purpose arises for both definitions. Why is “standard” right-hand division insufficient in this dialectical context? Or better, what dialectical role is served by left-hand division that division exclusively to the right would not serve equally well? My sense of the matter is that the Stranger’s focus on left-hand division in this context does not constitute a rejection of right-hand division as such. We should not forget that left-hand division was featured in the Phaedrus (section 3.1), whereas division to the right prevailed nonetheless through most of the Sophist. The point of left-hand division in the latter part of the Statesman, I suspect, has to do with alternative ways of arriving at successful definitions. As noted repeatedly in our earlier discussion, a successful definition specifies features that are both necessary and sufficient for the thing being defined. The task of finding necessary conditions falls to collection in the Sophist and to the use of paradigms in the Statesman. The task of arriving at sufficient conditions belongs to division in turn. In the methodology of the Sophist, division continues along the rightmost branch until a combination of features have been specified that belongs exclusively to the thing being characterized. The gist of this method is to keep adding features to the characterization until the thing in question has been completely isolated. An alternative way of arriving at the same result relies on a process of elimination. This way is illustrated by the Stranger’s procedure in the passages we have been considering. First he takes note of the related arts that have been separated from weaving in the initial definition (listed in Table 5.1). Then he mentions other (cooperating) arts that also must be set aside before the definition of weaving is complete (Table 5.2). The result (Figure 5.2) is a characterization of weaving by way of specifying what it is not. Weaving in effect is defined by eliminating other arts with which it shares relevant characteristics. To be sure, Figure 5.2 also shows weaving to be an art directly involved in wool working that combines warp and woof. By itself, however, this characterization does not seem particularly informative. And when the Stranger launches his discussion of “Excess and Deficiency in general”

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by asking YS why this shorter definition does not serve their purpose, we are put on notice that the alternative way – although roundabout – might sometimes be preferable. Obviously enough, this eliminative approach to definition works only when all things akin in relevant ways to the topic being defined have been identified and set aside. This explains, at least in part, the Stranger’s diligence in identifying and naming the arts kindred to weaving (listed in Tables 5.1 and 5.2). When names are not readily available, he (or rather Plato) resorts to neologism. The need for precise identification beyond general description (e.g., “tool-making arts”) lies in the requirement that all kindred arts be specifically distinguished from weaving. In this particular case, kindred arts comprise those involving the making or acquiring of things for the sake of prevention (Figure 5.1 and Table 5.1) and those directly responsible for the production or care of woolen garments (Table 5.2 and Figure 5.2). Once all kindred arts have been set aside, however, the art of weaving itself has been identified. A sufficient condition of that particular art is that it differs from all other arts determined to be similar to it in relevant respects.12 Whatever we are to make of this eliminative approach to definition in the overall scheme of Platonic methodology, this seems to be the approach followed in arriving at the final definition. A consequence is that this final definition of statesmanship differs from that of sophistry in two rather basic respects. It relies on paradigms rather than collection in its initial isolation of necessary conditions. And it relies on a method of elimination rather than one of increasing specification in arriving at sufficient conditions. Chapter 6 provides occasion for looking at details. 12

To get a better idea of how this eliminative method works, assume that X is distinguished from all things of kindred nature by the possession of features a, b, c, and d conjointly. Possession of these features thus is sufficient for X (i.e., (a ∧ b ∧ c ∧ d) → X). If these features individually are also necessary for X (X→(a ∧ b ∧ c ∧ d)), then X is defined by possession of these features (i.e., X↔(a ∧ b ∧ c ∧ d)). Now assume that , -, , and  comprise all things kindred to X in nature. It thus is sufficient for X that it be none of these things (i.e., (− ∧ −- ∧ − ∧ −) → X). Given that these things are different from X, it follows that not being any of these things is also necessary (i.e., X → (− ∧ −- ∧ − ∧ −)). Thus X is defined by its not being any of these things (i.e., X ↔ (− ∧ −- ∧ − ∧ −)). One method isolates X by the progressive adding of features that distinguish it from other things. The other method isolates X by distinguishing it from all other things with relevantly similar features. Either method, properly applied, defines X in terms of necessary and sufficient conditions. Similarities between this eliminative method and the dialectical method recommended at Parmenides 135E–136A are examined in the following chapter.

6 The Final Definition

6.1 Arts to Be Separated from Statesmanship The final definition begins (287B) with the Stranger’s observation that the art of the king (or statesman) has been separated from many others of similar sort, in particular from other arts concerned with herds. This was accomplished in the course of the initial definition. Directly parallel is the separation of weaving from other arts of prevention, accomplished by the initial definition of the weaver’s art (see Figure 5.1 and Table 5.1). But there are still countless ( " : 279A3) people who challenge the king in his role of caring for cities (
) 
 
 : 279A2). These others must be separated off as well. It was for this purpose expressly (279A) that the paradigm of weaving was introduced. By the time the final definition has been completed, statesmanship has been distinguished from four classes of skills that also pertain to the care of cities. For reasons that at first appear unclear, the Stranger is careful to enumerate the membership of each class in specific sequence. Let us begin our examination of this final definition with a consideration of the lists of skills (corresponding to those of Table 5.2) to be separated from the art of statesmanship. The first group of skills to be set aside fall under the general class of contributory causes (. . . . "  : 287B6–7), in contrast to that of direct causes to which the statesman belongs. This distinction between contributory and direct causes is carried over from 281D10–11, where it provided the first division of arts “concerned with all things done” (
)
   *  : 281D8–9) on the way to the final definition of weaving. In that earlier context, contributory causes included the arts of making 113

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spindles and shuttles and, in general, all arts providing tools for use in other arts. First to be listed under this category in the present context are arts responsible for the production of tools employed within the city (
 $ : 287D2). Tools are used for purposes of production. The next class of contributory arts has to do with the preservation of what is produced. To this class, the Stranger assigns the single name ‘vessel’ (' : 287E9). Continuing to identify arts by what they produce, he now begins listing additional contributory arts explicitly by number. Third is the class of vehicles ( S T5 : 288A9), fourth that of defenses (
-  at 288B6; defenses were contrasted with charms as preventive devices at 279D1), fifth that of recreations (J  : 288C6), and sixth what the Stranger calls “original and incomposite human possessions” (#
  L  !*
   ) 3 ! : 288E5) – that is, raw materials. Seventh and finally come all things pertaining to bodily nurture (  : 289A2). Included under this category are arts of the farmer, the doctor, the trainer, and the baker (289A3–4), item-by-item the arts representing the myriads said at 267E7–8 to challenge statesmanship for the role of nurturing the human herd. When these providers of nurture are finally separated from the statesman in the divisions that follow, that particular challenge will have been overcome. It is interesting to note that when the Stranger recapitulates this list of contributory arts at 289A9–B2, those dealing with raw materials are moved to the top. A rationale for this reordering comes with the observation that arts of the remaining six classes all rely on raw materials in one way or another. This means that the arts now listed first are somehow basic to the others. Moving arts dealing with raw materials from its former sixth position, moreover, reveals a seemingly natural subgrouping within the remaining six. Makers of tools, vessels, and vehicles all focus on nonliving objects, whereas the latter three are concerned directly with the needs of human beings.1 The Stranger’s final remarks on this group of contributory causes point out that not all civic arts fit comfortably into just one of the seven classes. Arts having to do with engraving, for example, might fall partly under recreations (as decorative, presumably the sense of  at 289B6) and partly under tools. Awkward cases like these, however, are said to 1

Mitchell Miller has contributed substantially toward assessing the significance of these and other subgroups of arts distinguished from statesmanship in the final definition. For his comments on the first set of seven, see Miller (1980), pp. 82–84.

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be of no great significance (   ! : 289B2–3). The Stranger seems intent on maintaining a fixed number of classes under the general category of contributory causes. Table 6.1 offers the final list of the arts falling under that general category, identified by respective product. Herdsman, along with others who provide nourishment in their management of living possessions, are thus set aside with the category of contributory causes. There is another class of living possessions, however, that must be dealt with separately. This is the class of slaves who, although owned by others, can play an active role themselves in civic affairs. The Stranger chooses to group slaves with other servants in subordinate roles, some of whom nonetheless may challenge the role of the king in fashioning the fabric of the state. Within the category of servants generally, slaves are least likely to lay claim to the kingly art (- . . . 5 : 289E1–2). Scarcely more pretentious in this respect are freemen engaged in various forms of commerce, among whom money changers, merchants, and retailers are named specifically. Next to be listed are heralds and clerks, who provide many services for the city’s magistrates. Being themselves subordinate, however, these people clearly do not count among civic leaders. All can quickly be set apart from the statesman himself. The only serious challenge to the king from the ranks of servants comes from soothsayers and priests, experts dealing with the intercourse between gods and men. So important is this role that in some countries a king must function as a priest as well. In Athens itself, the person who becomes king by lot (the King Archon) is assigned responsibility for the most solemn and ancient sacrifices. Although these hereditary kings and priests require careful consideration (
 : 291A3) in their own right, along with their subordinates, it is obvious that these experts too must be separated from the authentic statesman. table 6.1. Contributory Causes Separated at 287C–289C 1. Raw materials 2. Tools 3. Vessels 4. Vehicles 5. Defenses 6. Recreations 7. Nourishment

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Metaphysics and Method in Plato’s Statesman table 6.2. Servants Separated at 289C–290E 1. Slaves 2. Merchants, etc. 3. Heralds, clerks, etc. 4. Soothsayers and priests

Listed in order in Table 6.2, these classes of servants also are to be set aside. Like that of Table 6.1, this list is organized in a progressive fashion. For one thing, the list exhibits a hierarchy in prestige within the polis, paralleled by an ascending degree of pretension to the art of statesmanship. As Miller points out,2 there is also a progression in types of function served within the body politic. Both slaves and merchants provide for the material needs of society, although only the latter do so freely. Clerks and heralds serve in the communication of intelligence, and the priestly class deals primarily with spiritual matters. Putting the two lists together, we find a progression from the basic materials required for the physical existence of a city to a class specializing in its immaterial well-being. The next list (Table 6.3) of exclusions takes up a total of thirteen Stephanus pages. Let us proceed directly to the list of imitative polities itself and then pause for a brief survey of associated issues. This list is ordered according to the relative merits assigned these polities at 302E– 303B.3 Other orderings can be found at other places in this section. The number of imitative polities involved comes from bifurcating (5  ' at 302E7) single rule (kingly and tyrannical monarchies), rule by a few (aristocracy and oligarchy), and rule by the many (lawful and lawless democracies, respectively). As the artisans of Table 6.1 are identified by the products they provide, so here the rulers to be set aside are identified by the types of government they oversee. At 291A2–3, this group is described collectively as a “very large mob” (

" $5 ) of people, some of whom resemble lions and centaurs, others weaker animals like satyrs and shape changers. This image is repeated at 303C8–D2, where the Stranger announces that the troop of centaurs and satyrs has finally been separated from the statesman’s art. 2 3

Miller (1980), p. 85. Kingly monarchy is called first and best to live with at 303B2–3. Miller finds the same ordering; op. cit., pp. 101–08.

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table 6.3. Imitative Politics Separated at 291A–303D 1. Kingly monarchy 2. Aristocracy 3. Lawful democracy 4. Lawless democracy 5. Oligarchy 6. Tyrannical monarchy

In a less figurative mode, the Stranger also describes this group of imitators as a chorus of sophists. To be found among them, as he puts it, is “the greatest sorcerer of all the sophists” (U#
  .  .  : 291C3),4 and the one “most versed in that skill” (3  5  
 : 291C4). This characterization is repeated at the end of the section, where the whole group is referred to as the greatest of imitators and sorcerers, who as such turn out to be “the greatest sophists of the sophists” (  " . . . .  .  : 303C4–5). In contrast to the art of the statesman, which is based on knowledge (303C1), leaders of these polities are “experts in faction” ( 3: 303C2) instead. The fact that statesmanship is a form of knowledge, posited at the very beginning of the dialogue (258B3–5) and frequently reemphasized in the present passages (292B6, C2, 8, D3, passim), provides the basis on which statesmanship is separated from leadership of the imitative polities. As far as rule by many (the two democracies) and rule by few (aristocracy and oligarchy) are concerned, their difference from true kingship in this regard is readily apparent. There is no likelihood at all that the requisite knowledge should be possessed by all members of a polis and little more that it should be possessed by an appreciable fraction thereof (the Stranger mentions five per cent at 293E). In the case of rule by one or a very few (
 
 I ": 293A3–4), however, the grounds for exclusion are not so straightforward. In his attempt to make the nub of the distinction more apparent in this case, the Stranger introduces the analogy of the knowledgeable doctor. The mark of a good doctor, he points out, is the ability to act for the good of the patient, regardless of circumstances or manner of treatment. 4

Use of the singular in this expression makes it unclear whether the description applies to all imitators or just to the case of monarchy mentioned soon thereafter. This ambiguity is not present at 303C.

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In particular, the skilled doctor can benefit both willing and unwilling patients and can do so either with or without written rules. In the case of the genuine statesman, similarly, he has knowledge to guide his city justly (
7: 293D8) regardless of circumstances and regardless of whether he governs by law. At this, YS balks, saying that the possibility of just government without laws is hard to accept. The next ten pages are occupied with the role of law in the polis. Taking up the analogy of a physical trainer, the Stranger observes that a skilled trainer will make up general rules for his athletes to follow when he has too many to deal with on an individual basis. So, too, with the knowledgeable doctor and with a ruler who has the knowledge of a genuine statesman. When either doctor or trainer goes abroad, moreover, he will leave written orders for his charges to follow. But when the knowledgeable specialist comes back and finds that the rules laid down previously are no longer working, it would seem ridiculous ( ' : 296A2) if a true statesman were not allowed to change previously instituted laws for the city’s benefit. In the case of a true statesman, to be sure, such changes should be permitted even when the populace has not been persuaded to accept them willingly. If someone lacking the skill of the statesman were to abrogate established law by force, the result would be something shameful, evil, and unjust (1 : 296C6). When undertaken with the knowledge of a genuine statesman, however, even forcible changes in law will make things more just (: 296C9) than before. The defining mark (+ : 296E2) of a correct polity (I! . . .
: 297A4) is its being governed by “a wise and good man” (Q  # ) !#  : 296E3) who will manage in the interests of his subjects. The skill of such a man is stronger than law and always results in the distribution of full justice ( : 297B1) to the populace at large. The defining difference between genuine statesmanship and its imitations is that the former, and the former only, practices a skill of just government in the interests of the populace at large. This skill is born of knowledge and as such is stronger than institutionalized law. The true statesman, accordingly, is not bound by law. But such is not the case with his second-rate (3 : 297E4, 5) imitators. Because of the evil that would result when someone without the statesman’s knowledge suspends the laws for his own advantage (illustrated at 298A–300B with allusions to current events in Athens), it is part of the second-best way (3 
 %:5 300C2) to have laws and written 5

The same expression is used at Phaedo 99D1 in reference to the hypothetical approach to causation based on participation in Forms.

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rules that all parties in the state are required to obey. To provide a good imitation of the polity governed by kingly knowledge, any other form of governance must be law-abiding. As the Stranger remarked previously at 293E, imitations of the correct polity are fair or shameful to the extent that they have good laws (?   ": 293E4). By way of afterthought (
 : 302B8), the Stranger observes that although all of these suboptimal polities are difficult to live with, some are more difficult than others. With the three types of polity previously mentioned – monarchy, rule by a few, and democracy – rule according to law (  ": 302E1) is always preferable. Cutting each in two according to this principle yields the ordering shown in Table 6.3. Having set aside this “troop of centaurs and satyrs” (303C9–D1), the Stranger turns finally to three arts he describes as honored in themselves and akin (" : 303E9) to statesmanship. In order of first mention, these are generalship (: 303E10), the judicial art (: 303E10), and the part of rhetoric that uses persuasion in helping the king direct the daily business of the state (referred to simply as H ; at 304D3 and following). Although each brings its own sort of knowledge (
 : 305C9) to bear in the process of governing, each is subordinate (G
 : 305A8, also 304E1 and 305C7) to the king in putting that knowledge into practice. In his otherwise perfunctory discussion of these three subordinate arts, the Stranger emphasizes that each is controlled by the knowledge of the statesman. It is statesmanship that “controls the art of persuasion and speaking” (
 5 3; ) : 304D7). The knowledge of the statesman controls (15 " : 305A1) the art of generalship ( : 304E7–8) in waging or withdrawing from war. And those judges “who judge correctly” (. I!. 6  : 305B1) do so with reference to canons of justice laid down by the kingly lawgiver ( ! " -: 305B5). In any such case, the role of the king is not to act for himself (   . . .
 : 305D1–2) but rather to control those empowered to act (15 . "   
 : 305D2) in these capacities. Having the skill to perceive ( . " : 305D2) the right time for action he instructs his subordinates regarding the practical measures required. The kingly art remains practical in bearing, even in cases where others are responsible for carrying out his instructions. As a careful reader will note, the Stranger’s discussion of these subordinate arts follows a different order than that in which they are mentioned originally. The order in which they are discussed is that in Table 6.4.

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Metaphysics and Method in Plato’s Statesman table 6.4. Subordinates in Governance Separated at 303E–305D 1. Rhetoric 2. Generalship 3. Judgeship

The designation ‘subordinates in governance’ chosen for this group is due to their belonging to the class of governors (15 , separated from servants at 290B5–6) who are nonetheless subordinate to the genuine statesman. The contrasting designation of the statesman is ‘governing ruler’ (

3 " 15 at 304C1). It is not clear why rhetoric is last in order of mention and then is moved to first for purposes of discussion. If this reordering is more than coincidental, the reason may have something to do with the prestige of the professions involved. As a group, they are described as recipients of honor (  : 303E9). Given the basic concern for justice emphasized in contrasting the statesman with his sophistical imitators (293D9, 297B1), it may be that those who “judge correctly” are being singled out for special honor by making them the last to be distinguished from the statesman. Be this as it may, the judge’s art is the last skill to be set aside before statesmanship is left standing alone.

6.2 The Complete Sequence of Divisions The second (and finally successful) definition of weaving began with the division of arts exercised in doing things into contributory and direct causes. The same distinction is invoked at 287B, but this time is applied specifically to arts exercised within the city (
 : 287B6). Just as before we posited (!  : 287C8) tools related to weaving as contributory causes, the Stranger says, so now we must posit (! : 287D2) as contributory causes all arts that produce tools used in the city. With this posit, the second (and ultimately successful) definition of statesmanship begins. As we recall, the first definition began by positing (! : 258B4) the statesman among people with knowledge. As the definition progressed, the knowledge of the statesman was further specified as theoretical, selfdirective, and concerned with the keep of voluntarily constituted human herds. But now we find the second definition beginning in a quite different fashion, with a distinction between contributory and direct causes operating within the city.

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When the Stranger proposes to YS at 287B that they go back to the statesman, he is not suggesting that they resume the process of division that ground to a halt ten Stephanus pages earlier. The second definition is not a continuation of the first. If the second line of division were a continuation of that broken off at 276E, then all the arts separated off from statesmanship after 287B (Tables 6.1 through 6.4) would be forms of self-directive theoretical knowledge (see Figure 1.3). In point of fact, this is not the case of any one of these arts. Rhetoric, generalship, and judgeship are all kinds of knowledge, but they are not self-directive. Rulers of the imitative polities are said repeatedly not to possess knowledge at all. And although the priestly class is customarily thought to have knowledge about making sacrifices to the gods, this surely is not theoretical knowledge of the sort leading off the initial line of division. Moreover, because the express purpose of the paradigm of weaving was to help separate the statesman from farmers, bakers, trainers, and other caretakers of the populace, it would be necessary for all of these initially to be grouped together with the statesman previously in order for the separation to proceed. Although these other callings may employ their own proper arts, however, they are not arts based on theoretical knowledge. For the second definition to get underway, the statesman must be reclassified in terms of some skill (5 ) other than knowledge. This is not to strip knowledge from among his possessions. When the sophist was reclassified as productive rather than acquisitive on the way to the final definition of sophistry, this in no way suggested that he does not engage in acquisitive practices. All it meant is that the ensuing definition would characterize him in contrast with other forms of production rather than other forms of acquisition. The final definition of sophistry got underway with a shift from acquisitive to productive art. The final definition of weaving got underway with a shift from arts of prevention to arts exercised in doing things. The same thing now is happening in the case of the statesman. Instead of representing statesmanship as a skill involving theoretical knowledge as before, the Stranger reclassifies it as a cause directly responsible for getting things done within the city. In effect, it is reclassified as a practical art. Thus, we find the Stranger remarking, as he prepares to separate the statesman from the various servant classes within the city, that the contributory causes (Table 6.1) have already been separated from the practical action (
 : 289D1) of the king and statesman. The mark of

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statesmanship that separates it from governance in the imitative polities is knowing how to govern a city justly regardless of circumstances, which certainly is a matter of practical consequence. And when the Stranger observes at 305D that a king does not act as his own rhetorician, general, or judge, the sense is not that the activity of kingship has no practical effect at all. The sense is that the king is not engaged in subordinate activities like these on an everyday basis. But this does not keep statesmanship from being a thoroughly practical calling in its own right. To be sure, statesmanship may be the most highly practical art of all, in that it has the most far-reaching consequences in affairs of state. In effect, the second definition begins by relocating the kingly art under the general category of practical knowledge. Rather than undertaking an extended dialectical division of this general class of knowledge, however, the Stranger proceeds directly to the subcategory of art exercised in doing things within the state – that is, to the class of civic arts. The diagram in Figure 6.1 shows how the division proceeds from that point onward. Scholars who comment on this definition seldom fail to note that it involves nondichotomous division. Like the final definition of weaving (Figure 5.2), it also features further division along the left-hand branches. Indeed, all its nondichotomous divisions occur in the leftward sector of the figure. These matters are discussed in the following two sections. A prior question, however, is whether governorship of the imitative polities should be considered extraneous to the final definition. Reasons can be given for counting the Stranger’s discussion of these imitative polities as a digression.6 One has to do with what might be described as a ranking by merit within the groups separated from statesmanship in the course of the definition. Among contributory causes, providers of nourishment seem generally more worthy of esteem than producers of raw materials, insofar as the former (like Cronus in the myth) are concerned with vital needs of human beings. Within the class of servants, priests obviously play a more august role than slaves. As far as governing subordinates are concerned, moreover, reasons have already been considered why the judge might be deemed more akin to the statesman than either the general or the rhetorician. Without undue concern for details, the 6

In the work cited in note 1, Mitchell Miller repeatedly refers to 291A–303D as a digression. He uses the same sometimes dismissive term for the myth, for the section on paradigms, and for the discussion of Excess and Deficiency at 283B–289B. In evaluating this use of the term, we should be aware of Notomi (1999), section 1.4, which documents cases in which Plato uses digressions for serious philosophical purposes.

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civic arts

contributory causes

direct causes

1 2 3 4 5 6 7 governors

servants

1 2 3 4 in imitative polities

in genuine polities

1 2 3 4 5 6 subordinates in governance

governing ruler (= statesman)

1 2 3

figure 6.1. The final definition.

general order of these listings is from worse to better. Generally speaking, the higher a calling in order of listing, the more akin that calling to the role of the king. As ordered by the Stranger in his final wrap-up of imitative polities at 302E–303B, however, there is an explicit decline in worth as the list progresses. Tyrannical monarchy is worst of all, whereas kingly monarchy is mentioned at one point (301A9–B3) as sharing the name of the king himself. Whether or not the section on imitative polities is to be treated as a digression, it is related differently to the art of kingship than are the other groups set aside in the course of the definition. An even more striking departure from these other groups is the fact that governors of imitative polities have no role in the city governed by the genuine statesman. Given the nature of the Greek city-state, any durable polis will have producers of raw materials, vessels, and defenses; will rely on the services of slaves, merchants, and priests; and will have officials playing the crucial roles of generals and judges. But the “centaurs and satyrs” that rule in imitative polities are excluded from the domain of

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a genuine ruler. Here is another reason for describing the Stranger’s discussion of these deviant forms as some kind of digression. Regardless of how we describe it, however, the section of deviant polities is an integral part of the definition of statesmanship. Throughout the dialogue, the Stranger’s pursuit of a definition has been vexed by various groups vying for the title of statesman. Earlier in the dialogue, the competition came from merchants, farmers, trainers, and doctors, along with countless ( " : 268C2) other caregivers among the populace. These are considered as having already been set aside when the final definition begins at 287B and are reintegrated in the overall fabric of the state under the general category of contributory cause. Next are those who dispute the king’s role in shaping this overall fabric, who are then put in their place under the category of servants. Last to become visible, and seemingly the most threatening, is the very large crowd ($5 : 291A3) of “lions, centaurs, and satyrs” who challenge the statesman in his role of genuine ruler. It is precisely the purpose of the present set of passages to separate these deviant politicians from the statesman and to put them out of competition. As the Stranger says quite plainly at 291C5–6, the king must be set aside ( ; compare 5 at 303D1) from this crowd if his art is to be clearly distinguished. And something required for this purpose must be considered integral to the division currently underway. If there is anything extraneous to this task in the present section of the dialogue, it is the ranking by merit of the various imitative polities. The fact that this ranking is referred to specifically as a side issue (
 : 302B8) suggests that the final order of listing at 302E–303B should not be a crucial factor in our interpretation of this section.

6.3 Nondichotomous Division The final definition begins with a division of civic art into contributory and direct. This is a dichotomous division, and as such poses no apparent problem. In his very next remark, however, the Stranger alerts YS to the difficulty of bifurcating these two kinds of art, for reasons he says will become evident as they proceed. Because we cannot do it dichotomously (5 "  %  : 287C4), he advises, we should divide them limb by limb (V : 287C3), like a sacrificial animal. In any case, we ought always make cuts into the nearest number (( # 3 . . . ! # : 287C4–5).

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As suggested by parallel instructions in the “godly method” of the Philebus, the sense must be that we should cut things into the smallest number suitable under the circumstances (the number nearest to the low end of the number series). The instructions in the Philebus are to lay down a single Form and after that to look for two; failing to find just two, however, one should look for three or some other number (' W   1 !  : 16D4). In the Statesman passage, similarly, YS is told to make cuts into the smallest number available – if not into two, then into some neighboring number. Following these instructions, of course, we have a division of the contributory arts into seven, a division of the serving arts into four, and so forth. The analogy of the sacrificial victim should remind us immediately of Phaedrus 265E1–2, where dialectical division is likened to cutting things according to their natural joints. In the Phaedrus, the comparison is drawn by way of illuminating the effect of dividing things according to Forms ( & 0: 265E1). The same intent, presumably, carries over into the Statesman. The Stranger’s advice here is that one should cut things into the smallest number possible, as long as the cuts correspond to Forms. Commentators differ in the significance they attach to this departure from strictly dichotomous division. Some consider it a methodological breakthrough that makes the difference between success and failure of the dialectical enterprise.7 Others pass it by with the briefest mention8 or else overlook it entirely. Whatever one’s stance in this regard, it should be borne in mind that this is not the first appearance of nondichotomous division in the dialogues. Nondichotomous division prevails in both the Phaedrus and the Philebus. In connection with arguably the earliest mention of methodological  in the corpus (Phaedrus 266B4), to be sure, dialectical division is illustrated by an example that is notably nondichotomous (Figure 3.1). As far as the Statesman is concerned, there is an isolated tripartite division in the definition of weaving (Figure 5.2); and at 284E the bipartite division into kinds of measurement at least appears to be extended in a multipartite manner (see Figure 9.1). The only overtly methodological dialogue in which division is exclusively dichotomous is the Sophist. 7

8

In Miller’s view, notably, although bifurcation “would successfully isolate statesmanship as a kind, it would conceal its form, its essential character” (op. cit., p. 77). Part of the problem, for Miller, is that civic arts constitute an “organic totality” (p. 76) which strictly dichotomous division would obscure. Thus Benardete (1984) III.119; Rosen (1995), p. 140; and Lane (1998), p. 24, n. 30, and p. 59, n. 80.

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This overview suggests that the shift to nondichotomous division in the final definition of statesmanship, instead of an innovation, is little more than a return to a procedure employed previously. What needs explaining is not the appearance of nondichotomous division in the last part of the Statesman but rather its absence in the Sophist and in the initial definition of kingship. The exclusive practice of bifurcatory division in these two contexts probably is part of the Stranger’s discipline of “cutting things through the middle” (Statesman 262B6), which is discussed at length in Chapter 11. While bifurcatory division may be a good regimen to follow as a dialectical exercise, we have already seen ample reason to be assured that it is not a requisite for dividing things according to Forms. Another factor to bear in mind in this regard is that bipartite division is still present in the final definition of statesmanship. As a glance at Figure 6.1 should indicate, nondichotomous distinctions are confined to the leftward branches of the scheme. Division to the right is dichotomous from start to finish. In point of fact, this scheme could be made to look like one of the successful definitions in the Sophist (Figure 3.2 or 3.5) by simply eliminating the multipartite divisions in the leftward direction. If this were done, it is not immediately clear how the resulting characterization of statesmanship would suffer. One purpose of the definition, at least, is to separate the art of statecraft from kindred arts; and this does not require that the other arts be extensively itemized. While the final definition of statesmanship is notable for its use of nondichotomous division, it is no less conspicuous for its division in the leftward direction. This raises the interesting question of how these two distinctive features are related. Although there is a case of nondichotomous division to the right in the Phaedrus (Figure 3.1) and a case of dichotomous division to the left in the Sophist (Figure 3.4), in most occurrences these two features are found together. We may reasonably surmise that their purposes somehow are intertwined. Let us look more carefully into the function of leftward division.

6.4 Division to the Left At the beginning of the final definition of sophistry, the Stranger gives explicit instructions regarding the method to be followed. They are to “cut the kind they have laid down into two, always following the right-hand part of the cut” (Sophist 264D10–E2). In the final definition of statesmanship, he retracts both aspects of those instructions. What is gained by allowing leftward division in this latter context?

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The Stranger takes up nearly nineteen Stephanus pages in his description of civic arts to be separated from statesmanship, and these descriptions are lavish in detail. For one thing, he is careful to provide a precise numbering of practices separated off in the leftward direction. We shall return momentarily to this matter of numbering. Another dimension of detail found in these descriptions is the concrete character of the activities involved. Whereas the functions separated off to the right are general and abstract – having direct responsibility for things done, being responsible as governor, and so forth – those itemized to the left are part of the daily activity of a functioning state (genuine or otherwise). Comparable detail to the right is withheld until the final five pages of the dialogue. In compiling this list of practices, moreover, the Stranger is consistently attentive to the diversity of specialized interests represented within them. In introducing the class of people who provide defenses, for instance, he mentions clothing and armor as among their contributions, along with walls, enclosures of earth and stone, and countless other things ( " B: 288B4) as well. Comparable detail is provided in the case of raw materials, which include gold and silver, all that is mined, the material of carpentry and basketweaving, skin stripped from animals, bark stripped from trees, as well as cork, papyrus, and bindings (such as rope) made up from unsynthesized material (288D7–E4). Taking up the class of servants in turn, the Stranger calls for a careful look (X* !: 289D3) at the professions remaining, a scrutiny that becomes even more sharply focused (
     3 : 290C3) as it continues. By the time he comes to the class of imitators, of course – a class he says contains a very large mob (

" $5 : 291A2–3) of people – the Stranger is ready to commit a full ten pages to graphic discussion of this group before concluding (at 302C) that it can be subdivided into six groups of pretenders. With examples like this in view, the presentation to the left appears no less lavish in descriptive detail than that to the right appears abstract and colorless. What is to be made of this highly textured portrayal of the societies over which the governors preside? Shortly before the call for a new paradigm at 278E, we may remember, the Stranger observed that while the account of statesmanship to that point seemed adequate in general outline (
 A  K . A5 : 277C1–2), it had not yet received the clarity that would be imbued ( O  '   : 277C2) by a commixture of colors. We also recall that the Stranger’s remedy for this defect included a discussion of the role of paradigms in dialectic, an illustrative definition of weaving as a

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paradigm for the definition of statesmanship, and an extended analysis of measurement as it applies to dialectic in particular. We are now dealing with the part of the dialogue where the Stranger’s remedy is being put into effect. The clarity and resolution that up to now has been missing is being added in the form of colorful details regarding the many civic skills with which statesmanship is being contrasted. This much seems clear at least: one use to which leftward division is put in the final pages of the Statesman is that of providing a scaffolding for the descriptive coloration needed to bring the picture of statesmanship to life. In the methodology of the Sophist, we may note in retrospect, occasion for detail is provided by the process of collection. By way of illustration, one need only think of the collection performed at the start of the definition of angling, with its numerous examples of production (farming, care of animals, fabricating equipment, and imitation) and of acquisition (learning, cognition, commerce, fighting, and hunting). It is not unreasonable to suppose that, with the elimination of collection in the Statesman (Chapter 4), the role of providing enlivening detail is taken over by leftward division instead. But surely there is more to the story than this. Taken by itself, the need for detail does not account for the fact that the membership of each class separated from statesmanship is carefully enumerated. What does precise numbering have to do with leftward division? As a conceptual aid for getting a grip on this question, let us reproduce the essential structure of Figure 6.1 in simplified form.9 In the following diagram (Figure 6.2), think of A, B, and C as features attributed to X (the thing to be defined, here statesmanship) along the right-hand line of division, B and C as features dichotomously opposed to B and C along the left (as contributing cause, for example, is opposed to direct cause in Figure 6.1), and the sets , -,  and , , 6 as features multiply distinguished under B and C , respectively (as producers of raw materials, tools, vessels, etc., are multiply distinguished under the category of contributing cause). For present purposes, it is stipulated that having the features A, B, and C is both necessary and sufficient for being X and that X thus can be defined as a thing that has these specific features. Speaking in recognizably Platonic terms, we may say that what it is (
 & A, as at 9

For purposes of illustration, what is essential to this structure is that there is a plurality of multiply subdivided categories to the left (here B and C ), not the specific numbers of subclassifications involved.

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A B´

B C´

C (X = df ABC)

figure 6.2. Simplification of Figure 6.1.

Sophist 218C1) to be X is to have this set of features. Being X by nature is to possess features A, B, and C. What makes Figure 6.2 instructive for our purposes is the alternative way it illustrates of expressing a thing’s nature. Given the dichotomous division of B into C and C , the fact that being C is included in the nature of X entails the exclusion of C . Being X by nature entails not-being-C . In parallel fashion, given the dichotomous division of A into B and B , the fact that being B is included in the nature of X entails that being B is excluded, which is to say that being X entails not-being-B as well. Because being X entails each separately, it entails not-being-C and not-being-B conjointly, which is to say that it entails their conjunction.10 Continuing to interpret the intent of the procedure, we note further that not-being-B entails not-being-, not-being--, and not-being- all in conjunction. Not-being-C similarly entails the conjunction of not-being, not-being-, and not-being-6. By what is often called “hypothetical syllogism,” we now see that being X entails not being any one of , -, , , , and 6.11 10

11

The term ‘entails’ (of which ‘→ & here serves as a formal equivalent) is being used without commitment to any particular system of logic. Any formal system will accommodate the inferences in the text as long as it sanctions (a) the basic truth-functional operations and (b) something equivalent to what might be dubbed “definitional summary”: (P → Q) ∧ (Q → P) → (P = dfQ). This without prejudice to whether Forms are “intensional entities” as some commentators insist (e.g., J. M. E. Moravcsik(1973), “Plato’s Method of Division,” p. 175). The inference thus far is: (1) (2) (3) ∴ (4)

X → (−B ∧ −C ) −B → (− ∧ −- ∧ −) −C → (− ∧ − ∧ −6) X → (− ∧ −- ∧ − ∧ − ∧ − ∧ −6)

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Next comes a crucial inference involving the assumption that the class of things to be considered (here civic arts) can be broken down into a set of subclassifications that are mutually exclusive and also exhaustive. In terms of Figure 6.2 (with mutual exclusivity built in), this is the assumption that there are no things other than , -, and  that possess both features A and B , that there are no things other than , , and 6 that share the features A, B, and C , and that there is only one thing (X) with features A, B, and C together. The upshot is that there are exactly seven specific subclassifications of things that are A, such that not being a given one entails being one of the others. By this time, the crucial inference is clear: not-being-X entails being one of the remainder. By transposition, moreover, not being any one of the remainder entails being X, which is to say that being X is entailed by not being any one of , -, , , , or 6.12 The remaining step is to combine the results of the last two paragraphs. Because being X and not being one of , -, , , , or 6 entail one another, being X necessarily is not being one of these others.13 Being X by nature is being A, B, and C. By the same entailment, it is X’s nature not to be one of , -, , , , or 6 as well. Here is an alternative way of expressing X’s nature. Something very similar to this seems to be happening in the final divisions of the Statesman. The key factor in making a tactic like this work is a complete enumeration, within a specified range (that of A in Figure 6.2), of all alternatives to being the thing for which a definition is sought. The relevant range of things in Figure 6.1, of course, is that of arts incorporated within a polity. With this context clearly specified (
  at 287B6), the Stranger is particularly concerned within the next few pages to provide complete lists of the callings being distinguished from statesmanship. This explains his care in itemizing exactly seven subclassifications of contributory cause at 289B1–2, followed by his expression of confidence that any leftover cause of this sort (e.g., engraving) can be made to fit within one of the seven. It similarly explains his concern to get a close (289D3) and yet closer (290C3) look at the class of 12

The inference continues as follows: (5) −X → ( ∨ - ∨  ∨  ∨  ∨ 6) (6) −X → −(− ∧ −- ∧ − ∧ − ∧ − ∧ −6) ∴ (7) (− ∧ −- ∧ − ∧ − ∧ − ∧ −6)→ X

13

The final step invokes what is called “definitional summary” in n. 10 above: (8) {(4) ∧ (7)} → {X = df (− ∧ −- ∧ − ∧ − ∧ − ∧ −6)}

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servants, making sure that all members of that class have been set apart (
5!  : 291A4) before passing on to consider imitations of genuine polities. And although both governors of imitative polities and subordinates in governance seem to fall naturally enough within their respective subclasses to require no further explanation, the need for an exhaustive enumeration of alternatives may also be the reason these subclasses are so conspicuously itemized (at 302C8 and 303E10–304A1, respectively). By carefully dividing all major forms of civic caregiving into specifically itemized subcategories, the Stranger sets up his final definition of statesmanship with reference to what it excludes.

6.5 The Statesman as Weaver At the beginning of the dialogue, the Stranger set out with YS to give a full account ( !: 257C1) of the statesman. That task appears to be completed with the final division, separating the governing subordinates from the genuine ruler. With this final division, a set of features has been identified that belongs to all statesmen and to statesmen exclusively. The statesman now can be defined as someone who possesses this set of features. When this point had been reached with the sophist, the morning’s conversation ended with a summary (a “weaving together;” "
  : 268C6) of defining features. But this does not happen with the statesman. After apparently completing the definition at 305E, the Stranger extends the discussion for another five pages dealing with the statesman’s role in fashioning a viable state. This final section contains a wealth of observations, social and psychological as well as political, some connecting with the Republic and others with the Laws. As in the case of the great myth before it, most of this material has no direct relevance to the present study.14 Our concern in this section is limited to the methodological significance of the Stranger’s final remarks. The Stranger introduces this final section by suggesting to YS that they undertake next to look carefully (
 !' : 305E9) at statesmanship with reference to the paradigm of weaving. Up to now, the paradigm most directly involved in the definition of statesmanship has been the 14

Readers with special interest in the political content of this final section probably will be familiar already with the analyses of Miller (1980), pp. 106–13; Rosen (1995), pp. 179– 90; and Lane (1998), pp. 163–82. Diverse as they are, these approaches all provide valuable insights.

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definition of weaving (paradigm D in section 5.2), as distinct from weaving as such. From this point onward, the paradigm of primary concern is the art of weaving itself (paradigm B in section 5.2). With this paradigm in mind, the Stranger says, they should discuss both the kind of intertwining ("
  : 306A1) involved in statesmanship and the sort of fabric it produces for us. As Miller insightfully points out,15 the ensuing discussion breaks down into three parts, corresponding to three stages in the weaving of a finished fabric from wool. First is the preparation of the raw materials from which the fabric is to be produced. In the case of the statesman, the raw materials comprise potential citizens naturally endowed with either courageous (  : 306E7) or well-behaved (    : 307B2) characters. Left by itself, the courageous character tends toward excesses of vigor and aggression, whereas the well-behaved character tends toward lethargy and cowardice. Neither extreme can dominate in a viable state. The statesman’s task is to weave these naturally opposing characters together into a durable social fabric. But before this can happen, the characters involved must be properly prepared. Just as the weaver of woolens requires the services of carders and spinners to convert the raw wool into usable form, so the statesman relies on teachers and tutors to make young people ready for citizenry. The role of these auxiliaries is first to weed out characters who are unteachable. This corresponds to carding out burrs and dung in raw wool. Their next task is to educate the remainder in appropriate civic virtues, corresponding to the spinning of wool into warp and woof. Once the two types of character (the “warp” and “woof ”) have been properly prepared, the final step is to entwine them together in a durable fashion. In the case of the city, this role falls to the statesman and involves an intermingling of citizens on two distinct levels. One is the spiritual level ( ['] X"5': 309C7) where citizens of disparate character are imbued with common opinions about the beautiful, the just, and the good.16 The other is the animal level (# 67  L: 309C3), having to do with marriage and the rearing of children. Contrary to the common practice of like marrying like, the statesman must bring it about that courageous and well-behaved types generally breed with each other. This

15 16

Miller (1980), pp. 106–07. The sense is that citizens should be brought up with unified beliefs about what counts and does not count as virtue within the state, not that they become knowledgeable of the corresponding Forms.

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will prevent either type from domination in the long run, which in either case would hasten the downfall of the state. What this kingly weaving together (- " " : 310E8) accomplishes, the Stranger concludes, is the completion of the fabric brought about by the practice of statesmanship (

 : 311B8). This accomplishment brings to completion (
: 311C2) the finest (1 : 311C2) product of the statesman’s art, a civic fabric held together by his rule and direction. Using very similar terminology,17 the elder Socrates concludes the conversation by complimenting the Stranger for bringing to completion (
: 311C7) in a most excellent fashion (V: 311C7) his portrayal of the king and statesman. There are two facets of this closing conversation that are noteworthy from a methodological perspective. One has to do with the respect in which it brings the portrayal of statesmanship to completion. As noted previously, the initial definition of statesmanship, based on the paradigm of shepherding, is defective both in failing to separate the king from many other caretakers of the human herd and in lacking the coloration and texture needed to exhibit its subject with adequate clarity. The first defect is overcome by the final series of divisions, which specify features distinguishing statesmanship from its kindred arts. But the other shortcoming must also be remedied before the portrait can be considered finished. Lack of vividness is made up in part by the detailed descriptions of the various arts separated from statesmanship in the divisions located to the left of Figure 6.1 (see section 6.4). Although these details provide a nuanced and textured depiction of the city in which the kingly art is exercised, the portrayal of statesmanship itself that emerges along the right remains relatively colorless and abstract. As matters stand at the end of the formal definition (305E), this portrayal still lacks the vividness called for by the Stranger in explaining the need for a new paradigm to replace that of the herdsman. One role of the final five pages is to flesh out the formal definition with a description of the statesman’s practical responsibilities in weaving together the components of a durable state. In light of the Stranger’s own 17

Miller (1980), p. 113, calls attention to the proximate appearances of 
 at 311C2 and C7 and reads Y" at 311C7 as ‘in turn’ in place of the probably more standard ‘again’. Miller’s reading emphasizes the association between the statesman’s completion of the web of state and the Stranger’s completion of his portrayal of the statesman, in contrast to the other reading, which presumably would refer back to the earlier portrayal of the sophist.

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criticism in setting aside the initial definition, this final attempt will be complete only when descriptive details like these have been added as a finishing touch. Once the coloration and texture provided by these details have been worked into the Stranger’s account, it is time for Socrates to compliment him on a job well done. The second point of methodological interest has to do with a final twist on the Stranger’s use of the paradigm of weaving. Returning to section 5.2 once again, we recall the distinctions among paradigm A, the familiar character used in teaching letters, paradigm B, the art of weaving used as a paradigm for statesmanship, paradigm C, the actual use of A in teaching letters, and paradigm D, the actual use of B in the definition of statesmanship as a paradigm for the use of paradigms in dialectic generally. Prior to the present chapter, however, little attention has been given to the actual use of paradigm B in that capacity. As a consequence, little was said previously about how weaving serves as a paradigm for statesmanship or about how its use in this role is supposed to serve as a paradigm for the use of paradigms generally in dialectical inquiry. Turning to this topic earlier in this chapter, the first thing we learned was that the series of divisions leading to a definition of weaving provided a pattern subsequently followed by the Stranger in his treatment of statesmanship. This can be reinforced by a comparison of Figures 5.2 and 6.1. Cuts are made along the left in both lines of division, and in both there is a departure from strictly dichotomous distinctions. The probable import of these distinctive features has already been discussed (section 6.3 and 6.4). Another facet of the Stranger’s use of weaving as a paradigm for statesmanship makes an appearance in the final pages of the dialogue. Having isolated necessary and sufficient conditions for statesmanship in the lines of division terminating at 305E (the formal definition), he enters into a detailed discussion of the statesman’s role in fabricating the web of state. In this particular context, weaving serves as a template for specifying tasks that have to be accomplished in fashioning the final product. Uneducable culls must be set aside, courageous and well-behaved characters must be imbued with common civic virtues, and the results must be interwoven as warp and woof into the fabric of a durable state. Here is the most explicit application of the weaver paradigm as such to be found in the Stranger’s portrayal of the statesman’s art. Let us recapitulate the respects in which weaving contributes to the completion of the Stranger’s task. As far as the portrayal of statesmanship itself is concerned, the art of weaving serves as a template for specifying

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the practical responsibilities of the statesman’s art, and the stepwise definition of weaving sets the pattern followed by the series of divisions leading to the formal definition of statesmanship in turn. But the Stranger’s main task in this dialogue is not just to produce a definition of the statesman’s art. More importantly, his task is to help the participants in the dialogue become better dialecticians. This is the underlying purpose of paradigm D, which is the use of weaving (paradigm B) in the definition of statesmanship as a paradigm for the use of paradigms in dialectical inquiry at large. As just noted above, one aspect of the Stranger’s use of weaving in this role is to provide a template for the elaboration of practical details involved in the statesman’s art. These details must be integrated into the formal definition in order for the portrayal of the kingly art to be complete. Let us think of it this way. Just as the warp provides the structure into which the woof is interspersed by the weaver, and just as the contingent of courageous natures provides the structure into which the “woof ” of wellbehaved natures is interwoven by the statesman, so the formal definition provides the structure into which the dialectician interweaves descriptive details that bring clarity to the final product of his or her inquiry. This is what Socrates complimented the Stranger for accomplishing at the end of the present dialogue. And this may well be what the Stranger is prompting budding dialecticians to aim for in taking this accomplishment as a lead to follow in their own inquiries. The Stranger’s treatment of statesmanship is the last fully developed illustration of dialectical inquiry in Plato’s corpus. So we have no way of knowing whether the procedures followed here represent the author’s final thoughts on the use of paradigms in dialectic. Regardless of what we make of it in a broader context, however, the Stranger’s blending of formal divisions and informal descriptions in his portrayal of statesmanship amounts to a methodological technique of considerable interest just by itself.

part ii METAPHYSICS

7 Excess and Deficiency in General

7.1 From Methodology to Metaphysics The definition of weaving was developed (279C–283B) for the express purpose of providing a paradigm to follow in a renewed attempt to define the statesman. Rather than returning to the statesman immediately, however, the Stranger enters into an enigmatic discussion of “Excess and Deficiency in general.” The ostensive purpose of this discussion is to prepare the discussants to address the question of whether the definition of weaving was needlessly long. Although YS is quite forthright in saying that he has no misgivings in that regard (283B3–4), the Stranger suggests that doubts of that sort might nonetheless arise. And in case he begins to waver on the matter subsequently, there are some considerations germane to all such cases that YS should hear. Thus begins an extended interlude on metaphysical matters that commentators often dismiss as a mere digression.1 Here is how it begins. 283C3

1

So let us begin by examining Excess and Deficiency in general (
C   G
-  )  AX ), in order that we may reasonably praise what is said on a given occasion in discussions like this, or else censure it for being longer than it should be or just the opposite.

See, for example, A. E. Taylor (1926), p. 889. Julia Annas, in her editorial notes to Waterfield (trans.) (1995), p. 47, reads this section as a comment on digressions which itself (as a digression) she finds “lengthy and not obviously relevant.” An even more negative view of the section is found in Seth Benardete (1984), p. III.114, according to which its very project is “self-contradictory.”

139

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283D

(1)

Metaphysics and Method in Plato’s Statesman Then let’s do so. It would turn out auspiciously, I think, if we began talking about these things. What things? About length and brevity, and Excess and Deficiency in general (
 G
 5  ) X). I suppose the art of measurement pertains to all these. Yes. Then let us divide it into two parts. For this is what our present task requires. Do say how this division goes. Like this: on the one hand according to the association of greatness and smallness with each other, on the other according to the being [that is] necessary for generation (        ). What do you mean?

The expression G
-  ) AX at the beginning of this passage occurs twice in the Statesman and only once elsewhere in the authentic Platonic corpus.2 The other occurrence in the Statesman is at 285B7– 8, where the Stranger suggests that enough has been said about Excess and Deficiency and the kinds of measurement it admits. The section bracketed by these two occurrences (283C3–285B8) occupies the very middle of the dialogue (twenty-six-plus Stephanus pages on either side). The significance of this arrangement (if any) is considered later, when we compare the overall structure of the Statesman with that of the Philebus. An equivalent expression G
 5 ) AX (with G
 5 for G
- ) occurs at 283C11–D1, where the Stranger identifies length and brevity as a particular case of Excess and Defeciency. This is the only time this particular expression occurs in the entire Platonic corpus. In view of the infrequency of these expressions in Plato’s writings, it is not surprising that they have received little attention from recent scholars. We return to this matter of terminology in section 7.2. As indicated at 283C11–D2, length and brevity (Z " . . . ) -53 ) are included under the general heading of “Excess and Deficiency in general,” and are bound up in turn with the art of measurement 2

The other authentic occurrence is at Protagoras 356A2–3, where the expression is used in a sense not directly related to measurement. There are occurrences also at (the spurious) Definitions (415A), suggesting that the expression had currency in the early Academy. Capitalization of this expression in the present context is explained later in this section.

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( ). The Stranger next proposes that they divide the art of measurement into two parts. The division goes as follows. On one hand, things can be measured according to the association of greatness and smallness ( ! " )   : 283D7–8) with each other. On the other, they can be measured according to the being that is necessary for generation. With this formulation (marked (1) in the left margin) of the division, however, the Stranger’s examination of the art of measurement hits a snag at its very beginning. Neither YS nor the reader has any hint at this point regarding the identity of this being said to be necessary for generation. As discussed in detail when we return to this topic in Chapter 9, moreover, there are substantial disagreements about the proper translation of the expression in question. It comes as no surprise to find YS asking what the Stranger means. Within the next page and a half, the Stranger provides five alternative formulations of the difference between the two kinds of measurement, no two exactly alike. Two alternatives (marked (2) and (3)) occur within the following set of passages. 283D11 283E

(2)

(3)

284A

Undoubtedly it seems to you that the larger (# '6 ) ought to be termed larger in comparison with nothing other than the smaller ( %  ), and the smaller in turn smaller than nothing other than the larger? It does. But what of this? Wouldn’t we say, rather, that there are things exceeding the condition of due measure (  %  " 3 ), or exceeded by it, whether in word or in deed, and that the chief difference between bad and good in human affairs lies in this? So it seems. Then we must lay it down that the Great and the Small ( %  " )  %   %) both have being and are judged in these two ways, not just in relation to each other as we said a moment ago. As was said just now, we should speak rather of their existing relative to each other on the one hand and relative to due measure on the other. Would you like to know why? Yes, why? If someone admits the greater in relation to none other than something smaller by nature, it will never relate to due measure. Agreed?

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Metaphysics and Method in Plato’s Statesman That’s so. But with this account, wouldn’t we destroy the arts themselves and all their products; and in particular wouldn’t we obliterate the art of statesmanship we are now seeking and the art of weaving just mentioned? For it seems to me that all such arts guard against exceeding due measure or falling short of it, not as something nonexistent but as something hard to deal with in their practice. It is by preserving measure (#  ) in this way that everything good and fair is produced. What then?

Responding to YS’s question of meaning, the Stranger surmises that YS probably thinks that larger and smaller can be compared only with each other. This is the first of the two kinds of measurement in question. To see that there is another kind, YS should note that there are some things that exceed due measure and other things that fall short of it. As far as human affairs are concerned, the chief difference between bad and good ( [   ) ) ! ) lies in the relation of our words and deeds to due measure or the mean.3 In the second formulation, accordingly, one kind of measurement amounts to comparing larger and smaller with each other, whereas the second kind involves comparison with an appropriate mean. Apart from a shift from nouns to adjectives in describing the opposing parameters of size, formulation (2) agrees with the previous formulation in its depiction of the first kind of measurement. But their characterizations of the second kind are markedly different. Formulation (1) says nothing about comparison with due measure, and (2) makes no reference to a being that is necessary for generation. Formulation (1) makes its distinction with reference to a certain kind of being (one necessary for generation), and formulation (2) makes the same distinction with reference to a certain standard of assessment (the relevant mean). Formulation (3), however, refers at the same time to a mode of being and to a manner of assessment. As the Stranger puts it, the Great and the Small both exist and are judged () in two 3

Comparison with Aristotle’s doctrine of the mean seems obviously relevant. As characterized at Nicomachean Ethics 1106b36–1107a8, the mean falls between two vices, one due to excess (G
-  ), the other to defect (AX ). An example given in this context is courage, standing at the mean ( : 1107a33) between fear and excessive confidence.

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ways. With regard to judging, they can be assessed either relative to each other or relative to due measure. In this respect, formulations (3) and (2) are roughly equivalent. But (3) goes on to say that the opposing principles in question might exist either relative to each other or relative to an appropriate measure. The focus in (3) is on the status of the factors to be assessed, as distinct from the measures involved in the assessment. In formulation (3), moreover, the principles that get assessed are the Great and the Small, in contrast with greatness and smallness in formulation (1). For reasons elaborated later, I read  %  " )  %   % (in the genitive) at 283E8–9 as referring to the principle #  ) #   said by Aristotle, in his account of Plato’s thought (notably in the Physics and the Metaphysics), to cooperate with the One in the constitution of sensible things. In Aristotle’s account, the dual principle of the Great and the Small is the general form of contrariety covering more specific opposites like greatness and smallness in (1) and larger and smaller in (2). This explains the use of capital letters in expressions referring to that principle. By way of anticipation, this also explains the use of capitals in the expression ‘Excess and Deficiency in general’ translating 283C3–4 and C11–D1. As will be seen in section 7.2, G
 5 ) AX is an alternative designation used by Aristotle for the Great and the Small. Other synonymous expressions for the same principle will be pointed out in due course (section 7.3), and all will be capitalized in their English equivalents. At the end of the passage quoted earlier (284A5–B2), the Stranger explains why acknowledging the second kind of measurement is important. Without measurement relating to due measure, he declares, the arts themselves ( 5  . . . ) would be destroyed along with all of their products. This is true of the art of statesmanship and the art of weaving in particular. Although the Stranger does not say so in this particular passage, the same result would follow for the art of dialectic. In this manner, both the subject matter of the present inquiry and the inquiry itself depend on the legitimacy of the second kind of measurement. By way of summary, it is preserving measure (#  at 284B1, not just  ) in this way that “everything good and fair is produced” (
  ! )  
6 ). We return for a careful look at this dependency in Chapter 9. It should be noted in passing, however, that the measure upon which the production of all things good and fair depends may well be related to the being said to be necessary for generation in

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formulation (1). After examining a series of parallel passages from the Philebus in Chapter 8, we shall be in a position to decide whether they are in fact identical. The Stranger puts even more stress on the dependency of art on the second kind of measurement in the following text, which includes two further formulations of the distinction between kinds of measurement as well. 284B4

(4) 284C

284D

(5)

284E

Well, if we obliterate the art of statesmanship, the search for the knowledge of kingship from then on will be impracticable. Very much so. So just as in the case of the sophist we proved it necessary for not-Being to exist, lest the argument elude us on this issue, what alternative is there now to making it compulsory that the more and fewer be measured not only with respect to each other but also with respect to the inception of due measure (  %  "   )? For if there is no agreement on this, it certainly is not possible for the statesman indisputably to have gained existence, nor anyone else with knowledge of practical subjects. Then we certainly must do the same in the present case. This task will be even larger than the previous one, Socrates – and we remember how lengthy that was. But it is entirely fair to venture the following assumption about the topic. What? That sometime we will need what we have been speaking of just now for an exhibition of exactness itself. Regarding what has now been well and sufficiently proved, however, I believe that it comes to the aid of our argument in a magnificent fashion; namely, one must suppose equally that all the arts exist and that at the same time larger and smaller are measurable not only with respect to each other but also with respect to the inception of due measure. For if the latter is the case, the former exist also; and if the former exist, then the latter is the case as well. But if either is not, then neither of them will ever be. This is correct. But what comes next?

In the previous dialogue, sophistry was shown to depend on the existence of not-Being. In the present context, statesmanship is said to

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depend similarly on the preservation of due measure. Along with this claim goes a fourth formulation of the distinction between two kinds of measurement. According to this formulation, more and fewer (#
 . . . ) A , another opposition falling under the Great and the Small) must be measurable not only with respect to each other but also with respect to the inception of due measure. The phrase   %  "   here is ambiguous between due measure itself being generated and the generation of things that exhibit due measure.4 In view of 284A5–B2, which makes due measure responsible for the production (generation) of all things good and fair, the latter sense seems clearly preferable. The translation ‘inception of due measure’ is intended to convey that sense – the sense specifically of due measure becoming manifest in products that are artfully generated. The phrase in question is repeated in formulation (5), in which larger and smaller (the same opposites as those in formulation (2)) are said to be measurable both with respect to each other and also with respect to the inception of due measure. What is novel with this formulation is that it generalizes dependency on due measure to all of the arts ( 5 
: 284D4) and points out that a reciprocal dependency exists as well. To paraphrase the Stranger here, the arts exist only if larger and smaller are measurable with respect to the inception of due measure, and if the arts exist then larger and smaller are measurable in this fashion. The second kind of measurement goes hand in hand with the existence of arts that generate good and fair products. If either does not exist, then neither will the other. Between formulations (4) and (5), the Stranger makes two observations that require explication. One is that the present task will be even larger than that of establishing the existence of not-Being in the Sophist. The other is that what they have been talking about just now will be needed when they come to “an exhibition of exactness itself ” (
) # -L 
  ). What they have been talking about just now is the dependency of the arts on the second kind of measurement for their existence. This dependency pertains not only to statesmanship (
# at 284C2) but to any art involving knowledge of practical subjects (
  
 : 284C2). 4

Among commonly available translations of the entire dialogue, those of Di`es, Skemp, and Rowe offer readings according to which the generation in question is of things that exhibit due measure, whereas Benardete has due measure itself being generated. Jowett wants it both ways, rendering the term differently here and at 284D6. Waterfield waffles, giving a translation with no mention of generation.

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The task at hand that will be larger than in the case of not-Being, presumably, is that of showing why the second kind of measurement is necessary for the existence of the arts. Although nothing more is said on this topic in the Statesman, substantial help on the matter can be found in the Philebus. We return to this topic in Chapter 8. But what of the need for what they “have been speaking of just now” when they come to “an exhibition of exactness itself”? There are at least two problems here. One concerns the occasion on which this exhibition is supposed to take place. Although it is clear that no such occasion arises in the remainder of the Statesman, it is possible that the author is anticipating here the discussion of accuracy in the arts found at Philebus 55E–59C. The relevance of this discussion to matters at hand is examined in Chapter 10. The other problem is to understand what the dependency of the arts on the second kind of measurement has to do with accuracy. As we shall see, pursuing this matter leads us to the art of dialectic itself. The general idea, by way of anticipation, is that dialectic is revealed at Philebus 57E–58E as the most accurate among the arts, and that its accuracy has to do with dividing things according to Forms (Chapter 11). At 284E1, YS agrees with what the Stranger has been saying and asks what comes next. The Stranger responds as follows. 284E2 It is clear that we should divide the art of measurement, (6) cutting it in two as we said. As one part of it we lay down all those arts measuring number (! # ), length, depth, breadth, and speed according to contraries; as another, those measuring according to the mean, to the fitting, the timely, and the requisite – all that has been withdrawn from the extremes to the middle. Each of the sections you speak of is vast, and differs widely from the other. 285A What we have been saying just now, Socrates, turns out to be the same as what is said from time to time by many clever people, thinking themselves to be saying something profound – that the art of measurement pertains to everything that comes to be. For everything in the province of art shares in measurement in some manner or other. These people, however, are not accustomed to studying things by dividing them according to Forms (& 0). Thinking such different things as these to be alike, they throw them together straightway into

Excess and Deficiency in General

285B

285C

147

the same bin. In other cases, they do the opposite – dividing, but not according to parts ( ). What one ought to do, upon first perceiving a community among some plurality, is not desist until discerning within it all the differences that rest in Forms ( 0). When manifold unlikenesses are noticed among numerous things, once more, one should not allow oneself to give up in shame short of having captured all kindred things within a single likeness, enclosing them by some existing kind. But this is enough to say about these topics, and about what is deficient and excessive. Only let us bear in mind that two kinds of measurement have been discovered in relation to these, and remember what we say they are. We’ll remember.

This section begins with the sixth formulation of the distinction between two kinds of measurement. In formulations (1) through (5), the first kind has been described simply as a measurement of relevant opposites in comparison with each other. Most of the differences we have been observing among these formulations have to do with varying ways the second kind of measurement has been described. In formulation (6), however, there are distinctive features to be noted in the characterizations of both kinds of measurement. As far as the first kind is concerned, we note that instead of mentioning specific contraries that might be compared with each other (such as larger and smaller in formulation (5)), this formulation specifies several dimensions along which relevant contraries might be encountered. Dimensions mentioned are number, length, depth, breadth, and speed. This indicates that the first kind of measurement covers not only contraries of size (e.g., larger and smaller), but also longer and shorter, deeper and shallower, broader and narrower, and faster and slower. As we shall see presently, these are all included under Excess and Deficiency as a general principle of contrariety. In formulation (6), furthermore, the second kind of measurement itself is considerably broader than indicated in previous formulations. Whereas (2) through (5) focus on some aspect of due measure (#  ), formulation (6) mentions measurement not only according to due measure but also according to what is fitting, timely, and requisite (#

) # # ) #  : 284E6–7). To be sure, the range

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of measures included here might be even broader, as indicated by the conjoined phrase “all that has been withdrawn from the extremes to the middle” (
 ! & Q
 ( #  
7 ! . 5 : 284E7–8). Although it is reasonable to surmise that reference to middle (#  ) here has something to do with “cutting through the middle” at 262B6, we will not be able to make full sense of this reference until the final chapters of this study. The Stranger’s next concern in this section is with unnamed “clever people” who agree that measurement is involved in all that comes to be,5 but who are remiss in not studying things by dividing them according to Forms. These people err sometimes in not dividing things that are different (like the two kinds of measurement), thinking them alike, and other times in dividing but not according to parts. In Chapter 11, we shall see that not dividing according to parts entails not dividing according to Forms as well. This cursory survey of the topics treated between 283C and 285C has left us with a budget of problems that require further consideration. We need to know more about the being identified as necessary for generation in formulation (1) and about how it is related to the due measure that figures in the other formulations. We need to find out more about the Great and the Small in formulation (3) and about its relation to the more specific opposites in the other descriptions of the first kind of measurement. As far as the second kind of measurement is concerned, we want to become clear about how it is mutually dependent with the existence of the arts and about its involvement in the production of “everything good and fair.” And above all, we need to reach a better understanding of the principle of “Excess and Deficiency in general” that lies behind this examination of the two kinds of measurement. We return to these matters in Chapter 9. Our task in the meanwhile is to bring together some secondary material that will help us respond to these various needs. The next section traces observations by Aristotle and his later commentators on Plato’s use of the expression G
 5 ) AX.

5

The “clever people” in question are often identified as Pythagoreans. See Miller (1980), p. 69; Benardete (1984), p. III.117; and Annas (1995), p. 44, n. 41. A more likely attribution, it seems to me, is to followers of Protagoras, who is made to say in the Theaetetus (152A2–4) that man is the measure (  ) of all things with regard to being or notbeing.

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7.2 Excess and Deficiency in Aristotle and His Commentators As already noted, the terminology of excess and deficiency in the Statesman (283C3–4, 283C11–D1, 285B7–8) has received little attention from recent commentators. Considerably more importance was assigned to the expression G
 5 ) AX by ancient authors writing on Plato’s philosophy. The authors in question include first Aristotle himself, and then a group of writers between the second and sixth centuries a.d. who are generally known as the Greek commentators on Aristotle.6 Although the immediate concern of the latter was exegesis of various Aristotelian texts, most of these writers approached Aristotle with an extensive knowledge of Plato’s works. This, and the fact that they had access to materials bearing on Platonic interpretation that are no longer available, make them a valuable source of insight into how Plato was understood by his early readers. Particularly useful for present purposes is what these authors have to say about Excess and Deficiency in relation to other key factors in Plato’s late metaphysics. One thing we learn about the expression G
 5 ) AX from these sources is that Plato used it in a general sense covering a variety of more specific contraries. Another is that it can serve as an alternative designation for Plato’s (the) Great and (the) Small. At Physics 187a14– 17, for example, Aristotle mentions dense and rare as contraries that can be generalized into excess and defect,7 in the manner of the Great and the Small of Plato (#  . . . J ) #  : 187a17). Essentially the same message is repeated at Physics 189b8–11 (without direct reference to Plato), with more and less ( C ) = : 189b10) added to dense and rare as contraries that may be generalized into excess and defect. In his wide-ranging criticism of the Forms in Metaphysics A.9, moreover, Aristotle likens the Great and the Small of Plato to the rare and dense of the physical philosophers, inasmuch as these are excess and defect (992b1–7). Another text in which Aristotle refers to excess and defect as a general form of contrariety is the History of Animals (486b6–9 and 16–17). 6

7

An informative account of the early history of Aristotelian commentary in the Greek language is provided by Richard Sorabji’s general introduction to the series of translations currently being produced under his editorship, first appearing in Wildberg (1987) and reprinted in subsequent volumes of the series. The Oxford translators of the Physics, the Metaphysics, and the History of Animals render AX ‘defect’ (uncapitalized), rather than ‘Deficiency’ as in the present study.

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Aristotle’s reference at Physics 187a16–17 to excess and defect as a generalized form of contrariety is mentioned by each of the three Greek commentators whose works on the Physics have survived to the present. Themistius (fourth century a.d.) paraphrases Aristotle’s remark,8 observing that excess and defect are the most general contrary qualities, like Plato’s principle of the Great and the Small. In their comments on Physics 187a16, moreover, both Philoponus and Simplicius (alike sixth century a.d.) repeat Aristotle’s claim about excess and defect being a generalized form of contrariety, comparable to Plato’s Great and Small.9 The equivalence of G
 5 ) AX to Plato’s Great and Small is also alluded to in the commentary by Alexander (second–third century a.d.) on the Metaphysics. Commenting on 987b25–29, Alexander says that Plato’s dyad was called excess and defect, and goes on to equate excess and defect with the Great and the Small.10 Excess and defect are also mentioned several times in apposition with the Great and the Small in Alexander’s comments on 992a24 (122.19–24). Here are five philosophers from antiquity, no less qualified than we are to pronounce on Plato’s views, who have gone on record affirming that Excess and Deficiency are equivalent to Plato’s the Great and the Small. It seems unlikely in the extreme that Plato’s own sole use of the expression G
 5 ) AX at Statesman 283C11–D1 was intended in a radically different sense. Having noted the highly probable equivalence of Excess and Deficiency to Plato’s principle of the Great and Small,11 we are in a position to consider other expressions used by Aristotle and his commentators with apparently the same reference.

7.3 Equivalent Expressions in These Ancient Authors Another expression for the Great and Small is    " (the Indefinite Dyad), frequently used by Aristotle in the Metaphysics while discussing the views of Plato and like-minded members of the Academy.12 Interestingly enough, this phrase also appears more than one dozen times in Simplicius’ commentary on the Physics, even though it is not 8 9 10 11 12

Themistius, in Schenkl (ed.) (1900), 13.13–15. Philoponus, in Vitelli (ed.) (1887), 91.16–17. Alexander, in Hayduck (ed.) (1891), 54.8–11. From this point on, synonymous expressions for Plato’s principle of the Great and the Small are capitalized. Exact locations for references in this section are given in the Appendix.

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used in the Physics itself. In most of these occurrences it is used in conjunction with other expressions for the Great and the Small, and attribution is usually made to Plato explicitly. The phrase is also used more than one dozen times in Alexander’s commentary on the Metaphysics, again with Plato usually mentioned by name. Another occurrence is in Philoponus’ commentary on the Physics, where Plato once again is explicitly cited. A fourth apparent synonym for Plato’s principle appears at Metaphysics 1091b32, where Aristotle refers to the “contrary element” of the Great and the Small or the Unequal (# 1  ) as bad itself. The Unequal is also spoken of as equivalent to the Great and Small explicitly at 1087b11, with an indirect reference to Plato, and identified with it by implication at 1088a15 and 1091a24. Commenting on these and other passages, Alexander several times pairs the Unequal with the Great and the Small, as well as with Excess and Defect and the Indefinite Dyad, sometimes mentioning Plato by name as the thinker responsible. Yet a fifth synonym used by Aristotle is 1
 (Unlimited) itself, which in contrast with
s (Limit) is mentioned as first in the Pythagorean list of contraries at Metaphysics 986a23. The term # 1
 is then associated with the Platonic principle in question at 987b26, where Aristotle remarks that Plato differed from the Pythagoreans in constructing his Unlimited out of Great and Small. In commenting on this and subsequent passages, Alexander describes Plato’s Unlimited not only as the Great and the Small, but as Excess and Defect as well. In a parallel remark at Physics 203a10–16, Aristotle says that whereas the Pythagoreans identified the Unlimited with the even, Plato has two 1
, the Great and the Small. In their comments on this particular passage, both Philoponus and Simplicius affirm that Plato’s Unlimited was the Great and the Small, Simplicius also mentioning the Indefinite Dyad as an equivalent formula. Themistius agreed in his paraphrase, adding that the Unlimited was Plato’s “other nature” (D 3, matching the description of Plato’s dual principle at Metaphysics 987b33). We have learned so far that Aristotle referred to Plato’s principle of the Great and the Small alternatively as the Indefinite Dyad, the Unequal, and the Unlimited, in addition to Excess and Defect. Alexander and Simplicius use all five expressions as co-referential as well. All four commentators mentioned earlier join Aristotle in referring to this principle as the Unlimited. All save Themistius use the expression   " to the same effect. And all save Themistius and Philoponus refer to it as the Unequal as well as the Unlimited Nature.

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It is impossible to gauge the extent to which the terminology used by these four later authors for the Great and the Small is derivative from Aristotle, rather than from the dialogues themselves or from yet other sources. To rein in the assumption that it all came from Aristotle, however, we should note two other terminological equivalents that were not used in this connection by Aristotle himself. Because both of these expressions also occur in the Philebus, as we shall see in Chapter 8, it is natural to surmise that this dialogue is where they came from originally. One is  
 " 3 (the Nature of the Unlimited, sometimes rendered the Unlimited Nature), which occurs in the commentaries both of Alexander and Simplicius. As part of his remarks on Metaphysics 987b25, Alexander reports Aristotle’s claim that Plato made an underlying substance of Excess and Defect, also called the Great and the Small. Alexander then observes that these contain the Nature of the Unlimited, repeating an expression appearing three times in the Philebus (18A8, 24E4, and 28A2). Alexander is also paraphrased by Simplicius, in commenting on Physics 202b36, as stating that Plato said that the Dyad was of the Nature of the Unlimited, because the Great and the Small engage the More and Less (discussed later) which go on without limit. Two other uses of the expression occur in an apparent quotation by Simplicius of Porphyry. In one, Porphyry reports that Plato held certain opposites, including the More and the Less, to be of the Unlimited Nature. In the other, he suggests that the Indefinite Dyad is exhibited by a repeated segmenting of parts of a cubit into increasing smaller halves, adding the portion removed at each stage to the part remaining undivided. In this manner, Porphyry claimed, the Unlimited Nature is disclosed as one portion proceeds toward the Great and the other toward the Small. Simplicius prefaces this quotation with the remark that within it Porphyry is expounding on Plato’s enigmatic discourses on the Good, as recorded by Aristotle, Heracleides, and Hestiaeus, and that the passages quoted are from Porphyry’s writing on the Philebus (Simplicius, On the Physics, 453.25–31). Simplicius follows the quote by repeating that it pertains to Plato’s conversation on the Good and adds that Porphyry thought Plato’s utterances on this occasion probably fit in with what he wrote in the Philebus (ibid., 454.17–19). As will be seen in the next chapter, we can be almost certain that Porphyry was right. The other expression used by the commentators but not by Aristotle in reference to the Great and the Small is # C ) (Q) = (the More and (the) Less). We have encountered this expression already in

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Simplicius’ quotations from Porphyry and Alexander, both associating the More and Less with the Unlimited nature. Simplicius also uses the expression several times in his own account of Plato’s doctrines. Commenting on Physics 189b8, for instance, he mentions the More and Less and the Great and Small as contraries that sustain Excess and Defect (ibid., 204.6–8, 12–14). Other passages connecting the More and the Less with the Great and the Small appear in his comments on Physics 207a18. This expression for the More and Less, of course, is used time and again in the Philebus, in association with both the Nature of the Unlimited and the Unlimited itself. To bring the tally up to date, we have five co-referential expressions for Plato’s principle used both by Aristotle and by his commentators, and two others used by Simplicius, Porphyry, and Alexander. Each appears with sufficient frequency in relevant contexts to show that its association with the others is more than coincidental. Less frequently occurring locutions that may be noted in passing are #  
  (the Indefiniteness of the Unlimited), which appears twice in Simplicius’ commentary on Physics 202b36, and # 1  " (the Unequal Dyad) in Alexander’s comments on Metaphysics 1087b4. Up to the final decades of the twentieth Century, modern Plato scholars were almost unanimous in assuming that the views attributed to Plato in Metaphysics A could not be found in Plato’s dialogues. Given that assumption, some readers may still be surprised to learn that no less than five of these seven frequently used expressions for the Great and the Small play major roles in the Philebus and the Statesman. In the Statesman we find Excess and Deficiency and the Great and the Small itself. In the Philebus, there are several appearances each of the More and Less, the Unlimited, and the Unlimited Nature. The roles played by these expressions in the Philebus have been shown directly relevant to the claims about Plato’s views made by Aristotle in terms of the Great and the Small and the Indefinite Dyad.13 Our concern in the next chapter is to lay the basis for extending this relevance to the terminology of Excess and Deficiency in the Statesman as well. 13

See Sayre (1983), (1987), and (2005).

8 The Great and the Small in Plato’s Dialogues

8.1 The Purpose of This Chapter Chapter 7 identified seven expressions used equivalently by Aristotle and his commentators for Plato’s (the) Great and (the) Small. All but two of these appear in the Platonic dialogues. Of the five used by Plato, occurrences of G
 5 ) AX (Excess and Deficiency) and #  ) #  (the Great and the Small) are found in the Statesman. The remaining three, # 1
 (the Unlimited), # C ) = (the More and Less), and  
 3 (the Unlimited Nature, or the Nature of the Unlimited), occur in the Philebus. The tactic of the present chapter is to examine the use of these expressions in the latter dialogue in hopes of elucidating the nature of Excess and Deficiency in the middle section of the Statesman. Merely knowing that these three expressions occur in the Philebus, of course, tells us little about their meaning in that particular context. Of the three, # 1
 has received the most extensive discussion. Ancient commentary begins with Aristotle, who says in the Physics that Plato made the Infinite (or Unlimited) a substance in its own right (203a4–5), that it is present both in the Forms and in sensible things (203a8–10), and that Plato had “two infinites,” the Great and the Small (203a15–16). Commenting on these and adjacent passages, Simplicius equates the Infinite with the Indefinite Dyad and the Great and Small on Plato’s behalf (see Appendix). Similar connections are made by Alexander, Themistius, and Philoponus (see Appendix). Because none of these authors made much of an effort to explain the meaning of this terminology, however, they

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provide little help in understanding the nature of the Unlimited in the Philebus.1 Scholarly preoccupation with the nature of Plato’s indefinite principle has continued to the present. An informative survey of views through most of the last century was included in Gosling’s commentary on the Philebus (1975),2 augmented and updated by the present author’s Plato’s Late Ontology (1983). The latter work compares Aristotle’s account of Plato’s doctrines in the Metaphysics with the metaphysical sections of the Philebus, in hopes of shedding light on both texts by the comparison. The exegesis of Plato’s views in this book is largely mathematical, tying Plato’s Great and Small to work on irrationals being done by Eudoxus in the Academy at roughly the time the Philebus was written. It seems fair to say that, with the exception of some recent contributions by Mitchell Miller,3 little gain 1

2 3

As typical with Aristotle’s treatment of his predecessors, his discussion here of Plato’s view on the Unlimited is part of a more general examination of earlier opinions and is generally critical. The commentators, in turn, are primarily concerned with Aristotle’s texts and tend to avail themselves of Plato’s terminology without further explanation. An exception of sorts comes with Simplicius’ paraphrase (in Diels (ed.)(1882), 453.31– 454.16) of what Porphyry said about the Indefinite Dyad in his writing on the Philebus. According to Simplicius, Porphyry’s view was that the Indefinite Dyad (also referred to in this writing as the Great and the Small, the Unlimited Nature, and Excess and Deficiency) can be exhibited by segmenting part of a cubit into increasingly smaller portions and adding the portions removed to the part initially unsegmented. Porphyry’s idea apparently was that the part left unsegmented tends toward the Great while the part subject to segmentation tends toward the Small. While the possibility of carrying out this process of segmentation indefinitely shows that a cubit is continuous, as Porphyry (according to Simplicius) pointed out, it tells us little about the nature of the Great and the Small itself. One does not have to subscribe to the notion of an indefinite principle to acknowledge that a line can be divided indefinitely. Because Porphyry’s work on the Philebus is no longer extant, we cannot check whether it had more to say about the Great and the Small than Simplicius reported. J. C. B. Gosling (1975). Miller’s view is laid out in Miller (1990), (1999), and (2003). As laid out in these writings, Miller’s conception of the Unlimited is based primarily on his analysis of two examples in the Philebus. One is the example of musical pitch at 17B–D, the other that of phonetic elements at 18A–D. In the context of the former, Miller understands the Unlimited to be a continuum between high and low tones. At the high end of the continuum, high exceeds low, and at the low end “low predominates over high” ((2003), p. 27). Over the range of the continuum, there are infinitely many “possible balances of low and high” (ibid.), with a midpoint at which high and low are equal. The role of Limit in this scheme is to select sounds from the continuum “that are ‘musical’ in a normative sense” (p. 28). The proper selection constitutes “music in all its perfection (26A)” (ibid.). A similar analysis is given the division of phonetic sounds by Theuth at 18A–D. The continuum in this case ranges from “sounds uttered with the maximal release of breath to those uttered by the maximal cutting-off of breath” (p. 31). This continuum provides for many “different balances of the opposites,” a normative selection among which distinguishes between

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has been made during the last two decades in understanding the nature of Plato’s principle. Rather than revisit the previous comparison between the Philebus and Aristotle’s account in the Metaphysics, this chapter focuses on the main metaphysical passages in that particular dialogue with only occasional reference to comments by Aristotle. We shall also pass over the probable mathematical background of these passages in the Philebus. Our purpose, once again, is to examine the meaning of the three expressions used in this dialogue for the Great and the Small, with the hope of gaining a fuller understanding of Excess and Deficiency in the Statesman.

8.2 Three Synonymous Designations in the Philebus Let us begin with the Unlimited. The term # 1
 occurs (with the definite article) about twenty times in the Philebus. By present count, there are seven occurrences in the section dealing with the “godly method” (16C5–18D3) and ten in the section discussing the ontology underlying all that exists (23C4–27C1). The rest occur in subsequent passages referring back to this latter section. There are complications in the “godly vowels and mutes, in the middle of which there are certain unvoiced sounds (pp. 31–32). In accord with the way these various sounds fit together, Theuth collects them together under the single Form  5' , or element. Miller’s analysis of these examples highlights important features of each that must be taken into account. In my current estimation, however, there are several respects in which his analysis appears problematic. The basic problem is that the continuum of the Unlimited, as he understands it, is already laden with structure. For one thing, the continuum of vocal sound comes already provided with a “frame” of “opposites and middle” (p. 31). This seems contrary to Socrates’ characterization of the Unlimited at Philebus 31A9–10 as lacking beginning, middle, and end. Another problem in this regard comes with viewing the continua in question as providing many possible balances of their respective opposites. Balance (like equality) is a relation between determinate properties. But given the way Plato has Socrates describe the Unlimited (e.g., at 24C–D), it is totally lacking in determinate features. As far as the dialogue is concerned (25A–B, D–E), it is the role of Limit to impart relations of this sort. (Miller himself seems to acknowledge this in (1999), where he notes that fixing the proportions of the opposites on a continuum results from an instantiation of Unity (p. 230). On the surface, at least, this seems to conflict with what he says in the other papers.) How the Unlimited itself could consist of “possible balances of opposites” remains uncertain; possible or actual, a balance is a relation of determinate properties. Yet another problem of the same sort concerns his characterization of the midpoint of a continuum as a place where the opposites are equal. If there is any midpoint between two determinate degrees of high and low, however, it would be a place that is neither high nor low, not one in which high equals low (as in (2003), p. 27). Although these difficulties do not rob Miller’s account of its many acute insights, they suggest that it needs further development.

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method” sequence having to do with multiple senses of the term in question (discussed elsewhere4 ). For the moment, we limit our attention to the ontological section, where the term seems to maintain the same sense throughout. The Unlimited is the first to be examined of four ontological principles in this section. The others are Limit, Mixture, and Cause, listed and discussed in that order. The Unlimited is introduced with the help of an example, hotter and colder, which are characterized as having the More and Less residing within them. Because of this, hotter and colder never reach a termination ( : 24B1, 7), which renders them “entirely unlimited” (
 
 
: 24B8). What makes hotter and colder unlimited, in short, is the unrestricted presence of the More and Less within them. Continuing with the More and Less, Socrates goes on to mention other comparative terms (strongly and mildly, stronger and gentler, more and fewer) that have More and Less within them, and thereby are prohibited from having a definite quality (
# B : 24C3–4). To drive the point home, he observes that definite quantity and due measure (  : 24C7) evict comparatives such as strongly and mildly from the domain of the More and Less. The reason is that definite quantity is a kind of termination, bringing things to a standstill and putting an end to further progression within that domain. To forestall the need for more examples, Socrates then provides a general definition in terms of what he calls a mark ( ' : 24E5) of the Nature of the Unlimited (  % 
 " 3: 24E4). The characteristic mark of this principle is that it consists of everything we find “becoming more and less” ( C  ) =    : 24E7–8). All such things fall within “the class of the Unlimited” (#  % 
 "  : 25A1). Other members of this class, mentioned at 25C8–11, are drier and moister, faster and slower, and larger and slighter, all of which characteristically admit the More and Less. Other occurrences of # 1
 in this section pertain to the role of the Unlimited in combining with Limit to produce members of the Mixed class. The key passage in this sequence, of course, is the general characterization of the class of the Unlimited, which identifies becoming more and less (or More and Less) as the Nature of the Unlimited (or Unlimited Nature). Here within a few lines we find three expressions used in the Philebus for the Great and the Small. Their several uses in this passage, 4

Sayre (1983), ch. 3.

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moreover, are closely interrelated. Whatever is characterized by More and Less exhibits the Nature of the Unlimited, and whatever exhibits that character belongs to the class of the Unlimited itself. Two other references to the Unlimited Nature by name occur at 18A8 in the context of the “godly method” and at 28A2 where Socrates begins reflecting on the unlimited character of pleasure and pain. At 18A, Socrates repeats the advice of 16E–17A that when one starts with a single Form, one should not look for the Unlimited Nature before one has identified a specific number of other Forms in between. Attention to the intermediaries, Socrates says at 17A, makes the difference between dialectical and eristic discussions. At 28A, Socrates observes that if pleasure shares any part of goodness, this must be conferred by something other than the Unlimited Nature. For pleasure, like pain, admits varying degrees of intensity (i.e., is Unlimited), whereas good is a mixture of the Unlimited with Limit. We turn now to the More and Less. The expression C ) = (without article) occurs at 24E7 in connection with the mark of the Unlimited, as already noted. Whatever comes to be characterized by More and Less, Socrates says there, exhibits the Nature of the Unlimited. There are six other occurrences (all with article) in the section on ontological principles, all in connection with particular opposites that exhibit that character. Two other occurrences at 41D8 and 52C7 pertain to the unlimited character of pleasure or of its opposite pain. Particular opposites said here to fall under the More and Less, in addition to those mentioned earlier, are hotter and colder, strong and mild, stronger and gentler, and drier and moister; and in the context of music, high and low, and quick and slow. According to the summary characterization of the Unlimited at 24E–25A, a necessary condition for membership in this class is that the opposite in question admit of becoming more and less. As something becomes more dry, for instance, it correspondingly becomes less moist, and so for the other opposites involved. Being characterizable in terms of more and less, however, is not sufficient for membership in the class of the Unlimited. It is not hard to find many arrays of entities ordered by more and less that do not belong to this class. A representative example is the series of positive integers. Each item in this series is more than the one before it and less than the one following. But numerical relations are features explicitly said at 25A7–B3 to be excluded from the class of the Unlimited. Relations of number to number, along with those of measure to measure, fall within the class of Limit instead.

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Terminologically, what is unlimited (1
 ) is what lacks limit (-
). Ontologically, the class of the Unlimited is made up of everything that has not submitted to Limit. However designated, the domain of the Unlimited excludes whatever has been limited by number or measure. In effect, it excludes everything with fully determinate features, such as the sequential ordering of the positive integers. A short list of general features excluded by the Unlimited is given at 25A8–B1. Socrates here describes, as contrary to the More and Less, the equal (# 0 ), the double (# 
 ), and all things related “as number to number or measure to measure” (
# ! # ! # /  \;
#  ). This is the first of two descriptions of the class of Limit, a description to which we return in the following section. The other description of the class of Limit comes at 25E1–2, with the observation that it includes, as well as the equal and the double, whatever else terminates the conflict of opposites by “infixing number making [them] commensurate and harmonious” (3  L ) 3    !' ! # 
6). Among other such factors are definite quantity (#
# ) and due measure (#  at 24C7), the form of Limit said to bring about the condition of health at 25E7–8, and the kind of Limit at 26A2–5 that establishes the art of music when imposed on the unlimited opposites of high and low and fast and slow. In addition to Limit and the Unlimited, the other two ontological principles are Mixture and the Cause of mixture. Mixture is defined at 26D8–9 at the single class constituted by all the progeny (A ]
 ) of the other two principles, which is to say all “coming-into-being from the measures established by Limit” (  (   .   %
  
    ). And Cause is identified at 27B1– 2 as the Maker (  " % ) who produces what comes into being by mixing corresponding forms of Limit and the Unlimited. Mention in these passages of all things that come into being as a result of mixing Limit with the Unlimited should remind us of the being said to be necessary for generation at Statesman 283D8–9. We look more carefully at these passages when we return in the next chapter to the section on Excess and Deficiency in the Statesman.

8.3 The Definite, the Equal, and Their Privations Just as the Unlimited is what lacks limit, so the Unequal is something that lacks equality and the Indefinite Dyad something characterized by lack of definite features. While neither of these latter two privative terms is

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used by Plato in connection with his indefinite principle, their positive counterparts appear several times in the Statesman and the Philebus. By looking carefully at how # 0 and Q +  are used in these dialogues, we can gain at least a tentative idea of the significance that might have been attached to the privatives Q 1  and    " by Aristotle and his Greek commentators. Let us take the Indefinite Dyad first. In one grammatical case or another, there are six occurrences of # +  in the Statesman. All carry the sense of distinctive feature or defining characteristic. In his review of the divisions preceding the Myth of Cronus, the Stranger reminds Young Socrates that they are looking for “the defining features of the king” (#  % - + : 266E1). In the midst of his comparison of the statesman with the knowledgeable doctor, he calls upon “the truest criterion” (# + . . . ! * : 296E2) of correct city management. And in between, he talks about the defining characteristics of constitutions (292A6, 293E1), of medicine (293C2, no article), and of various other things that had come into question (292C5). Essentially the same sense is carried by the occurrence at Philebus 17D1, where Socrates refers to the notes defining (+ ") the intervals of the musical scales. In each of these occurrences, +  designates a feature distinguishing the thing possessing it from other things that are similar but not the same. In this sense of the term, accordingly, something is indefinite if it possesses no distinguishing feature. Carrying this sense over to the terminology used by Aristotle and his commentators, Plato’s Indefinite Dyad would be a pairwise classification of things related by More and Less, but otherwise without distinguishing characteristics. We turn next to the Unequal, privative of # 0 . One common use of 1  , of course, is to express a mathematical relation (that of having different numerical values), and it was often employed by Plato in that use. The term also carries the meaning of ‘disparate’ (like its English equivalent), in the sense of unevenly matched, as well as that of unjust or unfair. But it would be unhelpful to try to pack all those senses into the term as used by Aristotle and his commentators with regard to Plato’s dual principle. Both Alexander (commenting on the Metaphysics) and Simplicius (commenting on the Physics) follow Aristotle in treating Plato’s Unequal as equivalent to the Indefinite Dyad and the Great and the Small. Whatever else the Unequal amounted to, it must have been a principle of indeterminacy. Although Plato does not use 1   in this sense in the written dialogues, its positive counterpart 0  plays a featured role at Philebus

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25A7–8 and again at 25D11. As already noted, the former occurrence is part of Socrates’ initial characterization of Limit as comprising, first the equal (# 0 ) and equality, and after the equal the double and relations of number to number and measure to measure. The latter occurrence is part of the second characterization of Limit as including equal, double, and whatever else produces number making the opposites (of the Unlimited) commensurate and harmonious. Given the presumed equivalence of the Unequal with the Unlimited in subsequent commentary, what are we to make of the equal and equality as kinds of limit that impart number and commensurability to the indefinite principle in the Philebus? Contrary to what may be a natural first assumption, 0  here cannot be intended to include equality among numbers or other mathematical quantities. In the first characterization, it is explicitly stated that numerical relations come after ( ) the equality in question. This means that the equal is something that can be present independently of determinate numbers. At 24C–D, moreover, Socrates says explicitly that definite quantity does not reside in the Unlimited, which indicates that definite quantity must be a contribution of Limit. Because the equal comes first among forms of Limit, and numbers follow subsequently, an Unequal that lacks limit could not itself include numerical relations. But if numerical equality is excluded from the equal at 25A8–9 and 25D11, what is left? A clue comes from the language of Aristotle and the commentators. Several times in the Metaphysics (1083b23–24, 1083b31, 1091a24–25), Aristotle speaks of the equalization of the Great and the Small. Aristotle’s concern in these passages is with the Platonic generation of the numbers. Alexander follows suit in commenting on these passages, twice (On the Metaphysics, 768.22, 820.2) referring to the equalization of the Great and the Small by the One. For these authors to bring the One into the picture in this connection should come as no surprise, in light of Aristotle’s remark at Metaphysics 987b20–22 that the numbers come from the Great and Small by participation in the One. What this adds up to is that the Unequal has the potential, as it were, of taking on numerical relations, but does so only upon being subjected to the kind of limit coming with the equal and the double. The equalization Aristotle and Alexander speak of must be a matter of taking on determinate features that enable comparison in terms of numerical equality and inequality alike. As a result of the participation of the Great and the Small in the One, quantities emerge with features enabling them to be either equal or unequal to each other. Whatever else may be involved, equality comes into play when the Unequal participates in the One – which

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is to say, when it becomes equalized. This results in the production of quantities that can be compared as number to number, as in 3 = 3 and 3 = 4. And once equality becomes operative, the double follows, enabling further comparisons like 2 × 3 = 6. Before equalization, the Great and the Small is devoid of features determinate enough to admit numerical comparison. After equalization, the whole range of numerical relations somehow comes into being.

8.4 More and Less: Unlimited in Multitude There is another expression in several late dialogues that sometimes serve as a descriptor of the Great and the Small. So at least I have argued on several previous occasions.5 The term in question is 1
 #
!  (unlimited in multitude) or sometimes simply 1

!  (unlimited multitude). It occurs mostly in the Parmenides but can be found in the Theaetetus and the Philebus as well. This section deals primarily with its use in the Philebus. Although in one instance (Philebus 17E3) the expression is preceded by a definite article and thus invites translation as a nominative phrase, it most often functions as a descriptor and not as a name.6 At any rate, it should not be thought of as a synonym for the expressions designating the Great and the Small; and it was not so used by Aristotle or the later commentators. Nonetheless, its use by Plato in describing this principle can be informative. Let us look first at its use in the Philebus. Having explained the divinely revealed pathway of discovery in the arts (16C5–17A5),7 Socrates turns immediately to illustrate this method in a number of familiar skills. First mentioned is the skill of literacy, which of course is the skill being imparted in the paradigm of paradigms at Statesman 277E–278C. While vocal sound is singular ( : 17B3) for each and every one of us (unique for each person), Socrates observes, it is also indefinitely (or unlimitedly) multitudinous (1
  . . .
!: 17B4). Merely knowing its unlimitedness (# 1
 : 17B7) or its unity (# B : 17B7), however, does not make us knowledgeable users of 5 6

7

Sayre (1983), ch. 1, section 4, ch. 3, sections 1 and 2; (1996), ch. VI, passim. In commenting on this expression in (1996), I sometimes equated the Unlimited and the Unlimited Multitude (e.g., p. 132). In retrospect, treating the expression as a name or title seems unwarranted. An analysis by the present author of the “godly method” can be found in Sayre(1983), ch. 3, section 1.

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language. What makes us literate, rather, is knowing how many sounds there are and their various properties. A more specific description of what this amounts to comes at 18B–D with the story of Theuth, the Egyptian god who first developed the art of literacy. Theuth’s achievement began with the observation that vocal sound is Unlimited and that in this indeterminacy there can be perceived a plurality of vowels. He next discerned a certain number (! # : 18C1) of sounds other than vowels that do not require articulation. As a third step, he separated ( : 18C3) what are now called mutes. What Theuth has done thus far, it appears, is to isolate three general kinds of phoneme – vowels, semivowels, and mutes. His next move, as Socrates describes it, is to divide (: ; 18C3) each of these kinds down to the individual unit (D # D ": 18C4), distinguishing alpha and epsilon among the vowels, mu and nu among the semivowels, and so forth. After he had taken the count of these, both individually and collectively, his final step is to give them the name of “element” ( 5' : 18C6). Having constructed the whole system in such a fashion that no element could be understood apart from the rest, he considered this to be the single factor that makes them all a unity (
  . . . B : 18D1) and gave it a single name, the “art of letters” (  : 18D2). The story of Theuth deals with the kinds of discrimination that must be mastered to make ordinary mortals skilled in phonetic language. Before someone can learn the use of alphabetical characters, that person must be able to distinguish the phonemic elements to which the characters correspond. What Theuth is depicted as doing, however, is not on a par with what we do in distinguishing these elements. Theuth’s accomplishment is the establishment of the phonemic system itself. Starting from scratch, as it were, from the Unlimited in the case of vocal sound, Theuth has brought into being the system of distinctive sounds that provide a basis for phonetic reading and writing. As far as the beneficiaries of Theuth’s accomplishment are concerned, there is the grammatical theorist (or dialectician) who studies the system of elements established by Theuth in accord with the dictates of the “godly method.” Then there are the teachers and the students of grammar, who take advantage of techniques like those in the Stranger’s paradigm of paradigms to develop a mastery of phonetic language. Each in his own way, both the theorist and the student must become conversant with the phonemic system established by Theuth. To paraphrase Socrates at 17B9, what makes us all skilled in grammar is moving beyond the Unlimited of vocal sound to knowing the quantity and quality of phonemic elements.

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The second illustration offered by Socrates in elucidating the “godly method” is the art of music. In this case, vocal sound is divided into pitches and intervals rather than vowels and consonants. Knowledge in this domain is a matter of comprehending the number of intervals relating to high and low pitch, along with what serves as limits (+ ": 17D1) of these intervals, their quantity and quality, and how many arrangements (" : 17D2) of them there are. With these factors in view, Socrates observes, the men of old ( K
! : 17D2) instructed us to call those arrangements “scales” (^ : 17D3). Given their contributions to music theory, we may assume that reference here is to the early Pythagoreans – described at 16C7–8 as beings superior to us who lived closer to the gods. Whereas Theuth started with the Unlimited in vocal sound and established the system of elements that provide the basis of grammar, the godlike Pythagoreans started with high and low pitch (explicitly mentioned as an instance of the Unlimited at 26A2) and established the arrangements of intervals we call scales. Musical theorists study these structures with the help of the “godly method;” and music teachers provide instruction on the systems of intervals involved. While thus illustrating the “godly method,” however, the case of music also illustrates the coming-into-being of the offspring of Limit and the Unlimited at 26D9–10. In the case of grammar, the demigod Theuth acted as Cause in bringing Limit in the form of phonemic elements to the Unlimited of vocal sound, generating phonetic language within the class of Mixture as a result. In like fashion, the godlike Pythagoreans were causally responsible for bring Limit, in the form of determinate intervals, to the Unlimited range of sound with pitch, thus “establishing all sorts of music in their perfection” ( " 3
 * "  : 26A4). Here, surely, is an example of the generation of “good and fair” products said at Statesman 284A10–B2 to be dependent on the second kind of measurement. A third illustration of the “godly method” is appended to this second. Almost by way of afterthought, Socrates draws attention to features in bodily movement similar to those in vocal sound. Noticing these features, the ancients said they should be measured numerically (! . ! : 17D5) and called “rhythms and meters” (H"! _ ) : 17D6). Reference to numerical measurement here rather clearly anticipates the characterization of Limit at 25A7–B1, where it is said to include all things related as number to number or measure to measure. Starting with the Unlimited as it pertains to bodily movement (high and low, fast and slow, etc.) the ancients brought Limit to bear in the form of numerical

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measures. The result is movement that is disciplined by rhythm and meter, typical of activities like dancing and gymnastics. By grasping the unity of any domain of art in this manner, Socrates concludes, one gains intelligence about it. Failing this, however, the unlimited multiplicity (# . . . 1
 . . .
! : 17E3) in particular things makes one’s particular thoughts “indeterminate and neither reputable nor numbered” (1
 . . . )   &  ! : 17E4). This is a consequence of never having addressed the number (! # : 17E5) of anything. In the passages from the Philebus reviewed earlier, the expression 1

!  describes the status of the Unlimited before it has been mixed with Limit. From the ontological perspective, the Unlimited itself is the basic principle, with the longer expression serving as an auxiliary descriptor. In the Parmenides, however, the term 1
 #
!  takes on a life of its own. Let us examine its role in a few passages from this dialogue.8 The second hypothesis of the second part of the Parmenides (142B– 157B) begins with an existing Unity that (unlike the Unity of the first hypothesis) admits attribution of other characters. Parmenides’ first move under this hypothesis is to show that the unity of this existing unity is different from its existence. This shows it to be constituted by two parts: unity1 and being1 . He next points out that unity1 both exists and has unity (being one of two parts), and that being1 likewise exists and has unity, yielding a pair of second-tier parts: unity2 and being2 . Parmenides then sets up a recursive series in which each factor on tier n yields two new factors on tier n+1, ad infinitum. As he puts it, because oneness always possesses being and being oneness, each is “always becoming two” (3& )    : 143A1). The upshot is that the existing unity of this hypothesis is seen to be unlimited in multitude (1
 . . . #
! : 143A2). It is important to note that the unlimited multitude of factors here is not a numerically infinite set of determinate elements. Although the term 1

!  conveys the sense of infinite numerosity at 144A6, this is after the derivation of numbers between 143B8 and 144A4. The indefinite multiplicity cited at 143A2 is a plethora without determinate membership. Every item that appears within its range morphs immediately into a pair of other items, leaving an array of fleeting entities without fixed identity. 8

The present discussion of these passages draws on previous treatments in Sayre (1983) and (1996), where the readings summarized here are defended at length.

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As it stands, this indefinitely multitudinous array lacks the stability of a series admitting numerical relations. This can be seen by representing the recursive expansion of being and oneness as a progressively branching inverse tree and then projecting each node of the tree onto a straight line extended beneath it.9 As far as the line is concerned, the effect of the progressive expansion is that between any two points additional points are always appearing and that the pattern of points continues to expand in both directions. By assigning some mode of dimensionality to the array (e.g., lesser to the left, greater to the right), any two points can be compared as more or less. But none can be compared in terms of fixed measures. With this indefinitely multitudinous array at hand, Parmenides next brings to bear various limiting features – pair and triplet, double and triple, odd and even – that generate sets of entities with fixed identities. When these sets are arranged in serial order (e.g., the set of triplets following the set of pairs), the system of positive integers results. As Parmenides summarizes this result at 144A4, his argument shows that if there is one (the existing unity of the second hypothesis) then “necessarily there is number” (  . . . ! # 9 ). Before the imposition of limiting features, the indefinitely multitudinous array had the status of the Unlimited in the Philebus, admitting comparison only in terms of More and Less. By bringing limiting factors to bear – including the double of Philebus 25A9 and 25D11 – Parmenides produces the series of positive integers out of an unlimited multitude of unstable entities. In effect, he generates the mathematical numbers by an auspicious mixture of Limit and the Unlimited. Another passage in the Parmenides where the term 1

!  plays a key role follows in the train of the third hypothesis. Discussion of this hypothesis traces out the consequences of an existing Unity for things other than this Unity but related to it. The first part of this discussion distinguishes two senses in which parts of a whole participate in Unity; all are parts of a single whole, and each is a single part of the whole. In either case, however, at the time such things come to acquire unity they do not yet possess it, so that they are not unified at that time but indefinitely multitudinous (
! 1
: 158B6). By way of clarification, Parmenides suggests the conceptual exercise of considering what things other than Unity would be like if Unity were absent. This exercise involves picking out the smallest portion of these 9

For further details regarding this representation, see Sayre (1996), pp. 166ff.

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other things we are able to conceive and then observing that because this portion itself lacks unity it remains a multitude (
! : 158C4). If we consider the other things time and again in this fashion, we come to see that they are forever unlimited in multitude () . . . 1
 . . .
!: 158C6–7). The intended upshot of this conceptual exercise is the realization that, without the limiting factors provided by Unity that give parts and whole their distinct identities, things other than Unity would remain indefinitely multitudinous. A similar exercise in abstraction is undertaken in the context of the seventh hypothesis. Discussion of the seventh hypothesis focuses on consequences for things other than Unity if Unity does not exist. Without Unity, there is no single thing but rather multitudes (
!: 164C7) of things. The exercise here is to consider a given mass ($ : 164D1) of such things and from among them to select something that seems minimal (  : 164D2) in extent. Because Unity is lacking, however, comparisons can be made only between multitudes. Thus any mass, however small, must be indefinitely multitudinous (1
 . . .
!: 164D1). As a manifestation of indeterminacy, the unlimited multitude of the seventh hypothesis is indistinguishable from that of the second and the third. In the second hypothesis, indeterminacy arises from a partitioning process in which every part of an array is continuously becoming two. Under the third hypothesis, indeterminacy arises from abstracting the factor that provides their unity from otherwise distinct parts and wholes. And in the seventh, indeterminacy results from comparing multitude with multitude, in the absence of Unity as a fixed principle of comparison. In each case, the indeterminate factor by itself is always changing in character, but gains fixity under the limiting influence of Unity. One further distinctive appearance of the expression 1

!  in the Parmenides occurs in the context of the so-called Third Man argument at 132A–B. The argument begins with Parmenides’ observation that (in the early theory of the Phaedo and the Republic) Forms are posited by way of explaining the manifestation of common properties in changing sensible things. Taken by themselves, sensible objects are constantly in flux, from moment to moment “never remaining just as before” ( 
 ?3 A5: Phaedo 78E5). Forms, however, are completely determinate, each being “always the same as itself” () ?3  : Phaedo 80B1–2). The way sensible things gain properties that can be exhibited commonly (according to this theory) is by participating in unchanging Forms, thus coming to share their determinate properties.

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The Third Man argument (at 132A–B) challenges this account of the source of determinate properties in sensible things. If you posit the Form Large to explain the appearance of several large things, Parmenides argues, and then “look at all these in your mind” (; X"5; 
)
  0: ; 132A7), another “Large will appear” (   ': 132A7) by which all these “appear large” (   !: 132A8) in turn. The problem is that when the initial Large is compared in thought with the original large things, it is represented by a mental image. As a mental representation, however, it no longer possesses a determinate character. Thus another Large is required to account for its distinctive identity, along with the identities of the original large things. As Parmenides puts it, “another Form of Largeness will be displayed” (` 1 9  ! "   : 132A10), “alongside [the former] Largeness itself and the things partaking in it” (
&   # !  . . . )  5   %: 132A10–11). Once this second Largeness becomes an object of thought, however, yet another Largeness will be required as a source of determinate magnitude, and so on indefinitely. It is this ever-increasing membership of the group of things requiring a Form to account for their determinate properties, of course, that has led recent commentators to diagnose Parmenides’ problem as one of infinite regress. The shortcoming of this conception of participation, however, is not that it leads to an infinite regress. Forestalling the regress in one way or another would not remove the defect lurking in this conception. The shortcoming of this way of thinking about the relation between Forms and sensible objects is rather that it fails to account for the source of determinate properties in sensible things. What the argument shows is that when Forms are put to this use, they end up themselves being unlimited in multitude (1
 #
! : 132B2–3), like the sensible things that supposedly participate in them.

8.5 A Problematic Appearance in the Republic Our concern in the last two sections has been to review, in brief scope, the several passages in the corpus where Plato uses the expression 1

!  in describing the indefinite principle of the Great and the Small. It is unclear how much the discussion of the Third Man argument in the previous section contributes to this purpose. This is unclear for the simple reason that the argument is directed against the conception of Forms at work in the middle dialogues, whereas the Great and the Small is a feature of Plato’s later thought. The Third Man passage was included

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primarily because it is part of a dialogue containing other uses of the expression in question that are more directly relevant to the principle of the Great and the Small. This said, we should be aware that the expression 1
 #
!  also makes an appearance in Book VII of the Republic, that in this occurrence it carries the sense of being unlimited in multitude, and that the context in which it occurs also contains the very expression used at Statesman 283E8–9 for the Great and the Small. The expressions in question appear in the section where Socrates is explaining to Glaucon how contradictory sense perceptions can lead the soul to a contemplation of reality. An illustration invoked by Socrates involves the conflicting appearance of three adjacent fingers, the smallest, the middle, and the finger in between. Although there is no confusion about each of these being a finger, Socrates points out, things are otherwise with respect to their bigness and smallness (# !  . . . )   : 523E3), their thickness and thinness, and their softness and hardness. As far as softness and hardness are concerned, sensation relates these to each other and reports to the soul that the same thing is perceived as hard and soft. In response, the soul invokes intelligence and its power of reasoning to demine whether the report is of just one thing or two. The same interchange occurs with bigness and smallness. In the case of the fingers and their relative size, sight perceives great and small (Z . . . )  # : 524C3) not as separate but as comingled (singular "5"  : 524C4). By way of clarification, intelligence must contemplate great and small, not as comingled (plural "5"  : 524C7) but as distinct (plural   : 524C7). Is it not in some such way, Socrates asks, that we are first led to question what the Great and the Small (#  . . . ) #   : 524C11) is – that is, question its very nature ( . . .
& ) singular: 524C11)? What we want to note at this point is that the term #  ) #   not only is the same as that used at Statesman 283E8–9 but also is the term used by Aristotle and his commentators in reference to Plato’s indefinite principle. Moreover, !  )   at 523E3 is the very expression used at Statesman 283D7–8 in illustrating the relativity involved in the first kind of measurement. On the surface, at least, it appears that Socrates’ discussion of perceptual relativity in this section of the Republic is a preview of the Stranger’s discussion of measurement in the middle of the Statesman. Although the significance of this apparent anticipation remains uncertain, the overlap between the two passages is

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too striking to be coincidental. One possibility is that Plato, in writing this section, was thinking ahead beyond the criticisms of the first part of the Parmenides. Another is that reference to the Great and Small in the Republic was interpolated at a later date, after the bulk of the dialogue had been released to the public. At any rate, the section regarding the effect of confused sense perceptions on the intellect ends with a description of these confused perceptions as indefinitely multitudinous. It certainly is the case, Glaucon allows, that visual perception has this contradictory character. For we see the same thing simultaneously as one and as an unlimited multiplicity (1
 #
! : 525A4–5). With the observation that this can hold for other numbers as well, Socrates then begins his discussion of the role of arithmetic in the training of the guardians.

9 The Generation of Everything Good and Fair

9.1 Return to the Problems of Chapter 7 Anticipating that YS might come to consider their definition of weaving too long, the Stranger attempts to forestall such misgivings by undertaking an examination of Excess and Deficiency in general. He begins this examination by distinguishing two kinds of measurement, which he proceeds to describe in a variety of alternative formulations. In our initial encounter with these alternative descriptions (in Chapter 7), we found them sufficiently diverse to raise doubts about the nature of the intended distinction. In hopes of resolving these doubts, we undertook a brief survey of other relevant contexts employing the same terminology, looking first at Aristotle and his later Greek commentators (section 7.2) and then at other dialogues written roughly at the time of the Statesman (Chapter 8). It is time to return to the problems raised by these diverse formulations. While the reader may want to refer to the translations provided in Chapter 7 for details, it will be helpful to have a summary of these formulations at hand. In formulation (1), the first kind of measurement is said to concern the association of greatness and smallness with each other, whereas the second is said to engage a being that is necessary for generation. In formulation (2), the first compares the larger and the smaller with each other exclusively, whereas the second involves comparison with the condition of due measure (which is chiefly responsible for the difference between bad and good in human affairs). 171

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In formulation (3), the first has to do with the fact that the Great and the Small both exist and are judged relative to each other, whereas the second pertains to their existing and being judged relative to due measure. In formulation (4), the distinction has to do on one hand with more and fewer being measured with respect to each other, and on the other with their being measured with respect to the inception of due measure. In formulation (5), the distinction is a matter of larger and smaller being measurable with respect to each other and their being measurable with respect to the inception of due measure. An added claim in this regard is that all the arts are dependent on this latter, and vice versa. In formulation (6), the first involves all skills that measure number, length, depth, breadth, and speed according to contraries, whereas the second involves skills measuring things according to due measure, the fitting, the timely, and the requisite – all that has been withdrawn from the extremes to the middle. Let us set up a list of questions to address in attempting to reconcile these formulations. The most basic question concerns the principle of Excess and Deficiency in general. Although we have learned from Aristotle and his commentators that Plato treated this as a general principle of contrariety, and as such equivalent to the Great and the Small, we have yet to explore its significance in this section of the Statesman. Of particular interest in this regard is how Excess and Deficiency in the Statesman relates to the More and Less of the Philebus. These concerns set the topic of section 9.2. As far as the second kind of measurement is concerned, we need to pin down the identity of the being that is said to be necessary for generation in formulation (1). In particular, we need to understand its relation to the due measure that figures in the other descriptions of this kind of measurement. A subsidiary question is how the inception ( . . .   ) of due measure in formulations (4) and (5) relates to the generation (  ) at stake in formulation (1). These issues are addressed in section 9.3. If successful in clearing up these matters, we should be in a position to provide a general characterization of the two kinds of measurement, bringing together the diverse formulations contained in the dialogue. As far as the first kind of measurement is concerned, we must consider

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the relation between the particular contraries cited in connection with formulations (1) through (5) and the much wider range of contraries mentioned in formulation (6). Regarding the second kind of measurement in turn, we must relate the fitting, the timely, and the requisite of formulation (6) to the unelaborated references to due measure in formulations (2) through (5). And we must at least address the question of how these measures, along with possible others (
 !& Q
 at 284E7), have been withdrawn from the extremes to the middle. We return to these topics in sections 9.4 and 9.5. With respect to the second kind of measurement, a culminating question concerns its interdependence with the productive arts. Following formulation (3), the Stranger remarks that without this kind of measurement the arts themselves would be obliterated along with all of their products. Although the arts of statesmanship and weaving are mentioned as particularly vulnerable, he goes on to say that the production of all things good and fair (
  ! ) : 284B2) depends on this kind of measurement. This is restated in connection with formulation (5), where the dependency is said to hold in the other direction as well. Whereas at this point in the discussion it may not be too hard to understand how art generally depends on the second kind of measurement, it remains unclear how due measurement itself might be dependent on the arts. We come back to this problem in section 9.6.

9.2 Excess and Deficiency Revisited At Physics 187a14–17, Aristotle observes that denser and rarer are contraries which may be generalized (! ") into excess and defect (G
 5 ) AX), as with Plato’s the Great and the Small. At 189b8– 11, Aristotle adds the contraries of more and less (apparently distinct from the More and Less of the Philebus), repeating that these can be generalized (+) into excess and defect. In his commentary on Physics I.4 (Diehls (ed.) (1882), 189.9–11), Simplicius quotes Physics 187a15–17 directly, including the attribution to Plato, and goes on to speak of the Great and the Small itself as a principle of generalization (! ": op. cit., 190.13). In the Statesman we find Plato himself (through the Stranger) opening up a discussion of measurement with a reference to Excess and Deficiency in general (
C  . . . G
-  )  AX : 283C3–4), and shortly thereafter talking about the existence of the Great and the Small ( %  " )  %   %: 283E8–9). We have seen ample reason

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(section 7.2) to believe that reference in both cases is to the indefinite principle attributed to Plato by Aristotle and his commentators. The task of this section is to clarify the sense in which Excess and Deficiency is a general principle of contrariety. Among other things, this requires looking more carefully at its relation to the More and Less of the Philebus. Specific contraries mentioned during the Stranger’s interlude on measurement are (1) length and brevity (283C11, also 286C7), (2) greatness and smallness (283D7–8), (3) larger and smaller (283D11–12, also 284A1–2, D5), and (4) more and fewer (284B8). A more extensive list is alluded to at 284E4–5, with reference to skills measuring number, length, depth, breadth, and speed according to contraries. Of the specific contraries just mentioned, (3) and (4) pertain to number, (1) and (2) involve length, while (2) and (3) might apply to depth and breadth as well. Contraries of speed are left for Socrates’ discussion of the Unlimited in the Philebus. Continuing the list with entries from the Philebus, we add (5) hotter and colder (24A7–8, also 24D1, 4), (6) strong and mild (24C1–2, also 24C8D1 and 24E8), and (7) stronger and gentler (24C4). More and fewer is repeated from the Statesman at 24C5, 9. Each of these is mentioned in connection with the definition of the Unlimited at 24E7–25A2. In subsequent passages leading up to the first characterization of Limit, we find also (8) drier and moister (25C8), (9) faster and slower (25C9), and (10) taller and slighter (25C9–10). And then at 26A2, we find (11) high and low and (12) quick and slow, both relating to music specifically. Looking through this list, we find a variety of grammatical forms. Contraries (1) and (2) are designated by nouns with directly opposed meanings. Contraries (6), (11), and (12) are designated by directly opposed adjectival expressions. And the remainder involve either adjectival or adverbial comparatives, again directly opposed to each other. What these various instances have in common is that each consists of a pair of diametrically opposed factors. The fact that these opposing factors come in pairs is significant. By way of illustration, suppose that equal were added to greater and smaller, expanding the initial pair into a trio. Before this addition, greater and smaller can be compared only with each other. Two things might be related as greater and smaller, but that is the only comparison of size available. Given the trio of greater, smaller, and equal, however, other comparisons might be brought to bear. For example, two things might be neither greater nor smaller but equal to each other. Or if one thing is greater than another, then the difference between them is greater than if

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they were equal; and so forth. Similar results would follow if equality were added to the contraries of greatness and smallness. Greatness and smallness would still be diametrically opposed to each other. But comparison between them would not be restricted to this opposition. In addition to greatness and smallness there is now equality, toward which both extremes approach as a limiting factor. Let us put these observations in the language of the Philebus. Given a range of comparisons restricted to greater and smaller, two things can be compared only as more or less extensive than each other along the relevant parameter (e.g., size). As a pair of contraries thus restricted, greater and smaller belong to the class of the Unlimited. For as may be recalled from Chapter 8, the distinguishing mark of the Nature of the Unlimited is that it includes whatever seems to become more and less. Other members of this class are length and brevity from the Statesman, and hotter and colder from the Philebus, along with others listed earlier. With the addition of equal to the contrariety of larger and smaller, however, Limit has been brought to the Unlimited. As characterized initially at 25A7–B1, Limit comprises first the equal and equality, and then the double and all comparisons of number to number and measure to measure. Equal and double also lead the roster at 25D11–E2, where Limit is characterized as everything that puts an end to the variation between contraries, making them commensurate and harmonious by the introduction of number. In like fashion, the contrariety between hotter and colder is made commensurate by limits that remove their excesses and establish the seasons (a: 26B1). In general, “fair things of all sorts come into being among us” (+ 
   '  : 26B1–2) by the mixture of Limit with the Unlimited. We turn later in the chapter to consider the relevance of the passage just quoted to the “production of all good and fair things” at Statesman 284B1. In the Philebus, the Unlimited includes all contrary pairs so disposed as to be comparable only with each other. A designation used by Aristotle and the commentators for this principle is the Indefinite Dyad. By nature, contraries of this sort relate to each other only in terms of More and Less – more or less lengthy or brief, more or less hot or cold, more or less dry or moist, and so forth. As far as comparative measurement is concerned, such contraries bear relationship to each other exclusively. Measurement of this sort is restricted to comparison in terms of More and Less. This brings us back to Excess and Deficiency in the Statesman. As Plato’s general principle of contrariety, it is equivalent to the class of opposites that are characterized in the Philebus as comparable only in terms of

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More and Less. In section 8.3, we saw that this class does not include things that can be compared in terms of number. A group of four objects is less numerous than a group of six, double in number to a group of two, equally numerous with two such groups, and greater in number than a group of three. But comparisons of this sort involve measures like equal and double, which derive from the imposition of Limit on the Unlimited. Quantities with numerical properties do not reside in the class of things comparable only in terms of More and Less. They belong to the class of Mixture instead. At Philebus 26D9–10, Socrates talks about the offspring in the Mixed class that are generated (  ) from the Unlimited by measure achieved by means of Limit. With this in mind, let us return to the puzzling reference to a “being necessary for generation” at Statesman 283D8–9.

9.3 The Being Necessary for Generation The phrase        is obscure, as commentators often note, and the translation I have offered is obviously not the only one available. Among prominent translators of the entire dialogue, Jowett paraphrased “without which the existence of production would be impossible.”1 Di`es offered “les n´ecessit´es essentielles du devenir,” suggesting that the necessity in question is that of the laws governing the whole universe.2 Skemp expanded the text to read “the fixed norm to which [objects] must approximate if they are to exist at all.”3 Benardete opted for “the necessary (indispensable) being of becoming.”4 Rowe, wisely looking ahead to 284A–B, chose “what coming into being necessarily is.”5 And Waterfield settled for “the fact that there does exist something which is a necessary prerequisite for qualities to occur.”6 None of these renditions, however, offers much help in relating the “necessary being” in question to other formulations of the second kind of measurement. Turning next to piecemeal translations of recent commentators, we find Rosen’s “the necessary being of genesis,”7 apparently attaching the necessity to the existence of the process of generation. Miller reads

 as “essential being,” yielding “the essential being necessary to 1 2 3 4 5 6 7

Jowett (trans.) (1892). Di`es (ed. and trans.) (1935); p. 44, n. 1. Skemp (ed. and trans.) (1952). Benardete (1984). Rowe (trans.) (1997). Waterfield (trans.) (1995). Rosen (1995), p. 123.

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coming-into-being.”8 Santa Cruz translates   “production” and adds a universal quantifier, to come up with “la r´ealit´e qui est n´ecessaire a` toute production.”9 Most circumspect of the group, perhaps, is Lafrance’s “l’essence (nature, r´ealit´e) n´ecessaire du devenir.”10 A problem with this set of translations generally is that they provide little help in relating the being in question to the due measure figuring in the other formulations of the second kind of measurement (see section 7.1). One exception, perhaps, is Miller’s “essential being necessary to coming-into-being.” According to Miller, the coming-into-being here in question is that of words and deeds that originate in human action, which constitute the range of human affairs judged bad or good according to the due measure of formulation (2). The “essential being” necessary for this generation, in this interpretation, is that of the Forms that human actions are supposed to instantiate.11 By limiting the generation in question to human words and deeds, however, Miller’s account seems to leave out a good part of the production of “everything good and fair” said to be dependent on the second kind of measurement in connection with formulation (3). His account also offers little help regarding the sense in which all the arts depend on due measure for their existence, and vice versa (formulation (5)), or about what is meant by due measure being withdrawn from the extremes to the middle in formulation (6). It seems fair to say in retrospect, moreover, that none of the translations cited here shows any connection between the being said to be necessary for generation at Statesman 283D8–9 and the generation resulting from the mixture of Limit with the Unlimited at Philebus 26D9–10.12 Other difficulties commentators have experienced with these passages in the Statesman, to be sure, may be due in part to the inadequate attention they have given to this connection. At Philebus 26D9–10, Socrates refers to the offspring from the Unlimited by measure achieved with the help of Limit. What does this tell us about the being said to be necessary for generation in the Statesman? In point of fact, the ontological section of the Philebus distinguishes three factors that are necessary for anything to come into existence. One is the Unlimited, another Limit, and yet another the Cause responsible for 8 9 10 11 12

Miller (1980), p. 65. In Miller’s view, the “essential being” in question is that of the Forms. Santa Cruz (1995), p. 193. Lafrance (1995), p. 94. Miller (1980), p. 66. Lafrance is the only author of the group who draws overtly upon the Philebus in dealing with Statesman 283D, and 26D9–10 is not mentioned in his article.

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mixing Limit with the Unlimited. Inasmuch as the passages on measurement in the Statesman are not concerned with things actually coming into existence, the factor in question at 283D8–9 is not the responsible Cause. The passages instead are concerned with two contrasting ways in which things might be measured. One way consists in comparing contraries with one another. The contraries in question belong pairwise to what Aristotle and the commentators (speaking for Plato) called the Indefinite Dyad, Excess and Deficiency, or simply the Unlimited. This factor has already been cited at 283C11–D1 and at any rate is not the featured facet of the second kind of measurement. The second kind of measurement consists in relating one or another pair of contraries to a being that is necessary for generation. Of the three factors essential for generation in the Philebus, the only one left is Limit. In the Philebus, Limit contributes essentially to generation in providing measures by which one or another pair of contraries are made determinate and thus commensurate with each other. The being said to be necessary for generation in our Statesman passage, accordingly, must be the Limit that produces progeny in conjunction with the Unlimited. As a general formula, Limit mixes with the Unlimited to bring offspring into existence, regardless of the domain in which the offspring reside. But particular forms of Limit pertain to particular domains of existence, along with particular varieties of Excess and Deficiency. With regard to human action, a central form of Limit is that of due measure, which marks the difference between bad and good in that domain. Due measure is mentioned as a form of Limit at Philebus 24C8; and numerous pairs of contraries that are receptive to this kind of measure are discussed by Aristotle in connection with his doctrine of the mean (e.g., fear and excessive confidence, of which courage is the mean). But due measure is not the only form of Limit relevant to the second kind of measurement. In his discussion of formulation (3), the Stranger observes that the production of all things good and fair depends on the preservation of measure – not due measure (  ) in particular but measure (  : 284B1) in general. And in formulation (6), he mentions other particular forms of Limit that might be called for in other circumstances. There are lengths that are fitting for particular kinds of discourse, topics to be raised in a timely fashion, procedures requisite for rational inquiry, and so forth. In summary, what these considerations indicate is that the being said to be necessary for generation at Statesman 283D8–9 is Limit in the sense

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of the Philebus and that there are various forms of Limit including (but not confined to) the due measure featured in formulations (2) through (6). Let us return to the question of the relationship among these several formulations.

9.4 The First Kind of Measurement In the Philebus, the Unlimited is characterized as including all contraries that can be compared only with respect to each other. Comparison of this restricted sort is equivalent to the first kind of measurement in the Statesman. The Unlimited found in the Philebus is one among several designations of Plato’s principle of indeterminacy cited by Aristotle and his commentators. Another is Excess and Deficiency. It is thus appropriate for the Stranger to begin his discussion of measurement at Statesman 283C by calling for an examination of Excess and Deficiency in general. The first kind of measurement is described in formulation (1) as having to do with the association of greatness and smallness with each other. Greatness and smallness make up a specific dimension of contrariety falling under the general principle of Excess and Deficiency. Because relative length and brevity of dialectical definitions is of particular concern at this stage of the discussion, and because length and brevity here pertain to a great or small amount of time taken up in discourse, it makes sense for the examination to begin with the specific dimension of greatness and smallness. In formulation (2), the focus shifts to larger and smaller, which might be thought of as an adjectival version of greatness and smallness. YS thinks at first that larger and smaller can be compared only with each other. To correct this misconception, the Stranger points out that there is another kind of measurement in which larger and smaller are compared with due measure as a norm. A possible example (taken from Aristotle’s Nicomachean Ethics 1122a28–31) has to do with expenditures of money: expenditures that are larger and smaller than appropriate constitute vulgarity and niggardliness, respectively, in comparison with magnificence as an appropriate mean. Formulation (3) differs from its predecessors in two significant ways. Whereas (1) and (2) mention specific contraries that might be compared with each other (greatness and smallness, larger and smaller), (3) cites contrariety in its most general form. According to the testimony of Aristotle and the commentators, Plato’s Excess and Deficiency is the same principle as his Great and Small. As indicated previously, this is the

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only occurrence of the expression #  ) #   in Plato’s existing corpus, with the possible exception of Republic 524C11 (section 8.6). The other respect in which (3) differs from the previous formulations is its reference to two ways in which the Great and the Small might exist. On one hand, this general principle might exist by itself. In this mode of existence, it is equivalent to the Indefinite Dyad in Aristotle and his commentators and to Excess and Deficiency in the present context. On the other hand, the Great and Small might exist as a constituent of Mixture. In this capacity, as we shall see, it is an ingredient in things produced with the help of the second kind of measurement. Moving on to formulation (4), we find that the focus has shifted to the contrariety of more and less (#
 . . . ) A : 284B9). This presumably is not the same as the More and Less (# C ) = ) that provides the mark of the Unlimited Nature in the Philebus, inasmuch as it seems to lack the generality of the latter. What more or less amounts to here is more a matter of exceeding or falling short of due measure (conveyed by active G
- and passive G
-  in formulation (2), at 283E3 and 283E4, respectively). As the Stranger goes on to say, unless more and less can be measured not only with respect to each other but also with respect to the inception of due measure, neither the statesman nor anyone else with practical knowledge could have come into existence. Formulation (5) returns to the larger and smaller of formulation (2). The main difference between (5) and (4) preceding it is a generalization of the dependency of the arts for their existence on the second kind of measurement. This topic is addressed more fully in the following two sections. This brings us to formulation (6), which poses its own problems of interpretation. We should note for one thing that whereas all the previous formulations describe the first kind of measurement in terms of one or another form of contrariety, (6) addresses the relevant skill of measurement directly. As the Stranger puts it, the first kind of measurement comprises all the skills (5 : 284E4) measuring number, length, depth, breadth, and speed according to contrarieties. The skills involved here cannot be among those said a few lines earlier to depend for their existence on the second kind of measurement. If they were, then the first kind would depend on the second in turn, which is entirely foreign to the Stranger’s discussion of the two kinds of measurement. A consequence is that the skills of measurement itemized at 284E4–5 are not among arts yielding “good and fair” products (284B1), of which

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statesmanship and weaving have been mentioned as examples. In fact, the skills associated with the first kind of measurement are not productive arts at all. They are skills of assessment instead. According to formulation (3), the Great and the Small are judged (: 283E8) in two different ways. In one mode of judgment they are related to due measure, which engages the second kind of measurement. But in the other mode they are judged only in relation to each other. The skills mentioned at 284E4–5 must be skills that implement this other mode of judgment. What kinds of skills might the Stranger have in mind? They cannot involve fixed standards of comparison, like yardsticks, sundials, and calibrated scales. This would locate them within the context of the second kind of measurement. Possible illustrations of measurement skills not involving fixed standards of this sort can be gleaned from other dialogues. There is an oblique allusion at Republic 522D to Agamemnon’s inept deployment of troops at Troy, due to his inability to count. This would be an example of inexpert assessment with regard to general numerosity. Other generals might be able to perform assessments of this sort more aptly, thus illustrating skill in judging number (# ! # at 284E4) according to contraries of more and less. Another illustration might be flute playing, which is said at Philebus 55E–56A to lack precision and to proceed by “the hit and miss of practice” (   5
: 56A4). Inasmuch as tonal quality depends on embouchure, expert flute playing requires practice at hitting the right note by imprecise means. Yet another illustration might be sounding the depth of a harbor with an unmarked line and judging the indicated results as more or less than the draft of a ship. In the absence of specific help from the text, these examples give us some idea of how the first kind of measuring skills might come into play. A further problem of interpretation has to do with the character of the five dimensions of contrariety itemized at 284E4–5. It should be obvious immediately that this list is not randomly ordered. Beginning with number (no spatial dimensionality), it proceeds through length, depth, and breadth (one through three spatial dimensions, respectively), to speed (spatial motion through a fourth dimension, time). Reporting Plato’s thoughts at De Anima 404b20–21, Aristotle speaks of “the primary length, breadth, and depth” ( %
* "  " )
 " ) -! ") of which all things are constituted along with the Idea of the One (  % D # (). Metaphysics 1085a10–12 elaborates on this theme with the observation that lines come from long and short, planes from broad and narrow, and masses from deep and shallow (see also 992a11–13), adding that

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these contraries are forms of the Great and Small ( %  " )  %  %). This corroborates our conclusion that the contraries involved in the first kind of measurement at Statesman 284E4–5 belong to Excess and Deficiency – that is, to the Great and the Small. In line with considerations like this, some commentators have assumed that measurement of the first kind deals exclusively with quantity.13 Although the five dimensions of contrariety specified at 284E4–5 are quantitative, to be sure, to conclude that all such contraries are quantitative is surely erroneous. Among contraries explicitly mentioned in the Philebus, we find hotter and colder (not readings on a temperature scale, but qualitative feelings), strong and mild (to the taste), and drier and moister (to the touch). In the Statesman itself, moreover, formulation (2) alludes to words and deeds that exceed or fall short of the condition of due measure. An example from Aristotle mentioned previously is that of fear falling short of, and excessive confidence exceeding, courage as an appropriate mean. Within the classification of the first kind of measurement, fear and confidence would be judged solely with respect to each other. And neither fear nor confidence in any case is an attribute of quantity. For these and other reasons to be considered momentarily, we can set aside the assumption that the two kinds of measurement are divided by the distinction between quantity and quality. Measurement of the first kind compares contraries with respect to each other, regardless of whether those contraries are quantitative or qualitative. This is one substantial result of the Stranger’s examination of Excess and Deficiency in general.

9.5 The Second Kind of Measurement It has been noted previously that the section on Excess and Deficiency (283C–285C) occupies the very middle of the dialogue. Striking as this fact may be, we should not jump to the conclusion that it is more than coincidental. Mere coincidence seems less likely, however, in view of the equally striking fact that the middle sentence of this section – hence the middle sentence of the dialogue – emphasizes the necessity that more or less be measurable with respect to due measure. This is comparable in importance, the Stranger says, to the need to establish the existence of not-Being in their previous examination of the sophist. 13

Lafrance defends this assumption in (1995), p. 95, citing Di`es, Souilh´e, and Kucharski as having maintained the same view.

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In the context of the Statesman, due measure occupies the middle ground between the extremes of Excess and Deficiency. (Think again of courage as the middle –  at Nicomachean Ethics 1106B22, passim – between fear and excessive confidence.) This amounts to an occurrence of a reference to the middle between Excess and Deficiency being located directly in the middle of a section marked off at either end by references to Excess and Deficiency. Contrivance, in this context, is the opposite of coincidence. The probability of contrivance increases with Plato’s treatment of the beginning and ending of the dialogue. The dialogue’s first sentence refers to an introduction (of Socrates to Theaetetus and the Stranger), and its last sentence refers to a task completed (the portrayal of the statesman). Thus the dialogue begins with reference to a beginning, ends with reference to an ending, and includes reference at its midpoint to a mean or middle. The significance of these features of the dialogue becomes more apparent in comparison with the Philebus, which is distinctive in its lack of the same structural features. It has become commonplace among commentators on the Philebus to observe that we (as readers) join a conversation already underway at 11A and that the conversation continues after we fade out at 67B. As depicted in the written work, that is to say, the conversation between Socrates and his youthful interlocutors has neither beginning nor end. And what has neither beginning nor end perforce lacks a midpoint as well. The unbounded character of the Philebus is a concrete symbol of its concern with the Unlimited as a principle of indeterminacy. In like fashion, it seems fair to say, the precise marking of beginning, middle, and end in the conversation of the Statesman symbolizes its central concern with Limit in the second kind of measurement.14 14

A thematic treatment of “beginning, middle, and end” is associated with the Pythagoreans by Aristotle, who tells us at De Caelo 268a10–13 that they said the universe and everything in it is determined (N) by the number three, because that is the number of everything with beginning, middle, and end. Aristotle continues by observing that this is the reason we make use of the number three in worship of the gods, given the involvement of beginning, middle, and end in nature. In the present regard, it is relevant to note that Plato occasionally makes use of this Pythagorean formula as well. There are three passages in the Parmenides (137D5–6, 145A6, and 165A6–7) that treat having beginning, middle, and end as tantamount to having limit. There is an occasion at Laws 715E8–716A1 where the Athenian Stranger tells a story about a god who holds the beginning, middle, and end of all things in his hands. This passage from the Laws is cited at the very end of Aristotle’s (spurious?) De Mundo, alluding to the Pythagorean doctrine that beginning, middle, and end (being three) give the number of all that exists, where the doctrine is attributed to Plato by name. Another occurrence of this Pythagorean formula is at Philebus 31A9–11, the significance of which is discussed in the text following.

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In point of fact, there is a passage in the Philebus where a formulaic mention of “beginning, middle, and end” serves as a reference to Limit in general. By way of applying the results of his examination of the four ontological principles to the ongoing discussion of pleasure, Socrates observes at 31A9–11 that pleasure itself belongs to the class of the Unlimited because beginning (5 ), middle ( ), and end ( ) are always absent. To escape this classification, pleasure would have to possess Limit, which is tantamount to having a beginning, middle, and end. Lacking those features, however, it remains Unlimited, which means that it can be measured only with respect to More and Less. Let us return to the Statesman and the second kind of measurement. Formulation (1) characterizes this second kind as the part of measurement dealing with Excess and Deficiency according to the being that is necessary for generation. In section 9.3, we concluded that the being here in question coincides with the membership of the class of Limit in the Philebus. Whereas measurement of the first kind compares contraries of Excess and Deficiency with each other exclusively, the second kind of measurement compares such contraries with some form of Limit. Specific forms of Limit encountered in the Philebus include the distinctive phonemes Theuth imposed upon the Unlimited of vocal sound to establish the art of literacy, the particular intervals along the continuum of high and low pitch by which the Pythagoreans established the musical scales, the numerically measurable rhythms and meters that give rise to the art of gymnastics, and whatever climatic limits are required to transform excessive heat and cold into seasonable weather. Included also is the due measure (  : 24C8) that brings moderation to intemperate words and actions. Formulation (1) provides the most general description of the second kind of measurement. Whereas particular contraries (length and brevity, greatness and smallness) are involved in its characterization of the first part of measurement, this second part is singled out as measurement treating Excess and Deficiency in general with respect to Limit – that is, with respect to the being necessary for generation. In formulation (2), the second kind is illustrated in terms of human actions. Words and deeds are good if in accord with the conditions of due measure. If they either exceed or fall short of this norm, however, they also deviate from what is humanly good. To draw once again upon examples from Aristotle, courage is the mean between the excesses of fear and confidence, either of which counts as morally deviant.

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As noted previously, formulation (3) distinguishes both two kinds of measurement and two distinctive modes of being. As far as measurement is concerned, the second kind consists in judging the Great and the Small (or particular instances thereof ) relative to some appropriate form of due measure. Apart from reference to the Great and Small generally, there is little difference between this characterization of the second kind of measurement and that of formulation (2). An illustration of one would serve to illustrate the other as well. The main focus of formulation (3), however, is on differences in modes of being. On one hand, Great and Small exist with respect to each other exclusively, which amounts to existence as a general principle of contrariety (as Excess and Deficiency). On the other hand, the Great and Small exists as an ingredient of things falling under the class of Mixture. As portrayed in the Philebus, the class of Mixture comprises offspring generated when measures within the class of Limit are imposed on contraries of the Unlimited. These are the measures described in formulation (1) under the rubric of what is necessary for generation. The Stranger elaborates on this necessity in formulation (3) by pointing out that arts like statesmanship and weaving depend for their existence on the availability of due measure. It is by preserving measure (#  : 284B1) in the arts generally, he goes on to observe, that everything good and fair is produced. This reference to “good and fair products” is mirrored at Philebus 26B, where Socrates says that it is by the mixture of the Unlimited with Limit that “all sorts of fair things are brought into being” (+ 
  . . .  : 26B1–2). We look more closely at what this amounts to in the following section. Formulation (4) is expressed by the sentence that occupies the very middle of the dialogue. With regard to their current project of defining the statesman, what alternative is there, the Stranger asks, to making it compulsory that more and fewer be measured not only with respect to each other but also with respect to the inception of due measure? The implication seems to be that practical mastery of the art of statesmanship constitutes an ability to achieve due measure in political affairs managed under its guidance. It is in this manner that the statesman must be able to exercise his art with respect to the inception of due measure – that is, must be able to bring about results in accord with the mean. Formulation (5) returns to larger and smaller (from the first formulation) as a particular form of contrariety and repeats that these contraries can be measured both with respect to themselves and with respect to the inception of due measure. A new claim introduced at this point is

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that the relation between this second kind of measurement and all the productive arts is one of mutual dependence. Not only are arts like statesmanship and weaving dependent on due measure for their existence, as stated previously, but moreover the second sort of measurement itself is dependent on the existence of such arts. Section 9.6 is concerned with the dual character of this dependency. According to formulation (6), the second kind of measurement includes skills that measure “according to the mean, to the fitting, the timely, and the requisite” (284E6–7). This, of course, is in contrast with skills of the first kind that measure only “according to contraries” (284E5). It has already been observed (section 9.4) that the skills (5 : 284E4) here in question are distinct from the arts that generate good and fair products. Although the latter depend on the former for their existence, skills of measurement are not the same as skills of production. It was also argued in the previous section that the distinction in this formulation between skills that measure according to contraries, and skills of the second sort that apply fixed standards, does not boil down to a distinction between quantity and quality. Just as there are qualitative comparisons that belong to the former (e.g., between contraries of strong and mild), so there are assessments of quantity that fall within the latter. The express intent of the present inquiry into kinds of measurement, after all, is to find a measure of length appropriate for dialectical discussions. And length undeniably is a quantitative dimension. The apparent fact of the matter is that measurement of both kinds apply to both quantity and quality. Opposing armies can be compared merely as larger and smaller (as supposedly by Agamemnon) but also can be contrasted in size with what is requisite (#  ) for a given military task. And lengths of philosophic discussions can be compared as longer and shorter (the Theaetetus is longer than the Sophist) but can also be judged with regard to a length that is fitting (#

) for that kind of discussion. The distinction at hand is not between different kinds of things that can be subjected to measurement but between different ways in which things can be measured. Questions also might arise about the list of normative measures at 284E6–7. On one hand, it might be maintained that the fitting, the timely, and the requisite are all specific forms of due measure, which happens to head the list (#  ) #

) # # ) #  ). Although there is nothing in the grammar of the passage to indicate such an hierarchical order (all four terms being connected by )), possible support for this view might be found at 286D1–2. Shortly before returning

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to the definition of statesmanship at 287B, the Stranger articulates yet another formulation of the two kinds of measurement – this time in terms directly applicable to the length of dialectical discussions. As he puts it there, lengths can be compared not only in relation to each other but also in relation to what is fitting (#

: 286D2). Taking into account the relevance of the terminology to the particular circumstances at hand, one could read #

as a particular case of #  featured in formulations (2) through (5). A more plausible reading, however, seems to be that the fitting, the timely, and the requisite are all coordinate with due measure rather than subordinate to it. To bear this out, there are several uses of the term # (timely) in the Statesman in contexts where it could not sensibly be replaced by the term  . One is at 307B1, where the Stranger is talking about the timely employment of slowness in music; another is at 310E2 where he talks about an untimely growth of sluggishness over several generations. There is also an occurrence of

(fitting) in a passage where replacement by   would seem unnatural. The passage in question is 308E5–9, where the Stranger is talking about dispositions that are appropriate to the roles played by various citizens within the state. Because none of these passages deals with measures pertaining to moderation, they suggest that neither the fitting nor the timely is being treated at 284E6–7 as a subclass of the mean or due measure. As far as #  (the requisite) is concerned, its sense is too broad to be limited to a specific normative application. Another consideration is that it seems natural for the coordinate series of dimensions admitting contrariety in connection with the first kind of measurement – number, length, depth, breadth, and speed – to be matched with a comparably coordinate set of measures invoked by measurement of the second sort. Although little hangs in balance with regard to overall meaning, viewing these four more exacting measures as coordinate opens up an interesting perspective. This perspective may be laid out in a diagrammatic form. At 283D1–4, the Stranger divides the art of measurement into two parts. These two parts are described in various ways, which we have been sorting out in the preceding discussion. Then each of these two parts is divided further at 284E3–8, as follows (Figure 9.1). The final entry to the lower right refers to the extension of the list of normative measures at 284E7–8 – “all that has been withdrawn from the extremes to the middle” (
 ! & Q
 ( #  
7! . 5 ). We return to this expression in Chapter 11. For the moment, it is enough to note that

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art of measurement according to contraries number length width breadth

according to fixed measure due measure the fitting the timely the requisite

speed

(other)

figure 9.1. Subdivisions of the art of measurement.

there are other normative measures than those explicitly mentioned in the list. This scheme is interesting in two respects relevant to our previous discussion of division as a dialectical procedure. One is that division here is pursued in both left and right directions. In this respect, it is comparable to Socrates’ division of madness in the Phaedrus (Figure 3.1) and to the division of purification in his definition of the “noble sophist” (Figure 3.4). The other point of interest is its employment of nondichotomous division, previously present in the definition of madness and in the Stranger’s final definition of weaving (Figure 5.2). Although these antecedent departures from twofold division are easily overlooked, they provide precedent for the nondichotomous divisions that dominate the final definition of statesmanship.

9.6 The Interdependence of Art and Normative Measure At 284D, the Stranger asserts that the existence of art generally and the existence of the second kind of measurement are mutually dependent. In fact, he says this three times in rapid succession. First stated, the claim is that one must suppose equally (Q  at 284D4) that all the arts exist and at the same time that larger and smaller admit measurement not only with respect to each other but with respect to the inception of due measure. The second version says in effect that if the second kind of measurement exists then so do the arts, and vice versa. And in the third case the Stranger states bluntly that if either fails to exist, there will never be the other.

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The Stranger has stated previously (284A), of course, that arts like statesmanship and weaving could not exist without the second kind of measurement (i.e., normative measure). It is by preserving measure of this sort, he observes, that “everything good and fair is produced” (284B1). But now the dependency is extended in the other direction as well. In what manner might art and normative measure be mutually dependent? Insofar as the arts in question yield products that are good and fair, it is not difficult to understand how they must rely on measurement that adheres to normative standards. Practitioners would have to maintain such standards in fashioning their products; and such standards would provide guidelines by which these products are evaluated. With regard both to production and to subsequent assessment, arts of this sort depend on the availability of relevant norms. Dependency of art on measure in this fashion, we may note in passing, is consistent with the measures in question existing independently of the arts that employ them. This would be like Forms existing independently of particular instantiations. It is more difficult, however, to think of a sense in which measurement of the second kind might be dependent on the corresponding arts. Given the dependency noted earlier of art upon measure, no art could exist before the measures it employs. As far as temporal existence is concerned, the only possibility is that art and measure come into existence together. The sense in which a given art and its measures are interdependent, understood temporally, must be that both arrived on the human scene simultaneously. Help in comprehending this interdependence comes with the story of Theuth in the Philebus. As we recall, Theuth was credited with the invention of the art of literacy, by way of illustrating what Socrates refers to as the reverse (#    : 18A9) of the god-given method. As someone following this method is instructed to look for number (! # : 18A9) between unity (B : 18A7) and the Unlimited Nature (
 " 3 : 18A8), so someone beginning with the Unlimited (# 1
 : 18A9) is told not to head “straightway to the One” (
) # : !3: 18B1) but rather to take note of some number (! # . . .  : 18B2) that encloses each plurality (
!  B : 18B2). As Socrates recounts the story, Theuth’s achievement began with the observation that vocal speech is Unlimited (1
 : 18B6) and that in this indeterminacy there could be perceived a plurality of vowels. He next discerned a number (! # : 18C1) of sounds other than vowels that do not require articulation, after which he set apart what are now

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called mutes. His next move, as Socrates describes it, was to divide each of these classes down to the individual unit until he had found the number (! # : 18C5) of each. This done, Theuth gave the name ‘letter’ ( 5' : 18C6) to all of them together and designated the unified system, which he had initiated the ‘art of literacy’ (  5  ; 18D2). Although this story about Theuth has been interpreted in various ways, it seems clear that the art of literacy and the measures on which it depends are initiated as part of the same creative act. The measures on which “good and fair” speech depends are the vowels, semivowels, and mutes that Theuth marked off by number along the range of the Unlimited with which he began. To employ the art of literacy, once it has been brought into being, is to articulate one’s speech with respect to those measures, and to apply these measures is to employ the art of literacy. In this sense, the measures and the art are mutually dependent. In Socrates’ account of the story, the art of literacy and the measures it employs came into existence simultaneously. But the story probably is not intended to be historical. As a demigod, Theuth is not an agent who operates in the province of time. The mutual dependence between the art of literacy and its constitutive measures should be conceived as ontological rather than temporal. The same holds, we may conclude, for the productive arts of the Statesman and the normative measures with which they are interdependent. The focus of the Stranger’s discussion of measurement is ontological from start to finish. Such must be the focus as well of his remarks about the interdependency of art and normative measurement. We turn in the next chapter to the Stranger’s enigmatic remark at 284D1–2 connecting the second kind of measurement with a forthcoming “exhibition of exactness itself.” As we shall see, this exhibition also engages an ontological perspective.

10 Accuracy in the Art of Dialectic

10.1 Knowledge and Art in the Philebus In a seemingly offhand remark at Statesman 284D1–2, the Stranger alludes to a forthcoming “exhibition” (
  ) of exactness itself and says that on this occasion there will be need for the distinction between two kinds of measurement that he and YS have been discussing. As pointed out during our initial encounter with this passage in section 7.1, there is an examination of accuracy among the arts at Philebus 55D–59D that apparently answers to the Stranger’s prediction. Not only does this examination of accuracy make use of a distinction between two types of measurement very much like that in the Statesman, it also deals at length with the topic of dialectic which is the Stranger’s main concern in the passages directly following the prediction. Whether or not Plato had the Philebus (or plans for it) in mind when assigning this remark to the Eleatic Stranger, its treatment of accuracy in the arts is obviously relevant to the discussion underway at the middle of the Statesman. The task of the present chapter is to bring Socrates’ examination of accuracy to bear in setting the stage for a discussion in the following chapter of the procedure of dividing according to Forms. To someone accustomed to a sharp distinction between knowledge (
 ) and art (5 ) in other Platonic contexts, it may seem disorienting to find dialectic referred to as an art in the Statesman and the Philebus. The distinction between knowledge and art is maintained with some consistency in the Republic specifically, where the latter is often characterized as somehow inferior. At 522B4, for example, the arts generally are said to be merely mechanical (5  - "  . . . ]
); and 191

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at 533D4–6, arts (5 ) of mathematics are described as clearer than opinion but more obscure than knowledge ( "  " L / 
 ). In the context of the Divided Line, moreover, the various branches of mathematics are described as arts (511B1–2) and assigned to a level beneath that reserved for knowledge (533E5). Whatever its status in previous dialogues, however, by the time of the Philebus this terminological distinction between art and knowledge has all but disappeared. There are still some basic differences between skills that rely on rote training and guesswork, such as instrumental music at 56A, and other skills that incorporate forms of precise measurement. But Plato is no longer scrupulous in reserving the term 
  for the fruits of dialectic. At 57C6–7, for example, Protarchus observes (with Socrates’ agreement at 57D3) that there is a vast difference in perspicuity among different kinds of knowledge, mentioning branches of arithmetic and measurement (57D6) as studies that in their purest form constitute “knowledge that is especially precise” (
  -' & 9 : 57E3–4). More significant for present purposes, however, is the fact that the term 5  is frequently applied to the exercise of dialectic. One striking illustration occurs in connection with the “godly method” of 16C–E. Although Socrates credits the method with making the difference between dialectical (.: 17A4) and eristic discussion, he describes it initially as being responsible for making evident everything that has been discovered in the field of art (+ 5 : 16C2). The implication, it seems clear, is that proper products of the method are at once dialectical and count among works of art. Another indication that any previous terminological barriers between 
  and 5  have been relaxed comes at the end of the dialogue, where Socrates announces his final ranking of the human goods. Between intelligence and pleasure, the original contenders – which (in purified forms) place third and fifth, respectively – he places forms of knowledge, art, and right opinion (
   ) 5  )   I!: 66B9) indiscriminately.1 This makes it less surprising to find the two terms used synonymously elsewhere in the dialogue. As part of his observation at 57C that different forms of 
  differ vastly in perspicuity, for instance, Socrates cites certain 5  as being among the forms of knowledge thus 1

The only sharp distinction between states of mind in this ranking is that separating intelligence and wisdom ( % )   : 66B5–6) on the third level, and knowledge, art, and right opinion on the fourth. This accords with the priority of intelligence ( %) over knowledge and true opinion at 342C4–D2 of the Seventh Letter.

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distinguished. And at 58C1 he uses the two terms in complementary apposition to ask what form of art or knowledge exceeds all others in truth and precision, an apposition repeated at 58E3 in claiming that distinction for dialectic. The immediate relevance of all this to the division of disciplines undertaken at Philebus 55E is that the disciplines in question are not presorted under mutually exclusive labels “arts” and “knowledge.” The fact that Socrates begins with a distinction between types of 5  does not prevent the products of dialectic from showing up at a later stage of the division. Let us trace out the steps by which this happens.

10.2 Division of Arts with Respect to Accuracy Socrates begins his examination of the various disciplines by observing that if numbering, measuring, and weighing (!  . . . )  )  : 55E1–2) were dismissed from the arts, then the remainder in each case would be of little worth. This parallels the remark of his counterpart at Republic 522C to the effect that all art relies on arithmetic and calculation, as do knowledge and other forms of understanding. What we are asked to imagine at Philebus 55E is that all mathematical support has been removed from the disciplines in question. All that would be left is conjecture based on repeated experience. Although many people (
 ): 55E7) call this “art,” it is nothing more than guesswork built up by laborious practice. In lyre playing, for example, the performer finds each point on the string by practiced guesswork rather than measurement, which adds uncertainty and imprecision to the performance. Other such examples, Socrates says, can be found in medicine, agriculture, navigation, and military command. Factoring numbering and measuring back into the mix, however, we make room for crafts that employ instruments in their practice, like the straightedges and plumblines used in building. Because of their frequent use of measuring devices like these, such crafts have a degree of accuracy that makes them more artful than other branches of knowledge (5  .
. 
 . : 56B6). This contrast provides the first dichotomy in Socrates’ division of the disciplines. On the one hand there is a group of so-called arts (   2 5 : 56C4), like those of music, that involve less accuracy in their procedures. On the other are 2

The first group is so-called by the
 ), as noted at 55E7–56A1, despite its exclusion of numbering and measuring. According to Statesman 284D4–6, 5  properly so-called incorporate some kind of measure.

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arts like house building and shipbuilding that achieve greater accuracy through their use of measuring instruments. The second of these two groups admits further division. Rather than proceeding to this task immediately, however, Socrates draws attention to an important difference within the skills of measurement to which this group owes its accuracy. The skills in question – numbering, measuring, and weighing (55E1–2) – are both primary (
*: 56C9) among the arts and themselves arts of the highest accuracy (-: 56C8). The important difference pointed out by Socrates is that these primary arts admit differing degrees of accuracy among themselves. Further division of the metrically involved disciplines comes down to distinguishing different levels of accuracy within the primary arts that they incorporate. In the case of arithmetic, there is the difference between the way numbers are employed by common people (.
. : 56D5) and by “philosophers.”3 “Arithmeticians” of the first sort “reckon with unequal units” (    " ! % : 56D10), comparing two squadrons of ships, or two herds of cattle – or indeed, two of the smallest or largest things there are – without regard to a common measure. An example would be reckoning one squadron merely as larger or smaller than another, without counting the number of ships involved.4 This is the first reference in the present context to the type of comparative measure described in the Statesman as taken “according to the association of greatness and smallness with each other” (283D7–8), in contrast with that taken according to due measure. The “unequal units” with which the numerically unsophisticated general would operate might be the two individual squadrons themselves, which are judged larger and smaller on a comparative basis alone. Restricted to merely comparative measures like this, an “arithmetician” of the first sort would be able to judge two assemblages only as more or less numerous, even if they were “the smallest and the largest things in the world” (   . . . ) 
  : 56D11–E1).5 In contrast with this procedure of reckoning by unequal units, someone employing numbers in a “philosophic” manner would reckon the 3

4 5

The participle    3  at 56D5, 57C3, and 57D1, may refer to the studied or reflective use generally of the arts in question, as distinct from the more specific practice of dialectic cited at 57E7. Compare the supposed predicament of Agamemnon mentioned at Republic 522D. For explanation, see the note on p. 427 of Waterfield (1995). This is the only appearance in the present context of what might be called the “vocabulary of the Great and the Small” engaged in the methodological passages of the Statesman.

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comparative size of two different assemblages only after assuring that both could be enumerated according to the same unit.6 With this contrast in clear view, Protarchus has no trouble agreeing that there are two kinds of arithmetic. The same question arises about calculation and measurement (  ) : 56E7). Is there not a studied use of calculation to be compared with the calculation of the merchant, Socrates asks, and a philosophic geometry to compare with that of the builder? Are these respective arts of one sort only, or shall we say there are two of each? In response to these rhetorical questions, Protarchus casts his vote for two of each. Like the other primary arts mentioned at 56C9, calculation and measurement can be subdivided with respect to precision of application. As Protarchus goes on to exclaim, the difference in clarity among sciences exhibited here is “amazingly vast” (!" # . . . ! : 57C6). Not only are the primary arts far superior to the others in this respect, but when practiced in a genuinely philosophic manner they far surpass their common counterparts in the accuracy and truth (-7 ) !7: 57D1–2) of their employment of measure and number. The upshot so far is that there are two arts of arithmetic and two arts of measurement (3 ! ) ) 3 ): 57D6), and two branches as well of the many other arts following their lead. In each case (for example, the art of military command), the arts in question are divided with respect to degree of accuracy made possible by the primary arts of number and measurement upon which they rely. In brief, the source of accuracy in the arts overall has been identified as residing with the basic arts of numbering, calculation, and measuring, each of which itself admits differing levels of accuracy. As it stands, this sequence could plausibly count as what the Stranger calls “an exhibition of exactness itself” at Statesman 284D2. In following the demonstration thus far, moreover, we find explicit mention by Socrates of the two types of measurement figuring in the Stranger’s prediction. On the one hand is comparison of greater and smaller with each other, on the other a more exacting kind of measurement appropriate to the reflective (that is, “philosophic”) disciplines. But Socrates’ examination of accuracy in the disciplines is not yet complete. A place still has to be found for dialectic, which Socrates insists is inferior to no other with respect to accuracy. Two options appear 6

The stress here on equality of unit measures may hark back to the priority of equality over other numerical relations at 25A8 and D11.

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available. One is to locate dialectic indiscriminately among the other “very accurate” (-' & . . . : 57E3) disciplines, those already described as “philosophic” in viewpoint. But this seems inappropriate, given the distinctive character of its subject matter. What Socrates does instead, in effect, is introduce yet a further division within the group of disciplines that employ measurement in an exacting fashion. Up to this point, distinctions with respect to accuracy have been drawn with reference to the primary disciplines of numbering and measuring – dividing arts lacking such skills from those employing them – and within the latter distinguishing between those employing them in a common and in a “philosophic” manner. The final division in the sequence differentiates among disciplines employing these skills in a “philosophic” manner with regard to their respective subject matters. For some subject matters are more conducive to accuracy than others. On the one hand there is a discipline “concerned with what exists and is real and by nature is always the same” (
) # b ) # $  ) #  # )
"#: 58A2–3). Whatever else this discipline amounts to, it is one that “examines what is certain and accurate and overall the most true” (# L ) -L ) # ! 

': 58C2–3). Due to “the eternal existence” ( $  : 59A7) of its subject matter, dialectic achieves truth of the most accurate (-:; 59A11) character. On the other hand are disciplines concerned with what happens in the universe, how things act and are acted upon, and how they come to be originally. However reflective these latter disciplines may be, they are focused on what becomes, what will become, or what has come to be, rather that on what is always the same. The highest truth (# ! : 59B8) is not available to such studies; nor can any certainty (-- : 59B5) attach to disciplines without a secure subject matter. All that remains to complete the sequence of divisions is for everyone concerned to agree that dialectic is the discipline with the most accuracy and truth.7 Socrates’ examination of accuracy among the arts has revealed dialectic as the discipline with the most exacting subject matter, unique among the many disciplines in employing number and measure in the most exacting way. This done, Socrates and Protarchus return to their debate regarding the relative contribution of intelligence and pleasure to the human good. 7

Protarchus agrees at 58E, after Socrates assures him that the discipline in question is not in competition with rhetoric (`a la Gorgias) for superiority among the arts in eminence and utility.

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Now all this should be reassuring to the traditional Platonist who has grown accustomed to a firm distinction between being and becoming and to the distinction between reason and opinion that goes along with it. The term ‘reason’ ( %: 59D1) is reserved for the power of dialectic, whereas disciplines dealing with things in change are fixed on opinion (  : 59A1). Plato’s shift in the Philebus to a Pythagorean ontology8 has not dulled the distinction between the eternal and the temporal. Despite this orthodox outcome, there nonetheless is an aspect of Socrates’ examination of accuracy among the disciplines that remains unclear and more than a little puzzling. Dialectic first appeared within the class of arts that employ number and measure in an exacting manner, and then was distinguished from other arts of that class as the only discipline with unchanging subject matter. The eternal nature of its subject matter, however, does not change the fact that dialectic employs numbers and measures in its procedures. What is it to employ number and measures exactly in dealing with an eternal subject matter? No more help on this topic is available from the Philebus. To connect this portrayal of dialectic by Socrates with what the Stranger says as the conversation continues in the Statesman, we need to return to Aristotle’s characterization of Plato’s late philosophy in the Metaphysics.

10.3 Forms as Numbers In our previous discussion of Excess and Deficiency (Chapter 7), we noted that G
-  ) AX is one of five expressions used by Aristotle for Plato’s dual principle. The others are # 1
 (the Unlimited), # 1  (the Unequal),    " (the Indefinite Dyad), and #  ) #   (the Great and the Small) itself. This dual principle figures in several distinctive theses attributed to Plato in the first book of Aristotle’s Metaphysics. Three of these theses are of particular interest for present purposes: (1) that numbers come from the participation of the Great and the Small in Unity (987b20–22), (2) that sensible things are constituted by the Forms and the Great and the Small (988a11–14), and (3) that the Forms are composed of the Great and the Small and Unity (988a11–14).9 A further thesis involving this principle, with which we are not now concerned, 8 9

This is explained in ch. 1 of Sayre (1983). The meaning and credibility of these, and other theses attributed to Plato by Aristotle, are examined at length in Sayre (1983).

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is that well and ill (well and poorly done; see Physics 192a15) are caused by Unity and by the Great and the Small, respectively (988a14–16). Aristotle had other interesting things to say about Plato’s views regarding numbers. One is the claim at 987b14–18 that Plato said there are objects of mathematics ( ! ) located between sensible things and Forms, differing from sensible things in being eternal and unchanging and from Forms in being many alike.10 Another is the observation at 987b22–25 that Plato agreed with the Pythagoreans in saying that numbers are the causes of the existence of other things. This ties in with an apparent implication of theses (1) and (3) in tandem: inasmuch as both numbers and Forms come from the Great and the Small and Unity, there seems to be a sense in which Forms are numbers. This is also suggested by the apposition of  0 and  _ ! 3 at 987b22, which can be read as saying that the Forms (i.e., the numbers11 ) come from the participation in Unity of the Great and the Small. What is only implied by these passages is expressly stated at 1086a10–11 (see also 991b9–10, 1073a17– 20, and 1091b26): according to Aristotle, Plato also held (4) that the Forms are numbers. Although Plato’s terminology differs enough from Aristotle’s to make them hard to spot, all of these theses can be found in the dialogues.12 Of the four, the latter will provide most help in showing how dialectic is involved with number and measure. Because all four are interconnected, however, we should look briefly at the meaning of the first three theses. Thesis (1) corresponds to the derivation of number at Parmenides 142D–144A already summarized in section 8.5. To recapitulate briefly, the derivation begins with an unlimited multitude (1
 . . . #
! : 143A2) of parts implicated in an existing unity, establishes unique limits within this multitude that identify 2 (the first even number), 3 (the first odd number), and 1 (the numerical unit), proceeds to show how other numbers come from these by standard arithmetical operations, and then concludes on this basis that all numbers must exist.13 Although there is no evidence that Aristotle was thinking of this particular derivation in 10

11

12 13

This distinction among (i) Forms of mathematical objects, (ii) the numbers of mathematical calculation, and (iii) numerable sensible things is clearly drawn in the Philebus between 56C and 62A. See Sayre (1983), pp. 87–88, for discussion. Although both terms occur in the manuscript, editors vary on whether  0 or  _ ! 3 (if either) should be bracketed. The rendition of 987b22 in thesis (1) follows Ross. To show this was one of the purposes of Sayre (1983). Details of this derivation are discussed in Sayre (1983).

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attributing thesis (1) to Plato, the fact that it plays a featured role in the Parmenides shows that Plato had distinctive views about how number flows from the Great and the Small.14 Theses (2) and (3) are illustrated by the discovery attributed to the Egyptian deity Theuth in the Philebus. Again, we may recapitulate our previous discussion of this topic. Starting with an undifferentiated Unlimited (# 1
 : 18A9) of vocal sound, Theuth first apprehended the class of vowels, next a number of sounds that are not voiced (e.g., labials), and then separated out ( : 18C2) a third class to be called mutes. Having established the three main classes, he then subdivided each down to the level of units until he had got the number (! # : 18C5) of each. At this stage he gave these units singly and collectively the name ‘element’ (or ‘letter’;  5' at 18C6), and labeled the whole system ‘the art of letters’ (  5  : 18D2). Theuth starts with an undifferentiated range of vocal sound (more and less, open and voiced), marks off three major divisions (vowels, labials, mutes), and then subdivides further down to specific numbers of phonetic elements. As noted in our previous discussion, we have here a case of Limit being imposed on the Unlimited. With the vowels, for instance, the Unlimited is a continuum of sounds placed progressively further backward along the palate, which when subdivided yields a series of distinctive sounds (in English) A-E-I-O-OO. Similar divisions along other sound continua, having to do with lip formation and breath control, produce labials and mutes. Theuth’s creative act resulted in the establishment of unique cuts along the relevant continua that we now recognize as determinate phonetic elements. These limits are described not only by the term ! # (18C1, 5), according to the definition of Limit at 25B1 and 25E2, but also by the term 9  (18C2) itself. Here is an illustration of thesis (3). The Forms of the phonetic elements come with the unique cuts established along the continua in question. What the Great and the Small contributes to this result are the continua of sound to be divided, whereas Unity contributes the uniqueness that makes the elements distinctive. This creative act accomplished, there is now an art of letters for people to exercise in articulate speech. A sound articulated on a given occasion counts as an instance of A if it falls near the fixed cut identified as A along 14

For reasons laid out in Sayre (1983), ch. 2, sec. 3, it seems likely that Plato had a mathematically more sophisticated generation of numbers based on then-current work of Eudoxus in the Academy.

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the continuum of voiced sound. Similarly, if it falls near the cut marking off E, it counts as a voiced E. And if it falls indiscriminately somewhere between, it amounts to a sound without determinate phonetic character. The fixed cuts (points of division) in question are the unchanging (hence eternal) Forms A and E.15 In any given case, a particular sound owes its phonetic identity to its position relative to an unchanging reference point along a relevant vocal continuum. Here is an illustration of thesis (2). The Great and the Small going into the constitution of a given sensible phoneme is the vocal continuum along which the sound is situated. And the Form entering into its constitution is the fixed reference point along that continuum from which it receives its determinate character. We come now to thesis (4) assigned to Plato by Aristotle, to the effect that the Forms are numbers. The first question to be faced regarding this thesis is how to understand the term ! #. Like its English counterpart, the term carried a considerable variety of meanings in Attic Greek. The range of meanings in English can be instructive. To mention a few, there are cardinal and ordinal numbers, numbers of periodicals (“the most recent number of National Geographic”), number as general quantity (“the difference between many and few is a matter of number”), number as one of a group of performances (“her number came last on the program”), and number worthy of special attention (“cute little number” in a designer’s collection). Attic Greek used ! # in a comparable range of meanings. Notable for our purposes, in addition to the numbers involved in counting, are grammatical number (LSJ (1968), sense V), number in the sense of general quantity (LSJ, sense I, 2, as at Statesman 284E4), number as a measure of rank, value, or station (LSJ, sense I, 5), and number signifying fullness or completion (LSJ, sense I, 4, as at Laws 668D10). 15

As I interpret the story, Theuth established (set apart:  at 18C2) the fixed reference points along the vocal continua in question, rather than merely happening upon cuts that had somehow been established previously. In recognizing these cuts as Forms, we encounter the apparent anomaly of eternal Forms in some sense being generated. This accounts for Aristotle’s otherwise puzzling complaint at Metaphysics 1091a12–13 about the thinker (Plato) who said number is generated from Unity and the Indefinite Dyad attributing generation to eternal things. To defend Plato’s rationality, we should point out that the generation in question is not in time – no more so than Zeus’ creation of cosmic order cited at 28E (see 30D). Forms are “generated” only in the sense that they are no longer primitive (as in the middle dialogues), being constituted from Unity and the Great and the Small. Despite being constituted in this manner, Forms are still changeless and eternal.

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In Metaphysics M.6, Aristotle himself distinguishes number in three different senses recognized among his predecessors. First he mentions numbers none of whose units is comparable with those of any other. This appears to correspond to the type of arithmetic dealing with unequal units at Philebus 56D9–E2. Second is number with units that are all the same, which Aristotle identifies with mathematical number. This presumably corresponds to the other kind of arithmetic at Philebus 56E2–4 dealing with equal numerical units. And third is number exemplified by Two itself and Three itself (; " ; . . . ;  :; 1080a28), which exist in sequence but do not contain units. Having completed this survey, Aristotle pronounces without argument that these are the only ways in which numbers can exist (1080b4–5). This division of numbers into sensible, mathematical, and ideal seems to tie in with his claim on behalf of Plato at 987b14–18 that mathematical numbers exist between Forms and sensible things. What appears to be the same attribution is repeated at 1090b35–36 as the position that mathematical number is located between sensible number and ideal number, said to be held by those who first posited two kinds of number (presumably including Plato16 ). In this more specific form, the view attributed to Plato is that mathematical numbers (Aristotle’s second kind) are located between Form Numbers such as Two and Three (the third kind) and numbers assigned inexpertly to sensible things (the first kind without comparable units). Let us return to thesis (4) with this threefold distinction in mind. If Plato was among those whom Aristotle understood as maintaining that mathematical numbers are between Form Numbers and sensible numbers, then we can properly gloss 987b14–18 as implying that Plato maintained a distinction between mathematical numbers such as 2 and 3, which are eternal and many alike, and the Form Numbers Two and Three, which are eternal and each unique. One possibility, accordingly, is that by assigning thesis (4) to Plato, Aristotle meant that Plato maintained that Form Numbers are numbers, comparable to maintaining that the Form Good is good and the Form Beauty beautiful.17 16

17

At 987b27–28, Plato is said to differ from the Pythagoreans in speaking of numbers apart from sensible things, whereas they said that mathematical numbers are sensible things. This seems to be Julia Annas’s reading in Annas (1976), prompting her to refer indifferently to Form numbers and Number Forms (p. 24). As she duly notes, this leads to Third Man problems induced by thinking of Forms as perfect exemplars of properties shared by their instances.

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Given the contexts in which this thesis comes into play, however, it seems evident that the view attributed to Plato concerns Forms in general as distinct from Forms in the sense of ideal numbers. In citing Plato’s agreement with the Pythagoreans in saying that numbers cause the existence of other things (987b22–25), Aristotle surely is attributing to Plato a view comparable in generality to the Pythagorean tenet that the elements of numbers are the elements of everything else (986a1–2). Otherwise we would not find him worrying about numbers that would be assigned Socrates or Callias if Forms are numbers (991b9–11), or the consequences for animals and plants under the same hypothesis (1091b26– 30). It is one thing to say that Forms of numbers are numbers, and quite another to say this of Forms in general. The latter seems clearly to be the thesis attributed to Plato. Another possible reading of thesis (4) is that Plato assigned mathematical numbers to all the Forms, as distinct from identifying Forms with numbers. Aristotle seems to have something like this in mind when he wonders facetiously at 1084a21–25 whether, if the number of Man itself is 2 and that of Horse is 4, Man will be part of Horse. With respect to its plausibility as a view of Plato’s, this reading falls in the same category as that inspiring the procedure attributed to Eurytus at Metaphysics 1092b10–14, who was said to have arrived at the number of things (man and horse are mentioned) by tracing out images of their visible forms with pebbles.18 Yet another possibility, perhaps, is that Forms are ratios, a reading Aristotle seems to toy with at 991b13–20 and 1092b14–15. But this is an interpretation Aristotle quickly dismisses himself, on the grounds that qualities such as white, sweet, and hot (1092b16) cannot be caused by mathematical numbers. Given what Aristotle tells us about Plato’s later views in Metaphysics A.6, however, there is one overriding reason why Forms cannot be identified with mathematical numbers of any sort (integers or ratios). The reason is simply that Plato located mathematical numbers between Forms and sensibles and that Forms cannot be identical with things on a different level from themselves. As far as thesis (4) is concerned, it seems entirely unlikely that it should bear a meaning that renders it so patently false.

18

More information is provided by Alexander in his commentary on this passage (Hayduck (ed.) (1891) 827.8–17), saying that Eurytus used colored pebbles, presumably to achieve a shadowed effect, and that he assigned the numbers 250 and 360 to man and plant, respectively.

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In point of fact, there is another meaning to be assigned thesis (4) that makes it not only intelligible but arguably correct. We noted earlier that one sense of ! # in Attic Greek is that of measure. A man’s eminence is numbered by his rank in society. Aristotle employs the term in a closely allied sense in the Physics, where he speaks of time alternatively as the number and the measure of motion.19 Far from being an innovation on Aristotle’s part, moreover, this use of the term ! # corresponds to a standard use in astrology according to which number measures degree of progression of a heavenly body in a given period of time (LSJ (1968), sense XII). Although Aristotle’s convoluted criticism in the Metaphysics seems not to have allowed for this possibility, the reading of thesis (4) borne out by Plato’s Philebus is that Forms are numbers in the sense of measures. This sense is illustrated explicitly by the terminology of Philebus 17D4–6, where Socrates observes that the bodily motion (of a gymnast or dancer) should be measured by numbers (& ! . ! ) called rhythms and meters. These measures correspond to the numbered intervals and scales constituting the art of music in the immediately preceding illustration (17C11–D4). Other illustrations, considered in Chapter 9, include the law and order imposed by the goddess by way of limiting our unbridled pleasures, the temperate seasons produced by mixing Limit with excessive heat and cold, and the state of health established by the correct mix of Limit and the Unlimited. What these cases illustrate, of course, is the class of Mixture containing things generated by imposing number (! # : 25E2) on the conflicting opposites of the Unlimited. In his earlier description of the limits involved, Socrates included equal, double, and in general everything related “as number to number or measure to measure” (
# ! # ! # /  \;
#  : 25A8–B1). If number and measure are treated as synonymous in the Philebus, as they certainly seem to be, then thesis (4) can be elucidated as the claim that Forms are numbers in the sense of measures.

10.4 The Involvement of Dialectic in Numbers and Measures In section 10.2, it was proposed that Socrates’ discussion of accuracy in the arts at Philebus 55D–59D responds to the Stranger’s anticipation 19

Between 219b and 222a, motion is said with comparable frequency to be numbered or to be measured by time. The preferred expression is “time is number of motion in respect of before and after” (219b1–2, 220a24–25). Details are discussed in Sayre (1983), p. 110.

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at Statesman 284D1–2 of an exhibition of exactness itself. Whatever the merits of this proposal, Socrates’ discussion of accuracy in the Philebus is interesting in its own right. Dialectic is introduced into the discussion as belonging to the class of arts that are especially exact in their employment of measure and number (57D1–2). Within this special class, dialectic is further distinguished as being concerned with a subject matter that is real and always the same (58A2–3). Because of its eternal subject matter, dialectic is said to possess the highest degree of truth and precision among the arts (58C2–3). This, in brief review, is the source of our quandary at the end of section 10.2. To make sense of what Socrates is saying about dialectic in this passage, we need to make headway on a number of interrelated problems. One previously recognized problem is to determine a sense in which dialectic makes use of numbers and measures. An initial step toward resolving this problem was taken in the previous section where, with the help of Aristotle’s account of Plato’s views in the Metaphysics, it was proposed as likely that the author of this passage was thinking of Forms as numbers in the sense of measures. Given this conception of Forms in the Philebus, the initially baffling characterization of dialectic as exact in its use of measure and number (57D1–2) translates into a more familiar depiction of dialectic as exact in its dealing with the Forms. An associated problem that remains unresolved, however, is to understand how a discipline can be more or less exact in its dealing with Forms. If dialectic is fully exact in this regard, in what sense might another endeavor be less precise? Another problem to be addressed is how the eternal nature of dialectic’s subject matter contributes to its precision, and renders it supreme among the most exacting arts. We take a fresh look at these problems in the remaining two chapters. Before leaving the Stranger’s allusion to a forthcoming exhibition of exactness, however, we should look again at his remarks about the “clever people” (284E11) who think that measurement is universally bound up with generation. A shortcoming of these people, he says, is that they are not accustomed to dividing things according to Forms (& 0: 285A4). A consequence is that they fail to realize that there are two kinds of measurement, only one of which contributes to the generation of things. When these people do make divisions, the Stranger continues, the separations they make are not into parts (   : 285A7). As we shall see in the next chapter, failure to separate things into parts results in failure to divide them according to Forms as well.

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There is another reference to division according to Forms at 286D, where the Stranger is wrapping up the results of his discourse on Excess and Deficiency for the practice of dialectic in particular. The upshot is that no discussion is too long or too short if it increases the ability of the participants to divide according to Forms (& 0: 286D9). Should someone complain that a philosophic discussion is too lengthy (as the Stranger feared YS might do at 283B6–7), then it should be incumbent upon that person to show that a shorter discussion would have resulted in the participants’ becoming better dialecticians (287A1–3). Improving one’s capacity to divide according to Forms is tantamount to becoming a better dialectician. Making divisions is something that can be done expertly or inexpertly, precisely or in a manner lacking precision. The “clever people” in the first case divide things inexpertly, which amounts to their failure to divide according to Forms. On the other hand, the division of a dialectician, when done expertly, is clear and precise. Done expertly, it proceeds wholly according to Forms. But even dialectical division can be done with different degrees of precision. Insofar as the purpose of the ongoing conversation with YS is to make him a better dialectician, it is directed to the end of increasing his ability to make accurate divisions. Put otherwise, its purpose is to make YS more capable of dividing things according to Forms, along with other participants in the conversation. An accomplished dialectician is one who can divide according to Forms with unerring accuracy. If we can pin down what complete accuracy in this regard amounts to, we will be close to understanding the sense in which accomplished dialecticians are exact in their employment of measure and number. This sets the task of the remaining two chapters.

11 Division According to Forms

11.1 Relevant Texts in Other Dialogues To students of the middle dialogues, the Stranger’s talk of dividing things according to Forms may sound reassuringly familiar. Before returning for a closer look at the Stranger’s remarks in this regard, let us recall some similar remarks by Socrates of the middle period.1 At Republic 454A, Socrates tells Glaucon that people often are unable to distinguish between disputation and genuine discussion because they lack the ability to divide things according to Forms (  3 !  & 0  3  : 454A6). This failure is comparable to that of the “clever people” of Statesman 284E11, whose inability to distinguish the two kinds of measurement is attributed to exactly the same cause (   & 0 . . .  "  ": 285A4–5). At Cratylus 424C, in their discussion of letters and syllables, Socrates tells Hermogenes that vowels should be divided from other elements according to Forms (or classes2 ) (! . . .  0: 424C6). This brings to mind the story of Theuth in the Philebus. As we recall (from section 8.4), Theuth was credited with having first discerned vowels, semivowels, and mutes within the Unlimited range of vocal 1

2

The Socratic dialogues in question are the Republic, the Cratylus, and the Phaedrus, which very likely were made public before the Sophist and the Statesman. Scholars uncomfortable with dividing Plato’s corpus into periods may gloss this reference to the middle period accordingly. The ensuing survey includes only texts mentioning division according to Forms, excluding other uses of the expression  & (or ) 0. The term 9  invites translation sometimes as ‘Form’ and sometimes as ‘class’, occasionally in occurrences within the same passage. A case in point is Statesman 262D–263B, to which we turn in the next section. Note 14 also bears on this point.

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sound. In describing this achievement, Socrates refers to mutes as a third class ( . . . 9 : 18C2) to be set aside as distinct. The distinctions among phonemic sounds that Hermogenes is advised to observe correspond to those established by Theuth in the story of the Philebus. The Phaedrus contains three explicit references to the procedure of dividing according to Forms. One is at 265E1, in a passage familiar for containing the sole reference in the dialogues to collection and division as companion procedures. Division is described here as a matter of dissevering things according to Forms (’ 0 . . .   ), following their natural joints (& 1! . . .
" : 265E1–2) like an accomplished butcher. Shortly thereafter, Socrates declares himself a lover of divisions like these, when in the company of collection, and refers to people skilled in these procedures as dialecticians (266C1). It is interesting to note that this passage, in contrast with those cited previously from the Republic and the Cratylus, tells us something about what division according to Forms accomplishes if done successfully. It cuts things up along lines of articulation that exist by nature (
" ), here compared with the natural joints of a sacrificial animal carcass. The same metaphor is employed at Statesman 287C3, in connection with the Stranger’s sanction of nondichotomous division. The sense of the comparison, presumably, is that dialectical division should follow these natural lines of cleavage. Division according to Forms is tantamount to abiding by these prestablished lines of distinction. Another occurrence is at Phaedrus 273E1, in the context of Socrates’ disquisition on the importance of truth to the art of speaking. As he puts it, the art of speech requires an ability to distinguish various characters in an audience, comprehending each in a single Idea ( C7 (7: 273E2); this in turn requires being able to divide things according to Forms (& 0 . . . '!  $ : 273E1–2). Knowing how to divide according to Forms, in short, enables the orator to identify members of the audience by specific types. The other reference to dialectical division in the Phaedrus comes with Socrates’ summary of requirements for the artful use of speech at 277B– C. First, one must know the truth about things being discussed, which goes along with being able to define the things in question. Then one must know how to divide these things according to Forms (& 0 . . .   : 277B7) until reaching something individual. Other requirements are finding out the sort of speech appropriate for each kind of soul and being able to fashion one’s discourse accordingly. As commentators have

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been quick to note,3 Socrates portrays speaking as rhetorical art in which dialectic plays an essential role. There is one further reference to division & 0 in a dialogue that features Socrates as leader. Immediately after introducing the first two ontological classes (Limit and the Unlimited) at Philebus 23C, Socrates adds a third (Mixture) in rapid sequence. Immediately thereafter, he remarks that Protarchus must find him absurd for his enumeration and dividing into classes (& 0 : 23D2). After Protarchus politely refuses to comment, Socrates remarks that a fourth class (Cause) might also be needed. This is the last mention of division  & 0 in the Platonic corpus. Returning now to conversations featuring the Eleatic Stranger, we find two references to division according to Forms toward the end of the Sophist. Upon finishing his analysis of falsehood in judgment and speech, the Stranger asks Theaetetus to recall their previous divisions according to Forms ( & 0  : 264C1–2). He mentions first the division of copy making into making likenesses and making appearances (Figure 3.5) and then proceeds to recapitulate the entire sequence of prior divisions. At 267D he encounters the distinction between knowledgeable and unknowing mimicry, and finds it necessary to coin a term (i.e., 

  : 267E1) for the latter. The reason given for this need is a certain laziness on the part of their predecessors regarding “the division of kinds according to Forms” ( .  . & 0 : 267D5–6). This explanation of the need for neologisms merits careful attention. The predecessors in question are being faulted for backwardness in dividing kinds ( . ) according to Forms. On its face, this charge is puzzling. At crucial junctures in the Sophist, the terms   and 9  seem to be used interchangeably. One such juncture is the discovery of the “free man’s knowledge” at 253C, whereupon the Stranger describes dialectic as a matter of dividing things according to kinds (  : 253D1) and not taking the same Form (9 : 253D1) as different or a different one as the same. Another is his reference to the “very important kinds” (Z . . . .  . : 254D4) of Being, Rest, and Motion, the blending or failure to blend of which is a matter of philosophic discernment.4

3 4

See, e.g., Griswold (1986), p. 215. See also 259A4–5, with its reference to blending kinds ( ), followed at 259E5–6 with the claim that discourse is made possible by the blending of Forms ((. ); also 260B7 where not-Being is named as one kind ( ) among others.

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The charge against the predecessors, however, cannot be that they were lazy in dividing Forms according to Forms, or kinds according to kinds. If it were, the charge would be unintelligible. Even if a distinction were maintained between kinds and Forms, it is unclear what dividing kinds according to Forms might amount to. The purpose of dividing things according to Forms, presumably, is to make authentic distinctions – as vowels are distinguished from other phonemic elements in the Cratylus or types of soul are distinguished from each other by the orator in the Phaedrus. But how could division of kinds, however skilled, contribute to that purpose? The burden of the question is not about kinds as such but rather about the procedure of division itself. Phaedrus 265E1 speaks of dissevering things according to Forms, using butchery of carcasses as an analogy. But what gets dissevered in making the distinction between vowels and other phonemes? What corresponds to the carcasses in the analogy is left unclear. At Phaedrus 273E2, the art of speech is said to rest on the ability to divide things ( $ ) according to Forms. Yet we are not told what things get divided in the orator’s skilled distinction among various kinds of soul. Our goal for the remainder of this study was set at the end of the previous chapter. The announced purpose of the Stranger’s conversation with YS is to make its participants better dialecticians (285D6, 287A3). As the Stranger indicates, this involves making the participants better able to divide things according to Forms. Our concern at this point is to understand what division according to Forms amounts to, which requires a firm grasp on the sort of thing that gets divided as part of the process. There is another section of the Statesman concerned with dialectical division (262B–263B), to which we turn presently. By way of preparation, however, it will be helpful to review what other commentators have said about the matter at hand.

11.2 What Gets Divided? Some Familiar Answers According to one unreflective conception of Plato’s method of division,5 the procedure deals with Forms from start to finish. The dialectician begins with a Form that is relatively comprehensive (e.g., Knowledge at Statesman 258B4), divides it into other Forms of less generality 5

This conception corresponds to what Moravcsik calls “the crude model” on p. 168 of his “Plato’s Method of Division,” in Moravcsik (1973).

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(e.g., Practice and Theory at 258E5), and proceeds through Forms of increasingly lesser generality until arriving at the Form to be defined (e.g., Statesmanship). Given the progressive character of this procedure, what results from a given division (e.g., Practical Knowledge on one hand, Theoretical Knowledge on the other) must be of the same nature as what gets divided in producing it. Else the factor(s) yielded by the initial division would not themselves be available for further division in turn. Thus conceived, dialectical division is not just division according to Forms. It rather is division of Forms themselves. And what results from division are yet other Forms, which can be subjected to further division in turn. Before rejecting this conception out of hand, we might note that it is not entirely without textual support. For one thing, it seems compatible with the description of dialectic at Republic 510B and 511C as a procedure of inquiry that proceeds through Forms alone without involvement of sensible images (thus distinguishing it from mathematics). For another, there are several passages in the Sophist and the Statesman where the Stranger seems actually to be talking about division of Forms into other Forms. At Sophist 264C, as already noted, he recalls earlier “divisions according to Forms” ( & 0  : 264C1–2) in which “two Forms of image making were cut apart” (M !  9
 0 3 : 264C4) – the making of likenesses and the making of semblances. And at Statesman 258E7 the two parts Practical and Theoretical into which Knowledge is divided are referred to specifically as 0.6 Nonetheless, although we should not foreclose the possibility that Forms in some sense come into being (recall the case of Theuth in the Philebus), there is no conceivable way this could happen by the division of other Forms. Even if we grant that Forms in the later dialogues are somehow composite,7 it is hard to imagine “cutting up a generic Form with metaphysical scissors”8 in such a way that other Forms are produced as a result. One lesson to be learned from Socrates’ discomfiture in the first part of the Parmenides is that thinking of Forms as literally divisible into parts leads to unacceptable consequences. There is no call to attribute

6 7

8

Other passages admitting this reading, perhaps, are Sophist 265E5–8, and Statesman 262E6 and 287D8. In his Metaphysics, Aristotle attributes to Plato the view that Forms are composed of the Great and the Small (see Chapter 10) and Unity. I have argued, in Sayre (1983) and elsewhere, that this view of the Forms can be found in the Philebus. The phrase is Moravcsik’s, from op. cit., p. 168.

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this way of thinking to the Eleatic Stranger after it had been abandoned by Socrates under pressure from Parminides himself. A more plausible account comes with conceiving the relation between a given Form and other Forms into which it supposedly gets divided as a broadly logical relation9 and then thinking of division as a matter of making relations of this sort explicit. The relation in question can be illustrated by the Stranger’s division at Sophist 219Dff. of acquisitive art (now conceived as a Form, Acquisitive Art) into Exchange and Conquest, the latter into Open Conquest (Fighting) and Stealthy Conquest (Hunting), and so forth (see Figure 3.2). If we assume that all instances of Exchange and all instances of Conquest invariably are instances of Acquisition as well, we should be prepared to say that being an instance either of Exchange or of Conquest entails being an instance of Acquisition – in short, that both Exchange and Conquest entail Acquisition. Insofar as both Exchange and Conquest are bound up with Acquisition in this manner, we may think of their instances as alternative occasions on which the Form Acquisition is also manifested. Acquisition is manifested partially in instances of Exchange and partially in instances of Conquest. With this in mind, we may then say more simply that Exchange and Conquest are parts of Acquisition. When the Stranger divides Acquisition into Exchange and Conquest at 219D, accordingly, he divides the former into its parts. Conquest is similarly divided into its parts Combat and Hunting at 219E, and so forth along the line of division terminating with the Form Angling at 221B–C. Put more generally, definition of a practice x (e.g., angling) proceeds by positing a Form A (e.g., Art), which is divided into parts B (e.g., Acquisition) and B , the former divided into parts C (e.g., Conquest) and C , and so forth through M (Striking) and N (Diurnal), until the Form X (Angling) itself is reached as a part of N. In this sequence, each of A, B, C . . . , M, N, and X is a Form, and these Forms are so interrelated that X entails N, N entails M, . . . C entails B, and B entails A. The upshot is that x is defined by a set of Forms each of which is entailed by the Form X, and that X is unique in being the only Form with this exact sequence of entailments. According to this conception of division, nothing actually gets divided in the dialectical process. To talk of dividing according

9

This account corresponds to what is called the “new intensional mereology model” in Cohen (1973), p. 186ff., but without specification of any particular system(s) of logic (for Cohen, set theory and modal logic) to be used in elucidating the relation in question – hence reference to it as a “broadly logical relation.”

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to Forms is an elliptical way of referring to the procedure of making distinctions that engage lines of logical entailment. Although concern with Forms unquestionably is involved in the dialectical method of the Sophist and the Statesman, however, this way of conceiving that method is surely inadequate as it stands. One major problem is that it subscribes to a notion (previously criticized in section 3.3) of strict hierarchy in the sequence of division that simply does not fit the text. A good example of the problem appears in the definition of angling, where there are several features mentioned in the Stranger’s divisions that are not entailed by other features coming later in the sequence. There are instances of acquisition, for example, that are not artful (e.g., finding something valuable by accident), instances of conquest that involve no acquisition (e.g., winning a wrestling match), instances of hunting that do not result in conquest (e.g., looking for rare birds to photograph), and so forth. Hence Acquisition does not entail Art, nor Conquest Acquisition, and so on, as the present conception of division requires. Whatever the relation between successive entries in a given line of division, it cannot be a matter of entailment (however broadly conceived). Another problem with this conception of division is the direction it assigns to the “part-whole” relation among Forms in the first place. Inasmuch as angling is an acquisitive art involving conquest, this conception construes Acquisition as part of Art, Conquest as part of Acquisition, and ultimately Angling as part of a part (etc.) of Conquest. But if there is to be a relation of this sort among Forms at all, it seems much more natural to think of it as heading in the other direction. By way of analogy, consider the definition of man as a rational animal. Although being a man in some sense does seem to entail being an animal, it is counterintuitive to think of being a man as part of being an animal. This is because other things are fully animal without being anyway involved in humanity. A much more natural conception of their relation is to think of both being an animal and being rational as part of being a man.10 Similarly, it seems more natural to think of Acquisition and Conquest as parts of Angling, rather than vice versa as the present account of division requires. Yet another objection to this account is that there are features involved in several of the Stranger’s divisions that cannot plausibly be considered to have Forms. Examples cited by Moravcsik are the various ways of striking fish (e.g., from below) at Sophist 220D–E and “using short arguments” at 10

Cohen made this objection on the basis of the same analogy; see Cohen (1973), pp. 190–1.

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Sophist 268B.11 Another example is arts exercised in “doing something” at Statesman 279C8. Whatever the relation between these and the qualifying descriptions accompanying them, it seems not to be a relation between Forms.12 One remaining attempt to locate Forms in the direct line of division employs the concepts of classes and subclasses. In this way of thinking about the definition of angling, for example, Art is a generic class of Forms (not of particular instances) having Production and Acquisition as subclasses, and the initial division of Art amounts to distinguishing between these two subclasses. Acquisition is further divided into the subclasses Exchange and Conquest, and so forth until we reach a subclass – that of Angling – with no further relevant subclasses. Whatever other difficulties this treatment might encounter, however, it falls prey to the objection of the previous paragraph. There are too many features in the Stranger’s divisions that most probably do not correspond to Forms in the first place for division to be a matter solely of distinguishing subclasses of Forms. In view of difficulties like these, a seemingly more promising approach is to take Forms out of the line of division entirely and to think in terms of classes and subclasses of particulars instead. Glossing the definition of angling accordingly, we think of art as the class of individual artisans, divided into subclasses of productive artisans and artisans who specialize in acquisition. The subclass of acquisitive artisans is divided further into those acquiring by exchange and those acquiring by conquest, and so on until only the subclass of anglers remains, distinguished from all others with kindred concerns. One advantage of this approach is that it makes no mention of entailment relations among successive stages of division. In particular, it is compatible with the observation that many features in the Stranger’s division are specifications not applying exclusively to the features preceding them – that there are instances of acquisition that are not artful, instances of conquest that involve no acquisition, and so forth.13 For acquisitive

11 12

13

Moravcsik (1973), p. 173. Arguments like this based on assumptions about what does and does not constitute a Form for Plato of course are provisional at best. Plato never took a stand in his writings on where the borderline lies. The closest he comes is at Parmenides 130B–E, which portrays Socrates as unable to make a firm decision on the matter. This approach corresponds closely to what Cohen calls “the superclean model” in op. cit., p. 182. Although Cohen is not entirely clear on the matter, one difference may be that the “superclean model” seems to require that the entire extension of the class of acquirers be included within the class of artisans, etc.

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artisans to be a subclass of artisans generally there is no requirement that all people who acquire things do so artfully. Individuals in that subclass might all engage in acquisitive art, regardless of others who acquire by artless means. Another important feature of this approach is the ease with which it handles the Stranger’s repeated stipulation that divisions should be made “according to Forms.” If the subclass of acquisitive artisans is further divided into a subclass all members of which acquire by exchange and another all of which acquire by conquest, and if indeed there are Forms of Exchange and Conquest, then this is tantamount to dividing acquisitive artisans according to those two Forms. Dialectical division is properly executed, as the Stranger would have it, when it segregates subclasses each with members which all participate in the same relevant Form. This approach also fits in nicely with Plato’s tendency, noted earlier,14 to vacillate between the sense of Form and the sense of class in his use of the term 9 . When the Stranger speaks of cutting apart two 0 of image making at Sophist 264C4, we can comfortably read this as a matter of splitting the class of image makers into two distinct subclasses, rather than in the problematic manner considered earlier of cutting up Forms. Similar readings are available for his mention of two 0 resulting from the division of knowledge at Statesman 258E4–7, for that of dividing number into two 0 at Statesman 262E3, and so forth. According to this approach, in summary, division according to Forms is division of classes into subclasses of individuals, such that all members of a given subclass are instances of the same general Form. When properly accomplished, division results in a diminished class of individuals that can be further divided in similar fashion; and so on until the task at hand is finished. This clearly is the most promising (and probably most familiar) account of dialectical division to be considered thus far. When we bring it to bear on the passage in which the Stranger advises YS to make cuts “through the middle,” however, it encounters a difficulty that is not easily resolved. We turn now to that passage.

11.3 Making Cuts through the Middle Although the entire dialogue is required to reach an acceptable definition of statesmanship, a tentative definition is put forward within the first five 14

See note 2 and the associated text.

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pages. Statesmanship is initially characterized as (a) theoretical rather than practical, (b) directive rather than critical, and then in sequence (c) self-directive, (d) concerned with living creatures, and specifically (e) concerned with their collective rearing. Although problems are raised with (e) shortly thereafter, the Stranger’s first criticism comes with YS’s suggestion that collective rearing be further divided into a part concerned with people and a part concerned with beasts – the former, of course, to be identified with statesmanship. Here is the Stranger’s diagnosis of why that will not work. 262A8 Let us not separate one small part from many others that 262B are large – not without the help of Forms (0 "). Instead, the part removed should engage a Form (9 ) at the same time. It is best to separate what one is looking for straightway from the rest, if done correctly – as you thought was the case with the division advancing the argument just now, seeing that it led to humankind. But narrow cuts, my friend, are not without danger. It is safer to make cuts through the middle of things (  ); [this way] one is more likely to hit upon 262C Ideas ((). With regard to inquiry, this makes all the difference. What do you mean by this, Stranger? Rather than perfunctorily separating off the thing one is looking for (in this case, humankind) as a small slice of a larger group (living creatures), which the Stranger says poses a risk for dialectical inquiry, time should be taken to ensure that one’s divisions result in parts that correspond to Forms as well. And the surest way of doing this is to make cuts through the middle. One question raised by this remark is “middle of what?” Another is the question of sense: what does “cutting things through the middle” mean? There are passages in the Sophist that appear relevant to this latter question. One is at 229B, where the Stranger is in the process of defining “noble sophistry” and proposes cutting ignorance “down the middle” (  : 229B5) as an aid in categorizing the arts that correct it. The result is an unelaborated separation of stupidity from other types of ignorance. A seemingly related passage contains the Stranger’s summary of the divisions leading to the definition of angling. In this very succinct recapitulation, we hear that half (, "  : 221B3) of art is acquisitive, half of acquisition conquest, half of conquest hunting, half of hunting animal

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hunting, and so forth. Although there is no mention here of “cutting through the middle” as such, it seems reasonable to construe “dividing by half” as an equivalent procedure. Neither of these passages from the Sophist, however, provides much insight into what “cutting down the middle” or “dividing by half” might amount to. For help in this regard, we have no better place to turn than the Stranger’s response to the question put by YS at 262C2. Upon hearing the former’s advice to avoid small slices in favor of “cutting through the middle,” YS asks what this is supposed to mean. The Stranger responds. 262C3

262D

262E

263A

I must try to put it yet more clearly, Socrates, out of respect for your natural bent. As it happens, a complete explanation is not possible just now under present circumstances. Yet I must attempt to move the matter forward just a little bit for the sake of clarity. So what sort of thing were you saying wasn’t being done right in our divisions just now? Just this. It was as if someone tried to separate the human race ( !*
 . . .  ) dichotomously, dividing as most people do here by setting the Greeks aside as one group distinct from all the rest. Whereas all the other races (  ) taken together are addressed under the single name ‘barbarian’ – even though they are unlimited (
 ) and neither mingle nor speak with one another – and because of this single name are supposed to amount to a single kind ( ). Or again, someone might purport to divide number into two classes (0) by cutting 10,000 off from all the rest, splitting it off as a single class (9 ); and then upon making up a single name for all that’s left, maintain on the basis of this name that the remainder justify the introduction of another kind ( ) of number apart from the first one. The division would be better done, I should think – more dichotomously and accordingly to Forms (& 0) – if one were to cut number into even and odd, and humans (.  !*
  ) on the other hand into male and female, and were to split off Lydians, or Phrygians, or any other group, setting them counter to the rest, only when unable to find a division each term of which is at once a kind ( ) and a part.

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Before trying to come to grips with the contents of this passage, we should pay attention to certain aspects of its terminology. The term   occurs five times, twice in the expression 1 !
 . . .   meaning the human race. In the other three occurrences it is translated ‘kind’ (without capital). The term 9  occurs three times, once translated ‘Form’ (as also at 262B1) and twice ‘class’ (as also at 263B5, 7, 8, 9).15 A class here is understood as a collection of items grouped together for some particular purpose. The dialectician’s intent, according to the Stranger, is to group things together according to Forms. The passage contains two compelling examples of division gone awry, accompanied by carefully chosen alternatives in which these mistakes are avoided. In both faulty divisions, the mistake is said to be like that committed by YS when he divided collective nurture into a part concerned with people and a part concerned with beasts. In YS’s case, the cut fails to go “through the middle,” and as a result fails to correspond to a split according to Forms or Ideas. This defect is a consequence of a faulty division. But what should be done to get the division right? With these examples provided by the Stranger, we may reasonably hope to gain a better understanding of the difference between correct and incorrect division, and of how the difference hangs upon cuts being made “through the middle.” What exactly goes wrong in the division between Greeks and barbarians, and how is this remedied in the cut between male and female? Again, what specifically is the error in slicing 10,000 off from other numbers, and how is this avoided in the dichotomy between odd and even? One obvious difference has to do with the relative size of the subgroups resulting from the alternative divisions. While there are far fewer Greeks than barbarians, there is a one-to-one correspondence between odd and even integers, and a roughly equal (although variable) split between males and females. Upon first consideration, this suggests that “cutting through the middle” might be a matter of dividing into equal subgroups.

15

Translators differ widely in rendering the terms 9 , (, and   in this section between 262B and 263B. Rowe is consistent in translating all three terms ‘class’. Waterfield uses ‘class’ for 9  and sometimes for  , with ‘category’ for ( and sometimes for  . While Jowett translates all three terms ‘class’ on occasion, he sometimes renders both 9  and   as ‘species’ as well. Benardete uses ‘species’ and ‘genus’ for 9  and   respectively, and translates ( ‘looks’. Skemp uses both ‘Form’ and ‘class’ for 9 , and renders ( and   as ‘Form’ and ‘class’ respectively. These differences reflect wide variation among these scholars in how the section is understood.

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A tentative answer to the questions raised at the beginning of this section, accordingly, is that the procedure in question amounts to dividing classes into equally numerous subclasses. What gets divided are classes of individuals. And dividing these “through the middle” is a matter of splitting them into equal parts. In some manner (as yet mysterious), cutting classes into equally numerous subclasses is supposed to increase the likelihood that the inquirer will “hit upon Ideas” (( 1 
 "5 : 262B7). Whereas this understanding of “cutting through the middle” is intelligible with classes that have denumerable membership (like the positive integers), however, many other groups divided by the Stranger with apparent success cannot plausibly be thought to have a countable number of members. How could the class of all artisans of Sophist 219A be split up into numerically equal subclasses, to say nothing of artisans dealing with “all that is done” at Statesman 281D8–9. Even in the Stranger’s own example of male and female, there is little likelihood that these two subclasses of human being would ever turn out to be numerically equal. There are other reasons why “cutting through the middle” cannot be a matter simply of dividing into numerical halves. One is that ways are available of dividing numbers into half that have no relevance to dialectical inquiry. For example, the two subclasses resulting from separating the positive integers by alternate pairs (1–2, 5–6, 9–10 . . . in one group, 3–4, 7–8 . . . in the other) would be equinumerous but of no apparent help in dividing numbers according to Forms. Another reason for rejecting this understanding of “cutting through the middle” is that it is explicitly tied by the Stranger to dichotomous division. As he says at 262E3–4, the division of number would be done “more dichotomously and according to Forms” ( C & 0 ) 5) by cutting number into odd and even; and similarly by cutting humans into male and female. While thinking of dichotomous division in the abstract, it at least makes sense to specify that the two subclasses resulting from such division should in some sense be equally extensive. As noted time and again at previous stages of this study, however, strictly dichotomous division is set aside in the second part of the Statesman. An example is the nondichotomous division of genuine leaders who govern jointly with the statesman into the three subclasses of rhetoricians, generals, and judges (Figure 6.1, Table 6.4). It makes no sense at all to require that these auxiliary leaders be equal in number in order for the division in question to be dialectically sound.

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When the Stranger advises YS that inquiry would be better served by cutting number into odd and even, or humans into male and female, this advice presumably is not nullified by the shift to nondichotomous division in the final sections of the dialogue. The superiority of splitting number into odd and even is not keyed to the fact that odd and even numbers are equally numerous. Let us look further into the nature of this superiority.

11.4 Comparisons by Contraries and According to Measure Questions of numerosity aside, there is a conceptual feature of the distinction between Greeks and barbarians that prevents it from corresponding to a distinction between Forms. Whatever else Forms amount to in the late dialogues, they are what they are just in and by themselves. But Greeks and barbarians are what they are only in contrast with each other. From the Greek perspective, the class of barbarians comprises people occupying territories outside the borders of Greece. A barbarian is someone other than Greek, and a Greek is someone living in a land bounded by nonGreek territory. Greeks and non-Greeks take on identity in contrast with each other, meaning that neither group answers to an independent Form. Dividing human beings between male and female, on the other hand, sets apart two classes that can be characterized without reference to each other. Understood broadly across animal species, females produce eggs for fertilization, and males produce semen by which eggs are fertilized. Although a characterization of the reproductive process would refer to the functions of both sexes, the two functions involved – production of eggs and production of semen – can be described independently of each other. Characterization of the female as egg producer, that is to say, requires no mention of the process by which the eggs are fertilized, nor does characterization of the male as semen producer require mention of eggs. The Stranger’s other example of a faulty division is that between 10,000 and all the other numbers. As in the previous case of Greeks and barbarians, the basic problem here seems to be that the resulting two subclasses cannot be characterized independently. One class is identified as containing 10,000 alone, exclusive of all other numbers, whereas the other contains all numbers other than 10,000. As a consequence, the distinction between the two is dialectically insignificant. The two classes can be defined only relative to each other, which precludes their corresponding to eternally fixed Forms.

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A more significant division of numbers, the Stranger points out, would be to separate them into odd and even. Odd numbers can be defined as those that cannot be halved without remainder, and even numbers as those divisible into two equal parts. Although of course there are demonstrable relationships between these two definitions, neither incorporates explicit reference to features intrinsic to the other. Because odd and even numbers can be defined independently, the cut between them constitutes a division that is dialectically significant. The cut between them is a division made according to Forms. Why is making cuts in this manner dialectically significant? Part of the answer is that the descriptive independence of the subclasses initially distinguished is conveyed through subsequent divisions. In a manner of speaking, descriptive independence is transitive relation. When the class first posited (e.g., humankind) is divided into two independently characterized subclasses, a consequence is that each subclass (e.g., male) can be further divided in terms not dependent for their meaning on the identity of the other subclass (e.g., female). If this independence is maintained throughout a given series of divisions, the final subclass will have been specified independently of other subclasses that have been eliminated (in the present case, set aside to the left) as the procedure continues. Descriptive independence of this sort opens up the possibility that the subclasses involved correspond to Forms – entities that are what they are in and by themselves. Although maintaining descriptive independence throughout a series of divisions does not by itself ensure that all divisions have been made according to Forms, it at least is a necessary condition. This is a partial answer to the question of why descriptive independence of cuts between subclasses is dialectically significant. Another part of the answer has to do with the productivity of independent characterizations. In the division of humanity into male and female, to continue this example, the characterization of females as egg producers can be further qualified with reference to whether the eggs are retained for fertilization within the female’s body. And the description of the male as producer of semen can be made more specific by mention of whether the semen is discharged with or without copulation (e.g., as with mammals and fish, respectively). In neither case would these further specifications be available without prior distinction between male and female. To be sure, humankind in general could be divided into people who retain eggs within their bodies and those who do not (including

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males, children, and women past bearing). But this would be a division into parts only, and one which seems sufficiently unnatural as to be of no interest for dialectical purposes. The characteristic of retaining eggs within the body for fertilization is one that applies naturally only to individuals that are egg productive, which is to say that it applies only to individuals that can be independently identified as female. One problem with the distinction between Greek and barbarian (nonGreek), on the other hand, is that neither category admits further distinctions that would not apply to humankind at large. Greeks can be divided into literate and illiterate, and barbarians can be divided into light- and dark-skinned peoples. But the same divisions can be made within the human race generally. A consequence is that the distinction between Greek and barbarian contributes nothing to the further specification of particular subgroups of humanity. Inasmuch as the express purpose of dialectical division is to arrive at fully specified subgroups of this sort, the distinction between Greek and barbarian is dialectically useless. By contrast, the distinction between males and females opens up avenues of further specification that might prove fruitful for one or another dialectical purpose. Given that the two sexes can be independently characterized, each admits further subdivision in ways that are not available within the opposite subgroup. A consequence is that each can be further divided in ways that do not apply to humankind at large. Its productivity in opening up new lines of meaningful division is the main reason why dividing humankind into male and female is dialectically significant. In the case of the other faulty division between 10,000 and all other numbers, similarly, the problem is that the resulting subclasses cannot be characterized independently. The class with the single member admits no further specification. And because the remaining class admits all subdivisions pertaining to the integers generally (odd and even, prime and multiple, etc.), it opens up no further lines of specification on its own. A consequence is that the distinction in question contributes nothing of dialectical interest. There are no subclassifications of dialectical significance that could not be achieved just as well without it. When number is divided into odd and even, however, the result is two classes that can be defined without reference to each other. As a consequence, both odd and even admit further divisions that would not apply in the same manner to number in general. Even numbers can

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be further divided dichotomously into square and oblong,16 and odd numbers into primes and multiples of primes. Whereas number generally could of course be divided into squares and all others, this would have the same effect as separating Greeks from the rest of humanity. The result would be division into parts alone. It is only when numbers have already been divided into even and odd that the distinction between squares and oblongs (or primes and their multiples) can be applied in a dialectically significant manner. Put otherwise, when a distinction between square and oblong is appended to the property of being even, which has been previously distinguished from that of being odd, the upshot is a sequence of divisions according to Forms; whereas if number is divided directly into square and not square, the two groups thus separated are parts but not kinds. Whatever else dialectic amounts to, its business is to generate characterizations of increasingly greater specificity until the thing to be defined has been completely isolated from kindred things. This means that the features factored into the division at each stage must be chosen with an eye toward further specification. Division according to Forms yields kinds that can be further specified. Unless a division hits upon Forms or Ideas in this fashion (Statesman 262B7), the result will be segregation into parts that contribute nothing to a dialectically sound definition.

16

At Theaetetus 148A, an oblong number is defined as one produced by multiplying two unequal numbers, comparable to an oblong rectangle. It may be noted that odd numbers also include squares (e.g., 9) and oblongs (e.g., 15), but not dichotomously because they include primes as well. At this point in the Statesman, there is no provision for other than dichotomous division.

12 The Metaphysics of Division

12.1 Review of Outstanding Questions It is time to take count of questions raised previously that remain unresolved. These questions spring ultimately from the Stranger’s disclosure at Statesman 285D that the purpose of his conversation with YS is to make its participants better dialecticians. In Chapter 10, we concluded that becoming a better dialectician is a matter of becoming increasingly capable of making accurate divisions, which in turn boils down to an ability to divide things according to Forms. Chapter 10 ended with the question of what accuracy in this respect amounts to. Chapter 11 began with an attempt to make headway on this question by considering passages in other dialogues where Plato’s characters talk to dividing things according to Forms. One such passage is Phaedrus 273E, in which Socrates likens the dialectician’s ability to divide things according to Forms to the ability of a butcher to cut carcasses along their natural joints. This gave rise to a further question of what exactly gets divided in the dialectical process. A possible answer is indicated at Sophist 267D, where the Stranger faults earlier speakers of Greek for a certain laziness with regard to “the division of kinds according to Forms.” But nothing is said in this context about the nature of kinds or about the sense in which they might be subject to dialectical division. Shifting attention to this further question in section 11.2, we undertook a survey of current views regarding what gets divided in the dialectical process. The most familiar of these views holds that dialectical division is a matter of splitting classes of individuals into constituent subclasses, which can be broken down into further subclasses in turn. These subclasses then 223

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are severed into yet further subclasses, until the task of division has been completed. This familiar account of dialectical division was then tested against remarks made by the Stranger in his tutorial on division at Statesman 262B–263B. According to the guidelines laid down there, any part separated off in the process of division should always engage a Form (262B1– 2). To tie this in with the familiar account, we need to understand how parts and classes (or subclasses) are interrelated. In continuing his instructions to YS, moreover, the Stranger advises that Forms or Ideas are more likely to be encountered when one makes cuts through the middle of things (262B6–7). This poses a pair of additional questions. Once we have reached an understanding of how classes are related to parts in the Stranger’s account, we need to pin down what it means for them to be cut through the middle. Having done this, we need to understand why cutting things through the middle increases the likelihood of encountering Forms or Ideas. In section 11.3, an attempt was made to understand cutting through the middle as a matter of cutting things in half, as apparently specified at Sophist 221B. The upshot in this case would be that classes are cut through the middle when they are split into equally numerous subclasses. But this attempt ended in failure inasmuch as (among other reasons) there are many apparently successful divisions in the Sophist and the Statesman that yield subclasses without denumerable membership. As matters stand, the question of what cutting through the middle amounts to has yet to be resolved. The second additional question just mentioned is how cutting things through the middle is supposed to make it more likely that one’s divisions will hit upon Forms. To be sure, this is the very question asked by YS at 262C2. By way of answer, the Stranger points out the mistakes of dividing humankind into Greeks and barbarians, along with those of dividing number into 10,000 and all the rest. These divisions would be done more dichotomously and according to Forms, he claims (262E3– 5), if number were cut into odd and even, and humanity into male and female. The sense in which the latter divisions are made according to Forms was discussed in the final section of Chapter 11. But no further insight was forthcoming there into why divisions of this sort might be enabled by cutting things through the middle. Yet another complication arises with the Stranger’s observation that divisions of number into odd and even, and of humanity into male and female, result in parts each of which is a kind ( : 262E7) as well.

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This brings us back to Sophist 267D and its suggestion that kinds should be divided according to Forms. In addition to the initial question of the relation between parts and classes, we need to determine how both are related to kinds in turn. Here is a list of unanswered questions to be faced in this final chapter. First, what is the relation, in the Stranger’s account, among kinds, classes, and parts, and what does it mean to divide kinds or classes according to Forms? Second, assuming that kinds or classes are the things that get cut, in what sense can such things get cut through the middle? Third, in what conceivable manner might cutting such things through the middle make it more likely that one’s divisions will hit upon Forms or Ideas? A fourth question is left over from Chapter 10: In what sense is dialectic more exact than other arts in its employment of number and measure? If we can arrive at satisfactory answers to the first three questions, an answer to the fourth should come as a matter of course. We address these questions in the order indicated.

12.2 Classes, Kinds, and Parts How do kinds relate to classes, and how to parts? Although the questions are distinct, they must be answered together. The joint answer provided by the end of this section is that kinds are classes of things all sharing the same Form, while parts are groups of individuals that may or may not share Forms in common. But let us build up to this answer gradually. At 262E the Stranger advises YS that division should produce parts that are also kinds, which is the result to be expected of dichotomous division according to Forms. YS responds to this advice with the following query. 263A2

263B

Entirely right. But what of this, Stranger – what must be done to see more clearly that kind ( ) and part (  ) are not the same but differ from each other? That is no mean question, Socrates – excellent fellow that you are. We have already wandered further than proper from the topic proposed, and you’re urging that we digress yet further. For the present, however, let us retrace our steps, which is only reasonable. We will chase down these other things like trackers sometime at our leisure. But here is one thing you must avoid at all costs – you must never suppose you have heard me make a sharp distinction to this effect.

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Metaphysics and Method in Plato’s Statesman To what effect? Class (49 ) and part being different from one another. Then what instead? That whenever there is a class (9 ) of something, necessarily it is part (  ) of the very thing it is said to be a class (9 ) of. But there is no necessity that a part (  ) be a class (9 ). This rather than the other, Socrates, is the assertion that should always be attributed to me.

One thing to note immediately about this passage is that YS asks about the difference between kind ( ) and part, but that the Stranger answers in terms of class (9 ) and part instead. This suggests a close relation between class and kind. Another thing to note is that the term 9  invites the translation ‘class’ throughout this passage, in contrast with ‘Form’ earlier at 262B1 and 262E3.1 Why the Stranger is concerned not to be known as someone who maintains that class and part are different (B ) remains unclear.2 The view he wants to be known as endorsing, on the other hand, seems relatively perspicuous – namely, that all classes are parts but not vice versa. Lydians and Phrygians comprise parts of humankind; but because these subgroups do not correspond to Forms, they do not constitute dialectically significant classes. When humankind is divided into male and female, of course, the resulting classes (or subclasses) are also parts, but at the same time parts identified by Forms to which they correspond. Some parts are classes of the relevant sort and others not. Whereas a class is a part just as a matter of course, there is no necessity that a part be a class of the relevant sort. What is a class (9 ) of the relevant sort? One requirement stated by the Stranger is that a class is a part of what it is said to be a class of. In other words, a class is a subset of some more general grouping, of which it counts as a part as well. For example, the class of even numbers is both subset and part of the broader class of numbers generally. This means that classes and parts must be made up of the same type of constituents – numbers in the case at hand. The main difference between them is that classes are 1

2

As already noted, Jowett, Skemp, Rowe, and Waterfield all render 9  here as ‘class’. Plato uses this term in different senses within the same context elsewhere as well, for example Phaedo 100B4 and 102B1. One possibility is that the term B at 263B5 is intended to be read in the special sense of Sophist 258A11, in which things said to be different are logically opposed (    : 258B1) to each other. If so, then the Stranger’s point here is that class and part are not logically exclusive.

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constituted according to Forms, which is not a requirement in the case of mere parts. Whereas all members of a given class will participate in a given Form, parts might be constituted in a haphazard manner. The next question concerns the relation between 0 in the sense of classes and   in the sense of kinds. As noted earlier, Young Socrates asks about the difference between kinds and parts, but the Stranger responds in terms of classes instead. Substituting classes for kinds in this way runs counter to the prevalent view that kinds in the Sophist and the Statesman are equivalent to 0 in the sense of Forms.3 If kinds are classes of the relevant sort, they cannot also be the Forms according to which such classes are constituted. Moreover, although there is substantial evidence in the Sophist to support the view that   are Forms in that context, evidence in the Statesman runs strongly in the other direction.4 At some point after writing the Sophist, Plato shifted his use of the term   to a range of senses typically conveyed by the English terms ‘race’, ‘type’, and especially ‘class’.5 Among many passages in the Statesman where   carries the sense of ‘class’ is 263E3–4, where the Stranger advises against dividing the class of living animal as a whole with regard to herd rearing, lest they repeat the mistake of separating a small part from a large. Another is 260E4– 8, where he is talking about dividing the class ( ) of “self-directing” persons into the class ( ) of kings and another class without a name. And we have already alluded to 262D1 and 262E5, where   is used in the sense of ‘race’.6 In each of these cases, there is explicit mention of   being divided, which is enough in itself to show that they are not equivalent to Forms. 3 4

5

6

See, for example, Cornford (1935), p. 276; Moravcsik (1973), p. 171; and Waterfield (trans.)(1995), p. 4, n.7. Two places in the Sophist where   and 9  appear to be used interchangeably are 253C–D, describing the skills of dialectic, and 254Dff., dealing with the “very important Kinds” (Z . . .  . : 254D4). Of the approximately forty occurrences of   in the Statesman, on the other hand, the only instance I can find that might be interchangeable with 9  is that of 3   at 285B8 referring to the two types of measurement being discussed in that section. This transition may have been anticipated by two passages toward the end of the Sophist in which   cannot refer to Forms. One is 264D10–E1, where the Stranger proposes taking the kind they have posited (that of image making) and cutting it in two. The other is 267D5–6, cited earlier, which mentions “dividing kinds according to Forms.” Both refer to the division of kinds, whereas Forms are not things that can be divided. Other passages with   in the sense of ‘race’ are 266B1 and 270D1. The sense of ‘type’ is suggested at 285B8. And there are dozens of other passages where it carries the sense of ‘class’.

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Without assuming gratuitously that Plato has settled on a fixed technical vocabulary in either dialogue, we may conclude that just as 9  typically is used in the sense of ‘Form’ in the Sophist, so in the Statesman it is used typically in the sense of ‘class’. The fact that 9  itself can be used in both senses should not be allowed to confuse us. Within the context of the passage we have been examining (263A–B), at any rate,   and 9  in the sense of ‘class’ appear to carry the same meaning. This explains why the Stranger could respond to Young Socrates’ question about the difference between part and kind by making a careful distinction between part and class. As far as the relationship of part and kind is concerned, the upshot is that all kinds are parts but not all parts kinds. A consequence is that kinds and parts share constituents of the same ontological sort. The kind of odd number is made up of a certain subset of numbers, the kind of male person is constituted by a certain a subset of human beings, and so forth. The key difference is that all members of a kind participate in the same Form – the Form by which the kind is identified – whereas parts might be constituted by happenstance. Thus all constituents of the kind of odd number participate in the Form Oddness, whereas a subset of numbers thrown together randomly will share in no common Form other than number itself. By way of summary, a class is a set of entities of a common sort (numbers, people, productive arts), each participating in the same specific Form. A part, on the other hand, is a group of entities considered without respect to any features they may happen to share in common. Thus it is that all classes are parts, whereas there is no necessity that a part be a class. In the present context, moreover, the terms 9  (in the sense of class) and   are used interchangeably. This being the case, the question of what the Stranger means at Sophist 267D in speaking of dividing kinds according to Forms converts into the question of what it means to divide classes in that regard. Let us look more carefully at what this procedure involves.

12.3 Kinds Divided According to Forms The task engaging most of the Stranger’s effort in the Statesman boils down to teaching YS, and other relevant participants in the discussion, the right way of dividing classes and kinds. To get the process underway initially, the Stranger first divides knowledge generally into two classes (9: 258E7), the practical and the theoretical. A short while later, he tentatively divides

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the “self-directive” kind ( : 260E5) of theoretical knowledge into the kingly kind ( : 260E6) and another kind left unnamed. Before long, we find him criticizing YS for making a division equivalent to dividing human kind ( : 262D1) into Greek and barbarian, recommending a division of that kind into male and female instead (262E). At 263E3–4 he cautions against making too broad a division of the kind ( ) living creature; and so it goes. To these may be added the two instances at the end of the Sophist where the Stranger also speaks explicitly about dividing kinds. At 264D10–E1 he proposes dividing the kind ( ) of image making into two. And at 267D5–6, to repeat once again, he remarks on the inability of their predecessors to divide kinds ( . ) according to Forms. Drawing from both dialogues, we could assemble a representative list of passages in which the Stranger speaks unequivocally of kinds being divided and of kinds resulting from such division. Although the Stranger’s divisions in the first part of the dialogue are not always dialectically sound, for reasons examined at length in earlier chapters, we can now be confident about the sort of thing that gets divided. What gets partitioned in dialectical division are kinds, in the sense of classes. When division proceeds according to Forms, what results from the division are kinds as well. What it means to divide kinds according to Forms is to partition them in a manner that yields additional kinds, which is to say classes all members of which participate in the same Form. Sound dialectical procedure requires that all divisions be made according to Forms. As long as this requirement is met at each stage of a given series of divisions, the procedure deals with kinds from start to finish. As recalled previously, a review was undertaken in section 11.2 of answers found in current literature to the question of what gets divided in the dialectical process. According to the most familiar among these, division splits up classes of individual things and results in subclasses containing a portion of the same individuals. The answer indicated at this point in the present inquiry, on the other hand, is that kinds are divided in the dialectical process and that kinds result from this process as well.7 Given the conception of kinds as classes all members of which 7

Some readers may be reminded of the view expressed in Michael Wedin (1987), pp. 205– 33, to the effect that natural kinds might result from division (pp. 213, 230) as well as themselves be divided (pp. 209, 230). A natural kind for Wedin is a class all members of which belong to that class necessarily (p. 225), which is to say participate in the same “essence form” (p. 221, fn. 18) and thus have the same essential nature (ibid.). This conception is avowedly Aristotelian. Despite their similarities, the view put forth in the

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participate in the same Form, there is considerable overlap between the present answer and the familiar answer of section 11.2. Both answers hold that dialectical division deals with classes of entities, producing subclasses drawn from the same set of entities. But there are important differences between these two answers as well. One is that membership of kinds in the Statesman is not restricted by our answer to particular individuals. While classes of individuals are not ruled out (consider the division of the human race into male and female at 262E), the classes figuring in the line of division leading to the final definition of statecraft are primarily kinds of practical art. In effect, these classes are kinds with kinds as members. The same may be said of the kinds involved in the definition of weaving. Although it is natural to speak individually of the various arts in question, these arts are not themselves individuals in the sense relevant to the more familiar answer. A more crucial difference has to do with the way members of kinds in the Statesman are related to each other. To spell out this difference, we need to recall the difficulty the familiar answer had in dealing with the Stranger’s advice that dialectical division should make cuts through the middle. We have already seen (section 11.3) that cutting through the middle cannot mean simply dividing things into equally numerous subclasses. The purpose of the following two sections is to provide a more workable interpretation of this guideline.

12.4 Cutting through the Middle Revisited There are other references to “the middle” in both the Sophist and the Statesman that offer help in understanding the Stranger’s advice. One comes with his remark at Statesman 303A2–3 that “few is the middle between one and a multitude” (D # )
! " # I  ). In the context, the point of this remark is to make explicit two senses in which rule by a few is intermediate between single rule and democracy. In a law-abiding polity, rule by a few (aristocracy) is better than democracy present context differs from Wedin’s in several respects. One is that the present conception of kind does not include the notion of necessity. Socrates might fall within the kind of snubnosedness (see ibid.) as well as that of animality. Another difference is that collection and division are coordinate operations for Wedin (pp. 210, 215), whereas according to the analysis above collection is absent from the methodology of the Statesman (Chapter 4). Yet another difference is that Wedin sees division as proceeding “from higher to lower level kinds” (p. 214), which appears to be a version of the genus-species version of division criticized in section 7.3.

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but worse than kingship, whereas under lawless conditions it falls (as oligarchy) between tyranny and democracy. So rule by a few is middling (  : 303A3) in both respects – in number of governors and in excellence of government. One thing of immediate interest about this remark is that “a few” clearly does not fall at a mathematical midpoint between one and a multitude. Not only is a multitude without definite number, but moreover “a few” in its usual sense is not far removed from just one or two. Nor can it be a matter merely of “a few” falling some place or another between the two extremes. A group of many (
3 as opposed to I ) also falls between one and a multitude but would not be thought to stand as middle between them. The reason that “a few” counts as middle in the Stranger’s remark must have to do rather with its political context. From Plato’s perspective, rule by thirty or so individuals was qualitatively different from single rule and rule of the multitude,8 whereas rule by “the many” would be hard to distinguish from complete democracy. With respect to size of ruling group, that is to say, just “a few” is the most significant reference point in the broad middle ground between one and a multitude. Other passages employing the term   in a nonmathematical sense occur in the Sophist. In describing the conflict between the materialists and the friends of the Forms at 246B–C, the Stranger likens it to a neverending battle going on in the middle ( &4 7: 246C2) between the two parties. This clearly is a middle without mathematical features. It rather is a middle ground between factions with contrary interests. Another reference to “middleness” comes at Sophist 244E, where the Stranger is talking about Parmenides’ comparison of the wholeness of being with a well-rounded sphere. His comment here is that if being is like a sphere, it would have extremities and a middle (# . . .  : 244E6) as well. This mention of middle and extremities brings to mind Philebus 31A, where Socrates characterizes the class of the Unlimited as lacking beginning, middle ( : 31A9), and end. In this particular context, beginning, middle, and end are representative of determining factors that bring Limit to the Unlimited. As observed in section 9.5, other references to beginning, middle, and end can be found in the Parmenides (137D5–6, 145A6, and 165A6–7). In none of these passages is the middle a location found by counting. 8

Plato’s perspective in this regard undoubtedly was conditioned by the notoriety of the Thirty, a group of oligarchs mentioned at Apology 32C, Parmenides 127D, and Seventh Letter 324C.

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More importantly for present purposes, the Stranger’s comment about a sphere having extremities and a middle should also remind us of the distinction between the two kinds of measurement as formulated at Statesman 284E3–8. In this particular formulation of the distinction, the Stranger first cites the art of measuring contraries (like fast and slow, deep and shallow, long and short) with respect to each other. He then goes on to describe the second kind as measurement “according to the mean, to the fitting, the timely, and the requisite – all that has been withdrawn from the extremes to the middle (#  )” (284E6–8). In our previous discussion of this formulation (section 9.5), we postponed consideration of the final phrase referring to the extremes and the middle. It is now time to deal with this phrase by posing some obvious questions. What are the things that have been withdrawn from the extremes to the middle? What are the extremes from which they have been withdrawn? And what is the middle in which they come to be located? As we shall see presently (section 12.7), there are answers available to these questions that will also throw light on the Stranger’s advice at Statesman 262B6–7 that one is more likely to encounter Ideas by making cuts through the middle.

12.5 Cutting through the Middle and the Second Kind of Measurement In the Greek text, the phrase translated “all that has been withdrawn from the extremes to the middle” is affixed by conjunction ()) to the series of terms designating the mean, the fitting, the timely, and the requisite. This suggests that those four specific measures themselves are things that have been withdrawn in this manner. The longer phrase in question is an indefinite reference to things that have been withdrawn from the extremes to the middle, including the four measures named as specific instances. Other measures of this sort are mentioned in the Philebus. Returning once again to Philebus 26A–B, we find Socrates talking about the generation of the seasons (a: 26B1). As he explains it, the seasons come into existence by the introduction of Limit to the contraries of extreme cold and stifling heat (5 . )
 : 26A6). This has the result of removing all that is excessive and unlimited ( ) 1
 : 26A7), and in its place establishing conditions of moderation and balance (# . . . A  ) . . . 3  : 26A7–8). Although no specific measures are mentioned in the text, the forms of Limit involved in the

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creation of the seasons presumably would fall under the classification of the timely at Statesman 284E7 (the term  sometimes carries the sense of seasonable). Whatever measures are involved, they have the effect of replacing the extremes of cold and heat with the middle ground of seasonable weather. Another case mentioned in the same passage is that of the goddess (probably Aphrodite of 12C3) who brought moderation to humankind’s lust for pleasure. Perceiving the excess and general viciousness (3
 . . .
 : 26B7) of our pleasureful indulgences, the goddess imposed Limit in the form of law and order (  )   : 26B9– 10). The creative act with which she is credited here is a removal of pleasurable experience from extremes of licentiousness to the middle ground of proper order. (The opposite extreme, presumably, is the complete shunning of pleasure.) Whatever specific forms of Limit are involved, they presumably would fall under the category of #  (the requisite) at Statesman 284E7, insofar as law prescribes what ought to be done. In both cases we have forms of Limit applied to excesses of the Unlimited; and in both, the Mixture of these establishes norms of moderation in the middle ground between extremes. In both cases, moreover, the norms in question are products of divine Causation. Creation of seasonable weather is an act of the “marvelously wise intelligence” ( % . . .   . . . !"  : 28D8) that brings order to the universe at large. And the institution of law and order is attributed to the goddess invoked at the beginning of Socrates’ examination of pleasure. Both cases illustrate the creation of measure in the middle ground between opposing extremes. Let us return to the expression “all that has been withdrawn from the extremes to the middle” at Statesman 284E7–8. As noted earlier, this expression is appended by way of generalization to a list of four specific measures pertaining to the second kind of measurement – the mean, the fitting, the timely, and the requisite. In light of the preceding discussion of illustrative cases from the Philebus, we should now be prepared to identify the several factors involved in this expression. The things said to be withdrawn from the extremes to the middle are measures involved in the second kind of measurement, of which four specific types are mentioned explicitly. The extremes from which these measures have been withdrawn, in turn, belong to the various ranges of contraries that can be contrasted with each other by the first kind of measurement. Five such ranges are mentioned specifically at 284E4–5. Along the dimension of length ( ), for example, there is the immoderately

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long and the excessively short. Such extremes can always be compared with each other, albeit in a manner that is lacking in skill. In any artful treatment of length, however, there will be specific measures that are essential for the task at hand. There are appropriate lengths for speeches in courts of law, appropriate durations for exercises in athletic training, and appropriate intervals between soldiers in an infantry phalanx. The present conversation between the Stranger and YS is directed toward finding an appropriate length for dialectical discussion. Whatever the endeavor, its artful pursuit requires taking appropriate measure of this sort (measures on which the art is dependent; section 9.6) into account. Generally speaking, measures of this sort mark off a middle ground between their relevant extremes. In the language of 284E7–8, this is the middle to which they will have been withdrawn as part of the process of bringing Limit to the extremes concerned. The middle in question is the locus of moderation. Any artful endeavor must be pursued within the middle ground established by its appropriate measures; and any departure would be a return to either excess or deficiency. In like fashion, there are extremes to be encountered in the dimension of speed. Although such extremes can always be compared with each other in terms of greater or lesser, they also can be gauged by some appropriate measure. Whatever measure pertains in a given situation, it will establish a reference point of moderation between relevant extremes. Between extremes of recklessness and timerity, for example, there is a moderate speed to be maintained by a skilled chariot driver. And other norms govern the speed of a runner in rough terrain. Speeds that depart from the relevant reference point will be either excessive or deficient, and are to be avoided in endeavors requiring skill for their successful accomplishment. Considered without reference to moderating factors, any range of contraries exhibits Excess and Deficiency (Chapter 7). In the language of the Philebus, any such range would be said to belong to the Unlimited. Specific instances are indicated at Statesman 284E4–5 as falling within the dimensions of number, length, depth, breadth, and speed. Other instances mentioned in the Philebus are excessive heat and cold, extremes of licentiousness and (by implication) pleasure avoidance, and continua of sound that underlie the arts of music and of articulate speech. Whatever the dimension of contrariety, there are always extremes that can be compared with each other in terms of the first kind of measurement. In the case of artful endeavors dealing with such contraries, however, there is always a middle ground to be maintained by the application

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of appropriate measures. Four specific measures of this sort are listed at 284E6–7 – the mean, the fitting, the timely, and the requisite. Other instances in the Philebus are the phonetic elements incorporated in articulate speech, the intervals of pitched sound that complete the art of music, and the measures that establish the art of gymnastics, along with whatever measures are involved in seasonable weather and in lawful regulation of pleasurable experience. These are all instances of fixed reference points that have been withdrawn from the extremes of Excess and Deficiency and brought to a middle ground of moderation. Fixed reference points of this sort stand at the heart of the second kind of measurement.

12.6 Cutting Kinds through the Middle At Statesman 262B, the Stranger advises YS that cuts made through the middle of things are more likely to encounter Forms or Ideas. A parallel recommendation comes at 262E, where he points out that cutting number into odd and even, and humans into male and female, would be more dichotomous and according to Forms (& 0: 262E3) than other divisions mentioned previously. These remarks of the Stranger require explication. Our approach thus far has been to break the problems they pose down into specific questions. It is time now to see how the answers fit together. Section 12.2 was concerned with the sort of entity that gets split up in dialectical division. The conclusion reached there is that division is applied to groups of things that all participate in the same Idea. In the context of the Statesman (but not always in the Sophist), such groups are termed ‘classes’ and ‘kinds’ indifferently. In section 12.3 we addressed the question of what it means to divide kinds according to Forms. The answer forthcoming was that division of kinds according to Forms is division that results in subclasses that are kinds in turn. This result is tantamount to each subclass being such that all its members share a common property. Applying these answers to the Stranger’s remarks noted earlier gave rise to a pair of further questions. First, in what sense might kinds be divided through the middle? And second, in what manner might dividing kinds through the middle make it more likely that one will hit upon Forms or Ideas? The first question set the task of sections 12.4 and 12.5, a task to be continued in the present section. The second question is left for the sections following. Having determined earlier (section 11.3) that cutting a class through the middle cannot amount merely to dividing it into equinumerous

236

Metaphysics and Method in Plato’s Statesman

subclasses, we turned in section 12.4 to look at several passages in the Sophist and the Statesman that refer to middle in a sense having nothing to do with counting. Most instructive of these is Statesman 284E3–8, which characterizes the fixed measures engaged in the second kind of measurement as existing in the middle between opposing extremes. This second is the kind of measurement on which all arts depend, including statesmanship, weaving, and dialectic itself (section 7.1). Inasmuch as the remarks we are trying to explicate at Statesman 262B are part of a tutorial on dialectical division, it seems reasonable to think that the middle through which the would-be dialectician is advised to cut is closely tied up with the middle in which the fixed reference points of the second kind of measurement are said to exist. But an apparent problem emerges with this way of thinking. The middle ground in which a given reference point is located falls between the extremes of an array of contrary features. Typical examples are the contraries of hot and cold, and the high and low pitches of musical sound. In our ordinary way of thinking about classes, however, extremes of this sort appear wholly extraneous. As characterized previously, a kind is a class of entities that share some distinctive feature in common. This characterization says nothing about the presence of opposing extremes. This acknowledged, we should carefully note at the same time that opposition of some such sort is not ruled out by this conception of kinds and classes. There is no logical problem in conceiving of a class of entities with a given feature in common, all of which possess other features in varying degrees. For example, all living animals possess the feature of animality, even though some are very large and others very small. This logical point can be translated into an extended characterization of kinds as classes. As before, a kind is a set of entities all members of which participate in the same Form. With respect to the properties answering to that Form, the membership of the kind is fully determinate. All even numbers are evenly divisible by two, inasmuch as all participate in the Form of Evenness. At the same time, however, there might be other properties with respect to which membership of the kind remains indeterminate. Within the class of even numbers, some are much larger than others and some much smaller. In the language of the Philebus, the class of even numbers is limited with respect to the property of evenness but unlimited with respect to relative size. To put it succinctly, a kind is a class all members of which participate in the Form that determines the class’s identity, but whose membership remains indeterminate with respect to other properties. Membership

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of the kind might exhibit these other properties in varying degrees, constituting an array describable in terms of More and Less (from the Philebus). Within such an array there will be opposing extremes and a middle ground falling some place in between. When the membership of a kind constitutes an array of this sort with respect to a feature other than the kind’s defining property, it makes sense to speak of making cuts through the middle of the kind in question. Such cuts would fall within the middle between extremes of that other feature. At Statesman 262B, the Stranger instructs YS to make cuts through the middle as part of correct dialectical procedure. Such cuts would be properly made if the kind divided is split into subclasses in which features indeterminate in the original kind are rendered determinate. This is what it means to divide kinds according to Forms. The Forms involved are those that provide identifying characteristics of the resulting subclasses. When division goes properly, the result is the distribution of the membership of the initial kind into subclasses that are kinds in turn. If called for by the dialectical task at hand, these resulting kinds themselves can be further divided. Dialectical procedure begins with the positing9 of kinds that are determinate with respect to certain pertinent features but indeterminate in other features relevant to the project at hand. The role of division is to make these other features determinate in progressive stages. At each stage, one or another segment of the initial kind is isolated in subclasses constituted according to relevant Forms, yielding other kinds to be divided at subsequent stages. This process continues until all pertinent features have been segregated into relevant kinds. When all features essential to the subject of inquiry have been isolated in this manner, the dialectical task has been accomplished. The essential nature of the subject has been made explicit. When knowledge in general (
  
 : 258C6) is first posited (! : 258B4) at the beginning of the Statesman, for example, that totality was determinate in being limited to instances of knowledge, but indeterminate in many other respects pertinent to the nature of statesmanship. One dimension of indeterminacy concerned the many uses to which various types of knowledge might be put. This indeterminacy was 9

The language of positing is used frequently throughout the middle and late period in describing the beginning phase of inquiry; for instances, see Phaedo 100A3, Republic 507B6 and 596A7, Sophist 235A8, Statesman 258B4, and Philebus 15A5, 16D2, and 17C4. As pointed out earlier in this study, initial kinds are posited by collection in the Sophist and by use of paradigms in the Statesman.

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Metaphysics and Method in Plato’s Statesman

partially resolved by dividing knowledge into two classes, according to the Forms Practical and Theoretical. In the class of theoretical knowledge, indeterminacy remained as to whether such knowledge is used in making critical judgments or in issuing instructions. This indeterminacy was removed in turn by dividing theoretical knowledge into one kind that is directive and another that is critical. The process continuea in this fashion (not always expertly) until the completion of the initial definition. A dimension of indeterminacy is removed at each stage of this process by making cuts according to Forms in previously isolated kinds. Skillful dialectic is able to hit upon Forms that provide the measures required for the job, in accord with the provisions of the second type of measurement. These measures in any case will be those “fitting, timely, and requisite” to the dialectical task at hand. Such measures are described at 284E7– 8 as “withdrawn from the extremes to the middle” of the continua of properties pertaining to the kinds being divided. It is in this sense that dialectic makes “cuts through the middle.” Although making cuts in this manner does not guarantee encountering Forms, this is the way nonetheless in which the dialectician is “more likely to hit upon Ideas” (Statesman 262B7). How so?

12.7 Increasing the Likelihood of Encountering Forms The things said to have been withdrawn from the extremes to the middle at Statesman 284E7–8 are the fixed reference points integral to the second kind of measurement. This kind of measurement is essential to the art of dialectic. At 262B, fledgling dialecticians are encouraged to make their cuts through the middle, because this way they are most likely to hit upon Forms. It has been argued that the middle of 284E7–8 is also the middle through which dialectic should make its cuts. Why should cuts made in this manner increase one’s likelihood of encountering Forms? Let us return once again to the story of Theuth. Starting with the Unlimited of vocal sound, Theuth separated ( : 18C3), the vowels, the semivowels, and the mutes, and then divided each down to the number (! # : 18C5) of the individual phonemes. This provided a system of measured sound which children can refer to in learning letters and which dialecticians can classify in studying languages. Theuth’s contribution itself is not dialectical in character. The term  here is gramatically causal. Theuth established the vowels and other phonemes by imposing appropriate forms of Limit upon the Unlimited.

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Theuth brought the art of letters into being by establishing fixed reference points within the Unlimited range of vocal sound – reference points which impart phonetic identity to the sounds employed in ordinary speech. The forms of Limit involved in this creative act are referred to by such terms as ‘vowel’, ‘consonant’, and ‘mute’. Wherever human speech is effectively employed, one can be sure that phonetic elements of this sort are somehow involved. In the art of music established by the ancient Pythagoreans, similarly, the equivalent reference points are notes marking off fixed intervals within the Unlimited range of high and low pitch. Whenever music is pursued in an artful manner, limiting factors of this sort are sure to be found. Likewise, numerical measures like those called “rhythms and meters” at 17D6 will always be involved in orderly physical exercises like dance or gymnastics. And so it goes for other arts dependent on the second kind of measurement. The generic description applied to fixed reference points of this sort in the Philebus refers to them as numbers and measures (25B1, E2). And the generic role of these numbers and measures is to mark off an intermediate range of structure and order within a broader range of Unlimited extremes. In any given case, the existence of this intermediate range depends on the presence of fixed measures that set it apart within this broader range. Whenever a midrange of this sort between extremes is encountered, one can be sure that the enabling reference points are there to be found as well. The question posed at the beginning of this section comes into focus with the observation that Forms count among the fixed standards referred to as numbers and measures in the Philebus. Expanding on Aristotle’s cryptic claim in Plato’s behalf that Forms are numbers, section 10.3 argued that the sense of number in question is not that of arithmetic but rather that of metrics conceived more generally. Forms are numbers in the sense of measures. Just as motion is said to be numbered by time in the Physics, so human actions can be numbered by Absolute Justice, and works of art can be numbered by Absolute Beauty. What this means is nothing more nor less than that such Forms provide fixed standards by which these other things are measured. Without such standards, human affairs would be awash in Excess and Deficiency. Whatever their domain of relevance, Platonic Forms mark off a middle ground between extremes of the Unlimited. The middle ground in question is not located by numerical calculation. Nor is it a ground structured by a predetermined number of measures.

240

Metaphysics and Method in Plato’s Statesman

For purposes of dichotomous division that prevails at the beginning of the Statesman, to be sure, the middle ground must contain Forms suitably related for pairwise distinction. Thus the divisions between odd and even, and male and female, in the Stranger’s tutorial at 262B–263B. With regard to the nondichotomous division that dominates the latter part of the dialogue, however, there is no reason why the Forms involved should be associated in a pairwise fashion. There is ample support for this claim in the illustrations from the Philebus, with the many phonemes involved in the art of letters and the many notes and intervals implicated in the art of music. In any case, the measures in question establish a structured middle ground between their respective extremes. Measures of this sort are integral to the second kind of measurement. This is the kind of measurement on which all arts are said to depend (284D6–8). Such measures reside in the middle between various extremes (284E7–8). Every art thus relies on the presence of an appropriate middle ground between relevant extremes. Whatever the middle ground supporting a given art, we may be sure that the measures employed by that art are also present. The question at the beginning of this section has now been answered. One is most likely to hit upon Forms by making cuts through the middle for the simple reason that the middle itself is established by the relevant Forms. The middle ground goes hand in hand with its constituting Forms. One is likely to encounter Forms in cutting through the middle for the same reason that one is likely to encounter a fresh spring within the confines of a desert oasis. The reason is simply that the latter owes its existence to the presence of the former.

12.8 The Accurate Use in Dialectic of Numbers and Measures The final question to be answered is that left over from Chapter 10. In what sense are accomplished dialecticians exact in their employment of measure and number? As the previous section prepares us to recognize, the measures and numbers employed in dialectic are the Forms themselves. An accomplished dialectician is one skilled in making divisions accordingly, which means according to Forms. What division according to Forms amounts to has already been examined.

Appendix Equivalents for the Great and the Small in Aristotle and His Commentators∗

Aristotle: Physics, Metaphysics (the) Great and (the) Small – (#)  ) (#) () 

187a16–17† 192a11–12 203a16† 209b33–35† 987b26† 988a13–14† 988a26† 992b1–7 1083b24 1083b32 1085a9 1087b7–10 1088a15–16 1089a35–36 1090b36–37 1091a10 1091a24 1091b32

Alexander: On Aristotle’s Metaphysics 54.12 54.7–11† 56.13–18 56.32† 60.4–5† 86.12 117.26–27 122.10† 122.19–23 203.29–32† 228.13–14† 796.12–17 796.36–38† 797.3–6† 797.14–15 800.29–30 801.8–12 808.1–2† 809.15–16 809.32–33† 820.2†

Themistius: Paraphrase of Aristotle’s Physics 13.13–15† 80.25–26† 93.31

Philoponus: On Aristotle’s Physics 91.28–29† 92.27–30† 123.15† 388.10† 389.17–18† 395.1–7† 473.5–9† 480.12–13† 541.12†

Simplicius: On Aristotle’s Physics 150.12–15† 151.7† 151.12–15† 189.9–11† 204.6–8 204.14† 248.1† 248.5–8 431.8† 453.25–36† 454.6–13 454.32–36† 455.5† 455.9–11† 455.15–16† 458.11–15† 493.17–18† 499.4–6† 503.13–17†

(continued)

241

Appendix

242

Appendix (continued) Aristotle: Physics, Metaphysics

Alexander: On Aristotle’s Metaphysics

The Indefinite Dyad –    "

1081a14–15 1081a22 1081b21 1081b26 1081b32 1082a13 1082a30 1083b36 1085b7† 1088a15–16 1088b28–29 1089a35–36 1091a5

56.18–20† 58.2–3† 70.7† 85.17–24 86.1 117.26–27 122.10† 123.3 203.27–32† 228.13–14† 705.24–25 780.19† 796.36–38† 797.14–15 800.29–30 808.1–2† 809.32–33† 817.35–36†

The Unlimited – # 1


203a4–9† 203a15† 206b27–28† 987b26†

54.1–2 54.7–11† 56.20† 58.2–3† 60.4–5†

The Unequal – # 1 

1087b17–10 1088b28–29 1091a24 1091b32

56.13–17 228.13–14† 615.17 750.24–25† 796.12–17 797.3–6† 800.29–30 801.8–12 809.15–16 809.32–33†

(the) More and (the) Less – (#) C ) (#) =

Themistius: Paraphrase of Aristotle’s Physics

80.25–26† 80.28† 93.31

Philoponus: On Aristotle’s Physics

Simplicius: On Aristotle’s Physics

92.27–30†

150.12–15† 151.7† 151.12–15† 181.28 453.25–36 454.6–13 454.32–36† 455.5† 458.11–15† 499.4–6† 503.13–17†

388.10† 389.17–18† 395.1–7† 473.5–9† 480.12–13†

248.5–8 453.25–36† 455.9–11† 455.15–16† 458.11–15† 493.17–18† 499.4–6† 503.13–17† 247.35† 150.12–15† 248.10–13† 431.11†

204.6–8 248.1† 248.5–8 248.10–13† 453.25–36† 454.25–36† 455.9–11† 503.26–27†

Appendix

243

Appendix (continued) Aristotle: Physics, Metaphysics

∗ †

Themistius: Paraphrase of Aristotle’s Physics

Philoponus: On Aristotle’s Physics

54.7–11†

The Nature of the Unlimited –  
 " 3 Excess and Defect – G
 5 ) AX

Alexander: On Aristotle’s Metaphysics

187a16–17† 189b8–11 992b–17

54.7–11† 56.13–18 122.19–23 123.2–3

13.13–15† 22.17†

Compilation incomplete; subject to emendation. = Plato mentioned by name.

91.28–29†

Simplicius: On Aristotle’s Physics 453.25–36† 454.6–13 455.9–11† 150.12–15† 151.12–14 189.9–11† 204.6–8 204.12–14† 454.6–13 454.32–36 503.26–27†

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Index Locorum (excludes citations in the Appendix; translations of extended passages marked ‘tr’)

alexander Commentary on Aristotle’s Metaphysics 54.8–11 150n.10 122.19–24 150 768.22 161 820.2 161 827.8–17 202n.18 aristophanes Lysistrata ll.574 ff. aristotle Categories 1b16–24 De Caelo 268a10–13 De Anima 404b20–21 History of Animals 486b6–9 486b16–17 Metaphysics 986a1–2 986a23 987b14–18 987b20–22 987b22 987b22–25 987b25 987b25–29 987b26 987b27–28

96

61n.14 183n.14 181 149 149 202 151 198, 201 161, 197 198n.11 198, 202 152 150 151 201n.16

987b33 988a11–14 988a14–16 991b9–10 991b9–11 991b13–20 992a11–13 992a24 992b1–7 1073a17–20 1080a28 1080b4–5 1083b23–24 1083b31 1084a21–25 1085a10–12 1086a10–11 1087b4 1087b11 1088a15 1090b35–36 1091a12–13 1091a24 1091a24–25 1091b26 1091b26–30 1091b32 1092b10–14 1092b14–15 1092b16 Nicomachean Ethics 1106b22 1106b36–1107a8

249

151 197 198 198 202 202 181 150 149 198 201 201 161 161 202 181 198 153 151 151 201 200n.15 151 161 198 202 151 202 202 202 183 142n.3

Index Locorum

250 aristotle (cont.) 1107a33 1122a28–31 Physics 187a14–17 187a15–17 187a16 187a16–17 187a17 189b8 189b8–11 189b10 192a15 202b36 203a4–5 203a8–10 203a10–16 203a15–16 207a18 219b–222a 219b1–2 220a24–25 Politics 1252a11–12 Posterior Analytics 100a10–100b5

142n.3 179 149, 173 173 150 150 149 153 149, 173 149 198 152, 153 154 154 151 154 153 203n.19 203n.19 203n.19 18n.3 39

philoponus Commentary on Aristotle’s Physics 91.16–17 150n.9 plato Apology 23B1 32C Cratylus 424C 424C6 Critias 109B Definitions (spurious) 415A Euthydemus 291C ff. Gorgias 464B–C 464B9 464C1 521D7 521D7–8

73 231n.8 206 206 19n.6 140n.2 18n.3 67 67 67 67 67

Ion 538D Laws 668D10 715E8–716A1 813D 881B6 886B7 933D7 Meno 80B6 81D1–4 85C 85C7 85C9 85C10–11 85D1 85D7 Parmenides 127D 130B–E 132A 132A–B 132A1 132A2 132A2–3 132A3 132A7 132A8 132A10 132A10–11 132B2–3 132D1–2 135E–136A 137D5–6 142B–157B 142D–144A 143A1 143A2 143B8 144A4 144A6 145A6 158B6 158C4 158C6–7 164C7 164D1 164D2 165A6–7

57n.5 200 183n.14 19n.6 11n.1 11n.1 90n.10 11n.1 88n.9 88 86 77, 86 87n.9 86 86 231n.8 213n.12 42 167, 168 42 42 42 42 168 168 168 168 168 73 112n.12 183n.14, 231 165 198 165 165, 198 165 165, 166 165, 183n.14 183n.14, 231 166 167 167 167 167 167 183n.14, 231

Index Locorum Phaedo 72E–76E 78E5 80B1–2 87B–C 99D1 99E–100A 100A3 100B4 100B5 101D–E 102B1 Phaedrus 237E3 238A2 238C2 238C3 243B5 244D2 244E2 245A1 245B1 248C–E 248D4–5 249B–C 249B7 249B7–C1 249C 249C2 249D 249D1 249D5 250A 250A1 250A6 250B5 253D1–3 257A4 258E–259D 262D1 265B 265D 265D–266C 265D3 265D3–4 265E 265E1 265E1–2 265E3–4

40 167 167 93n.1 118n.5 51n.13 237n.9 226n.1 51 51n.13 226n.1 53 53 53 53 53 53 53 54 54 54 18n.3 38 38 38, 86, 88 39, 41 37, 38, 86 54 53 40 88 38, 40 88 88 37 40 54n.1 73 53 40, 41 52 40, 52 40 223 38n.3, 41, 52, 125, 207, 209 41, 52, 125, 207 52

266A 266A2 266A5 266A6 266A7 266B 266B4 266B4–5 266B5 266B5–6 266B7–9 266C1 273E 273E1 273E1–2 273E2 277B–C 277B7 Philebus 11A 12C3 13C8 14C9 15A 15A5 15A5–6 15A7 15B6 16C–E 16C–17A 16C2 16C5–17A5 16C5–18D3 16C7–8 16D1–2 16D2 16D4 16E–17A 17A 17A4 17B–D 17B3 17B4 17B7 17B9 17C4 17C11–D4 17D1 17D2 17D3

251 54 52 41 53, 54 53 41 41, 86, 125 41 41 41 37 86, 207 223 38n.3, 207 207 207, 209 207 38n.3, 207 183 233 73 48 50 48, 49, 50, 237n.9 48 48 48, 49, 49n.12 192 48 192 162 156 164 50 49, 237n.9 125 158 158 192 155n.3 162 162 162 163 237n.9 203 160, 164 164 164

252 plato (cont.) 17D4–6 17D5 17D6 17E3 17E4 17E5 18A 18A–D 18A7 18A8 18A9 18B–D 18B1 18B2 18B6 18C1 18C2 18C3 18C4 18C5 18C6 18D1 18D2 23C 23C4–27C1 23D2 23E 23E4 23E5 23E6 24A7–8 24B1 24B7 24B8 24C–D 24C1–2 24C3–4 24C4 24C5 24C7 24C8 24C8–D1 24C9 24D1 24D4 24E–25A 24E4 24E5 24E7 24E7–8

Index Locorum

203 164 164, 239 162, 165 165 165 155 155n.3 189 152, 158, 189 189, 199 163 189 189 189 163, 189, 207 199, 200n.15, 207 163, 238 163 190, 199, 238 163, 190, 199 163 163, 190, 199 208 156 208 49 49 49 49 174 157 157 157 156n.3, 161 174 157 174 174 157, 159 178, 184 174 174 174 174 158 152, 157 157 158 49, 157

24E7–25A2 24E8 25A 25A–B 25A1 25A1–2 25A3 25A7–8 25A7–B1 25A7–B3 25A8 25A8–9 25A8–B1 25A9 25B1 25C8 25C8–11 25C9 25C9–10 25D 25D–E 25D5–6 25D6–7 25D8 25D11 25D11–E2 25E1–2 25E2 25E7–8 26A 26A–B 26A2 26A2–5 26A4 26A6 26A7 26A7–8 26B 26B1 26B1–2 26B7 26B9–10 26D8–9 26D9–10 27B1–2 28A 28A2 28D8 28E 30D

174 174 49 156n.3 157 49 49, 49n.12 161, 174 164, 175 158 195n.6 161 159, 203 166 199, 239 174 157 174 174 49 156n.3 49 49 49 161, 166, 195n.6 175 49, 159 199, 203, 239 159 155n.3 232 164, 174 159 164 232 232 232 185 175, 232 175, 185 233 233 159, 178 164, 176, 177, 177n.12 159 158 152, 158 233 200n.15 200n.15

Index Locorum 31A 31A9 31A9–10 31A9–11 41D8 52C7 55D–59D 55E 55E–56A 55E–59C 55E1–2 55E7 55E7–56A1 56A 56A4 56B6 56C–62A 56C4 56C8 56C9 56D5 56D9–E2 56D10 56D11–E1 56E2–4 56E7 57C 57C3 57C6 57C6–7 57D1 57D1–2 57D3 57D6 57E–58E 57E3 57E3–4 57E7 58A2–3 58C1 58C2–3 58E 58E3 59A1 59A7 59A11 59B5 59B8 59D1 66B5–6 66B9

231 231 156n.3 183n.14, 184 158 158 191, 203 193 181 146 193, 194 193 193n.2 192 181 193 198n.10 193 194 194, 195 194, 194n.3 201 194 194 201 195 192 194n.3 195 192 194n.3 195, 204 192 192, 195 146 196 192 194n.3 196, 204 193 196, 204 196n.7 193 197 196 196 196 196 197 192n.1 192

67B Protagoras 356A2–3 Republic 343B 364C4 454A 454A6 455C 506E4 507A–509D 507B2 507B6 507B6–7 507B7 510B 511B1–2 511C 522B4 522C 522D 523E3 524C3 524C4 524C7 524C11 525A4–5 533D4–6 533E5 540A8–9 540A9 596A6 596A7 Rival Lovers 138C Seventh Letter 324C 342C4–D2 Sophist 216A4 217B3 218C 218C1 218D–E 218D5 218D8 218D9 218E3 218E4 219A 219A–B

253 183 140n.2 19n.6 90n.10 206 206 96 85 83 42 42, 237n.9 42 42 210 192 210 191 193 181, 194n.4 169 169 169 169 169, 180 170 192 192 83n.5 73 42 42, 237n.9 18n.3 231n.8 192n.1 18 55 44, 45n.10 55, 58, 94, 129 81 55 75 15, 44, 56, 74, 84 75 56n.3 218 46

254 plato (cont.) 219A5 219A6 219B–C 219B1 219B11 219C7 219D 219E 220A8–9 220D–E 221B 221B–C 221B3 221C2 221C4 221C5 221D 221D–223B 223B 223C 223C–224D 223D 223D6 224C 224D–E 224D1 224E 224E2 225A–226A 225E 226A 226B–231B 226C1 226C8 226E–227A 227C2–3 228B8 228D4 229A8–9 229B 229B5 229B7 230B 230D8 230E3 231B 231B7–8 231B9 231D 231E4

Index Locorum

56 56 68 46, 56 46, 56, 56n.2 56 211 211 55 212 37, 224 56, 211 56n.4, 57, 215 56n.3 62 44, 56, 75 62 55 47 47 55 55 47 45n.10 55 62 63n.17 63 56 47, 63n.17 62 56 76 76 66 67 67 67 67 215 215 56n.4 45n.10 65 65 65 65 44 63n.17 65n.19

231E5 232A4 232B6 233D3 233D9–10 234–237 234A5 234A8–10 234B 234B–237A 234B2 234B3 234B3–4 234C 234C6 234E 235A8 235B 235B–C 235B8 235B8–9 235D1 235D8 236B1 236C 236C1 236C6 236C6–7 236C7 237A 237A–264B 244E 244E6 246B–C 246C2 250B 251A7 251D 253A12 253C 253C–D 253C7 253D1 253D2–3 253D3 253D5 253D5–6 253D5–7 253D7 253D8 253E2

65n.19 44 44 44, 76 44 68, 70 44 45 44, 69 69 44, 46, 69 44 44, 45 56 69 67 237n.9 69 45n.10 69 45, 76 69 77 69 69 69 69 69 69 69 68, 69 231 231 231 231 45n.10 77 45n.10 82 37, 43, 208 227n.4 93 43, 55, 82, 208 55 43 43 43 43n.9 43 43, 43n.9 38n.3, 43

Index Locorum 253E4–5 253E5 254D 254D4 258A11 258B1 258B4 258B6 258C4 258E 258E4 259A4–5 259D7 259E4–6 259E5–6 260B7 260C7 260D2 261A8 261B11 261C5 262B2 262B6 262C2 262C6 262C8 262D4 262D7 262E1 262E7 263A1 263E3–4 264C 264C1–2 264C4 264D5 264D10 264D10–E1 264D10–E2 264E 264E1 264E1–2 264E3 264E3–265A1 265A2 265A4 265B 265B6 265D6 265E5–8 265E11

84n.6 43 227n.4 208, 227n.4 226n.2 226n.2 120 35n.15 35n.15 103 35n.15 208n.4 35n.15 94 208n.4 208n.4 35n.15 35n.15 35n.15 35n.15 35n.15 35n.15 148 224 94 94 94 35n.15 35n.15 35n.15 35n.15 229 69, 210 208, 210 210, 214 35n.15 109 70, 227n.5 126 55 71, 109 70 70 58, 70 70 35n.15, 68 69 68 35n.15 210n.6 35n.15

266A2 266A10 266B 266D9 267A10 267B1 267D 267D2 267D5–6 267E 267E1 267E4–5 267E7 268A1 268A7 268B 268B3 268B10 268C6 268C8–D4 268D3 Statesman 257C1 258A 258B 258B–261E 258B–277A 258B3–5 258B4 258B6 258B9 258C4 258C6 258D5 258D9 258E 258E4 258E4–7 258E5 258E7 258E8–11 259B–C 259C1–4 259C10 259D1 259D7 260B4 260C–266A 260C7

255 35n.15 68 69 68 68 46 16, 208, 223, 225, 228 16 208, 227n.5, 229 16 16, 68, 208 16 16 16 68 213 68 17 94 70 46 131 15 26 16 100 117 11, 16, 120, 209, 237, 237n.9 17, 35n.15 17 35n.15 237 17 17 18, 103 35n.15 214 16, 102, 210 210, 228 17 102 11 12 12, 17 35n.15 16 35n.15 35n.15

256 plato (cont.) 260D2 260E4–8 260E5 260E6 261A8 261B11 261B13 261C 261C1 261C5 261C9 261D 261D–275D 261D3 261D5 261E 261E1–2 261E2 261E8 262A 262A2 262A8–262C2 (tr) 262B 262B–E 262B–263B 262B1 262B1–2 262B2 262B6 262B6–7 262B7 262C2 262C3–263A1 (tr) 262D 262D–263B 262D1 262D7 262E 262E1 262E3 262E3–4 262E3–5 262E5 262E6

Index Locorum

35n.15 227 16, 229 229 35n.15 35n.15 12 20 16 35n.15 67 21 22 21 21, 22 22, 23 21 21 12, 16 21 12 215 3, 38, 217n.15, 235, 236, 237, 238 28 22, 209, 217n.15, 224, 240 22, 217, 226 224 35n.15 12, 22, 56n.4, 126, 148 224, 232 22, 218, 222, 238 216, 224 216 59n.8 206n.2 227, 229 22, 35n.15 225, 229, 230, 235 35n.15 38n.3, 214, 226, 235 218 224 227 210n.6

262E7 263A–B 263A1 263A2–B10 (tr) 263B 263B5 263B7 263B8 263B9 263E–268D 263E3–4 264C 264D 264D5 264D10–E1 264E 264E1 264E1–2 264E3–265A1 265A 265A2 265A4 265B 265B–266B 265B11 265B–266E 265D6 265E8 265E11 266A2 266B 266B1 266B3 266E 266E1 266E6 266E7 267A8–267C3 267B 267D 267D2 267E 267E1 267E4–5 267E7 267E7–8 268A1 268B10 268C 268C2 268C6

35n.15, 224 228 35n.15 225–226 3 217, 226n.2 217 217 217 22 227, 229 69 23 35n.15 70, 229 23 71 70 70 22 70 23, 35n.15 69 23 23 23 35n.15 23 35n.15 35n.15 69 227n.6 23, 24n.7 23 160 23 23 24 26n.9 16 16 16, 22, 103 16 16 16 92, 114 16 17 24, 101 24, 92, 124 131

Index Locorum 268C8–D4 268C9 268D5–6 268D9 270D1 275A1 275A3 275A4 275B 275B4 275B5 275D8–E1 275E5–6 275E6 276A4–5 276B 276B7 276B7–C2 276D6 276E 276E7–8 276E8 276E10–14 277A 277A1–2 277A5–6 277B 277B4 277C1–2 277C2 277C3 277C4 277C4–6 277D 277D–278E 277D1 277D1–2 277D1–4 277D3 277D7 277D9–278C7 (tr) 277E 277E–278C 278A5 278B4 278C 278C5 278C6 278E 278E–279A

70 35n.15 25 25 227n.6 26 26 13 92, 101 27 97 21 22, 25, 92 13 26 101 26, 92 92 26, 27 18, 70, 71, 103, 121 26 27 26 13, 101 77 26 81 13, 26, 77, 97 127 127 26 27, 81n.4 81 5, 28, 85, 96 28 27, 77 98 92 77 85 78 27 29, 83, 162 90n.10 99 79 91 85 75, 81, 96n.4, 127 98

278E6 278E7 278E8 278E9 278E10 279A 279A–283A 279A2 279A3 279A7–8 279A7–B2 (tr) 279A8 279B 279B–283B 279B2 279C–280A 279C–283B 279C7–8 279C7–280A1 279C7–280A6 279C8 279D1 279E 280A3 280A3–4 280A3–5 280A7 280A8–E4 280B–E 280B–281B 280B–281D 280B3 280B6 280B7 280C–281B 280C–282B 280C–283A 280E 281A3 281A–D 281C9 281D 281D–283B 281D1–4 281D8–9 281D8–283A8 281D9 281D10 281D10–11 281D11 282A1–4

257 75, 98 99 75, 84 92 92 80, 92, 101, 113 13 92, 113 113 85 93 80, 98 38, 91, 98 28 94 100 100, 139 101 103 104 101, 213 114 16 104 104 102 101 105 105 100 101 35n.15 101 35n.15, 105 96 109 109, 109n.11 108 95 106 107 103 100 108 17, 113, 218 107 102 81 113 80, 102, 107 38

258 plato (cont.) 282D5 283A4–8 283A10–B2 283B 283B–289B 283B2–3 283B3–4 283B6–7 283C 283C–285C 283C3–4 283C3–D10 (tr) 283C3–285B8 283C11 283C11–D1 283C11–D2 283D 283D1–4 283D7–8 283D8–9 283D11–12 283D11–284B3 (tr) 283E3 283E4 283E8 283E8–9 284A 284A–B 284A1–2 284A5–B2 284A10–B2 284B1 284B2 284B3–284E1 (tr) 284B6–7 284B8 284B9 284C 284C2 284C7 284D 284D1–2 284D2 284D4 284D4–6 284D5 284D6

Index Locorum

95 110 110 31, 33n.12 122n.6 33n.12 139 205 179 2, 3, 14, 28, 30, 148, 182 143, 149, 173 139–140 140 174 140, 143, 149, 150, 178 140 177n.12 187 141, 169, 174, 194 159, 177, 178 174 141–142 180 180 181 143, 169, 173 189 176 174 143, 145 164 143, 175, 178, 180, 185, 189 173 144 32n.11 174 180 17 17, 145 32n.11 188 190, 191, 204 195 145, 188 193n.2 174 145n.4

284D6–8 284E 284E1 284E2–285C3 (tr) 284E3–8 284E4 284E4–5 284E5 284E6–7 284E6–8 284E7 284E7–8 284E11 285A4 285A4–5 285A7 285B2–6 285B7–8 285B8 285C 285C4 285C4–D7 (tr) 285C8–D3 285D 285D–286B 285D4 285D5–7 285D6 285D9–E4 285D9–286B2 (tr) 285D11–E1 285E4 286A–B 286A3 286A4 286A5–6 286A6 286A7 286B 286B4–E3 286B–287B 286B1–2 286B4–5 286B4–E3 (tr) 286B9 286C7

240 4, 125 146 146–147 187, 232, 236 180, 181, 186, 200 174, 180, 181, 182, 233, 234 186 147, 186, 187, 235 232 233 148, 187, 233, 234, 238, 240 204, 206 38n.3, 204 206 204 37 140, 149 227n.4, 227n.6 83 29 29 29 4, 28, 84, 95, 99, 110, 223 82 34 34 14, 30, 209 84n.7 82 84 82, 84 96n.4 83 84n.7 32, 34, 83 84, 84n.7 82, 83, 85 32n.11 33 28 81, 83 32 31 32n.11 174

Index Locorum 286D 286D–E 286D1–2 286D2 286D8–E4 286D9 286E 286E1 286E3 286E3–287B2 (tr) 286E5 287A 287A1–3 287A2 287A2–3 287A3 287B

287B–305E 287B2 287B6 287B6–7 287B7 287C 287C–289C 287C3 287C4 287C4–5 287C8 287D2 287D4 287D8 287E9 288A9 288B4 288B6 288C6 288D7–E4 288E5 289A2 289A3–4 289A9–B2 289B1–2 289B2–3 289B6 289C–290E 289C1 289D–E 289D1 289D3

205 110 186 32, 187 34 33, 205 30 34 33 33 33n.12 30 205 34 34 14, 34, 110, 209 14, 17, 70, 85, 102, 103, 110, 113, 120, 121, 124, 187 100 99 120, 130 113 80, 81 28, 38 115 124, 207 124 124 120 114, 120 103 210n.6 114 114 127 114 114 127 114 114 114 114 130 115 114 116 35n.15 18 17, 103, 121 127, 130

289E1–2 290B5–6 290C3 291A–303D 291A2–3 291A3 291A4 291C3 291C4 291C5–6 292A6 292B6 292C2 292C5 292C8 292D3 293A3–4 293C2 293D8 293D9 293E 293E1 293E4 296A2 296C6 296C9 296E2 296E3 297A4 297B1 297E4 297E5 298A–300B 300C2 301A9–B3 302B8 302C 302C8 302E–303B 302E1 302E7 303A2–3 303A3 303B2–3 303C 303C1 303C2 303C4–5 303C8–D2 303C9–D1 303D1

259 18, 115 120 127, 130 117, 122n.6 116, 127 115, 124 131 117 117 124 160 117 117 160 117 117 117 160 118 120 117, 119 160 119 118 118 118 118, 160 118 118 118, 120 118 118 118 118 123 119, 124 127 131 116, 123, 124 119 35n.15, 116 230 231 116n.3 117n.4 117 117 117 116 119 124

260 plato (cont.) 303E–305D 303E9 303E10 303E10–304A1 304C1 304D3 304D7 304E1 304E7–8 305A1 305A8 305B1 305B5 305C7 305C9 305D 305D1–2 305D2 305E 305E–311C 305E9 306A1 306A2 306E7 307B1 307B2 308E2 308E5–9 309B7 309C3

Index Locorum

120 119, 120 119 131 120 119 119 119 119 119 119 119 119 119 119 122 119 119 14, 28, 102, 131, 133, 134 6 131 95n.2, 132 95n.2 132 187 132 95n.2 187 95n.2 132

309C7 309E10 310E2 310E8 311B8 311C1 311C2 311C7 Theaetetus 148A 152A2–4 172D1 176E3 207D–E Thirteenth Letter 363A5–8 Timaeus 48E5–6

132 95n.2 187 133 133 28 133n.17 133n.17 222n.16 148n.5 43n.7 73 79n.2 35n.15 73

simplicius Commentary on Aristotle’s Physics 189.9–11 173 190.13 173 204.6–8 153 204.12–14 153 453.25–31 152 453.31–454.16 155n.1 454.17–19 152 themistius Paraphrase of Aristotle’s Physics 13.13–15 150n.8

Index of Names (19th century to present)

Anderson, Daniel E., 62n.16 Annas, Julia, 139n.1, 148n.5, 201n.17

Kucharski, P., 182n.13

Benardete, Seth, 97n.6, 125n.8, 139n.1, 145n.4, 148n.5, 176, 176n.4, 217n.15 Brandwood, Leonard, 35n.15

Lafrance, Yvon, 177, 177n.10, 177n.12, 182n.13 Lane, M. S., 4, 5, 19n.5, 19n.6, 96n.3, 125n.8, 131n.14

Campbell, Lewis, 106n.9, 109n.11 Cherniss, H. F., 1 Cleaver, Frank L., 62n.16 Cohen, S. Marc, 58n.7, 211n.9, 212n.10, 213n.13 Cooper, John, 11n.1, 24n.7 Cornford, F. M., 60n.12, 64n.18, 69n.21, 227n.3

Meinwald, Constance, 60n.12 Miller, Mitchell, 4, 6, 19n.4, 19n.6, 24n.7, 25n.8, 100n.8, 114n.1, 116n.2, 116n.3, 122n.6, 125n.7, 131n.14, 132n.15, 133n.17, 148n.5, 155n.3, 156n.3, 176–177, 177n.11, 177n.8 Moravcsik, J. M. E., 58n.7, 60n.10, 129n.10, 209n.5, 210n.8, 212, 213n.11, 227n.3

Diels, Herman, 155n.1 Di`es, Auguste, 145n.4, 176, 176n.2, 182n.13

Notomi, Noburu, 65n.19, 122n.6

El Murr, Dimitri, 96n.5, 106n.9

Rosen, Stanley, 24n.7, 25n.8, 125n.8, 131n.14, 176, 176n.7 Ross, W. D., 198n.11 Rowe, Christopher, 4, 11n.1, 24n.7, 97n.6, 145n.4, 176, 176n.5, 217n.15, 226n.1

Fowler, H. N., 97n.6 Gaiser, Konrad, 1, 11n.1 Gosling, J. C. B., 155, 155n.2 Griswold, Charles, 38n.3, 39n.4, 208n.3 Hayduck, Michael, 150n.10, 202n.18 Jowett, Benjamin, 97n.6, 145n.4, 176, 176n.1, 217n.15, 226n.1 Kato, Shinro, 86n.8 Kr¨amer, H. J., 1

Owen, G. E. L., 5, 30n.10, 84n.7

Santa Cruz, Maria Isabel, 177, 177n.9 Sayre, K. M., 34n.14, 36n.1, 39n.5, 48n.11, 51n.13, 61n.15, 68n.20, 153n.13, 157n.4, 162n.5, 162n.6, 162n.7, 165n.8, 166n.9, 197n.8, 197n.9, 198n.10, 198n.12, 198n.13, 199n.14, 203n.19, 210

261

262

Index of Names

Schenkl, Henricus, 150n.8 Skemp, J. B., 97n.6, 145n.4, 176, 176n.3, 217n.15, 226n.1 Sorabji, Richard, 149n.6 Souilh´e, J., 182n.13 Taylor, A. E., 139n.1 Teloh, Henry, 60n.12

Vitelli, Hieronymus, 150n.9 Waterfield, Robin, 97n.6, 139n.1, 145n.4, 176, 176n.6, 194n.4, 217n.15, 226n.1, 227n.3 Wedin, Michael, 229n.7, 230n.7 White, Nicholas, 11n.1, 60n.10, 60n.11 Wildberg, Christian, 149n.6

General Index

Agamemnon, 194n.4 Alexander Aphrodisiensis, 150, 150n.10, 151, 152, 153, 154, 160, 161, 202n.18 analogy at Phaedo 87B–C, 93n.1 of knowledgeable doctor, 113, 117 of physical trainer, 118 of sacrificial animal, 125 See also division according to “natural joints” Aristophanes’ Lysistrata, 95–96 Aristotle’s doctrine of mean, 142n.3, 179, 183, 184 basic kinds in Philebus, 49 See also Unlimited, Limit, Mixture, Cause becoming better dialecticians. See purpose of Statesman conversation Cause, principle in Philebus, 49, 157, 158–159, 164, 177–178, 208, 209 contributory cause in Statesman, 102, 103, 107, 113–115, 120, 122, 124, 125, 126, 128, 130 (contrast direct cause in Statesman) cuts “through the middle,” 3, 12, 22, 23, 24, 37, 56n.4, 59n.8, 126, 148, 214, 215–218, 224–225, 230–231, 235–236, 237, 238, 240

degrees of generalization among Forms, 60–61, 209–210, 212 See also division by genus and species dialectic, 3, 4, 5, 52, 55, 74, 77, 84–85, 95, 96–97, 98, 99, 111, 127, 128, 134, 143, 146, 158, 188, 191, 194n.3, 195–197, 204, 205, 207, 209–210, 212, 217, 218, 219–222, 223–224, 225, 226, 227n.4 See also purpose of Statesman conversation dialecticians, purpose of becoming better. See purpose of Statesman conversation Diogenes, 24 direct cause in Statesman, 102, 103, 107, 108, 113, 117, 120, 121 (contrast contributory cause in Statesman) division according to Forms, 3, 22, 31, 33, 35n.15, 37, 41, 52, 54, 55, 87, 125, 126, 146, 148, 191–193, 204, 206, 206n.1, 209–214, 216, 217, 218, 220, 222, 223–225, 226, 227n.5, 229, 235, 238 according to “natural joints,” 41, 52, 54, 124, 125, 207, 209, 223 See also analogy of sacrificial animal by genus and species (Aristotelian), 60–61, 61n.14, 61n.15. See also degrees of generalization among Forms dichotomous, 6, 19, 22, 37, 38, 55, 64, 70, 101, 109, 110, 124, 125–126, 129, 134, 188, 216, 218, 219, 222n.16, 224, 227n.5, 235, 240

263

264

General Index

division (cont.) left-hand, 6, 54, 55, 64, 64n.17, 65–66, 71, 101, 103, 105, 108, 109–111, 112, 122, 126–131, 134, 188, 220 nondichotomous, 5, 6, 14, 37, 38, 55, 64, 122, 124, 126, 188, 218–219, 240 See also cuts “through the middle” right-hand, 6, 54, 55, 64, 64n.17, 65–66, 70, 71, 72, 105, 108, 109, 111, 126, 127, 128, 188 terms for in Statesman, 35 due measure, 141, 142–143, 144, 145, 147, 148, 179, 183, 184, 185–187 elenchus, 44, 45n.10, 65–67, 77, 87 Eudoxus, 155, 199n.14 Eurytus, 202n.18 Excess and Deficiency (G
 5 ) AX), 2, 14, 29, 30, 32, 110, 111, 122n.6, 139–140, 143, 147, 148, 149–150, 151, 152, 153, 154, 155n.1, 156, 159, 171, 172, 173, 174, 175, 176, 178, 179, 182–183, 184, 185, 197, 205, 234, 235, 239 See also Appendix Forms as numbers. See numbers, Forms as “godly method” in Philebus, 48, 49, 50, 125, 158, 162, 163, 164, 192 Gorgias, 64, 196n.7 Great and Small ((#)  ) (#) ()  1, 2–3, 141, 142–143, 145, 148, 149–150, 150n.11, 153–155, 155n.1, 156, 157, 160, 161, 162, 168, 169, 170, 172, 173, 179–180, 181, 182, 185, 194n.5, 197–198, 199, 200, 200n.15, 210n.7. See also Appendix equalization of, 161–162 Hippias, 64 Homer, 19 imitative polities, 116–119, 123–124, 127, 131 Indefinite Dyad (   "), 2, 150–151, 152, 153, 154, 155n.1, 159, 160, 178, 180, 197, 200n.15. See also Appendix kinds, 236–237

and classes, 226–227, 230 and parts, 3–4, 228 and Forms, 227–230 divided according to Forms, 223, 227n.5, 228, 229, 235, 237 division according to, 37, 43, 45, 55, 82, 208, 209, 229 Limit, principle in Philebus, 49, 151, 156n.3, 157, 158–159, 161, 164–166, 175–176, 177–179, 183, 184, 208, 231–233 measure, 142, 143. See also due measure Mixture, principle in Philebus, 49, 157, 159, 233 More and Less ((#) C ) (#) = ), 2, 152–153, 154, 157–159, 160, 166, 172, 173, 174, 175, 176, 180, 184, 237. See also Appendix myth, Cronus, 6, 12–13, 14, 19, 21, 25, 26, 32n.11, 92, 122, 122n.6, 131, 160 charioteer, 53 Nature of the Unlimited ( 
 " 3), 2, 152–153, 154, 155n.1, 157–158, 175, 180, 189. See also Appendix necessary and sufficient conditions (in a definition), 47–48, 58, 58n.6, 59, 64–65, 89, 111–112, 112n.12, 128, 134 neologisms in definition of weaver, 96, 101, 106–110, 112 nondichotomous division. See division, nondichotomous not-Being in Sophist, 6, 32, 32n.11, 144, 145, 146, 182, 208n.4 number(s) in Parmenides, 165–166 in Philebus, 158–159, 189–190, 194, 195, 197, 198 in Statesman, 146, 147, 180, 181, 187, 216, 219–220, 221–222, 224–225, 228, 235, 236, 238, 239, 240 in Theaetetus, 222n.16 Forms as, 1, 3, 200–203, 204, 239 paradigm(s), 13, 16, 19, 26, 27, 28, 37, 44, 74, 83, 84, 86, 87, 88, 90, 92, 94, 96–97, 111, 122n.6, 127, 135 in learning letters, 5, 28, 29, 77–78, 79, 81, 82, 83, 85, 93, 97, 99, 134 of angling, 15, 74–76, 77, 97

General Index of shepherding, 5, 13, 19, 20, 21, 22, 27, 28, 75, 77, 88, 97, 133 of use of paradigms, 5, 13, 28, 29, 77–81, 85, 89, 91, 92, 96–97, 98–100, 101, 103, 134, 151, 162, 163 of weaving, 5, 6, 13, 14, 17, 19, 28, 33, 38, 75, 80, 84, 85, 87, 90, 91, 93, 94, 96, 97, 98, 99, 100, 113, 121, 127, 131–135, 139 requirements for proper use, 79–81, 89, 93, 96n.4, 98–99 verbal, 81–83, 85, 89, 93, 99 See also verbal accounts, importance of Philoponus, 150, 150n.9, 151, 154 Porphyry, 152, 153, 155n.1 Prodicus, 64 Protagoras, 64, 148n.5 Pythagoreans, 148n.5, 151, 164, 183n.14, 201n.16 purpose of Statesman conversation, 3–5, 14, 15, 19, 29, 30, 33, 34, 35, 35n.15, 82, 95, 99–100, 110, 135, 205, 209, 223

265

sophist of noble descent, 44, 46, 56, 65–67, 71, 76 Sun, simile of, 83n.5, 84 Theuth, 155n.3, 156n.3, 163, 164, 184, 189–190, 199, 200n.15, 206, 207, 210, 238–239 Themistius, 150, 150n.8, 151, 154 Thesaurus Linguae Graecae (TLG), 6, 35n.15, 106n.10, 106n.9 “Third man” argument, 25, 42, 167, 168–169, 201n.17

recollection (  ), 37, 38–40, 87, 88, 90 in Meno, 77–78, 79, 86, 87, 88 in Phaedrus, 52, 54, 86, 88, 89, 90

Unlimited (# 1
 ), 2, 49, 151, 153, 154, 155, 155n.3, 156, 156n.3, 159–161, 162n.6, 163–165, 166, 174–176, 177–178, 179, 183–184, 185, 189–190, 197, 199, 203, 206, 208, 231, 233, 234, 238–239 Unlimited Multitude ((#) 1

! ), 153, 162, 162n.6, 168–170, 198 Unlimited Nature. See Nature of the Unlimited Unequal (# 1  ), 151, 159, 160–162, 197. See also Appendix “unwritten teachings,” so called, 1, 153

Simplicius, 150, 151, 152, 153, 154, 155n.1, 160, 173

verbal accounts, importance of, 14, 32, 34. See also paradigms, verbal