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THE ASCENT FROM PHILOSOPHICAL STUDIES SERIES

Editors:

WILFRID SELLARS, University of Pittsburgh

KEITH LEHRER, University of Arizona

Board of Consulting Editors:

J ON A THAN BENNETT, Syracuse University

ALLAN GIBBARD,

ROBERT STALNAKER,

ROBERT G. TURNBULL,

VOLUME 37 TERR Y PENNER Department of , The University of Wisconsin at Madison, U.S.A.

THE ASCENT FROM NOMINALISM

Some in 's Middle

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DORDRECHTj BOSTONj LANCASTERjTOKYO Library of Congress Cataloging in Publication Data

Penner, Terry, 1936- The ascent from nominalism.

(Philosophical studies series; v. 37) Bibliography: p. Includes indexes. 1. Plato. 2. . 3. -History. 4. Nominalism-History. I. Title. II. Series. B395.P347 1987 111'.2'0924 86·31641 ISBN-13: 978-94-010-8186-3 e-ISBN-13: 978-94-009-3791-8 DOl: 10.1007/978-94-009-3791-8

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All Rights Reserved © 1987 by D. Reidel Publishing Company, Dordrecht, Holland Softcover reprint of the hardcover I 5t edition 1987 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical induding photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner ACKNOWLEDGEMENTS

Much of this work was conceived and executed between 1971 and 1975, though some of it was done much earlier, and a few bits are quite recent. My greatest debts, other than to , Plato and Aristotle, are first to my teach~rs in Gr~ek philosophy, , G.E.L. Owen and John Ackrill, and, perhaps most influential of all, my for• lIer colleague ; second, to the wr i tings of Frege and Quine; also to related writings of Geach, Church, Goodman, Carnap and Kaplan; third, to writings in philosophy of mathematics by Godel, Bernays, Church, Hilbert, Weyl, Gentzen, Goodstein and Boolos; .fourth, to writings of such modern causal theorists as Donnellan, Kripke, Putnam and Stampe; fifth, to conversations with (on Quine), Montgomery Furth, Mark Steiner, Richard Kraut (on Aristotle's universals vs Plato's Forms). Alan Code (on Quine's attitude to the ), Dennis Stampe and Berent Ene;; and also to a conversation (for so I call it) that I overheard between and on whether or not the world was we 11 lost. Readers who know Putnam's 'On Properties' and Sellars's ' and Existence' recognize how lIuch lowe to those important papers. Two books that I read in the early 1970's encouraged me to con• tinue on this Platonist venture once I was embarked on it: Murdoch's The Sovereignty of Good (in spite of its Wi ttgensteinianism) and Cudworth's Treatise on Eternal and ImlRutable Moral ity (in spite of its and its ) . Various different versions of the essential arguments of §§1-7 and 9 of 'The Nominalist' were presented at the Uni• versity of Minnesota in Fall i973; to the Western Division of the A.P.A. in April 1974 (to which Marc Cohen read an ex• tremely helpful reply); and in the spring of 1975 to Simon Fraser Uni versi ty. The material of §8 was presented at a Plato conference at the University of Marquette in Spring 1976, and, in an improved version, as a last minute substi• tute paper at the A.P.A. in May 1985. Except for §6, 'Aris-

v vi ACKNOWLEDGEMENTS totle's Dilemma' was written for my graduate seminars at the University of Calgary in spring 1975. Clarifications II and III were written for my students at Wisconsin in the later 1970's, in order to introduce them to certain views of Pla• tonic passages which were in opposition to my own. (But the objections to Shorey and Hackforth in the former go back to my graduate seminars at Princeton in the 1960's). Clarification VI, on the 'Third Man ', is really a separate story. For an account of my debts in that work see p. 404, n. 2. To all the audiences I mention, for questions and diffi• culties, my thanks. lowe a huge debt to Joan Kung, who selflessly and gen• erously took the time to give me a mass of extremely helpful detai led comments on the penul t imate draft. Many improve• ments in the present draft lowe to her suggestions. She also attended some of the seminars in the mid 1970's from which this book grew, and there too forced me to improve what I was saying. Robert Turnbull also read the entire pen• ultimate draft and gave me much good advice. Valuable com• ments of Keith Lehrer's pushed me to clarify my attitude to Russell as a Platonist in the Introduction. But my greatest debt by far is to several generations of undergraduate and graduate students at Wisconsin--far too many to mention. Jor special and numerous contributions to this manuscript, I must however mention David Ring, Tony Chu, George Rudebusch, Ruth Saunders, Lila Luce, Alan Code, Harry Nieves, Paul Warren, Marty Barrett, Melinda Hogan and Donna Rae McCormick. The last three undertook to proofread the manuscript for me, and ended up making so many useful suggestions for small changes resul ting in vast improve• ments, that the original final version became a penultimate version, and I' ended up responsible for my own • reading. Finally, I must also single out, as a prime source of for me, working on the passages discussed here in undergraduate tutorials. I consider myself fortunate indeed to have worked with so many most extraordinarily tal• ented young people. This book is certainly the better for that good fortune. The earliest financial support of this work came from a summer research grant from the American Council of Learned Societies in 1973, for some work on and the rule of of identicals as applied to thinking about Pla• to's parts of the soul doctrine and Freud's mature doctrine of the ego, id and super-ego. This work took a more general ACKNOWLEDGEMENTS vii turn, and became a study of Fregean attitudes to (connected with this work on ipentity in psychological con• texts) and the effect of such ettitudes on our of Plato. [See p. 339f of the present volume for some in• dications of my treatment of Pireud and Plato on parts of the psyche.] The Graduate School of the University of Wisconsin also supported the very beginning of this work in a research grant for the fall of 1974--a study of Plato's Forms and the paradoxes of , and theory. [Work done then is embodied in the present volume especially in Clari• fication VI as well as in p. 346, n. 43 and p. 358, n. 53.] The Graduate School also gave me a grant for technical help in preparing the manuscript in the academic year 1985-86. Both The Ascent from Nominalism and the next volume I shall be publishing, Plato and the of , in an important sense grew out of the work supported in the early 1970's by the ACLS and by the Graduate School, and I am ex• tremely grateful to those two bodies for the essential part they played in the (eventual) appearance of this work. In preparation of the camera-ready manuscript, I have principally to thank Janet Holt, Scott Berman and, especial• ly, Donna McCormick; and for related technical help, Anne Gunther, Dave Dean, Ginny Krohn, Read Gilgen, and, especial• ly, Don Crawford and Berent En~. I was also assisted in countless ways, both large and small, by John, Jane and Louise Penner; and especially by Rosemary Penner, to whom this work is dedicated. PREPACE

When I started out as a teacher of Greek phi losophy, I wasn't clear on exactly how it was that Aristotle differed from Plato on the existence of universals. But I felt sure that, with his greater subtlety and greater feel for what we now call the '' of statements about things and attributes, it was Aristotle, of the two of them, who was the more likely to be right. So too with Plato's infinite known as 'the Third Man', which Aristotle fatal to the : without being clear exactly how, I felt sure Aristotelian universals would be more defensible against such infinite regresses than the Platonic Forms. Not only were Aristotle's positions more moderate and sensible-looking, and based upon a wider range of logical and grammatical distinctions--of a sort that stu• dents of Frege, Russell, Wittgenstein and Ryle would be sen• sitive to; it was also the case that Plato's rather extreme views seemed all too emotionally surcharged with mystical and ascetic longings brought on by epistemological and even political disappointments with the world of temporal flux. The philosophical errors were deep, it is true; but they un• doubtedly called for patient and detailed diagnosis from a logically and linguistically discriminating standpoint. I was aware of intellectual currents running against the Aristotelian passion for simply getting the logical form right and then letting the ontology look after itself. Even Frege, the first and greatest modern master of logical gram• mar, showed an ontological candor that kept Plato before one's . The same was true of early Moore and, by fits and starts, Russell. And some few more recent masters--one thinks immediately of Quine and Davidson--showed that same unblinking attention to one's ontological commitments, how• ever unwelcome. But I was not shaken from my Aristotelian complacencies till the late 1960's when Mark Steiner intro• duced me to Hilbert's great paper on the infinite. At the time I was working on an annotated of Aristo• tle's complex and subtle account of continuity and infinite

viii PREFACE ix divisibility in VI. I had been assuming at that time that Aristotle's elimination of to the infinitely large in his account of the potential inf inite--like the elimination of the infinitely small from nineteenth century accounts of limits and continuity--gave us everything that was important in a theory of the infinite. Hilbert's paper showed me that this was not obviously so. Suddenly other about Aristotle's (apparently) judicious toning down of (supposed) Platonic extremisms began to crumble. The upshot of work I had been doing earlier on Plato's '' began to look different from the way it had before. I was confronted with a possibility I had not till then so much as entertained. What if the more extreme posi• tions of Plato on these issues were the more likely to be correct? The present work is the first instalment of the result• ing reassessment of Plato's metaphysics, and especially of his theory of Forms. It has occupied much of my teaching and scholarly time over the past fifteen years and more. The central question wi th which I concern myself is, "How does Plato argue for the existence of his Forms (if he does )7" The of making this the central question is that if we know how he argues for the existence of Forms, we may get a better sense of what they are. Starting here in our lAay restore some needed distance to our view of the Forms. It may make us stop thinking in terms of 'Plato's well-known Forms' and lead us to wonder a little, in Socra• tic fashion, "Well, what are they anyway?" The answer I come up with to the question how Plato argues for the Forms is this. In his middle dialogues (to which the present work restricts itself), Plato takes it that to establish that there is a Form of (or of equality or or health)--or a Form of the shuttle (or of the real nature of cutting), or a Form of whatever it might be--he needs to show that nominalism is false about beauty, equality, cutting or whatever. That is, he needs to show the failure of a nominalist program like the following: to explain what we are talking about when we use gener• al I ike 'beauty', 'equality', 'the shuttle' or 'cut' without referring to anything other than particu• lar spatio-tellporally locatable objects (beautiful sights and sounds, equal sticks and stones, particular aaterial shuttles or acts of cutting at particular spa• tia-temporal locations). x PREFACE

We can put this program in slightly more modern-looking garb as follows. Suppose that for various we want to, or need to be able to, assert certain sentences containing these general words. Then the program is to show how these sentences can be thought of as true without our having to suppose those general words stand for anything other than such concrete objects as sights, sounds, sticks, stones and the like. The challenge to the nominalist is: if you claim that beauty doesn't exist, then stop talking about it. To paraphrase : what we (f ind ourse I ves constrained to] think and speak of (we should admit] must be. This account of how Plato argues for the Forms is rath• er unusual. And indeed there might seem to be serious for questioning it. For it may seem to make the Forms and Plato's ways of arguing for them too unspecific. For exam• ple, if anything is clear about Plato's Forms, it is surely this: that they are discovered rather than invented. That is, Plato's Forms are not just creations of our linguistic, conceptual or cultural activities (as some would say that of a state are, for example). Rather, Plato thinks of his Forms as things which would have existed whether or not any had ever thought or spoken of them. But if on my view Plato argues for the Forms by arguing simply that nomi• nalism is false, he will have entirely omitted to give us any reason for thinking that what there is lIIore to beauty than beautiful perceptibles is something we discover rather than merely create. And there is a related difficulty. What good will it be to show nominalism false if one is attempting to establish the existence of (transcendent) Forms as opposed, say, to immanent universals? After all, Plato is surely only half way to where he wants to go when he has shown that there are things and properties, qualities or whatever. He still has to show that beyond these properties or qualities that we all believe in, there also exist these super-objects, the Forllls. So if Plato argues for the Forms in the way I say he does, I need to explain why he omits to show that these Forms are more than mere conceptual constructs; and I also need to explain why he omits to show that the Forms are more than mere immanent universals. My of these two difficulties flows from a suggestion of Vlastos and others, that the theory of Forms is the first systelllatic theory of abstract objects in the history of Western thought. I do not, as is often done, take PREFACE xi this suggestion in a merely forma way, to excuse what are taken to be Plato's obvious logical blunders. Rather I use it in a more substantial way. First, in connection with Plato's failure to argue that beauty and so forth are more than conceptual constructs, I use this suggestion to argue that since the Forms are the first abstract objects to ap• pear on the scene of at all, it would not have occurred to Plato that it would be necessary to argue against any of anti-metaphysician other than a nomi• nalist. (Constructivism and are, fro. a gene• tic point of view, fall-back anti-metaphysical positions, once nominalism has been defeated by the appearance of Pla• tonism or realism. No more could naive radical be immediately succeeded by Hume and Kant without an interven• ing theory of real a priori independent of the human . ) Similarly, in connection with the charge that Plato fails to give arguments to get him beyond the properties or qualities or characteristics we all believe in, the present suggestion is: the charge is entirely anachronistic. No one in Western philosophy believed in properties or qualities or characteristics till after the Forms appeared. What I am saying is this: all of those classic objects of thought for the --properties, qualities, Aris• totelian universals, Fregean , extensions of predi• cates, sets, meanings, uses of words, forms of life and the like--all of these entities appear upon the philosophical scene by reaction to Plato's theory of Forms or to its de• scendants. So it is not as if we all believe in properties and qualities, or uses of words, and Plato in a fit of meta• physical extravagance postulates now useless doubles of these ordinary properties. No one in Western philosophy could believe in a kind of thing--ordinary properties--till Plato introduced the Forms. Not only did Plato invent the 'quality' (poio-tes, 'such-ness'), he was the first Western philosopher to have the very idea of a , quality or attribute. So then, the general method I find Plato using in argu• ing for the Forms is: to defeat nominalism about beauty, equality, health, the shuttle, the real nature of cutting and so forth. But what arguments does he actually give? What I find in the middle dialogues is in two sorts of anti-nominalist arguments. One sort, of which I do not myself approve, I call 'the argument from incorrigible conceptual states'. Such arguments are closely related to xii PREFACE the idea of a priori , and to its unwitting stalking horse in the and the , the theory of recollec• tion. The other sort of argument, which I call, following Aristotle, "the argument from the sciences", I myself ac• cept, and think extremely important. But though I reject one of the arguments and accept the other, I find both arguments formidable and worth investigating. Much of the book is tak• en up with identifying these arguments in the Platonic text and explaining how I think they work and (to a degree that may surprise) defending them and their implications. I also try to say what sorts of things the Forms will be if these are the sorts of arguments Plato gives for their existence. If one accepts the argument from. incorrigible conceptual states, the Forms will be entities a bit like meanings--not meanings as culturally created patterns of be• havior ("uses") invented by , but meanings as those real properties or attributes we "bring before our " when we mean something by a word (as in the sorts of appeals G. E. Moore used to make against some of his philosophical opponents, most famously, Mill). If, on the other hand, one looks to the argument from the sciences, the Forms will be the sorts of real natures the scientist in his or her re• search program seeks to discover--the real nature of the atom, the real nature of the weak force, the real nature of chemical bonding (cf Plato's concern with the real nature of cutting), the real nature of cancer (cf Plato's concern with the real nature of health) or perhaps of the growing cell, and so forth. Both arguments make the Forms properties of a certain sort (though the identity conditions will eventually show up as crucially different in the two cases). In the first case, they will turn out to be properties of a sort that will be useful for semantics and logic (theories of and the• ories of ). In the second case, they will turn out to be properties useful for a theory of objects of in• quiry in , and so in metaphysics and . (For present purposes, let us think of mathe• matics--for Plato, geometry--as a science) With both argu• ments, it is supposed, the properties are discovered, not invented: they would have existed whether not hUllans had ever thought or spoken of them. (I use the term 'property', but I prefer 'real nature', which sounds less like a predi• cate and more like a nameable--an in the Platonic manner) . The sort of picture I present of the Forms conflicts PREFACE xiii with the powerful diagnoses of Platonist extremism that are to be found in the exegetical tradition of Vlastos, Ryle and OWen·--the tradition in which I was educated and from which, by far, I have learned most. Take the view that the Forms are paradigms, and in some sense 'perfect' objects, while sensible particulars 'fall short' of the Forms. This is tak• en to be a com.itment to the doctrine I call ' Lit• eral Self-Predication'. Beauty is the supremely beautiful object, Equality the one thing that is just equal, and so forth. (Forms as super-objects, as projections into another world, of disappointments in this world.) A key.point for lie here is this. If Plato is held to be committed to the that the Form of Largeness is itself a large object, he is being held to be committed to some• thing that, taken to the foot of the letter, makes no sense. (How could an abstract object like a Forll, which is supposed to be entirely non-spatial, be a large objec~) So Plato is being held to be committed to a view he couldn't have had in mind. (I'm not saying the view is meaningless. I'm saying it's so silly a view that he couldn't possibly have said to himself, "This view is true".) How can such beliefs be attributed to a great philo• sopher like Plato? The answer from within the tradition of Vlastos, Owen, Ryle and others is roughly this: because of conceptual confusions and mistakes of logical grammar. Real enough hUMan disappointments, compounded by misleading anal• ogies that are deep within language, tempt to metaphysical extravagance, generating all sorts of queer and mysterious entities and theories, with all sorts of unnoticed absurdi• ties. It is the duty of the clear-headed reader of Plato, while appreciating his great pioneering work, to track down the symptoms of his confusions and to diagnose his errors. I think of this period of the last fifty years or so within this particular Anglo-American tradition of the study of Plato as an age of diagnosticism. By , I have tried to make the beliefs attribut• ed to Plato in the present· study beliefs he 'could have had in mind'. This is not, I think, just an a priori imposition, pecul iar to my interpretations, and produced by simple cussedness on my part. It is the product also of philosophi• cal differences I have with the diagnostic tradition. That tradition is associated with a whole complex of philosophic• al doctrine which do not persuade lIe--doctrines about log• ical types' and ; about sentences and predicates not being treatable as nalles; about things known being prop- xiv PREFACE erly always propositional rather than being objects (the world as the totality of not things); about the inevi• tability of the paradoxes if category-distinctions are not observed and self-reference not proscribed; about the inter• est of showing Plato committed to 'two worlds' (as if it were clear what the is between two worlds and one wor Id containing two sorts of things), or to 'queer' or 'mysterious' entities (as if abuse constituted refutation), or to 'misleading' philosophical positions (as if 'mislead• ing' were a term of philosophy rather than of ); about the ease with which systems of modern logic may be app lied to t rad i tionai metaphys ical problems; about the metaphysical innocence of the notions of and lo• gical form; about the obviousness of certain proscriptions on involving existence, identity and psycholog• ical contexts. And so on. Thus my own divergent readings of the relevant passages flow not only froll (I hope) careful readings of the Greek text, but also, at least in part, from philosophical differ• ences with the certainties of the age. Somehow, I began to feel, modern philosophers and modern historians of had picked up an unjustified confidence about how much easier it is to 'do phi losophy nowadays wi th all the semantical and logical tools we now have at our service than it was for this wonderful primitive, Plato. By contrast, I was coming to the view that fundamental philosophical prob• lems are so hard that we always end up doing them by the seat of our pants--that our own attempts on those problems have not been so stunningly successful that we can afford to patronize Plato's arguments wi th diagnosis instead of letting his arguments raise questions for us (and even for our logical and se.antical techniques). Thus I came to look on strange-looking passages in Plato, and strange-looking locutions in Plato's Greek, with more sympathy than I had before. I even came to believe that it was almost entirely due to this unjustified philosophical confidence I have been speaking of that interpreters have been so quick on the draw when dealing with those passages which apparently comlli t Plato to such silly positions as the claim that the Form Largeness is itself a supremely large object. It will be apparent that I think one has to think through a good deal more fundamental philosophy than is usually supposed if one is to examine the views of a great philosopher like Plato. Indeed perhaps I should take the time here to make the following pOint. It is my view that it PREFACE xv is only possible to give an adequate interpretation of a classical text in philosophy to the extent one has oneself solved the philosophical problems being dealt with in the text. (It is not a matter of first figuring out, from a neu• tral philosophical standpoint, what the philosopher means, and then assessing the merits of the philosopher's posi• tion.) I can perhaps explain why I think this as follows. Most interpreters of philosophers have learned froll logicians and mathematicians of the past century or so just how much elaboration is necessary to get exact statements of the assumptions of arguments. Consider showing the truth of '2+2 = 4' by the methods of --including proper explanation of what are: functions? concepts? sets? sets of sets? quantifiers? An argument in Plato or Leibniz or Berkeley will in general be about matters rather more complex than '2+2 = 4'. Yet such arguments are given very succinctly by comparison with what a formal logician or a worker in foundations of mathematics will require. (For a simple case, see Gig, §6 for Frege's exposure of Leibniz's fallacious argument for '2+2 = 4'.) What this means is that to spell out more exactly an argument in a text before us, we must supply lemmas, assumptions and unstated premisses of various sorts. But where are we to get these lemmas, assump• tions and unstated premisses? "From other writings of Plato, Leibniz, Berkeley (or whoever's argument is in question)." But those writings too will depend upon lemmas, assumptions and unstated premisses of the author in question I "Very well, supply those gaps in the arguments by the most reason• able assumptions you can think of consonant with all the passages you know." Why reasonable rather than unreasonable or even stupid assumptions? Because Plato, Leibniz, Berkeley (or whichever great philosopher we are examining) are not fools, but clever thinkers who might be expected to come as close to the truth on any given matter as is possible, con• sonant with the rest of what they think. So now we come to it! To determine what they thought about the claim that p, we need to know what the truth is about p, so we can attrib• ute to the great philosopher in question a view as close to the truth as is consonant with the rest of what the philoso• pher thinks. (I have no doubt whatever, incidentally, that Plato would have entirely concurred with these remarks on interpreting a (lreat philosopher. See Phdr 259E-278B esp. 260A-262B, 277B on the of rhetoric requiring of the truth of the matters on which persuasion is sought. Plato's view here of course descends from Socratic views of xvi PREFACE the nature of literary criticism in the and of the nature of rhetoric, desire and power in the Grg. See also the distinction between true and false pleasure in the Phlb, as well as p. 311ff below.) But the above remarks are only meant as indications. Fuller discussion of these topics will be offered in the second instalment of the present study, Plato and the Philosophers of Langugage, and in my book on Socratic knowledge. At any rate, I hope these remarks will help to explain why the book discusses just the things it does. The first dialogue, 'The Nominalist', takes up incorrigible conceptual states, nominalism and Universal Literal Self-Predication. The second dialogue, 'Aristotle's Dilemma', takes up argu• ments from the sciences and resultant problems involving ex• i stence, identi ty and psychological contexts. (The first part of 'Aristotle's Dilemma' could actually double as a way of introducing the Fregean and Quinean problems of involving psychological contexts.) It also addresses some questions about logical form. Following the two dialogues, there is a series of 'Clarifications' directed in often quite substantial ways to important passages and arguments passed over in the two dia• logues. Most important of these are: the second (on oppo• sites and Forms of opposites); the third (on 'degrees of re• ality', being and , and Aristotelian ); and the sixth and seventh (on the Third Man Argument and the paradoxes). The sixth is in fact a substantial treatise, taking a radical look at the illusion of exact formulation of the logic of arguments in the history of philosophy. Lying behind these explorations of passages in Plato's middle dialogues are a of key philosophical themes which I address myself to in the Introduction. The reader is invi ted to feel free about the Introduction--either to plunge straight into it, or to postpone it till after read• ing the two dialogues, consulting it as that may seem desir• able given the philosophical situation that arises with reading the dialogues. In fact, the first section of the Introduction [pp. 1-9] may be difficult reading for those unfamiliar with modern discussions of theories of logical types. The dialogues, by contrast, should be fairly easy reading on their own; the reader can, in a measure, sit back and let me do the work. The analytical table of contents is designed to help with decisions as to the most helpful order of reading for the individual reader. The reader may also find helpful the account of the strategy of the present PREFACE xvii volume on pp. 11-20. All in all, most readers will probably find it best to begin right away with the dialogues and return to the Introduction later or as needed. I have tried, as far as poss i ble, to remove from the footnotes traditional source indications; the reader will usually find these within the text, in square brackets. I have also tried to eliminate less important cross- within this study from the notes; the reader should be able to find such cross-references by consulting the index of subjects. The notes are thus largely restricted to substan• tial philosophical discussions or digressions of a sort I think the reader should have available to him or her without their feeling any pressure to pursue them if not so in• clined. The text can be read without looking up the notes. I find it convenient to use numbered sentences quite a lot--something readers may find annoying. In an attempt to minimize the annoyance, I have tried for the most part to repeat or summarize such numbered sentences when they are not in the immediate vicinity. I also find it convenient to indent bi ts of text which are not actual quotations but rather my own paraphrases or adaptations of particular views. Accordingly I here violate the usual convention and use quotation marks if I am giving an actual quotation. A word about the dialogue form. The reader may be sur• prised, and even dismayed, to see that I will be employing the dialogue form for the central portions of this work. I make no for this other than to say that I found the form natural in itself, and that the form usefully • izes the way I see the doing of history of philosophy as in• volving a constant between (a) what we find sug• gested in the classical text, and (b) the likely reaction of the best modern philosophical to the same problems as are raised in the classical text. My character 'Plato' speaks of course for the sugges• ti ons I find in the Platonic text, while the character 'Gottlob' (that is, Frege) speaks if not for all that is best within of language, at least for much that is good (and certainly for that Fregean and Quinean part of modern which happens most to have influenced lie). I have found the unfolding of such a dialectic between classical text and powerful opposing mod• ern opinion valuable both to myself and to my students. I should add that I have tried to avoid being 'cute'; I have tried only to write in a style that I felt would be condu• cive to exposition of argument, to proper emphasis, and to xviii PREFACE philosophically natural reaction. The dialogue form is not meant to charm, but to enhance the rational discussions of what I think is of permanent interest in , by pit• ting it against some of the most educated and sophisticated opposition I think Platonism can find: the opposition of the modern analytical philosopher.

Madison, Wisconsin, August 1986. ANALYTICAL TABLE OF CONTENTS

INTRODUCTION

1. Some Views of the Forms; a Prolegomenon for Analytical Philosophers p. 1 Aristotle's t-reatment of Plato's Theory of Forms as a bit of metaphysical extremism, and some similar modern criticisms: Logical Form and· Diagnosis (p. 1). The Platonist Request for Clarification of these Criticisms, and modern Responses ap• pealing to theories of Logical Types and theories of the Logical Form of the (p. 4). A further, appar• ently unanswerable, modern riposte: Plato is committed to Universal Literal Self-Predication (p. 8). An earlier view of Plato: the Forms and Laws of Nature (p. 10).

2. A General Strategy for the Present Volume p. 11

The two main sorts of existence arguments in the middle dia• logues (p. 12). Remarks on the structure of the rest of this volume (p. 16).

3. Nominalism What p. 20

A strategy for defeating Nominalism: anti-deflationary argu• ments and ontological commitment (p. 23). Anachronistic character of interpretations that have Plato believing both in Immanent Characters and in Transcendent Forms (p. 24).

4. Incorrigible Conceptual States What p. 26

Anachronistic character of the possible charge that Plato's anti-nominalist argument for the Forms begs the question against conceptualism (p. 28). Incorrigible conceptual states and a priori truths (p. 30). Plato's middle period Forms as meanings or meaning-like entities (p. 32).

xix xx ANALYTICAL TABLE OF CONTENTS

5. The Frege-Quine Objections p. 33

Psychological contexts and inferences involving existence and identity (p. 34). Moore's argument against the 'Natural• istic ' not on the whole objected to as involving psychological cnntexts (p. 35).

6. Plato's other main Middle Period Argument for the Exis• tence of Forms--th~ Argument from the Sciences p. 40

7. On giving Plato a Position he 'could have had in mind' p. 43

Contrast of the present interpretation of passages like T'haedo 74 with Vlastos' s claim that Plato thought that Largeness was literally a large object (p. 44), and with Owen's claim that Plato thought that Equality Itself was perfectly equal (p. 48). A further difficulty in attributing to Plato a position he 'could have had in mind': how can the Forms be 'Paradigms' if they are not Literally Self-Predica• tional? (p. 52).

THE NOMINALIST

1. The Recollection argument of the Phaeao, commonly thought to presuppose the existence of the Forms, actually provides an argument (against nominalist opponents) for their existence. p. 57 2. The opponents in the (the 'lovers of sights and sounds') and in the Parmenides (Zeno, at least if his argu• ments against plurali ty are to be concl usi ve) also repre• sented as nominalists. p. 62 3. Various difficulties for the existence argument of the Phaedo. p. 69 4. The basic idea of the argument: that the equal we per• ceive we can confuse with the unequal we perceive; but the equal we conceive is, in clear cases, unconfusable with the unequal we conceive. p. 71 5. I ncorr igible conceptual states and Moore's argument against the 'Naturalistic Fallacy'. p. 78

6. Forms of opposites as the opposites ~themselves). How to understand the locution 'the F-itself I. p. 86 ANALYTICAL TABLE OF CONTENTS xxi

7. The quasi-theological predicates of the Forms. The Forms and Universal Literal Self-Predication. p. 95 8. Peculiarities of the contrast in Republic V between Knowledge and Opinion. The notion that the objects of opin• ion "lie between being and not-being". p. 106 9. Confusing the questions 'What is F-ness?' and 'What things are F?' Deficiencies of sensible F's as (nominalist) answers to the question 'What is F-ness?' The notion that Forms ar~ "separate". p. 113 10. Doesn't the of the Form of the Beautiful in the Upward Path in 210--212 compel the self--predi• cative notion that sensible particular F things are always less F than the F-itself? p.121 11. Examination of Symposium 210-212 shows the latter sug-• gestion to be a consequence of confusing the questions 'What is beauty?' and 'What things are beautiful?' p. 127 12. Plato's argument being an anti-nominalist argument from certain sorts of psychological states to objects of those states, we must turn to look at the (from a Fregean point of view) suspicious notion of objects of thought. p. 139

ARISTOTLE'S DILEMMA

1. The Platonic 'something or nothing?' question, objects of thought, and 'existential generalization from wi thin psychological contexts'. p. 141 2. 'Intensional' objects, 'extensional' objects and the in• ference from the existence of of Santa Claus to the existence of Santa Claus himself. Difference between a thought being directed and there being something the thought is directed towards. p. 147 3. Intensional/extensional and the taking of equal sticks to be unequal sticks or of the Morning Star to be other than the Evening Star. 'Substituting for identicals wi thin psy• chological states'. p. 150 4. Platonic worries about 'logically parallel' arguments. The suggestion in Aristotle's discussion of the 'Argument from Thinking' that he is aware of the dangers of inferences in psychological contexts involving existence and Identity; xxii ANALYTICAL TABLE OF CONTENTS and a difficulty for this view--Aristotle's endorsing of the Argument from the Sciences. (Aristotle's Dilemma) p. 153 5. The plausible (though in fact incorrect) suggestion that we are unable, in clear cases, to confuse equality with in• equality compared with the suggestion that there are such things as of contradictoriness. p. 160 6. The idea of a science of logic that is neutral on mat• ters of fact and real existence. Logical Form and the Pla• tonic Forms. p. 166 7. How Frege violates his own inferential restrictions--in Arguments from the Sciences--and even in his own theory of psychological contexts. p. 174

CLARIFICATIONS

1. The Recollection Argument at Ph.;. ·tlo 72A-77A. p. 181

The way in which sensible particulars 'fall short' of the Forms: contrast with traditional and diagnostic interpreta• tions (p. 184). How the recollection argument depends upon the existence of the Forms (p. 186). The possibility that Moore's concern with conceptual incorrigibility derives from Archer-Hind and Jackson on Phaedo 74B6-C5 (p. 187). Is the intrinsic implausibility of the theory of recollection from a previous life a serious defect in the Platonic theory of the soul and of its knowledge (p. 188)?

II. Are Forms of Opposites just Opposites? Plato's Final Argument for the of the Soul at Phaedo 102A• 107A. p. 191

III. Between Being and Non-being: Why is the Object of Know• ledge Being while the Object of Opinion is "What lies between Being and Not-being"? p. 206

A. The problem of Identity through Change (p. 207). B. ' problem and some doubts about the Aristotelian solution (p. 209). C. A first approximation to Plato's view of identity through change (p. 210). D. Aristotle's view contrasted with the views of Geach and Quine (p. 213). E. Plato's considered view (p. 214). F. How for Plato • cleitean flux would, but for the Forms, destroy all trans• temporal identity (p. 216). G. This-es and such-es: trans- ANALYTICAL TABLE OF CONTENTS xxi .ii

temporal identity in the (p. 221) H. Some interim conclusions (p. 224). J. A difficulty: how can there be any• thing which 'becomes' but 'is not'? (p. 225). K. Why does Plato restrict his 'What is X?' questions to Forms? How come he doesn't ask 'Wlldl .1rt-, these sensible F particulars?' (p. 226).

IV. Other Middle Period Passages with the Formula 'The F Itself' which are to be read with Caution. p. 232

A. Republic 505A2. The many surely do not think that the well-known Platonic is identical with pleasure: they too must be doing an ontological reduction (p. 233). How it is that Plato can deny that the good is identical with the knowledge Socrates supposes to be: the good is what that knowledge is knowledge of (p. ;~31). B. Republic 479D3-E5. The many conventions (nomima) that the lovers of sights and sounds identify beauty with are not universals but just the many sights and sounds--as they would have to be if the lovers of sights and sounds were nominalists (p. 235). C. Republic 515B4-517E3. The real question allegorized in the Cave passage is 'What is jus• tice?', and the pervasive shadow allegorize the nominalist answer to that question. The objects of knowledge and opinion [of what is] are not but objects like the Form of justice and (for nominalists) par• ticular perceptible just people and events--objects from the worlds of being or becoming (p. 237). D. 439C8-E6. The Forms, self-predication and changelessness (p. 242). E. The alleged near absence of Forms in the . Ab• sence of the formula 'The F-Itself' not necessarily a that the Forms arp absent (p. 243).

V. Aristotle's Lost Work On the p. 245

The Argument from the Sciences (p. 246). The One over Many Argument (p. 247). The Argument from Thinking (p. 249). The Third Man Argument (p. 250).

VI. Formulating the Third Man Argument p. 251

A. Vlastos' s 1954 analysis and the later introduction of sets into more properly generalized versions of the argument (p. 257). B-E. Three principal defects in this analysis: the relation of Non-identity and Self-Predication to One xxiv ANALYTICAL TABLE OF CONTENTS over Many (p. 263); the use of sets in formulating the argu• ment (p. 267); the failure to see that the regress is an ex• planatory regress (p. 269). The Vlastos finds in the premisses of the Argument (p. 271). F. Digression: how come the contradiction in the premisses of the argument did not surface till 30 years ago (p. 272)? G. Textual con• siderations in favor of the epistemological version of my (1967) (p. 279). H. Further reflections on how Vlastos got a contradiction in the premisses of the theory of Forms: the paradoxes of logic, semantics and (p. 282). J. A moral drawn from our comparison of Vlastos's version of the Third Man with the Paradoxes (p. 287). K. Why should a self -predication assumption be involved in the consistent ex• planatory (and epistemological) regress we have been examin• ing? Meaning-like entities and reflexivity without self• predication. (p. 291). L. Conclusion (p. 298).

VII. Aristotle on whether 'The Universal man is [a] man' is true in the same sense as 'Socrates is [a] man' is true. p. 300

Synonymous and paronymous predication in Aristotle's logical works (p. 300) Categorial division trees (p. 303). Synony• mous predication and being predicated in the same sense (p. 306).

VIII. Plato and the Philosophers of Language p. 311

A preview of problems to be discussed in the second instal• ment of the present study. Fregean theories of psychological contexts and logical form (p. 311). Conceptual incorrigibil• ity in the Theaetetus (p. 314). Protagorean and perceptual incorrigibility in the Theaetetus (p. 317).

NOTES to Introduction p. 318 to I The Nominalist I p. 362 to 'Aristotle's Dilemma' p. 382 to Clarification Two p. 394 to Clarification Three p. 396 to Clarification Four p. 399 to Clarification Five p. 399 to Clarification Six p. 404 ANALYTICAL TABLE OF CONTENTS xxv to Clarification Seven p. 421 to Clarification Eight p. 423

BIBLIOGRAPHY p. 424

INDEX OF PASSAGES CITED p. 432

INDEX OF PERSONS AND SUBJECTS p. 440 ABBRBVIATIORS

HJRKS OF PLATO

Crat: Cratylus Prm: Parmenides Euthyd: EuthydealUs Prtg: Grg: Rp: Republic Lach: Smp: SYIIPosium Lys: Sph: Phd: Phaedo Stm: Phdr: Tht: Theaetetus Phlb: Tm: Timaeus

WORKS OF ARISTOTLE

Catg: Categories Post. An.: Posterior De Int.: De Interpretatione Analytics Eud. Eth.: Eudemian S.E.: De Sophisticis Met. : Metaphysics Elenchis Nic. Eth.: Top.: Topics Phys. : Physics

OTHER WORKS

APQ: American Philosophical Quarterly ASPM: Allen (Ed.). Studies in Plato's Metaphysics ASSV: Aristotelian Society. Supplementary Volulle BP: Benacerraf and Putnam: Philosophy of Mathematics: Selected Readings CO: Frege. ' and Object' (1892a). in Geach and Black (Eds.). Philosophical Writings of CQ: Classical Quarterly EP: Paul Edwards (Ed.). Encyclopedia of Philosophy FK: Fodor and Katz: The Structure of Language: Readings in the Philosophy of Language

xxvii xxviii ABBREVIATIONS

FLPV: Quine, From a Logical Point of View FS: Feigl and Sellars: Readings in GB: Geach and Black: from the Philosophical Writings of Gottlob Frege Gig: Frege, Grundlagen der Arithmetik, (1884), tr. by J. L. Austin as Foundations of Arithmetic Ggs: Frege, Grundgesetze der Arithmetik (1893, 1902), tr. in part by Montgomery Furth as Basic Laws of Arithmetic. HC: Hamilton and Cairns (Eds.), Collected Dialogues of Plato JHP: Journal of the History of Philosophy JHS: Journal of Hellenic Studies JP: Journal of Philosophy JSL: Journal of Symbolic Logic PAS: Proceedings of the Aristotelian Society Phr: PPL: Penner, Plato and the Philosophers of Language (unpublished) PQ: Philosophical Quarterly PR: Philosophical Review PS: Philosophical Studies PSc: Philosophy of Science RM: Review of Metaphysics SR: Frege, "On " (1892b) Str: Strawson,

FREQUENTL Y USED SENTENCES

LSP: Universal Literal Self-Predication [see pp. 8f, 43ff, 257ff and so forth]. TMA: Third Man Argument [see p. 279ff, 251ff below] NI: Non-identity Assumption [po 257] SP: Self-Predication Assumption [po 257] OK: One over Many Assumption [po 257] EON: Explanatory One over Many Assumption [po 270] PH: Heracleitean thesis [po 210J