R.M.DANCY
The Sage Sclwol of Philosophy, Cornell University, Ithaca, N.Y., U.S.A.
Other publications in Synthese Historical Library 4. Proceedings of the Third International Kant
SENSE AND CONTRADICTION: A STUDY IN ARISTOTLE
This study is an attempt to clarify by reference to Metaphysics r3, the initial section of
r4, which concerns argument against people who deny the law of non-contradiction. 'Antiphasis', the interlocutor who denies the law of non-contradiction, is shown to be a "humus-heap of sophistic paradoxes, all turning on a failure to grasp the notion of sense". The author deals with what he terms the first and second refutations, and argues that some of Aristotle's views on sense and substance grew out of an attempt to handle problems set by the sophists.
Ccmgress held at the University of Rochester, March 30April4, 1970 edited by L. W. BECK
S. Bernard Bolzano: Theory of Science A Selection, with an Introduction edited by JAN BERG Translated from the German by Burnham Terrell 6. Patterns in Plato's Thought Papers arising out of the 1971 West Coast Greek Philosophy Conference edited by J. M. E. MORAVCSIK 7. The Propositional Logic of Avicenna A Translation from al-Shifa': al-Qiyas With Introduction, Commentary and Glossary by N. SHEHABY 8. Commentary on 'De Grammatico' The Historical-Logical Dimensions of a Dialogue of St. Anselm's by D. P. HENRY 9. Ancient Logic and Its Modern Interpretation Proceedings of the Buffalo Symposium on Modernist Interpretation of Ancient Logic, 21 and 22 April, 1972 edited by J. CoRCORAN 10. The Logic of the Articles in Traditional Philosophy A Contribution to the Study of Conceptual Structures by B. M. BARTH Translated from the Dutch by E. M. Barth; enlarged edition 11. Knowledge and the Known Historical Perspectives in Epistemology by ]AAICKO HnmKKA 12. Language and Logic in the Post-Medieval Period by B. J. AsHwORTH 13. Aristotle: The Nicomachean Ethics Translated with Commentaries and Glossary by HIPPOCRATES G. APOSTLE
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SENSE AND CONTRADICTION: A STUDY IN ARISTOTLE
SYNTHESE HISTORICAL LIBRARY TEXTS AND STUDIES IN THE HISTORY OF LOGIC AND PHILOSOPHY
Editors: N. KRETZMANN,
Cornell University
G. NucHELMANS, University of Leyden L. M. DE RuK, University of Leyden
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J.
BERG,
F.
DEL PUNT A,
Munich Institute of Technology
D.P. HENRY,
J.
HINTIKKA,
Linacre College, Oxford
University of Manchester
Academy of Finland and Stanford University
B. MATES,
University of California, Berkeley
J. E. MURDOCH, Harvard University G. PA TZIG, University' of Gottingen
VOLUME 14
R.M.DANCY
SENSE AND CONTRADICTION: A STUDY IN ARISTOTLE
D. REIDEL PUBLISHING COMPANY DORDRECHT-HOLLAND
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Library of Congress Cataloging in Publication Data M Dancy,R Sense and contradiction : a study in Aristotle. (Synthese historical library; v. 14). Bibliography: p. Includes index. 1. Aristoteles-Logic. 2. Essence (Philosophy) 3. Substance (Philosophy) 4. Contradiction. I. Title. II. Series. 75-2148 160 B491.L8D36 ISB~ 90-277-0565-8
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A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science. Bertrand Russell, 'On Denoting' (1905), in Logic and Knowledge: Essays 1901-1950 (ed. by R. C. Marsh), George Allen & Unwin Ltd., London 1956, p. 47.
TABLE OF CONTENTS
PREFACE
IX
INTRODUCTION
XI
CHAPTER I
I ARISTOTLE'S
PROGRAM
I. The Unprovability of the Law of Non-Contradiction A. The First Consideration: the Cognitive Priority of the Law B. The Second Consideration: the Logical Priority of the Law II. Arguing 'by Way of Refutation' CHAPTER II
I. II. III. IV. V.
I THE
FIRST REFUTATION: GENERAL STRUCTURE
The Plot of the Argument On the General Strategy Where Antiphasis Might Balk Where Antiphasis Does Balk: Two Sub-Plots Summary
CHAPTER III
I ON
1
1 3 7 14 28
29 34 38 43 54
ANTIPHASIS' CHARACTER AND
UPBRINGING
59
I. Antiphasis' Thesis II. Some Sophistry
59 63
CHAPTER IV
I. II. III. IV.
I THE
FIRST REFUTATION: THE TREATMENT
OF ANTIPHASIS
74
On Contradiction Uttering and Signifying Signifying and Defining Conclusion
75 79 82 91
vm
TABLE OF CONTENTS
CHAPTER
vI THE
SECOND REFUTATION
I. On Substances, Essences, and Why We Need Them II. Antiphasis' Commitments as to Essences
I ON
CHAPTER VI
SENSE AND ESSENCE
I. Subjects and Predicates; Essences and Accidents II. Essence and Falsehood III. Words and Essences CHAPTER VII APPENDIX I
I CONCLUSION
I De interpretatione 14
APPENDIX II
I De interpretatione 11. 21a. 25-27
APPENDIX III I
94 94 104 116 117 127 131 142 143 153
Metaphysics r3. 1005b11 to 4. 1()()7bl8: Text
and Translation
156
BIBLIOGRAPHY
166
INDEX LOCORUM
175
(a) Plato (b) Aristotle (c) Other Ancient Authors
175 176 184
PREFACE
This study began as a paper. It got out of hand. It had help doing that. Oswaldo Chateaubriand, Ronald Haver, Paul Horwich, Bernie Katz, Norman Kretzmann, Stanley Martens, Stephen Pink, Michael Stokes, Eleanor Stump, Bill Ulrich, Celia Wolf, and a lot of other people questioned or criticized or helped reformulate one or another of the arguments and interpretations along the way. In spite of (maybe partly because of) their efforts, the book is full of mistakes. At least, induction over previous drafts indicates that irresistibly. But I do not, right now, know of any particular mistakes. All but a couple of the translations are mine (the exceptions are noted). That is not because existing translations are bad, but because some uniformity was essential. The translations often make unpleasant reading. So, often, does Aristotle; I have tried to be literal. A text and translation of the passage on which the book centers is in Appendix III. Footnotes cite literature by author and (sometimes abbreviated) title. Details are in the bibliography. I do not profess to have covered all the literature. An enormous amount of editorial work was done by Margaret Mundy. She was not able to undo the errors that remain. In particular, the footnotes are often numbered oddly: '4', '4a', '4b', etc. This is not an obscure way of ranking footnotes, but a mistake I made that would have been expensive to correct.
INTRODUCTION
Metaphysics r4 contains argument against people who deny the law of non-contradiction. This study is an attempt to clarify the initial and most important stretch of that chapter, 1005b35-1007b18. None of the arguments in r4 is enough to prove the law, Aristotle thinks, because he thinks that it cannot be proved. Considerations he presents in r3 bear on this claim. They require us to use a different technique in r4: there we get outlines of debates, of dialectical arguments, for use against someone who tries to defend the denial of the law of noncontradiction. Chapter I below is concerned with these matters. I shall call the interlocutor who is denying the law of non-contradiction 'Antiphasis'. Antiphasis is, for all I know, a construct of Aristotle's: this study does not attempt to identify him with any historical figure. r4 contains debates with him. The first one, 'the first refutation' from here on, has for its backbone a direct argument for the law of non-contradiction, and for its ribs, attempts to counter moves on the part of Antiphasis. Chapter II is concerned with the backbone, and gives a preliminary investigation of the ribs. The direct argument is neat but, I think, not to be trusted. It depends on a view about sense (or what is signified, which is what Aristotle says, and that may be a little different) that may well be wrong. For it depends on saying that, where a word has a sense, we can give its sense in other words, and that this is a source for non-trivial necessary truths. The counterplay against Antiphasis is not at all neat. Understanding it, even seeing Aristotle's point in including it, requires consideration of the sort of thing he would have taken himself to be up against. This consideration is the undertaking of Chapter III. Chapter IV attempts to reconstruct the counterplay. What emerges is that Antiphasis is a humus-heap of sophistic paradoxes, all turning on a failure to grasp the notion of sense. Aristotle took the sophistry to be pretty poor stuff: he thinks of Antiphasis more as perverse than genuinely confused. And our sources for the sophistry (espe-
XII
INTRODUCTION
cially Plato's Euthydemus) certainly make its perpetrators look perverse. But that perversity should not blind us to the difficulty of straightening things out. It may have blinded Aristotle some. (It is here that I take the quotation from Russell that is this study's epigraph to apply.) For Aristotle's grasp of the notion of sense is not as firm as he thinks. The second major stretch of debate with Antiphasis, 'the second refutation' from here on, accuses him of destroying 'substance' and 'essence'. Understanding this requires consideration of Aristotle's distinction between essences and accidents. And here we run into trouble. The trouble comes in putting the essence-accident distinction together with the views on sense. We are forced to make this connection partly by the second refutation itself: it is not really independent of the first, and it is not easy to relate the two without considerably reducing the force of the first. But the trouble here is, I think, manageable. Chapter V is concerned with the second refutation. But there are other reasons for connecting essence and sense. For Antiphasis' sophistry turns as much on confusions over essence as on ones over sense. And Aristotle inherits some of this: first, he shows a tendency to conflate the distinction between what a word signifies and what it is true of with the distinction between the accident of a thing and its essence, and, second, he shows a tendency to identify the sense of a word with an essence. The trouble here is less manageable. Chapter VI deals with it. If any of this is right, it will show how some of Aristotle's views on sense and on substance grow out of an attempt to handle problems set by the sophists.l And however trivial he thought those problems to be, if they played that role, they are more important to him than he thinks. And since, as Plato and Aristotle saw these problems, false moves in connection with them resulted in some form of subjectivism or relativism, they are intrinsically more important than he thinks. NOTE
So also Aubenque, Le probleme de l'etre chez Aristote, pp. 94-134. Larkin, Language in the Philosophy of Aristotle, p. 22, n. 43, says she disagrees: Aristotle is answering Plato's problems. This is silly. Plato's problems in the Cratylus and the Sophist are
1
plainly ones set him by the sophists, and if Aristotle is handling them, he is handling problems set by the sophists.
CHAPTER I
ARISTOTLE'S PROGRAM
Aristotle says outright that the law of non-contradiction cannot be demonstrated: you can't prove everything, and among the things you can't prove there is this (r4. 10063 5-11).1 But, he says, it is possible to prove it 'by way of refutation' (eA.eyKnKU>c;;), if only the man who would deny it will say something (1006 3 11-13). I. THE UNPROVABILITY OF THE LAW OF NON-CONTRADICTION
He does not mean that it is not possible to construct some sort of deductive system in which the law of non-contradiction appears as a conclusion from other principles as axioms. 2 This possibility perhaps never occurred to him; still, the end of his first proof-by-refutation is a direct argument for an easily generalizable instance3 of the law, and that argument is virtually formalized as it stands. It reads (1006b28-34): Necessarily then, if it is true to say of something that it is a man, it is a biped animal (for this is what 'man' signified); but if this is necessary, it is not possible for the same thing not to be a biped animal (for 'it is necessary that it be' signifies just that it is impossible that it not be); so it is not possible for it to be true to say at the same time of the same thing that it is a man and is not a man.
It does not take much imagination to picture a deductive system with de-
finitions and rules of inference strong enough to capture this argument (although it takes a great deal more imagination to picture a system that satisfies both this requirement and others that logicians have placed on deductive systems)4. But a deduction of the law of non-contradiction in any such system would not, for Aristotle, constitute a proof of the law. There is one terribly architectonic argument for this, and I shall pretty much pass it by. The law of non-contradiction and other principles Aristotle calls "common beliefs" (Met. B2. 996b28), "common principles" (An. post. A 32. 88 3 36), just "common [things]" (A 10. 763 37, b10, A 11. 773 30), 43 or sometimes "axioms" (a~u:Olta-ra, Met. r3. 10osa2o, b33-34,
2
CHAPTER I
An. post. AlO. 76b14, A2. 72a17, A7. 75a41, 42), 4 b are trans-generic (An. post. AlO. 76a37-b2, 32. 88a36-b3). That places them outside the scope of demonstration, for a demonstration stays within a genus, and a chain of them constitutes a science, which is thus tied to a genus (cf. Met. B 2. 996b33-997a11, esp. 997a2ff., and An. post. A2. 71b17ff. A7). 4 c Aristotle refers to such considerations in r3 (cf. 1005&19-33), but he would not be entitled to rely on them there. For r3 is concerned to alter the rigid picture to which these ideas lead, and to allow the 'philosopher' room to discuss the 'axioms' (cf. 1005&33-b2, bS-11). r2 prepared the ground for this; according to that chapter, there can be a 'science of being' despite the fact that beings do not constitute a single genus. So it will no longer do to say: since the 'common principles' are trans-generic, no science can deal with them, and so there can be no proof of them. Aristotle might have kept the part of this argument that is supposed to show the 'axioms' indemonstrable (and so kept the claim that a demonstration cannot step outside of a single genus), and rejected the idea that the solitary scientific method is that of demonstration. His 'science of being' would then not have proceeded by demonstration. 4 d But he does not say this; indeed, he gives no specific reply to this argument. 4 e So I shall pass it by. It is possible to discern other considerations working in r3 to render the law of non-contradiction unprovable. Even in the Posterior Ana/ytics, where the above considerations were dominant, a proof had to satisfy conditions beyond that of being monogeneric, and beyond those of validity or even soundness. It had to start "from things true, primary, immediate, better known than, prior to, and reasons for (at·tiow) the conclusion" (An. post. A2. 71b20-22; cf. Top. Al. 100a 27-29, 30-b21, e3. 158b2-4 w. An. post. A2. 72a7-8, etc.). The 'reasons' demanded here are not merely considerations that might happen to convince one or another person initially disposed to deny the conclusion; they are reasons which are naturally prior to that conclusion (An. post. A2. 71 b33-72 3 5 w. Top. Al. 100&29-30, Top. e1. 155b7-16, etc.; there may be more than one such set of reasons: cf. An. post. A 29). And where the projected conclusion is the law of non-contradiction, there are no such reasons available. It is possible to discern in r3 two sorts of considerations 4 f in favor of this view, run together in an argument to show that the law of non-contradiction is the 'firmest' of all laws (lOOSbllff.). One is that there is noth-
ARISTOTLE'S PROGRAM
3
ing better known than that law (1005bi3); the other is (in effect: cf. 1005b14-17, 32-34 with An. post. A2. 723 5-8, 14-18)5 that there is nothing more primary. These considerations ought to be kept distinct; the first is fishy, especially in the light of the argument that supports it, and the second, although more promising, is not argued for in r3. Either of them would be enough to show that no deduction of the law could satisfy the conditions Aristotle places on a proof: they rest on the paradigm ways (apart from simple invalidity and question-beggingness) in which an argument may fail to be a proof in Prior Analytics B16. 64b30-33. We should look at these considerations more carefully: they (especially the first) show a structure that operates in r4 as well. A. The First Consideration: the Cognitive Priority of the Law The law of non-contradiction, Aristotle alleges, is the best known of all principles. This is because what people don't know, they make mistakes about (I005bl3-14), and it is impossible to be mistaken about the truth of the law of non-contradiction (b 11-13, 22-23; cf. KS. 1061 b34-1 0623 2). So it is impossible not to know the truth of that law. The first of the two premisses leading to this conclusion is false: people with true beliefs do not make mistakes either (cf. Plato, Meno 96d and ff.). This is hardly essential; we can take Aristotle to be trying to say: where someone doesn't know something, it is possible for him to be mistaken; since it is not possible to be mistaken here, no one fails to have knowledge here. This revision of the first premiss does not leave it indisputable, 6 but there are enough troubles over the other premiss to make cavils about this one look mean. The other premiss is that it is impossible to be mistaken about the law, that is, it is impossible to believe it false. And for this we are given the following argument (1005b26-32): ... and if it is not possible for contraries to belong at the same time to the same thing ... , and the contrary of a belief is the belief in its contradictory, it is apparent that it is impossible for the same person to believe at the same time that the same thing both is and is not; for someone who went wrong about this would have contrary beliefs.
There is an aura of circularity about this argument, but some of that can be dispelled. The argument relies on a corollary of the principle of noncontradiction, to the effect that contraries cannot belong to the same thing at the same time (this corollary Aristotle establishes in r6. 1011 b15-22).
4
CHAPTER I
So the argument relies on the law of non-contradiction. But this does not make it circular, since it is in no sense an argument for the law of noncontradiction. It is an argument to the effect that if the law is true, it cannot be believed false, and Aristotle is perfectly clear that this is all it is (cf. r4. 1006&3-5). The troubles in the argument lie elsewhere. One is that the law of non-contradiction, which, we are here to see, cannot be disbelieved, is stated in modal form:7 it is impossible for the same thing to belong and not to belong to the same thing at the same time etc. (1005bl9-20; cf. 4. 1005b35-l006&2, etc.). So someone who believes this false need not believe that there is anything that actually possesses both of two contradictory predicates; he need only believe that there could be such a thing. This is not very serious; it is a little hard to picture someone saying: there might be such a case, but I grant that no one could ever believe that there was one. He might, I suppose, say thatB if he were of a sort of Kantian cast, and felt that the laws of thought characterized thinkers more than what they thought about.9 This is a confusion of enormous interest, but rather too much to handle here. Another, related, trouble with the argument is that someone might believe it false that nothing ever possesses two contradictory predicates without believing of anything in particular that it is both a so-and-so and not a so-and-so.1o He might believe it false because (he thinks) he can prove it false, but not believe that he knew of a case in which it comes out false. (Apparently some Greeks believed it possible to trisect an angle with compass and straight-edge without believing of anyone that he had actually done it.) This is not a very serious trouble either, for the same reason: someone who tried to evade Aristotle's argument by printing this out would be accepting an argument that shows it impossible to believe of something that it both is and is not so-and-so, but insisting that it does not touch him, because he only believes that somewhere there is something that both is and is not so-and-so. He would be admitting that if he ever found it, he could not believe that he had found it. The serious trouble with the argument lies elsewhere. Anyone inclined to reject its conclusion will easily find a premiss in it he is equally inclined to reject. And there are people inclined to reject its conclusion; I am, and so, I think, was Aristotle, at least sometimes.
ARISTOTLE'S PROGRAM
5
In Chapter IV, we meet people who "say that it is possible for the same thing to be and not to be, as well as that they think [that it is possible]" (I005b35-1006a2). We are already supposed to have seen that these people are wrong on the latter count, assuming that they are wrong on the former (1006&3-5). So when they say that it is possible for the same thing to be and not to be, they cannot be expressing a belief they actually have (3. 1005b25-26). This is a hard line to stick to; Aristotle himself does not stick to it. In r5, he distinguishes between those who think the law of non-contradiction false as a result of honest confusion and those who adopt the position that it is false merely for the sake of argument (1 009a 1822); all of these people are brought back in at the beginning of r6, and some of them are convinced of the falsehood of the law in 1011a3 and not convinced of it in 1011a10 (cf. r4. 1008b10-27;11 we are going to have to spend some more time with these people later). The author of K has the same difficulty recalling that nobody can believe the law false: he begins Chapter 5 (1061b34-1062a2) by saying that it is impossible to go wrong over the law, and then says that Heraclitus may have "adopted the belief" that opposite predicates can be true of the same thing "without understanding for his own part what he was saying" (1062&31-35). Some fairly famous people have said things that made it ~ound to others as if they wanted to deny the law of non-contradiction. Hegel, 12 Engels, 13 and Kierkegaardl4 did; some writers on Quantum Mechanics have come close. 15 Maybe Heraclitus16 was against the law. Anyone who says something that looks like a denial of the law of non-contradiction presents us with an exegetical problem: is that what he really means? Does he really believe that the law of non-contradiction has to go? But that is a problem, and an exegete who said: no, none of these people really meant that, none of them believed the law wrong, because nobody can believe it wrong, as we learn by studying the logic of belief, would be a very poor exegete indeed. But that seems to be what Aristotle is telling us: here, that they could not have believed what they were saying; in the next chapter, that they could not really be saying it (or, at least, meaning it). The argument he gives us for that depends on a premiss to the effect that"- believes of x that it is F" is contrary to"- believes of x that it is not F" (1005b28-29: "the contrary of a belief is the belief in its contradictory"). To the extent that one is inclined to suppose that these peo-
6
CHAPTER I
pie might have believed what they said they believed, one will be inclined to deny that these predicates are contrary (unless one is inclined to reject the law oneself). That is, the argument will look circular, with the circle closing at this premiss. Aristotle gives no reason in r3 for accepting this premiss. Is there any? De interpretatione 14 was taken by Alexander (in Met. 270. 24-25) and Thomas Aquinas (in Met. n. 602) to provide reason for accepting it; more recent commentators1 6a tend to find that chapter hopeless. There is a lot of confusion in it, but there are also arguments for our premiss, that believing something is contrary to believing its contradictory. Here is a highly distilled version of two of those arguments (the distillation is carried out in an appendix to this study). Suppose Callias is just. Then someone who believes of him that he is just is right, someone who believes of him that he is not just is wrong, and someone who has no beliefs on the issue is neither. Nobody can be both right and wrong. So nobody can believe of Callias both that he is just and that he is not just. But somebody might be neither right nor wrong, if he believed neither. So believing of Callias that he is just is contrary to believing of him that he is not just. (This comes from 23b7-27 and 27-32 under torture: see appendix.) It had better be kept clear that this argument does not show that the belief that Callias is just is contrary to the belief that he is not. Aristotle does not keep this clear in De int. 14. He takes the argument (or the arguments he actually gives, from which this is derived) to show that the beliefs are contrary, and hence that the statements that express those beliefs are contrary (cf. 23&27ff., and appendix). Elsewhere, Aristotle knows perfectly well that these two statements, 'Callias is just' and 'Callias is not just', are not contrary but contradictory (Cat. 10. 13b27-35; cf. De int. 10. 20&16-30). Here he comes out on the opposite side. So his result cannot really be put as 'believing something is contrary to believing the contradictory of that belief'; it would have to read, rather, 'the belief, about x, that something is true of it is contrary to the belief, about x, that the contradictory of that something is true of it'.16b If Aristotle had kept straight on the distinction between believing something and the belief one has, the result he would have had would not be that the statement, about Callias, that he is just is contrary to the statement about him that he is not, but that saying of him that he is just is
ARISTOTLE'S PROGRAM
7
contrary to saying of him that he is not: that is, that you cannot say both of two contradictory things of him. This result is close to matters that will concern us in dealing with r4. What, then, about the argument itself? It depends on the claim that someone cannot be both right and wrong at the same time. And that is not as plausible as it may look. People are not simply right or wrong; they are right or wrong in believing something, or saying something. If Callias is just, one would be right in believing him just, wrong in believing him not to be just. So someone who had both beliefs would be, to put it misleadingly, both right and wrong at the same time: right in the one belief, wrong in the other. Indeed, at that rate, most of us are both right and wrong at almost any time, since most of us, at any given time, have some beliefs that are true and some that are not. It is silly to put it this way; someone who says 'nobody can be both right and wrong at the same time' plainly means by 'at the same time' something like 'in the same belief', so that these cases would not strike him as challenging what he says. But the point remains: people are not simply right or wrong at a time; they are right or wrong as to what they believe. It would not help to try to revive Aristotle's argument by lumping the belief that Callias is just together with the belief that he is not into a single belief, with reference to which someone would have to be both right and wrong if he held it. For if the law of non-contradiction holds, he is not both right and wrong in the belief that Callias is just and not just: he is simply wrong.
B. The Second Consideration: The Logical Priority of the Law The law of non-contradiction is "by nature the principle [or 'startingpoint'] for all the other axioms" (r3. 1005b33-34); this priority over other axioms dictates that "everyone who proves [anything] comes back to this belief in the end" (1005b32-33).16c And it is a further consequence of this priority that anyone who is to learn anything will have to accept this law (1005b15-17; cf. A.n. post. A 2. nat6-18, and perhaps A 10. 76b23-24): however much the rigid picture painted in the Posterior A.nalytics may have faded, Aristotle still tends to see the matter of teaching and learning as one of presenting and accepting proofs17 (cf. A.n. post. AI. nat-17, Soph. el. 2. 16Sa38-bll, Top. Z4. 141a26-31, Met. AlO. 992b24-33, etc.).
8
CHAPTER I
Placing the law of non-contradiction at the head of "all the other axioms" would set it over such laws as that of excluded middle. 1 7a We need not be concerned with this particular aspect of Aristotle's views: his response to deniers of the law of excluded middle in r7 may presuppose some sort of acceptance of the law of non-contradiction, but he makes no explicit appeal to the latter law.Is It would be enough if we could see reasons for the weaker view of B 2. 996b27-31 that includes the law of noncontradiction, the law of excluded middle, "and other such premisses" (Kai ocrat liA.A.at -rotaU-rat 1tpo-ramn~, b30-31) among the "demonstrative principles, ... I mean the common beliefs from which everyone conducts proofs" (cf. B l. 995b8-10, An. post. A10. 76b14-15, A 7. 75&41-42). That is, it would be enough if we could see what it is that gives priority at least to the simpler laws of logic. Seeing that need not involve finding any of the simpler laws of logic lurking as premisses in every argument, even if these passages make it sound that way. Elsewhere Aristotle is more cautious:I9 at An. post. A 10. 76b14-15 he talks of the 'axioms' (which include the simpler laws of logic) as "the things from which in the first instance [people] conduct proofs", which suggests that they are premis~es in those proofs, but he has just said that proofs are conducted by means of (Sta) the axioms from (&K) things previously demonstrated (76b10-ll; cf. A 32. 88a36-b3; but notice that 'Sta' covers premisses in Top A l. 100&26, a28, 93.158b2-3, 7, Soph. el. 1.165&2). Some of our contemporaries might say: these 'axioms' are really rules of inference, not premisses2° (but it would be a little tricky to state the law of non-contradiction as a rule: see below). In any case, Aristotle himself points out that the circumstances under which the law of non-contradiction is needed as a premiss are limited (A 11. 776 10-21). So what we should have to show, to make out Aristotle's case, is that the law of non-contradiction, or any other law we want to pick, is somehow presupposed by every demonstration, or by the practice of proving or arguing. We should have to show that failure to observe the simpler laws of logic would ruin demonstrations. Put that way, it may seem as if the question answers itself: the laws of logic are the regulative and constitutive principles of arguing; they are prior to anything anyone might want to prove because in their absence there is no such thing as proving. But it is not that simple, for none of this tells us what the laws of logic are, and so gives no priority to the law of
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9
non-contradiction, that of excluded middle, that of distribution, or whatever, over anything. I have brushed aside the task of showing the law of non-contradiction prior to any other particular (simple) law of logic, but that leaves the task of showing the law of non-contradiction, or that of excluded middle, or some other particular law of logic to be prior to the non-logical conclusions people want to demonstrate. Some quantum mechanics have wanted to (do something like) reject the law that distributes conjunction over negation ('p(q v r) ::::> (pq v pr )'); they have wanted to say something a little like "It doesn't follow from the fact that the particle got here either through this slit or through that one that it either got here through this slit or got here through that one". 21 They are, that is, concerned to deny the validity of an argument, and so concerned to reject a presumptive law of logic. They are not concerned to deny all the laws of logic at once, but only that law which would make this argument valid.22 Some Hegelians and neo-Marxists have acted as if they wanted to reject all the laws of ('formal') logic at once, sa and their fish are in a different kettle. But it will not do to say against the quantum logicians "But look, in the absence of laws of logic there would be no arguments at all, even yours", for this tells us nothing about the law of distribution. The pattern that is supposed to show the priority of the law of noncontradiction, or of whatever law you pick, is close to that of a 'transcendental argument'24: we are supposed to see that there is a certain practice, that of arguing, and that the law of non-contradiction is fundamental to that practice. The point here is that if this pattern is to be used in support of any particular presumptive law oflogic, what has to be shown is that that particular law is fundamental to the practice. The Hegelian and neo-Marxist rejections of 'formal logic' ought, I think, to be taken as abandoning the practice, or, at least, demoting indulgence in it to lower courts of appea1.25 It may be that Gorgias' treatise On Nature, or that which is not was a similar sort of rejection of the practice, 26 and Aristotle may have written a response to it,27 but the task of supporting the claims of r3 is not that of responding to any such position. It is the more specific one of showing Leibniz right in saying2s: the principle of contradiction is the principle of all truths of reason, and if it is given up, all reasoning is given up.
Aristotle does not take up this task. It may sound, from the end of r3,
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as if he had concluded that the law was fundamental to argument on the ground that it cannot be disbelieved: after giving his argument for this latter claim (our 'first consideration'), he says (1005b32-33) That is why everyone who proves [anything] comes back to this belief in the end (81.0 navt~ of. dno8Et1CV6vt~ d~ ta6tTJV dvayouow AaxatTJV 86l;av).
But it would be a mistake to suppose that he takes the connection between our two considerations to be that the second follows from the first: it is rather that the impossibility of disbelieving the law entitles people who are proving things to fall back on it without further argument for it. Aristotle's picture is this: Knowledge largely comes of proof, and knowing anything as a result of proof depends on knowing the ingredients of the proof. Some of these ingredients will be known by prior proofs, whose ingredients will also have to be known, and so on. A properly constructed chain of such proofs will constitute a branch of knowledge, a 'science', the boundaries of which will be determined by a genus. And there will be a range of ingredients in its proofs knowledge of which does not come of further demonstration (cf. An. post. A3, esp. 72b18-22). One's knowledge of these primary ingredients (or, at least, one's confidence in them) must be firmer than one's knowledge of (or confidence in) any of the things whose knowledge rests on them (cf. An. post. 12&25-32, Top. Z4. 141&28-30, etc.). Some of these indemonstrable, primary ingredients will be peculiar to the genus covered by the science, others common to it and other genera (A 10. 76&37-38). The 'peculiar' ones you need not have when you come to class (A2. 72&14-16): you will have to accept them to get on with learning the science (cf. Soph. el. 2. 165b1-3, 11. 172&27), but they can be motivated for you (not proved to you: Soph. el. 11. 172&12-13), perhaps by engaging in a bit of dialectic (Top. A2. 101&36-b4; cf. Top 95.159&28-30).28a The 'common' ones are stickier, for even dialectic operates within these (cf. Soph. el. 11. 171 b6-7, 172a23-b1 ). So if you do not have these when you come to class, you might as well not come. But, fortunately, these ingredients (our 'simpler logical laws' are included, especially that of noncontradiction) are intrinsically credible (An. post. A 10. 76b23-24; cf. Soph. el. 11. 172&33). In the particular case of the law of non-contradiction, indeed, no one can believe it false. So it is all right that everyone who proves anything comes back to this belief in the end.28b That, I take it, is what stands in back of 1005b32-33. So Aristotle does
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not undertake to show the law of non-contradiction fundamental to all proof or argument in r3. He might have had trouble showing that. On the face of it, there are a great many arguments that do not depend for their validity on the law of non-contradiction. The construction in Euclid's First Proposition depends on an argument to the effect that (Pl)
(The line) AC is equal to AB, and BC is equal to AB,
(C)
AC is equal to BC.
so
If we treat (P2)
Things equal to the same thing are equal to each other
as a premiss (for Aristotle it would have been an 'axiom'),29 the whole argument has the form '(Pl) and (P2); therefore (C)'. Suppose someone is bent on breaking the law of non-contradiction. He might say "Not (C)". But if this is to count as breaking the law of non-contradiction, he will have to say " ... and (C)". So there is no reason why he should reject the argument. He might try asserting the negation of either premiss. But, again, he can only break the law of non-contradiction by asserting the premiss or premisses he has negated as well, and, again, this need not involve rejecting the argument. Part of the trouble is that the law of non-contradiction is not a rule of inference, anyway. Modus ponens is a rule of inference: it tells you what to infer from what. The law of non-contradiction does not tell you what to infer, or what not to infer. If it tells you anything about what to do or not to do, if it is a rule at all, it tells you what to reject, or what not to accept. Then it can be compounded with rules of inference (modus to/lens, say) to give other rules of inference (reductio ad absurdum). But then it is not something on which every inference depends.29a. The situation may seem a little more like this: Part of the point of the practice of inferring is that it gets us from things we accept to other things we are then bound to accept. The law of non-contradiction is fundamental to our accepting things; accepting what someone says (whether as a result of argument or not) seems to conflict with rejecting what he says, and accepting the contradictory of what he says seems to be one way of
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rejecting what he says. 30 You may sound as pleasant as possible when you say "Yes, what you say is so; and so is the opposite", but I should find it hard to count that as agreement. Leibniz may be getting at something like this when he says that the principle of contradiction must be 'primitive',31 since otherwise there would be no difference between truth and falsehood; and all investigation would cease at once, if to say yes or no were a matter of indifference.
But this sketch of the situation is at best preliminary. First, relating acceptance, rejection, agreement, and formal contradiction in this way sounds dangerously close to the argument we were just considering to the effect that believing something is incompatible with believing its contradictory. And whatever doubts may have been raised about that argument have parallels for this one: one can imagine Lenin and Mao agreeing that the particle was there at noon and wasn't there at noon; or, at least, one can imagine them saying something to that effect to each other, and giving all the signs of agreement. But we are not really done with this sort of argument yet. Second, the notion of what one is 'bound to accept' is far from clear. If we were logicians, we might be judged incompetent for accepting too many contradictions; our jobs might turn on that, and so we might be bound to reject them. One of Wittgenstein's interlocutors says "But there is a contradiction here", and one of Wittgenstein's personnae responds "Well, then there is a contradiction here. Does it do any harm here?" 32 And one of the responses to all of this is: if you say that sort of thing, you're no longer doing mathematics. 33 But things are not that clear. Some mathematicians have allowed that the law of excluded middle breaks down in some cases; they still talk like mathematicians. So we might indulge in a practice sufficiently like mathematics, or logic, to warrant the label, and still find it feasible to allow a contradiction to go by here and there. When we are told that we are bound to accept the consequences of what we already accept, and bound to reject their negations, it is not at all clear what we are being told. What is the penalty for breaking the law? (Someone is bound to say: but if you accept a contradiction, you're committed to everything, because a contradiction entails anything. This is a conversational gambit. There is a formal argument to show that a contradiction entails anything. 34 But there are formalizations of element-
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ary logic in which that formal argument fails. 35 There are reasons for not employing these latter formalizations: they are extremely difficult to work with. But they are not impossible to work with. So the claim "a contradiction entails anything" comes at best to this : the easiest formalization of elementary logic to work with is one in which a contradiction entails anything. So what that claim at most supports is that it is easier to accept the law of non-contradiction than to reject it. But that does not mean that the penalty for rejecting it is acceptance of everything.) The law of non-contradiction is certainly in some way fundamental to the business of accepting or rejecting what people say, agreeing with them, and so on. (If Mao, after agreeing with Lenin that the particle was there and not there at noon, goes on to say "and it also wasn't both there and not there at noon", things begin to fall apart; cf. r4. 1008&3-7, 30-34.) And in that way it is fundamental to argument. A valid argument might be characterized as one in which you cannot consistently accept the premisses and reject the conclusion. The notion of consistency is fundamental to this characterization, and the paradigm inconsistency is an outright contradiction. 36 But this puts some difficult notions (accepting and rejecting) between the law of non-contradiction and the notion of validity. Wholesale, or arbitrary, abandonment of the law of non-contradiction might leave us without a handle on the notion of intellectual agreement. But, first, it is not clear how much we need that sort of intellectual agreement, and, second, even allowing that we need a good deal of it to cope with things, it is not clear how much of it we would be giving up if we let the law of non-contradiction slip now and then. This inconclusiveness is disappointing. But there is enough here to get on with. The wholesale or arbitrary abandoning of the law of non-contradiction might leave us without a notion of acceptance, or agreement, and that gets especially clear if we consider what it would be like to try to prove to someone who has abandoned it wholesale, or who abandons it when he feels like it, that he is wrong in doing that. He might reject the consequences of what he had accepted, allowing that they are consequences; he might accept them and accept their negations; he might do anything. There would be no way of proving the law to him, and no way of getting him to reject its denial, if he did not want to. Against this background, let us see how Aristotle thought we might cope with someone who wanted to deny the law of noncontradiction.
14
CHAPTER I II. ARGUING 'BY WAY OF REFUTATION'
In 1()()6a5-ll, Aristotle says that the law of non-contradiction cannot be proved; in all-12, he says that it can be proved by way of refutation.a? There is no point in picking at his words: either the second use of 'prove' here is looser than the first, and that does happen elsewhere in Aristotle38 (cf. Rhet. ri3. 1414a31-37, Soph. e/. 5. 167b8-9 and ff., An. pr. B27. 7Qa6-7), or, better, 'proving by way of refutation' is no more a sort of proving than a dead man is a sort of man (cf. De int. 11. 21a5ff. on '&:ttA.&q,', 'simply'; on proving 'simply', cf. K5. 1062a2-3, quoted just below, and Met. A 5. 1015b838a, An. post. A9., esp. 76a13-15, etc.). The sorts of procedures he has in mind are discussed in some detail in Topics essb and the Sophistic refutations; from here on, we shall make a good deal of reference to these books. sse He does not mean that it is possible to prove the law by a reduction to absurdity. He does not use the word 'refutation' (&A.erxoq,) to mean that, but to mean an argument that comes out with a conclusion that is the opposite of what your opponent wants to assert (cf. An. pr. B20. 66bll, Soph. el. 5. 167b21-27, 1. 165a2-3, 15. 174bJ9-23, Rhet. B22.1396b22-27, 23. 1400b26-29, ri 7. 1418bl-4.)39 What is essential here is the presence of an interlocutor whose views you are attacking, and who responds to your attacks: the refutation proceeds by getting him to grant things that lead to the downfall of his view. Aristotle makes the essential presence of an interlocutor pretty clear when he says (1006at5-18): I mean 'proving by way of refutation' to differ from 'proving' in that [here,] in proving [the law of non-contradiction], one might seem to beg the question, but where someone else is responsible for this, there will be a refutation, not a proof.
So the author of Metaphysics K 40 is not far off in paraphrasing this: he says (5. 1062a2-3; cf. a30-31, and r4. 1006a25-26): "In such matters there is no proof simply, but against a particular person, there is" (1tepi 'tiDV 'tOtoi:mov ci1t'A&q, Jl&V OUK &crnv (mooet~tq,, 1tpoq, -r6voe o& &crnv). I hereby christen Aristotle's interlocutor, the man who wants to deny the law of non-contradiction in r4, 'Antiphasis'. Let us have one thing clear now: Antiphasis, for all I know, never existed. In chapter III, I shall try to construct a position for him using various historical elements. But iYf ~ for my purposes, only a construction out of those elements and what Aristotle says to him.
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Thomas Aquinas paraphrases the phrase "against a particular person"41 as "ad hominem" (in Met. n. 2213); Ross translates it that way. That Latin is a literal translation of the phrase "npoc; 'tOV liv9pO>nov", which Aristotle uses in a similar connection in the Sophistici elenchi (22. 178b17, picking up similar phrases from 8. 170&13, 17, 17-18, 20. 177b33-34, 33. 1836 22, 24; cf. Top. 911. 161 6 21).42 But under that translation, the phrase suggests sophistry and illusion: isn't the argumentum ad hominem a well-known fallacy? Cohen and Nagel in their Introduction to Logic and Scientific Method48 tell us that The fallacy of the argumentum ad hominem, a very ancient but still popular device to deny the logical force of an argument (and thus to seem to prove the opposite), is to abuse the one who advances the argument.
And we have only to look at such passages as r4. 10066 13-15, 1008b7-12 (cf. 10076 19-20) to find Aristotle suggesting that if his opponent doesn't play along, he is no better than a plant. That is abuse, isn't it?44 So we had better consider the general question: is Aristotle recommending that we deal with Antiphasis by perpetrating sophistry and illusion 1 The answer to this question is that he is not. But it is not obvious that this is the answer. I think we can see what Aristotle is recommending by seeing how the charge misfires. First, consider the charge in its most general form: Aristotle is selfavowedly arguing ad hominem. Here we have been misled by very recent history.45 When Locke made the phrase 'argumentum ad hominem' part of the vocabulary of modern philosophy, he did not make it describe a fallacy, or anything like what Cohen and Nagel give us. He meant to be enumerating (Essay IV xvii. 19, his italics):46 four sorts of arguments, that men, in their reasonings with others, do ordinarily make use of to prevail on their assent; or at least so to awe them as to silence their opposition.
And the third of his "four sorts of arguments" is to press a man with consequences drawn from his own principles or concessions. This is already known under the name of argumentum ad hominem.
This is no fallacy.47 And it describes Aristotle's procedure pretty well: he begins by getting Antiphasis to say something (10066 11-13), and it is Antiphasis who is responsible for his own downfall (6 17-18, 25-26). There is no suggestion in this that the argument against him will tum on fallacies.
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But we cannot leave it at that. In the Sophistici elenchi, Aristotle contrasts argumentative moves that are directed 'against the man' with ones that are directed against his argument. And the ad hominem moves are very second-rate at best. A dissolution of somebody's argument that is ad hominem is not really a dissolution (20. 177b31-34, 22. 178bl6-23). We found in Metaphysics K 5 a contrast between a proof 'simply' and a proof ad hominem. Aristotle has, in the Sophistici elenchi(8. 1703 12-19), a similar contrast between a refutation 'simply' and a refutation ad hominem; ominously, sophistical refutations are of the latter sort, 4 8 and sophistical refutations, of course, do turn on fallacies, falsehoods, and other foul things (cf. Soph. el. 1). But it would be a mistake to rely on these impressions of shady dealing to conclude that the contrast drawn in Metaphysics K between a proof and an ad hominem proof is that between proof and sophistry. The argument he is about to take up, there and in r, is one in dialogue, against an interlocutor. Every argument in dialogue is an argument against someone (cf. Top 91.155bl0, De caelo B 13. 294b7-13), and every refutation, as r uses the word, is an ad hominem refutation. Some are merely ad hominem; that is true of the pseudo-dissolutions of the Soph. el., but it is not the business of dialectic to increase our stock of these (cf. Rhet. A2. 1356b33-37). Some of these arguments in dialogue can be converted into proofs; these are the ones that obey the priority restrictions touched on before, and other restrictions: at least in the Organon, the restriction that they stay within a genus. Other arguments in dialogue are not rewritable as proofs. Some of these are not rewritable as proofs because they are simply bad arguments: here we find sophistic refutations. Others are not rewritable as proofs because they fail to obey the restrictions, even though they are not simply bad arguments. (Cf. a parallel point made about definitions: some are intelligible 'simply'; some to particular people, who may need a definiens composed of words they understand; Top Z 4 .141 b}S142316.) For example, in Physics A 2-3, Aristotle attacks the Eleatics. They had said that what is is one and unchanging (184b25-26). The arguments Aristotle works up against them are not, he insists, the sort of thing a serious physicist (student of nature, natural philosopher) should take up in doing serious physics. Rather, they are to be taken up in discussing interdepartmental affairs (cf. 1853 2-3 with 1853 20) "consideration [of these
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matters] is of philosophical interest", exet yap q>tA.oao
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thesis were an independently plausible one (a 'simply' plausible one: "&t ()' fiv()o~oc; d1tA.illc; ft 9tcnc;", Top. 95. 159bl6-17}, the conclusion toward which Aristotle would be driving, the negation of that thesis, would be implausible: so he would be expected to concede to Aristotle only what is independently plausible, or, at least, less implausible than Aristotle's projected conclusion. (159bl6-20). Or if his thesis were not independently plausible, but plausible to him, his guide in answering would be his own views (159b26-27). And if the answerer is defending the view of someone else, it's clear that he ought to grant or deny each point with an eye to the thought of that someone. That is why those who bring in the views of others, e.g., that good and evil are the same thing, as Heraclitus says, 5 1 b will not admit that contraries cannot belong to the same thing at the same time- not because this is not plausible to them, but because, in line with Heraclitus, that's what one ought to say. Those who trade off theses with each other&lc also do this: they aim at answering as would the [original] poser [of the thesis]. (8 5. 159b27-35)
So taking up a thesis 'for the sake of argument' does not make one immune from critici~m. But, in the case of Antiphasis, there is a special difficulty. His thesis is a peculiar one: it is the denial of the law of non-contradiction, and that is something with a high degree of independent implausibility. Indeed, if Aristotle were right in saying that it could not be believed, it would be off the end of the scale. And where the thesis is implausible, the answerer is expected to concede only things more plausible than its negation, the proposed conclusion (5. 159b8-16, 6. 16()&14-16, 11. 16lb30-33). But the proposed conclusion is the law of non-contradiction, than which nothing more credible can be conceived. These features make things like the law of non-contradiction terribly difficult to deal with by dialectical methods (cf. 93. 158&3I-b4). Most often, dialectical debates discuss things no more abstract than the principles that govern particular sciences (cf. Top. A2. 101&36-b4).5ld But they can be carried out over inter-science principles (cf. Top. 93, 14. 163b17-20, Soph. el. 11. 172&18-20), and that is what is going to happen in r4. In r2 we are reminded of the difference between dialectic and philosophy: roughly, dialectic is the skill of arguing either way on anything that comes up, especially inter-departmental affairs; philosophy chooses among the arguments and lays out the truth (cf., with r2. 1004bi7-26, Top. A 1. 100&18-21, 91. 155b7-16, 11. 161 &24-37, 14. 163b9-16, 164bl-4, Rhet. A4. 1359b10ff.).5le It is difficult to see what the finished science of
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philosophy would look like (cf. p. 2 above), but dialectic is plainly the way into it, and r3 tells us that it will cover laws like that of non-contradiction. So we need some sort of lever with which to pry Antiphasis loose from his denial, and that lever is to be provided by the simple fact that he is willing to argue with us. Any dialectical debate, the one with Antiphasis included, has to stay within laws of logic (cf. Soph. el. 9. 170&34-b3, bS-11, 11. 171b6-7, 172&19-21). Then if Antiphasis is going to join us in argument, he will have to leave some logic standing. And so, Aristotle thinks, he will be responsible for his own downfall, "for while he does away with argument, he puts up with argument" (4. 1006&25-26: &.vatpii'lv yap Mrov 01toJ,ltv&t Myov cf. 6. 1011&21-24).52 At bottom, those who, like Antiphasis, demand that they be shown wrong in denying the law of non-contradiction, or in espousing extreme subjectivism, demand something impossible: they are asking to be contradicted, but they themselves propound contradictions at the drop of a hat (6. 1011 a 15-16 ;sa cf. Plato, Euthd. 286de). It ir. in this sense that the arguments of r4 are essentially ad hominem: Antiphasis' willingness to take up an argument seals his doom. So far, there is nothing on which to base a charge of sophistry. Still, we noted that the dependence of the practice of argument on laws of logic does nothing to support any particular law of logic. So there is going to have to be more to the argument than simply pointing out to Antiphasis that he is willing to argue. And what more there is brings us close to another argumentative technique commonly accounted dubious. Aristotle is terribly concerned not to "seem to beg the question" (4. 1006&17, 1008b1-2). And a glance at KSwill suggest that that is as far as his concern goes (1062&5-11): Against somebody who makes opposite assertions, someone who is showing him wrong ought to get [from him] 58a something that is the same as the claim that it is impossible for the same thing to be and not to be in one respect at the same time, but which he does not think is the same; for only in that way can [anything] be proved against someone who says that it is possible for opposite assertions to be true of the same thing.
One common feature of Aristotle's talk of begging the question in the Organon is the idea that where some premiss of an argument is really the same as, or merely a more general form of, the conclusion, however disguised, the question has been begged (cf. Top. 913. 162b34-163&13, Soph.
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el. 5. 167&36-39, An.pr. B 16. 64b38ff.). So, it appears, Aristotle's concern is not to avoid begging the question, but to avoid seeming to beg the quesstion. In the Topics (911. 161bll-18), he remarks that blame for begging the question in an argument in dialogue should be heaped on the respondent, who failed to see it happening. And, although that certainly squares well with Aristotle's claims in r that it will be Antiphasis who is responsible for his own refutation, it is likely to seem cold comfort. If the refutation of Antiphasis turns on his failure to see his way past Aristotle's questions, won't that refutation be ad hominem in a bad way? At least, you won't be able to run the same refutation on him twice. How serious is this charge? A bald accusation of question-begging is not worth much;54 it depends for its force on just how close the disguised premiss is to the proposed conclusion. If the disguise is a good one, the argument that draws the conclusion out of it may be of enormous value just because it removes the disguise. Aristotle drops one of his arguments on the ground that the charge of question-begging would be too easy; the argument would look like this (1008&34-b2): Aristotle: When an assertion is true, isn't its negation false? Antiphasis: Yes. Aristotle: And when the negation is true, isn't the assertion false? Antiphasis: Yes. Aristotle: So the assertion and negation can't be true at the same time.
He does not say just where this begs the question; presumably it is at the first step. It would be a more obvious case of begging the question if one of the steps were Aristotle requesting Antiphasis to concede that nothing can be true and false at the same time, but he does not record this step. In any case, Aristotle is plainly right to drop this argument: the disguise here is not good enough to make its removal interesting. One theme that crops up more than once in Aristotle's remarks as to what a dialectician ought to do when he has to deal with theses involving things as fundamental as the law of non-contradiction is: we need a definition (Top. 93. 158&33, 37-b4, bl6-17, 20-22, Met. r7. 1012&21-22). Most of the time, he seems to be thinking of a definition for some key logical term: 'contrary', 'true', etc. But the first of the arguments ofr4, to which I am about to turn, is an attempt to show that an instance of the law of non-contradiction is lurking in the definition 'man' signifies biped animal,
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or in any definition in that form. Removing that disguise is of some interest. And removing it from definitions in this form is of interest, since if Antiphasis is going to argue with us, he is going to have to say something, and so allow that some words signify something. Aristotle's idea is that allowing that is allowing that some such definition as the above will work. If so, it is Antiphasis' willingness to talk at all that commits him to the law of non-contradiction, and we have got what we wanted. Let us look at the argument.
NOTES Kirwan (AM 90) suggests that Aristotle might mean only that we do not need a proof of it. I do not see this. K 5. 1062"2-4 (which he cites) says the stronger thing (but seen. 4f below on K), and is borne out by r 3. 1005b13-14, 6. 1011 8 11-13; cf. also An. post. A 3, where Aristotle goes from 'you can't prove everything' to 'there are some things that can't be proved' (Kirwan, p. 91, denies this, but cf. 72b18-22). a He'd have been wrong if he had meant that. In Russell and Whitehead's Principia Mathematica, a work of later antiquity, the law of non-contradiction (3.24) is proved via the law of excluded middle (2.11), a 'DeMorgan' law (3.1; 3.01), etc. a If Anscombe ('Aristotle', pp. 39ff.) and others were right, this would not be so: cf. Chapter V, Section II below, and next note. 4 Particularly given the occurrences of 'necessarily', 'possible', and so on. A lot turns on the scope of these words: Anscombe (foe. cit.) takes them to cover the apodosis of the conditionals and the second conjunct of the conjunctions that follow them; I take them to cover the entire conditionals and conjunctions. Nothing in the Greek tells either way. Mine is a simpler way to begin with; I think it is a simpler one all the way through. But cf., again, Chapter V, Section II. 4" The expression 'common [things]' is ambiguous between propositions and properties; so is 'common principles'. This sort of difficulty becomes important much later (in Chapter VI below). 4 b Although 'al;(roJ.la' covers also the basic elements (propositions or properties) peculiar to a science, as in Met. B 2. 997"7: cf. Ross' note ad An. pr. B 11. 62"13 (APPA 452). The word comes, I imagine, of dialectical practice: it signifies the demand one places on one's interlocutor, and is the noun-correlate of the verb 'al;toOv', which Aristotle uses for the placing of that demand (the question would have the form 'isn't this so?'): cf. Top. 9 1. 155b15, 156"23-24, 3. 159"4, 7, 6. 1608 7, 10. 160b29, 13. 163"3, Met. r 4. 1006"10, 19. Cf. also Kirwan, AM 86. 4c Cf. Ross, AMi. 229-30 (ad 997"2-11). 4 d This seems to be Owen's suggestion: cf. "Logic and Metaphysics" pp. 178-79. Cf. also 'Aristotle on the Snares of Ontology', p. 84. 4e Cf. Kirwan, AM 86-87. 4f K 5. 1062"3-5 only mentions the first of them. There is some doubt as to the authorship of K: cf. DUring, Aristote/es 278-79. According to S. Mansion, 'Les apories de Ia Metaphysique aristotelicienne', published in 1955 (n. 47, p. 152), no one since Natorp ('Dber Aristoteles Metaphysik, K, 1-8, 1065"26', published in 1888) has really had 1
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serious doubts. But she raises some herself (cf. n. 67, pp. 160-61), and some of my friends have raised others. So I have tried to avoid relying on K. 6 I do not agree with Ross (APPA 509 ad 11 b19-23) that 'primary' in b21 and 'prior to' in b22 have to do with different sorts of priority. Ross thinks that 'primary' in b21 just means 'immediate'; i.e., "that the premisses must be such that the predicate attaches to the subject directly as such, not through any middle term". But 72•8 defines 'immediate premiss' as 'premiss to which none is prior'. So Aristotle's picture must be that, as you run back through the proofs to their premisses, and through the proofs of those premisses to their premisses, and so on, you are getting closer to the primary, immediate premisses: and one premiss is prior to another if it is closer to the primary ones. 8 Cf. Wittgenstein, PI p. 221: "'I know .. .' may mean 'I do not doubt .• .' but does not mean that the words 'I doubt .. .' are senseless, that doubt is logically excluded." 7 This point and the next are raised by Barnes, 'The Law of Contradiction', p. 308. a Barnes, 'The Law of Contradiction', pp. 307-08, seems a little worried about the modality of Aristotle's conclusion: it is not possible to believe the same thing to be and not to be; I do not see why. The premiss is "it is not possible for contraries to hold of the same thing", and if beliefs in contradictories are contrary beliefs, it follows that it is not possible for those beliefs to attach to the same person. Barnes does not make his worries into an objection, and seems willing to allow these occurrences of 'possible' to stand. 9 Lukasiewicz, in 'On the Principle of Contradiction', pp. 506-09, sounds something like this. 1o Cf. Barnes, 'The Law of Contradiction', p. 308. 11 Kirwan, AM 106-01, notes and comments on this inconsistency; he thinks it better to deny these people their beliefs. lll Cf. Science of Logic 2, 67. Contrast McTaggart's interpretation (which, I think, is right), in Studies, pp. 8-10. 1a Cf. Anti-DUhring, p. 132 (quoted below, Chapter II, Section II). 14 Cf. Concluding Unscientific Postscript, pp. 510-11, Philosophical Fragments, Chapter III. Contrast the interpretation of N. H. Soe, 'Kierkegaard's Doctrine of the Paradox.', pp. 218-20. 15 Cf. Putnam, 'Is Logic Empirical?'; Finkelstein, 'Matter, Space and Logic'. There is no suggestion here of giving up the law of non-contradiction, but I have heard it suggested in discussions of the issues dealt with in these papers. See also p. 9 and n. 21. 18 He certainly said things that make it look as if he was: cf. DK 22 B 10, B 49&, etc. And by the time of Sextus, he was taken to be against it: cf. HP I 210-11, II 63. Later people infiuenced by him were given to uttering similar paradoxes: cf. [Hippocrates] De victu I 4, 5, 11, 15 (Kirk suggests the later fourth century for the writing of this, and Peripatetic infiuence: cf. Heraclitus, p. 169n.), and [Hippocrates] De nutrimento 19, 44, 45 (with which cf. Heraclitus, DK 22 B 60). (Kirk's suggestion for the date of this is the first century A.D.: ibid., p. 117). 18a Bonitz, AM 186 makes no comment on De int. 14 other than "(cf. de interp. 14)". Cf. Barnes, 'The Law of Contradiction', p. 307. Kirwan (AM 89) thinks it may not be relevant. 18b This paraphrase preserves a feature of Aristotle's discussion in placing 'x' outside the context set up by 'believes that'. This helps preserve an ambiguity like that men-
ARISTOTLE'S PROGRAM
23
tioned inn. 4a above: here, in the word 'belief', which might cover the entire proposition believed (that Callias is just) or the predicable (that ... is just). The latter sticks to the letter of the construction 'believes of x that he is just', and, so taken, the construction is 'referentially transparent'; the former alternative would make it 'referentially opaque'. It may be that this difference is at issue in Plato's discussion of false belief in the Theaetetus: cf. C. J. F. Williams, "Referential Opacity and False Belief in the Theaetetus". That would be of some importance: false belief and false statement are going to occupy us later (cf. Chapter III, Section 10. 16c Or "come to this ultimate belief". I have used Kirwan's translation of the phrase. 1 7 cr. Barnes, 'Aristotle's Theory of Demonstration'. But I do not want to endorse all of Barnes' views. 17a That need not commit him to the view that all the rest of the laws of logic are derivable from the law of non-contradiction (cf. Wieland, Die aristotelische Physik 2 p. 212, n. 11): only, perhaps, that any proof of any other law would involve it, and that this is the only law of which that is true. This, I think, is still a mistake, but it is not the same mistake as that of saying that all logical laws can be justified solely by the law of non-contradiction (as, it seems, Kant says: cf. Critique B 190, and Kneale and Kneale, Development of Logic, 357-58). 1s cr. Maier, AS i 83: Aristotle does not try to derive the law of excluded middle from that of non-contradiction. Depending on how one reads De int. 9, one might take it that Aristotle would be prepared to give up excluded middle without giving up non-contradiction in the face of certain facts about the world (those mentioned in 198 7ff.). Cf. here D. Frede, Aristoteles und die 'Seeschlacht', Ch. iv. 19 For the following, cf. Ross, APPA 531-32 ad 75 8 41-42, and Mure's n. ad loc. in the Oxford translation. 20 The locus classicus for this distinction (not the terminology) is Lewis Carroll's 'What the Tortoise Said to Achilles' (1895). But it ought to be noted that Carroll's argument comes nearly straight out of Mill's System of Logic II. vi. 5. 21 Cf. refs. in n. 15, and the exposition in Fine, 'Some Conceptual Problems of Quantum Mechanics'. 22 Fine, pp. 10-14, argues against these people. One of the arguments he gives looks like it involves something like the mistake I am talking about in the text. We begin (p. 12) with a hypothesis H, assumptions A, and a (purported) logical consequence C. The law of logic that gets us C from Hand A is labelled 'L'. The quantum logician wants to accept H and A but reject C; so he want~ to reject L. For that to work it must be that 'Hand A imply C' is a consequence (this is the word Fine uses) ofL. Fine asks "why is it a consequence of L that Hand A imply C? Presumably the answer here is to be provided by showing that this consequence is derivable from L. But now we seem to be in trouble, because the reason we would normally offer in order to show that C does follow from Hand A is that 'Hand A imply C' is derivable from L. Thus the very same grounds that support (9) ["It is true that H and A imply C is a consequence of L") manage themselves to undermine (10) ["It is false that H and A imply C"]." But those grounds (showing that 'Hand A imply C' is a consequence, in this case, presumably, an instance, of L) only undermine the rejection of 'Hand A imply C' if we regard ourselves as committed to L, and we can show that 'H and A imply C' is a consequence of L without doing that: I take it that the quantum logician is trying to say that. It may take logical laws of one or another sort to show that it is a consequence of L that Hand A imply C, but these logical laws will not be L itself.
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CHAPTER I
cr. Trotsky, In Defence of Marxism, 49-52, Novack, An Introduction to the Logic of Marxism, Cbs. II-III, Lefebvre, Dialectical Materialism, 41-42. These attacks on 'formal logic' seem to me to be grossly misguided, and, Engels' authority notwithstanding, completely inessential to anything a Marxist needs to say. 114 Leibniz, New Essays, IV. xvii. (p. 571) refers to a similar pattern as an argument "ad vertiginem". 86 So, I think, Hegel: cf. n. 12 above, and Lefebvre, Dialectical Materialism, 41-42. 88 On this line, the treatise (DK 82 B 3) is not a "pure farce" (Reinhardt, Parmenides 39), or (merely) a reductio ad absurdum of Eleatic methods (Grote, Greece, vol. 7, pp. 51-52, Verdenius, Parmenides, 15, Bracker, 'Gorgias contra Parmenides', esp. p. 427, but cf. p. 438). I think, but will not here argue, that Gorgias is best seen as attacking Eleatic canons of argument, but taking it that those canons are the canons of argument. His message is: you see what reason does for you; it leads you into absurdities. So all there is is persuasion; cf. my Encomium on Helen (DK 82 B 11), esp. Sections 8, 13, and what Plato says about me in Ph/b. 58ab. (cr., perhaps, Sicking, 'Gorgias und die Philosophen', esp. pp. 232, 240ft". Guthrie, History, vol. 2, pp. 17, 102 n. 1; vol. 3, pp. 180, 192-96, 199-200, seems to sit on a fence here.) 11 7 cr. DK ii. 283; Diogenes Laertius V. 25 (Long, p. 209.2). But it seems to me equally possible that the book Diogenes refers to is the third book of the pseudoAristotelian treatise MXG (On Melissus, Xenophanes, and Gorgias). Notice that Diogenes (Long, p. 209.3-.4) tells us of a book each on Xenophanes and Zeno, and that the mistitling 'On Xenophanes, Zeno, and Gorgias' for MXG survives as late as Bekker's text (p. 974). Cf. G. Kerferd, 'Gorgias on Nature or That Which Is Not'. as Gerhardt IV. 237; Margaret D. Wilson, 'On Leibniz's Explication of "Necessary Truth"' p. 406. Mrs. Wilson notes a correspondence between Leibniz' interests and those of Aristotle in r. Cf. New Essays, pp. 13-14, 77: there are suggestions here of a more general argument, to the effect that the law of non-contradiction is fundamental to the practice of communicating. This argument is the subject of the rest of this study. (It would come to much the same as the above if arguing turned out to be fundamental to communicating: cf. Bennett, Rationality, 49ft'.) asa Cf. Owen, 'TtOsvat 'tli. cpatV6Jl&va'. BSb This departs from Kirwan's exposition in two ways. First, Kirwan says "Aristotle eschews the stronger claim, implied by Posterior Analytics I 10. 76b24, that [the law of non-contradiction] must be believed" (AM 90). I am not clear that Aristotle was alive to the distinction. Second, Kirwan says that the most that could be "supported or explained by the thesis that" the law of non-contradiction "cannot be disbelieved" is that no argument calls the law into question, not that every argument relies on it. The above reading of Aristotle's view would 'explain' the stronger of these. But there is a distinction here that we shall have to confront. 89 Perhaps also for Euclid: on the terminology here, cf. Proclus, In Eucl. I (Friedlein pp. 193f.), Heath, Euclid, vol. 1, pp. 221-22. 29a Cf. Mill, System of Logic, II. vi. S. 30 Black, 'The Justification of Logical Axioms', makes a case for treating modus ponens similarly. Cf. p. 21: " ... the form of words 'Understanding and accepting premisses of the form p and I/ p then q, but not accepting the corresponding propostion of the form q' describes nothing at all." 31 'On Locke's Essay', p. 14; cf. New Essays, IV. xviii (p. 587). sa Remarks on the Foundations of Mathematics, I, appendix I, Section 11 (p. 51). 118
ARISTOTLE'S PROGRAM
a.
25
Anderson, 'Mathematics and the "Language Game"', pp. 488-89 (Benacerraf and Putnam). 84 Suppose p and not-p. Then p. Then either p or q. But not-p; therefore q. a. Lewis and Langford, Symbolic Logic, p. 250; also Lewis, Mind and the World-Order, p. 208. 85 Particularly Anderson and Belnap's 'E': for a concise presentation and bibliography, cf. Hughes and Cresswell, An Introduction to Modal Logic, pp. 298-301 ; also pp. 335-39. 86 This inspires another attempt to enliven the idea that a contradiction entails anything: cf. Hughes and Cresswell, p. 336. 8 7 This involves taking the referent of the pronoun 'toirtou' in •12 to be that of the same pronoun in &4: "But we just now took it that it is impossible for the same thing to be and not to be at the same time, and by means of this we showed that it is the firmest of all principles .... But even about this, it is possible to prove by way of refutation that it is impossible ...•" (•3-5, 11-12). The intervening lines discuss the view that it is possible to prove everything, and that suggests another interpretation: that in •11-12 Aristotle is saying he can prove by way of refutation that it is impossible to prove everything. Then the argument would end at 1006•28. (This interpretation is one Norman Kretzmann tried out in discussion.) But it seems to me that the argument against people who think it possible to prove everything, or anything, is given, very briefly, in a.s-9; that the concessions Aristotle wants from his opponent in •12-24 are clearly intended for use in attacking the denial of the law of non-contradiction (cf., e.r., a.21 with b8-9), and that even in a.28 it is that denial that Aristotle is after (although this depends on keeping "t'bstE o(nc liv niiv oilt~ 1eai of>x oilt~ l!xot" in •28: cf. Chapter II, n. 8 below). 88 Ross, APPA 501 ad 10•7-8 (a misprint: it should read '6-7'); Patzig, Aristotle's Theory of the Syllogism 185-86 n. 12; Barnes, 'Aristotle's Theory of Demonstration', 127 and n. 18, and pp. 138-39; Hintikka, 'On the Ingredients of an Aristotelian Science', p. 57. Hintikka says that Barnes has "badly exaggerated" this point; he does not say what the exaggeration consists in. 88• Cf. Ross, AMi. 299 ad Joe.: to prove 'simply', "i.e., not with a qualification nor merely ad hominem". The suggestion that we are here dealing with an argument that is "merely ad hominem" I take up below. 88b For discussion of these procedures, cf. Grote, Aristotle, Chapter IX, Section VIII (pp. 353ff.) and Chapter X; Robinson, 'The Historical Background of Aristotle's Topics VIII'; Ryle, 'Dialectic in the Academy' (1965) (this is virtually the same as Plato's Progress, Chapter IV), 'Dialectic in the Academy' (1968) (this is a little different); Brunschvig, introduction to Topiques; and, most particularly, Moraux, 'La joute dialectique'. 88c The Soph. el. may or may not be the last book of the Topics: cf. Brunschvig, Topiques xviii-xx. as a. Lukasiewicz, 'On the Principle of Contradiction', p. 495. (But Lukasiewicz has his troubles. On the same page he finds 1006•15-18, quoted just below, unintelligible, even an 'embarassment'. He is a paradigm of the failure to understand that the argument of r 4 is a dialectical one.) An. pr. B 20. 66b14-15 tells us that where we have a refutation, we have a syllogism, but not conversely: presumably because not every syllogism has a conclusion denying something somebody would like to assert (the second of Ross' two explanations ad Joe., APPA 470). 40 Cf. n. 4f above. As far as I know, the contrast between 'proving simply' and 'proving against a particular person' does not occur elsewhere in Aristotle, but there 88
a.
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CHAPTER I
are plenty of occurrences of contrasts between other argumentative devices used simply and used against a particular person: see below. cr. Alexander's comments, in Met. 272.30-35. 4 1 Moerbeke's translation has "ad h101c" (§935). 48 "Ad hominem" is the phrase used by Boethius to translate "np~ tov dv9pomov" in Soph. e/. 178b17 (1031°12). A good deal of useful material on the history of this term is to be found in Hamblin, Fallacies: cf. esp. pp. 41-42, 160ff. He suggests that the translation by Boethius is the source for the label. 48 P. 380. 44 cr. Anscombe, 'Aristotle', p. 39. 46 cr. Hamblin, Fa/ku:ies, for the history: index, s. v. "Arguments ad hominem". 46 Fraser v. II, pp. 410-11. 47 cr. Leibniz, New Essays, ad loc. (pp. 576-77), and Fraser's n. ad loc. 'Argumentum ad hominem' starts to sound like a bad thing, apparently, in Whately: cf. Hamblin, Fallacies p. 174; also Johnstone, Philosophy and Argument, pp. 73tf. 48 Waitz apparently takes it to be sufficient for a refutation or whatever to be sophistical that it be ad hominem: cf. Org. ii. 567 ad 177b33. 4 9 For the translation, I rely on authority: cf. Ross, AP 461 ad loc., and Charlton, AP, translation ad Joe. 5o I here follow Bonitz, Ind. 32()1>3-6, Charlton, AP 53-54. Aristotle might as easily have had in mind the thesis that everything is in constant change (cf. Bonitz, Ind. 32()1>1-3): note the conjunction of theses in Top. A 11. 104b19-22. The two are often closely associated: cf. also Chapter III, Section II below on Plato's Theaetetus. 61 This simplifies the situation some. r 5 begins by identifying the denial of the law of non-contradiction with the 'thesis of Protagoras', and alleges that the two positions stand or fall together (1009•6-7: cf. Chapter III, Section I below). The rest of r 5 deals with confusions that are supposed to lead, specifically, to Protagoreanism. r 6 apparently attempts to undermine Protagoreanism by showing it absurd, and this apparently completes the program by dealing with those who defend the position 'for the sake of argument'. So, in 5. 1009•15-22, Aristotle is looking in two directions: backwards to 4, which was an attempt to show the denial of the law of non-contradiction untenable, and forwards to 6, which will attempt to show Protagoreanism (really equivalent to the denial of the law of non-contradiction) untenable. cr. 6. 1011"15tf., and Ross AMi. 279-80 ad 1011•3, Kirwan, AM 105-06, 113. 61a cr. Wieland, Die aristote/ische Physik2 p. 212. 6lb Or as the author of the Dissoi Logoisays: cf. DK 90, Chapter I (v. 2, pp. 405-07); in Sprague's translation, pp. 155-57. 61c cr. Waitz, Org. ii. 518 ad 159b34; Moraux, 'Lajoute dialectique', p. 280. 614 cr. Brunschvig, Topiques 116-17, nn. 1, 2. &le This glosses over difficulties: cf. Kirwan, AM 84-85 ad 1004b17, Cope, lntr. to the Rhet. 67tf., Aubenque, Le prob/eme de I'Dtre, 295-302, Owen, 'Dialectic and Eristic', 103-08, Moraux, 'Lajoute dialectique', p. 288, n. 3. 68 Ross translates "'J.iyycx;." here as 'reason', but has 'account' in •14; Kirwan has 'statement' throughout. Alexander interprets it as 'statement' (in Met. 275.14-15. Ross uses 'argument' in K 5. 1062•11, 13. I don't think a great deal turns on this. Antiphasis has agreed to participate in an argument with Aristotle; to do that, he'll have to make some claim or other, somewhere. If he won't do that now, he'll destroy the argument; if he never does that, he does away with all discourse.
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y~ sbtsiv detoOcnv, sOOI>c; tvavtia Myovt~". I am more attracted than Ross is (AMi. 280-81 ad loc.) by Alexander's reading of this (in Met. 318.13-20; Kirwan shows some favor toward this: cf. AM 113). In any case, the general substance of the paraphrase I have given is preserved in all but two of Ross' six possible interpretations. One of the two others is the one that Ross opts for: these people claim the right to contradict themselves, and, in doing that, they contradict themselves. But I cannot see that this would make any real point. 53• 'A:qmtov'. Cf. Top. A 13. 105•23, and Brunschvig's n. ad Top. A 9. 104•1 (Topiques i. 126 n. 2). 64 For Aristotle's thoughts, cf. Top. 9 13. 162b31ff. and 11. 161 b15-18 (where, if the question has been begged, it is the answerer's fault, not the arguer's: cf. Moraux, 'La joute dialectique', p. 286). In general, cf. Robinson, 'Begging the Question' (with special reference to Aristotle).
sa 1011•16: "tvavrla
CHAPTER II
THE FIRST REFUTATION: GENERAL STRUCTURE
Metaphysics r4 contains a battery of arguments with Antiphasis: part of Aristotle's strategy, apparently, is to drown him in argument. This is a strategy recommended in the Topics (914. 163b4-6) for forcing somebody to your conclusion, and Antiphasis, who has taken up the Heraclitean thesis for the sake of argument, is asking for precisely that: to be forced to Aristotle's conclusion (cf. r5. 1009&16-18, 6. 1011&15-16). The first argument in the batteryrunsfromroughly1 1006&1I to 1006b34; I am referring to it as 'the first refutation'. It makes much use of the expression 'for something to be a man' ('-ro civ9pmncp dvat', &33-34, bJ3, 24, 24-25, 27). After the statement of the first refutation, we get a passage (1006b341007&20) that begins (b34-&l): "The same argument [works] also for not to be a man" (6 ()' ao-ro~ Myo~ tcai. tni -roO l.tt'l si.vat liv9pronov). 'The same argument' here refers to the first refutation, and Aristotle is saying that it can be run based on the expression 'not to be a man' instead of 'for something to be a man'. The primary difference here seems to be the presence of the negation.2 But Aristotle does not go on to give us anything like a revised version of the first refutation with the negative expression replacing the positive; indeed, a few lines later he is back to taking the positive one as the basis (1007&8-9: "if, when he is asked [the question] simply, he adds in the negations, ... "; &17-18: " ... in answering the question whether it is a man ... "). Instead of giving us the revision, Aristotle provides incidental comments that are as easily, or more easily, applicable to the unrevised first refutation. So I shall treat this passage as an appendix to the first refutation, and use the material in it accordingly. s This chapter and the fourth, below, deal with the first refutation. In this one I shall try to get at its main outline. The main outline gives us an argument that is, or is nearly, formally complete (Section 1). There is reason to be suspicious of it anyway {Section II), and there is at least one way of attacking it {Section III). And besides, there is more to the refutation than appears in the main outline (Section IV).
THE FIRST REFUTATION: GENERAL STRUCTURE
29
Understanding what there is in the refutation over and above its main outline requires consideration of the role of Aristotle's imaginary interlocutor, Antiphasis. So Chapter III below takes up the background against which Aristotle is constructing his interlocutor, and Chapter IV applies some of the material in Chapter III to what is left over in the first refutation. 1007&20-b18 contains an argument closely related to the first refutation; I shall call it 'the second refutation'. 4 It is considered in Chapter V below. The material on Antiphasis' background from Chapter III is going to be important here, as well. I. THE PLOT OF THE ARGUMENT
The questioner in an argument in dialogue tries to get the answerer to grant him premisses that will entail the denial of the answerer's thesis. 4a These premisses are the 'necessary premisses': they are necessary, needed, to construct the final argument that shows the answerer wrong (cf. Top. 91. 155b20, 29, 11. 161 b28-30). Aristotle recommends saving them for the end (91. 155b29-30): you build up arguments (some of which will be 'inductive', some deductive; sometimes you won't need to argue: cf. 155b35-38) to support those premisses, but you keep your cards close to your chest (cf. 156&11-22; all of 156&7-157&5 is devoted to telling you how to 'hide the conclusion'). When Aristotle comes to lay down his hand in our argument, here are the cards he has (1006b28-34, quoted above, Chapt. I, p. 1): (1)
Necessarily, if anything is a man, it is a biped animal (1>28-30).
This is supposed to follow from a definition,
(D)
Biped animal is what 'man' signifies (b30).
But, by the definition of 'necessarily' (b31-32), (1) amounts to (2)
It is not possible for anything that is a man not to be a biped
animal (b31). And, using the definition (D) for 'man' again, we can replace 'biped animal' in (2) to get 'it is not possible for anything that is a man not to be a man', which amounts to
30
CHAPTER II
(3)
It is not possible for anything to be a man and not to be a man (b33-34).
That is Aristotle's conclusion, and it is an instance of the law of noncontradiction. I shall call the argument for it, starting from the 'necessary [i.e., required] premiss' (1) and invoking the definition (D), the 'clincher'. The actual text for the clincher involves the phrase 'it is true to say of x that it is F'. I have suppressed this in the above paraphrase, only for the sake of brevity. It is clear from the text itself that Aristotle feels free to move back and forth between 'it is true to say of x that it is F' and 'x is F'; and whatever else we are to make of the definition of truth in r7 (101lb25-27), it warrants that freedom.4aa There is no reason not to grant it to him. The argument that begged the question at the end of the last chapter (from 1008&34-b2) did not beg it by using this transition, or by assuming this definition of truth; rather, it begged the question in assuming that truth and falsehood were exclusive, or, perhaps, that the truth of 'xis not F' entailed the falsehood of 'xis F'. No such assumptions are lurking here. One might feel less charitable toward the definition of 'necessarily' that gets us from (1) to (2). It is common enough in Aristotle: cf. AS. 1015&3335, e.g. But would Antiphasis let it go by here? I am not sure. But I think it would be fair, if he tried to stop the argument here, for Aristotle to say: when I say 'necessarily, if anything is a man, it is a biped animal', I only mean to be putting into logician's jargon what I said earlier (at 1006&3234): if anything should be a man, it would be a biped animal. I got you to accept that. Now I'm just rephrasing it: if anything should be a man, it would have to be a biped animal, necessarily it's a biped animal, it couldn't fail to be a biped animal, it's not possible that it not be a biped animal. This strikes me as pretty intuitive. And it's all I meant when I put the law of non-contradiction in the form 'it's impossible for the same thing to belong and not to belong to the same thing at the same time, back in 1005b19-20. You said you wanted to deny that. If, all of a sudden, you want to mean something by 'necessary' or 'possible' other than what I mean, you owe me an account of what you mean. It might be that there's no real disagreement between us, that you're not denying anything I want to say. This response hardly takes care of all the difficulties that modal words
THE FIRST REFUTATION: GENERAL STRUCTURE
31
bring with them. But still, it seems to me enough for present purposes. Some of your, and my, residual doubts might be allayed by the realization that it does not leave Antiphasis speechless: most of the rest of this book centers on what he might like to say, assuming that he would have accepted Aristotle's use of 'necessary' and 'possible'. Then it looks like (3) follows from (1) by the invocation of (D), and that (1) itself comes of (D), and (3) is an instance of the law of non-contradiction. Still, it is only an instance of that law. So the clincher does not, by itself, show that the law is right. This is our first brush with a difficulty: Aristotle often acts as if Antiphasis' thesis were, not simply that the law is false, that something somewhere does or could have and lack some predicate or other, but that the law breaks down all the time, that everything that has a predicate also lacks it. Our conclusion, (3), goes against the latter, but not against the former. This difficulty will be of importance later; it is not now. For the definition (D) that gets us that conclusion is itself intended as an instance of a more general pattern that would work for any significant word, or, at least, any significant predicate. The initial stages of the argument set this up. First Aristotle gets Antiphasis to say something: that much Antiphasis will have to do if there is to be any more point in talking to him than there would be in talking to a plant (4. 1006&12-15). I don't think it matters a lot what he says: Aristotle says that we needn't demand that he say that something is so, or that it is not so; if we demanded that, Antiphasis might charge us with begging the question (1006&18-21; cf. 1008&34-b2: I want later to come back to the question why this would be begging the question). All that matters is that he utter a word, 4b and one which signifies something, to himself and to others (1006&21-24; cf. b8-9);4c and his uttering of any such word is also not a matter of saying that anything is so, or that it is not so (with 1009&19-20, cf. De int. 4. 16b26-30, 3. I6b19-22, An. post. B 7. 92b19-25). Imagine Antiphasis balking at this. Aristotle would have two connected replies. First, there just is no arguing with Antiphasis: that at least depends on his saying something that signifies something. This reply, though, will not carry us far though: Antiphasis might agree, by saying
32
CHAPTER II
'yes', and insist that this word 'yes' be the word that signifies something. That would not do, since in the long run we need a word that will fit where 'man' does in (D) and (1)-(3): a word, roughly, that can stand in predicate position, and 'yes' won't do that. So even if it doesn't matter a lot what Antiphasis says, it does matter a little. 5 But then Aristotle might fall back on a second line of reply. In taking up this argument, Antiphasis has committed himself to defending the denial of the law of non-contradiction. So far, that seems to mean that his thesis is that some predicate both belongs and does not belong to some subject. And that does seem to commit him to the idea that there are some words that both fit in predicate position and signify something. So once Antiphasis has entered an argument with us, he does seem stuck with Aristotle's opening move: he has to allow that there are utterable predicate-words that signify, so he might as well utter one. It emerges well on in the argument (1006&31) that he happens to have uttered 'man': (U)
Man.
And now we want him to concede explicitly that his word does signify something. Perhaps Aristotle has him doing that as early as 1006&18-22, but I doubt it&; in any case, he has him doing that when he says (1006&28-
30):7 First, it is clear that so much is true: that the word signifies for this to be or not to be. s
It is only in the next line that it emerges that Antiphasis has uttered 'man': plainly Aristotle intends the format of his argument to apply whatever the (predicate-) word happens to be. So far, we have Antiphasis conceding
(S)
'Man' signifies something.
To get from here to (1), the premiss for the clincher, we need more. We need a concession to the effect that we can fill in for the 'something' in (S): we shall have it filled in by 'biped animal'. But this concession has to be as general as the argument: Antiphasis has to be conceding that we could have filled in for the 'something' in (S) no matter what term occupied the place '"man"' does in (S). To Aristotle, this move is too innocuous to mention (unless &28-30 constitutes mention of it); for the moment, we can
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let him have the move. But we ought to make it explicit. Then we have (almost-D) 'Man' signifies biped animal. But (almost-D) is not (D), and would not warrant (1): (1) would not be true if 'man' also signified winged quadruped. So we need a concession to the effect that, at least for the course of the argument, 'man' will signify only what (almost-D) says it does. By the time Aristotle gets down to 1()()6bll-13, he has got this concession; he lays it out in 1006&31-34: Again, if 'man' signifies one thing, let that be biped animal. And this is what I call signifying one thing: if this [e.g., biped animal] 9 is a man, then if anything should be a man, this will be for it to be a man.
It would be nice if we could unpack the phrase 'for it to be a man' here, and the phrase 'for this to be or not to be' in the preceding passage (&2830, quoted above). I cannot. Roughly, I think he means: any significant word will have associated with it conditions under which it will be correctly applied. A statement of those conditions for a word such as 'man' will tell you what it is for something to be a man.1o (He talks in the first of the two passages above as if the word signified those conditions; he talks later as if the conditions, or maybe a statement of them, did the signifying. So things are pretty loose here.) Then the concession he wants over and above (almost-D), that 'man' signifies one thing, could be put: whenever 'this is a man' or 'there's a man here' are true, they are true under the same conditions. Indeed, anything that is to count as a man can only do so if it is a biped animal. That is, necessarily, if anything is a man, it is a biped animal. That is, (1). All this Aristotle sees built into our (D), "biped animal is what 'man' signifies" (I shall continue to refer to this as a definition, although it is a little more than that: as it is phrased, it makes 'man' univocal). So, naturally, he expects trouble here: he labors in a34-b11 to soften Antiphasis up so that he will accept (D) with its implication of uniqueness, and there are repercussions and further labors in b15 and following. We shall come back to that. The overall structure of the argument ought to be clear: If we are going to talk about the law of non-contradiction, we'll have to allow that there are words that can stand as predicates and signify things. Antiphasis picks one:
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w.
He concedes that it signifies something: (Sa)
'W' signifies something.
He concedes that we can specify what it signifies; let it signify s. Then (almost-Da) 'W' signifies s. He concedes that we can hold its significance constant, at least for the duration of our talk: (Da)
Sis what 'w' signifies.
Then we have him; by (Da), (Ia)
Necessarily, if anything is a w, it's an s.
So (2a)
It is not possible for anything that is a w not to be an s.
So, by (Da) again, (3a)
It is not possible for anything to be a w and not to be a w.
So the law of non-contradiction holds for any significant predicate-word 'w'. There is no such thing as a failure of it, since a failure of it would be
nonsense. II. ON THE GENERAL STRATEGY
This argument has the effect of building the law of non-contradiction into the practice of using words significantly, of communicating. Aristotle has had followers along this trail: we found Leibniz on it in the previous chapter, and we could also have found Spinoza,u McTaggart,12 Quine,1s and, no doubt, others. One way of summing up the effect of the argument might be this: if you accept a contradiction, you will not be able to give a sense to it; in particular, in Aristotle's version, you will not be able to give a sense to the predicate-term that figures in that contradiction. Aristotle gives us no general theory that supports these views: no theory of significance, communication, necessity, and so on. I want to ask: what sort of theory would we need here? And how much could we expect from it?
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One :floor plan for such a theory might be this. (It is supposed to be pretty stark.) We want to say that the fact that 'man' is significant guarantees that where it is true that something is a man, it can't also be true that that same thing is not a man. So we might say: the conditions under which 'man' is truly applicable are what give it a sense, and they rule out the possibility that both it and its negation should be truly applicable. We have to say, then, something about truth and significance, and something about truth, negation, and conjunction. On the first matter, Quine says;14 in point of meaning, ... a word may be said to be determined to whatever extent the truth or falsehood of its contexts is determined.
And that much, if the paraphrase of Aristotle's talk of 'for something to be a man', etc., in Section I above is right, Aristotle swallows. (He couldn't have swallowed Quine's more extreme view that 'the unit of communication is the sentence and not the word',15 because he couldn't have got it into his mouth. He did not have a firm enough grasp of the notion of a sentence for this.16) On the second matter, that of truth, negation, and conjunction, Quine has this to say (I here assume that 'assenting' amounts to overtly taking something for true: I want to soft-pedal the more behavioristic aspects of Quine's views, at the risk of some distortion):17 The semantic criterion of negation is that it turns any short sentence to which one will assent into a sentence from which one will dissent, and vice versa. That of conjunction is that it produces compounds to which (so long as the component sentences are short) one is prepared to assent always and only when one is prepared to assent to each component.
We can imagine Aristotle swallowing something like this (although, again, he would be more likely to concentrate on the terms within sentences than on the sentences). The result of putting these two views together is the expected one. Levy-Bruhl (an anthropologist) once characterized the mentality of certain 'primitives' as 'prelogical'. That meant that the thought of these 'primitives' "does not bind itself down, as our thought does, to avoiding contradiction" .1s Quine says, with reference to his 'semantic criteria' :1 9 This approach ill accords with a doctrine of "prelogical mentality". To take the extreme case, let us suppose that certain natives are said to accept as true certain sen-
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tences translatable in the form 'p and not p'. Now this claim is absurd under our semantic criteria. And, not to be too dogmatic about them, what criteria might one prefer? Wanton translation can make natives sound as queer as one pleases. Better translation imposes our logic on them, and would beg the question of prelogicality if there were a question to beg.
This cannot be right as it stands. Here is an English translation of a native original: Motion itself is a contradiction: even simple mechanical change of place can only come about through a body at one and the same moment of time being both in one place and in another place, being in one and the same place and also not in it. 80
The last clause of this is pretty short, and works with conjunction and negation to get a contradiction (its author is hardly denying that there is any motion). And it is correctly translated. Granted, translation from Engels' German is not 'radical' translation; it is not even translation that requires checking by field linguists in Germany. And Quine is considering translations more like that: translations of languages from scratch. But this is irrelevant for Quine: radical translation, translation from scratch, is only taken up by way of illustration of a thesis or bunch of theses that hold as well for English hearers understanding English speakers:21 we are as honor-bound to paraphrase each other's remarks in ways that preserve the simpler laws of logic as we are to translate those of the aborigine that way.aa It may seem that shifting from talk of significance and intelligibility to talk of translation brings with it only an illusion of clarity. We can, no doubt, translate things we do not understand. (Maybe machines do that whenever they translate.) So it does not follow from the fact that we can translate Engels' German that we can understand it. Perhaps this would not do for a defense of Quine, but Aristotle need not be committed to Quine's ideas about the usefulness of looking at translation. But it will not do for a defense of Aristotle, either. The general picture is supposed to be that to the extent that one accepts what looks like a contradiction, one cannot give any significance to the predicate-term in it (one cannot be right in accepting definitions like (D)). (For Quine, I guess, one cannot give any significance to the whole contradictory sentence.) We may not be able to understand why Engels says what he says, or what his view 'amounts to'; we may think he could only say that sort of thing as a result of confusion. But I do not see that this has anything to
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do with what he means by 'in the same place'. He probably means by that what anybody would mean by that. At any rate, whatever he means, what he says is contradictory. It is supposed to be; he wanted it to be. What is right about this sort of view as to the relation of significance to logic seems to me to be this. Suppose you are trying to settle what someone means by a given word, say 'boojums'. If you have only one utterance of his containing 'boojums' to work with, and that utterance is 'that is both a boojums and not a boojums', you will get nowhere. For any aspect of the situation obtaining when he comes up with that sentence that you might associate with 'boojums' will have its presence denied by 'and not a boojums'. Things are no better if you have only the sentences 'that is a boojums' and 'that is not a boojums', uttered on the same occasion with no detectable shift of reference. And things are no better if you have a lot of utterances from him containing 'boojums', where all of them are of this sort. But this leaves a lot of room. If he comes up with a great many sentences containing 'boojums', and not too many contradictory ones (I have no idea what the least upper bound might be), you can use the non-contradictory ones to get at the contradictory ones. The situation is not much different where he is an otherwise competent member of a linguistic community in which the use of the word 'boojums' is well established. I do not, offhand, know of any other place in which Engels uses the phrase translated above as 'in the same place'. But there is nothing wrong with his German here; he is not foaming at the mouth and speaking in tongues. He even seems prepared to argue for his point. That he is prepared to argue for it is of some importance in figuring out whether he means what he seems to mean. You may think him confused, that he has mistaken the force of his arguments, or whatever. But given that he is arguing for it, it is terribly hard to deny that he is denying the law of non-contradiction, or that he means what we all do by the simple words in which he presents his conclusion. Aristotle might have read a brief poem of Anacreon's (Fr. 83) :23 'Eptoo 't& 1)11~& Ko{nc sptoo Kai ~aiVOJ.UltKOO ~aivo~at.
In another possible world, he might have translated it into English: I love and do not love, And I am mad and not mad.
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For all of that, he might have said: that's poetry for you; anything goes; Anacreon didn't mean it literally. But he also knew of men who, like Engels, were persuaded. In rs, he gives one of the arguments that lead people to deny the law of non-contradiction: (1009&23-26): The [belief]ll4 that contradictories and contraries hold at the same time [comes to] those who see contraries coming to be from the same thing: so if it is not possible for what is not to come to be, the thing must have been beforehand such as to be both [contraries] equally.
Socrates used to be pale, but went dark under the sun; so, these people say, he must have been dark beforehand, and so far forth, not pale, but pale as well. Aristotle thinks this confused, a matter of mistaking the force of the argument. Really, he thinks, the argument only shows that he must have been potentially dark beforehand, and so he was in a way (viz., potentially) not pale when he was pale (cf. 1009&30-36). These people, however, drew a different conclusion: that Socrates was, flatly, pale and not pale. This conclusion denies the law of non-contradiction. It only does so if the words in which it is expressed mean something like what we would expect them to mean. That they do mean something like that you can see from the argument. So it is hard to see how Aristotle or anyone else is in a position to say: these people are not signifying anything to themselves or anyone else by 'pale' or 'dark'. All of this forces us to look again at the argument plotted in the previous section. That argument is a little too good to be true. III. WHERE ANTIPHASIS MIGHT BALK
Suppose, instead of the apparatus of (U), (S), (D), and (1)-(3) of Section I, we had tried this on Antiphasis : (lb)
Necessarily, if anything is a man, it's a man.
So, by the definition of 'necessarily' and so on, (3)
It is not possible for anything to be a man and not to be a man.
This differs from what Aristotle tries on him only in suppressing all talk of significance. But it would hardly get past Antiphasis, and that makes the talk of significance pretty important in Aristotle's argument. Against
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the little argument '(lb); so (3)', it is all too easy for Antiphasis to say this: "(3) only follows from (lb) using certain rules of inference. For the time being, I'll waive those rules, and take them as built into the sense of (lb). But then {lb) is only a thinly disguised variant of the law of non-contradiction. So if I'm going to play the part of a conscientious objector to the law of non-contradiction, I'll have to ask for further support for (1 b). And you did say that in defending what you call 'Heraclitus' thesis' I was supposed to concede only what he would. I don't know all that much about Heraclitus, but neither do you. But I did think you were going to give me a little more by way of motivating the law of non-contradiction than formal games: certainly if I were Heraclitus, I wouldn't concede you a premiss that is a simple logical variant of the law of noncontradiction. I'm going home." But when Aristotle argues with him, he doesn't go home. Presumably he stays around because the premiss for the clincher is not (lb) but (1), and (l) is not a simple formal variant of the law of non-contradiction: it takes (D) to tum it into that law. Besides, the theory is that we can give Antiphasis support out of his own mouth for (1), as we are not able to do for (lb): (I) comes of his willingness to take up 'Heraclitus' thesis' in argument, to talk about it. Does it, really? Here I want to outline a case for saying that it doesn't: for saying that the practice of communicating, of using words significantly, does not by itself require our accepting any necessary truths. A full defense of this case is not possible here, and many would not accept it without a full defense. But it is enough for present purposes if you can see that someone might accept a case of this kind without being totally mad. 25 Antiphasis, as much of him as can be seen in Aristotle's treatment of his objections, comes close to making out a case of this kind, but only close: we can use this case to get clearer on what he is up to. If we are to communicate, and use a word that behaves in the ways that Indo-European languages require of predicates to do it, we shall have to show some sort of agreement in our use of that word. This agreement is occasionally founded in a shared definition, but it need not be, and, indeed, only rarely is. You and I may find that we agree generally on what we call 'men' (usually we won't find that out; it is simply given). And we
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may find out that we look for the same sorts of things when we run into hard cases. But we may, neither of us, think that any of the things we look for is sufficient to show that what we have on our hands is a man, and we may not think that any of them is necessary for what we have to be a man. We may not even be able to say what all the things we look for are; at any rate, we would find it impossible to give an exhaustive list. And this impossibility need not be due to the brevity of life or the fallibility of the human intellect: there just may not be an exhaustive list. Still, we might mean the same thing by 'man': we agree, generally, on what to call 'men', and so on. We need not agree all the time, or in all conceivable cases. Consider a case in which we do not agree. Dr. Frankenstein, an enterprising biologist, has manufactured a dead ringer for a human being by synthesizing a reduction of vinegar and tarragon with the yolks of three eggs and butter. He calls his creation 'Bernie'. It is not hard to imagine you and me disagreeing as to whether to count Bernie as a man. Suppose I say not, and you say so. I might say: but look, it didn't come about in the normal biological manner. We might agree that that is relevant. But I might still believe, with you, that test-tube babies were babies. Or I might say: well, it didn't have human parents. We might agree that that is relevant. But I might still believe, with you, that Adam was a man. I might, in other words, not feel right about counting Bernie as a human being, and go some way toward formulating what seems wrong with counting him as a human being.26 But I might not feel that any of the things I list against that classification is associated with a generally necessary condition for the application of 'human being'. And I might not feel that, if only I had the mind for it, I could give some terribly long list of conditions whose disjunction is necessary for the application of 'human being'. You agree that the things I point to are relevant; you disagree when it comes to the question whether Bernie is a man. You point out that it is biped, and an animal (suppose I don't disagree that it is an animal). You might still believe, with me, that chickens are not men. You point out that it doesn't have wings. You might still feel, as I do, that chimpanzees are not men. You point out that it is rational. You might still be able to imagine a Martian or two that would fit all this and yet not be a man. I might concede that all of the things you are giving me are relevant, that you are making out a good case. But we might both agree that none
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of the things you give me is sufficient to show that Bernie is a man; and neither of us need feel that it is only human stupidity that keeps you from getting together a terribly long list of conditions whose conjunction is sufficient to guarantee that something is a man. Maybe our disagreement over whether Bernie is a man is beyond resolution. Do we therefore mean different things, signify more than one thing, by 'man'? We needn't; we almost certainly don't. When you ask me how many people are coming to the party, and I count Bill, Steve, and Norman, all these people I count as people in the same sense in which you would count them as people. But this does not mean that either of us has anything available that we would want to defend as a definition for 'person', and it does not mean that either of us thinks that there is a definition somewhere, we just don't happen to know where. So disagreement over whether to count something as a man is not necessarily a reflection of different definitions, nor does it always demand resolution in terms of shared definitions. And the agreement we normally enjoy is not necessarily a reflection of shared definitions, either. Where does any of this touch Aristotle's argument against Antiphasis? It may seem that it doesn't touch it at all. The definition Aristotle attaches to 'man' in r4, 'biped animal', is only a sample. That is, if you look at the generalized version of the argument (the one that runs from (Ua) to (3a) at the end of Section 1), you can see that it no more matters what Antiphasis will grant as a definition of 'man' than it mattered that he picked 'man' instead of 'platypus' in the first place. (And cf. here An post B4. 91&27-28). All that matters is that it is in principle possible to fill in for 'something' in (Sa). But if Antiphasis had been moved by the spirit of the above remarks, it would have been precisely this 'in principle' possibility that he rejected. He would have said this: "I don't see any reason to suppose that my admission that 'man' signifies something forces me to allow you to fill in what it signifies. But you have to fill that in to make (1) any different from (1 b). That is, if you tried to say: let's have 'man' signify man, and only that, I wouldn't have accepted the stipulation, since you say you mean by that that, if it's true to say of something that it's a man, it is, necessarily, a man. Then we're back where we started: as long as I allow you the rules of inference you've packed into 'necessarily' and so on, you're just playing formal games with
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me. What I question is the idea that my using 'man' significantly requires my acceptance of necessary truths like that one, or like the law of noncontradiction." To many people, views of this sort are tantamount to relativism or subjectivism. Their feeling seems to be that if our words do not have statable conditions of application, there are no constraints on our use of them: anyone can say what he pleases, and there will be nothing that counts as his being right or wrong. In the face of this feeling, it is worth pointing out that there has been no question so far but that Bill, Steve, and Norman are all men, that it is true that they are, and not true 'for' someone, but just true. Even in the case of Bernie, where we disagree, it is not necessarily a matter of each of us saying what we like, without the possibility of being wrong. Suppose you try to persuade me to invite Bernie to the party, and I refuse to, on the ground that he's not a human being. Then our disagreement is more than a matter of diverging linguistic preferences: it is a disagreement over how to treat Bernie.27 And I may well be as wrong as are those who talk as if blacks were sub-human, and suit their actions to their words. Or again, suppose I invite Bernie, but persist in withholding the titles 'man', 'human being', 'person', etc. from him. I might still be wrong - as wrong as are those who persist in saying things like 'there were four men and a few niggers there'. Granted, this, on the face of it, is not the sort of rightness and wrongness that interests logicians. But you can imagine someone saying that this is the sort of rightness and wrongness in the absence of which there would be no such thing as the sort of rightness and wrongness that interests logicians. I cannot argue that this is so here. Here the important thing is that rejecting the idea that communication can only take place where there are statable necessary and sufficient conditions for the application of words does not land one in subjectivism. This point is of some importance in connection with our text. We have just now envisaged Antiphasis balking at the transition from his admission (S) to the definition (D). That, in the text, is where he does first balk: that is, it is when Aristotle asks him to concede that 'man' signifies just one thing, and spells out that concession, that he stops to treat objections he expects Antiphasis to offer. But these objections of Antiphasis' are not along the same lines as the one above, and the biggest difference is that
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Antiphasis' objections are ones that would lead to subjectivism. This we can see by taking a closer look at Antiphasis' position. One advantage of looking more closely at Antiphasis is that it makes Aristotle's argument look better. If I am right, it is still not waterproof, partly because Aristotle is one of those people who sees rejection of the idea that words only have significance if there are necessary truths governing their application as tantamount to subjectivism. I think there are other alternatives. IV. WHERE ANTIPHASIS DOES BALK: TWO SUB-PLOTS
In the course of the first refutation, Aristotle attempts to deal with two lines of objection he expects from Antiphasis. One of the things that is unclear is what motivates these two lines of objection: this is reflected in an unclarity as to just what the objections are. Here I want to consider the passages in which they are treated, to locate the points of unclarity that will require a further look at Antiphasis. The first of the two lines of objection would block the stipulation of uniqueness of significance that Anstotle uses to get to (D). The second would block the use he makes of (D), With its stipulation of uniqueness, in the clincher; it has to do with the introduction of negation. A. The First Line: 'man' Signifies More Than One Thing Here Aristotle imagines Antiphasis simply denying that 'man' signifies one thing; he responds (l006aJ4-bll) But it makes no difference if it signifies more, if only they are definite: for then a different name might be granted to each account: I mean, e.g., if he denies that 'man' signifies one thing, and [says it signifies] many things, for one of which the account was 'biped animal', although there are many others, as long as they are definite in number; for then a different name might be granted for each of the accounts. If that weren't granted, but he said that it signifies infinitely [many things], it is plain that there wouldn't be any argument. For not signifying one thing is signifying nothing, and when words do not signify our dialogue with each other is destroyed, and, really, [so is] dialogue with oneself: for it is not possible to think without thinking one thing, and if it is possible, one name could be granted to this thing.
As far as I can see, this response does not touch the pattern of objection outlined in the previous section. Antiphasis is offered the dilemma: either 'man' signifies a listable plurality of things from which you can pick one,
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and then we can work the argument with that, or it does not, and you can never pick one- but then you can never signify anything in particular by 'man', and we're back where we started. The presupposition hidden in all of this is that the list of things signified by 'man' will have for entries sets of necessary and sufficient conditions for the application of the word, and that was what Antiphasis would be denying if he were moved by the spirit of the last section. There is more to the matter than this. Aristotle pictures Antiphasis denying that 'man' signifies one thing; Aristotle responds by suggesting that he pick one; Antiphasis tries saying that he can't pick one, because 'man' signifies infinitely many things. If he got as far as trying to say this, what would he be trying to say? It may seem that there is no real question here; that no one need ever have got as far as saying anything of the kind; that Aristotle is just covering all the possible cases. The dilemma has an air of mathematical exhaustiveness about it; it sounds as if it were based on the disjunction "'man' signifies either just one thing, or finitely many things, or infinitely many things". Since Aristotle believes that there are only finitely many phrases available for definitions (Soph. el. I. 165&10-11: he would be right about that if there were some finite upper bound on the number of words possible in such phrases), and since he apparently believes (cf., e.g., Top. A15. 106&1-8) that for each distinct sense of a word there will be, in the long run, some unambiguous phrase that defines the word in that sense (cf. Top. A15. 107b6-12), he would be entitled to conclude that no word can signify infinitely many things. But then he would be concluding that a word cannot signify infinitely many things for the wrong reason. For in our text, he wants to say that if a word signified infinitely or indefinitely many things, it would signify nothing, because there would be no way of picking out any particular thing it signified. And that is altogether different from saying that it can't signify infinitely or indefinitely many things because there wouldn't be enough phrases to give all the definitions. And I see no other way of getting to the conclusion that the word signifies nothing from the third alternative if the three alternatives are: one, finitely many, infinitely many. 2B Nor do I see any way of getting to that conclusion from the third alternative if the three alternatives are: one, so many, indefinitely many (we
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just don't know how many). Rather, the alternatives have to be: one, so many, an indefinite blur (in which we can't find even one). Then the third alternative is really a view to the effect that the word 'man' signifies something, but there is no saying what it signifies, because there is no way of picking out any particular thing that it signifies. So it may seem that the third alternative is really quite close to the objection of the last section. But it is not. I might talk about heads in connection with Hegel's chapter on phrenology; I might later talk about heads in connection with some of my counter-cultural friends. Each of these formulations of what I would be talking about uses the word 'head' in just one sense,29 but a different sense each time. There are two senses of the word 'head' in play in that sentence: count them. But one's ability to count them, to distinguish them, does not depend on one's being able to give necessary and sufficient conditions for the application of the word in either sense. Aristotle appeals to our ability to think of things: he says that if the word signifies indefinitely many things, we won't be able to use it in talking even with ourselves, we won't be able to think with it. Again, that is no help against the objection: if I think about heads in connection with Hegel and then think about heads in connection with the drug scene, I am thinking about heads in a perfectly definite sense in either case. So the third alternative does not get at that objection, either. Does it get at anything? It might, of course, be a misguided attempt simply to cover all the possible cases. On the other hand, it might tie in with a locatable confusion about significance. That, eventually, is what I am going to try to make it do.
B. The Second Line: On Negation In comparison with what Aristotle has to say here, the first line of objection was a breeze. I am going to try to straighten out some of the logic of this, and leave holes for the fenceposts I shall cart in later. Aristotle takes it that what he said in connection with the first line of objection leaves him room to stipulate that 'man' signifies biped animal and only that; he now tries to cash in on that. In l006bll-14, he says: Let the word signify something, and one thing, as we said in the first place. Then it is not possible for 'for something to be a man' to signify just what 'for something not to be a man' does, ....
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It is not easy to see how this is supposed to follow. Aristotle adds a qualification: this is not possible, he says, if 'man' not only signifies of one thing, but [signifies] one thing. (1006bl4-15).
This suggests that there is more packed into 'signifies one thing' than we have got at so far; but when we look for the extra packing, all we find is that 'signifying one thing' has to be kept distinct from 'signifying of one thing', where the latter amounts to 'is true of one thing'. (Cf. here 1007a34b}: "an accident always signifies a predicate of a certain subject"; this parallel is not altogether apt, since in this later passage Aristotle would deny that 'man' signifies a predicate of a certain subject: cf. Chapter VI below). That this is what the distinction amounts to is clear from the way in which Aristotle forces Antiphasis to accept it l1006b15-18):29a For we are not taking that to be signifying one thing, namely, [signifying] of one thing, since then even 'educated', 'pale' and 'man' would signify one thing, so that all would be one thing; for they'd be synonyms.
The argument in this passage is this. If it were enough for two expressions to signify the same thing that they be true of the same thing, 'educated', 'pale', and 'man', all of which are true of one thing, say, Socrates, would signify the same thing: they would be synonyms (here 'synonyms' is used as in Top. 913. 162b37, Rhet. r2. J404b39-140Sa32, rather than as in Cat. 1. Ja6-J2; cf. r4. 1006b25-27).30 But if they all signify the same thing, then being educated, being pale, and being a man all are the same thing. The appendix to the refutation bears out the implication that there is a step here beyond the three words' signifying the same thing: that the absurdity to which Antiphasis is driven is not just that three obvious nonsynonyms are synonyms, but that 'all things are one'.31 What Aristotle says is this (1007a4-8}: And if he says that 'pale' as well signifies one and the same thing [as 'man' and 'educated': cf. &2-3], we shall say again just the same as we did before, that all things will be one, and not just the opposites. But if that isn't possible, there will follow what we said, if he will answer the question.
So the absurdity, which Antiphasis is expected to see as an absurdity, is that 'all things are one', that something like Eleatic monism is true. And if Antiphasis is expected to crumble under this consequence, he is not an Eleatic monist. But how would it follow, from saying that for two words to signify the
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same thing is for them to be true of the same thing, that all things are one? In 1007b18-26, Aristotle tries a different tack for forcing this same conclusion on Antiphasis. There, the argument seems to be this. Antiphasis is taken to be saying that "all contradictories are true of the same thing at the same time" (1>18-19), that is, that everything that has a predicate true of it also has the contradictory predicate true of it. (The importance of this will be clearer in chapter III §1 below.) He is also taken to be committed to the law of excluded middle (b21-22: the introduction of Protagoras here, which I am for the moment ignoring, will also find a place in Chapter Ill). Take, then, anything you please, and any predicates you please: say 'battleship', 'wall', and 'man'. They will all be true of that thing: "the same thing will be a battleship, a wall, and a man" (1>20-21); for, by the law of excluded middle, either it's a battleship or it's not a battleship, and, by the general denial of the law of non-contradiction operating here, if it isn't a battleship, it is a battleship. And so on for the other predicates. Sla Going from here to saying 'all things will be one' is difficult: Aristotle seems to be thinking, very loosely, that 'this one thing is a battleship, a wall, and a man' amounts to 'a battleship, a wall, and a man are all one thing', i.e., that there is only one thing (since the same moves work for every predicate). In the long run, I am afraid that he is doing just that. But it is worth noting that we could support him if we saddled him with the 'identity of indiscernibles' : with the claim that where there are two distinct things, there is a predicate true of the one but not of the other. We could then say: if there are two distinct things, a and b, one must have a predicate, say 'F', that the other lacks. But if one of them, say b, lacks 'F', it has 'not F' (by the law of excluded middle), and so (by the generalized denial of the law of non-contradiction) it has 'F'. Since everything both has and lacks every predicate, there are no predicates by which distinct things can be discriminated; so nothing is distinct from anything else. Similar concessions would support the step we are interested in, at 1006b16-18. We would have to give Aristotle the identity ofindiscernibles again, and a further principle, call it 'the principle of ubiquitous likeness', to the effect that any two things share some predicate or other.31 b Suppose, then, that predicates true of the same thing signify the same thing.
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Suppose that 'F' and 'G' are true of a, and that 'F' is true of b. Then 'F' and 'G' signify the same thing (since both are true of a), and (assuming that predicates that signify the same thing are both true of the same thing) both must be true of b. So there is no predicate that will distinguish a and b, and (by the identity of indiscernibles) they cannot be distinct. This is a wildly speculative reconstruction of a train of thought in which Aristotle himself may never have filled in the gaps. (He nowhere, to my knowledge, pledges allegiance to the identity of indiscernibles. ale) I shall not spend more time on it: for most of us, there is enough absurdity in saying that 'pale', 'educated', and 'man' all signify the same thing, without the added absurdity of Eleatic monism. There is one thing this passage shows to be packed into the stipulation that 'man' signifies one thing that ought not to go without notice. When Aristotle first introduced and unpacked that stipulation, all he seemed to want was the concession that that single word could have (for the duration of the argument) one significance and no more. What is now in question, though, is not the conditions under which a single word has a single significance; it is, rather, the conditions under which two (or more) words or expressions have a single significance, i.e., the same significance. This is not a wholly separate issue: the considerations that bear on two expressions' having a single significance would also bear on two occurrences of the same expression having a single significance. And it is clear enough, if we look at what Aristotle said when he introduced the stipulation, that he has been thinking all along of the word 'man' as something that can be used repeatedly with the same significance (1Q06a32-34): if 'man' signifies biped animal, and only that, then anything to which 'man' is truly applicable will have to be a biped animal. But all this leaves us no clearer as to how it is supposed to follow, given that Antiphasis has allowed us to pick one thing that 'man' signifies, that, with this single significance, a statement of the conditions for applying 'man' cannot amount to a statement of the conditions for withholding it: in Aristotle's words, that 'for something to be a man' cannot signify just what 'for something not to be a man' does. In the long run, I think, it does not follow, and Aristotle does not have to think it follows. But then, why does he say it? His moves take on a semblance of sense once we realize that the notion of signifying something is simply not a part of Antiphasis' repertoire, and
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that Aristotle has to give him the notion pretty much from scratch. Roughly, what happens is this. Antiphasis is denying the law of non-contradiction. His denial of it has some generality: he wants at least to say that for some predicate, anything that has it also has its negation. Aristotle is trying to show him that if that is so, the predicate fails to signify anything. He says: suppose it does signify something; then take one thing it signifies. But Antiphasis, without a clear grasp of the difference between 'one thing it signifies' and 'one thing of which it is true', does not understand what he is being asked to do. He knows he wants to sa) that whatever the predicate, here 'man', is true of, its negation, 'not a man', is true of. Aristotle has just asked him to let biped animal be the one thing that 'man' signifies. And Antiphasis feels that he is then committed, by his thesis, to saying: well, if a biped animal is a man, it's also not a man. And Aristotle tries to get him to see the confusion he is in: once that is straightened out, the main line of the refutation takes over. The next two chapters will be concerned to make this way of seeing the argument more plausible. For now, let us just accept what Aristotle says: 'for something to be a man' does not mean, or signify, what 'for something not to be a man' does; a statement of the conditions for applying 'man' does not amount to a statement of the conditions for withholding it. Notice that this is not, formally, the same as saying that a statement of the conditions for applying 'man' does not amount to a statement of the conditions for applying 'not a man'. ("For something not to be a man" does not have the same structure as "for something to be not a man".) The conditions for withholding a term generally coincide with those for applying its negation only given the law of excluded middle. A nasty stretch of text, which we are about to encounter, turns on this difference. If the interpretation outlined in the last paragraph is right, Antiphasis has fallen into making the conditions for applying 'a man' coincide with the conditions for applying 'not a man'. So the concession we are letting Aristotle have, that the conditions for applying 'a man' do not coincide with those for withholding it, does not amount to a concession that Antiphasis was in error: that is something Aristotle has yet to show. He doesn't do it right away. What happens next is that he seems to tip his hand. He says (10Q6b18-20): And it won't be possible for the same thing to be and not to be3B except by a homonymy, as if what we called '[a] man' others were to call 'not [a] man'.
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It is hard to see how he managed to get this. What he had before (what we let him have, anyway) was that 'for something to be a man' and 'for something not to be a man' signify different things; but that does not mean that 'is a man' and 'is not a man' can only be true of the same thing if the one signifies what the other does. That, we might say, would be to confuse signifying one thing with signifying of one thing (being true of one thing), and we have just been told not to do that. Again, I think the answer lies in the part Antiphasis plays in the debate. If we were right a few paragraphs ago as to Antiphasis' confusion, Aristotle's point is clear enough: Antiphasis' response to 'let a biped animal be a man' (where that is supposed to stipulate one thing that 'man' signifies), namely, 'all right, but it's also not a man', is going to save the denial of the law of non-contradiction only by making 'a man' and 'not a man' coincide in significance, and that could only be so if 'a man' worked homonymously (as if someone were to argue that Helen is both a man and not a man, since, although she's a human being, she's a female human being).32aa So Aristotle is not saying, quite generally, that the only way for the law of non-contradiction to fail is by a homonymy, nor is he saying that his argument so far has proved that, but that what Antiphasis has said will only cause a failure of the law by a homonymy. And he points out (1006b20-22): But that isn't the problem - whether it is possible for the same thing at the same time to be and not to be a man [where it's just a matter of] the word- but [where it's a matter of] the thing. asa
If he really had thought that he had already shown the law to follow from what preceded (if, that is, he had been tipping his hand in b18-20), he might as well have stopped right here. He does not. He goes on for another half-dozen lines, and then puts the clincher to us. That, on my reading, is because he is responding to a specific confusion of Antiphasis'. That confusion would threaten (D), and so threaten the first line of the clincher. It would force us to replace (1) by: (1')
Necessarily, if anything is a man, it is a biped animal, and so also if it is not a man.
That might not be as serious as the threat it would issue to the substitution that gets us from (2) to (3): starting from (2), and using
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Biped animal is what 'man' signifies, and what 'not a man' signifies,
we would get (3')
It is not possible for anything to be a man, and not a man, and not not a man.
And that would certainly foul things up royally. So Aristotle tries to make it clearer what he is asking for when he tries to get Antiphasis to pick one thing that 'man' signifies. He points out that what is in question is not whether the word 'man' and the expression 'not a man' can be true of the same thing at the same time, but whether they can be true of the same thing at the same time without homonymy: without a different significance attaching to 'man' from the one to the other. In Topics A18. 108&20-37, he recommends attending to the beha-vior of homonyms as a way of insuring that the debate stays on the same track; he introduces this recommendation by saying that attention to homonymy is useful "in order that one's arguments should turn on the thing itself(Ka't' ao'to 'tO 1tpii:yj.la) and not be directed [merely] against the word" (&20-21 ). We just found him preaching the same gospel to Antiphasis. The claim that Antiphasis' way of saving his denial makes men homonymous from 'man' to 'not a man' follows from two things: one, that Antiphasis is making 'man' and 'not a man' coincide in significance, and two, that they could only coincide if men were homonymous from one to the other. Conversely, then, if 'man' signifies one thing (if men are not homonymous from 'man' to 'not a man'), 'man' and 'not a man' must signify different things. He now undertakes to show that this last is so, on the basis of the concession he already has: that 'for something to be a man' and 'for something not to be a man' do not signify the same thing. There ought not, really, to be much to it. But Aristotle makes -very heavy weather of it. I suspect that he is following some of his own advice from the Topics: he is hiding the conclusion by first getting something from which what he wants (the concession that 'man' and 'not a man' signify different things) will follow (namely, the concession we have already allowed him; cf. Top. 91. 156b27-30). The words in which he gives us the argument are, I am sorry to say, Greek for these (1006b22-28):
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But if 'a man' and 'not a man' don't signify something different, it is clear that 'for something not to be a man' [doesn't signify anything different from] 'for something to be a man', so that for something to be a man will be for something to be not a man; for they will be one. For that is what 'being one' signifies: as a jacket and a coat are one, if the account is one. But if they are to be one, 'for something to be a man' and 'for something not [to be] a man' signify one thing. But it was shown that they signify something different.
We are going to have to dismantle this. It is not a pleasant task. The argument is a reductio. The premiss to be shown false is: (P)
'A man' and 'not a man' signify the same thing.
It is to be shown false by showing that it entails something already shown false. The only candidate we have for something already shown false is: (C)
'For something to be a man' and 'for something not to be a man' signify the same thing.
The trouble is that Aristotle seems to start things off by going from (P) to (C) without anything in between, and then seems to go on from (C) to (Cl)
For something to be a man is for something to be not a man.
And besides, he seems to finish the argument, not by saying that (C) has been shown false, but that (C2)
'For something to be a man' and 'for something to be not a man' signify the same thing.
has been shown false. We can avoid the second of these two problems by treating 'for something not to be a man' as amounting, as far as sense goes, to the same thing as 'for something to be not a man•sa. The merely verbal variation between them comes into the argument because of the format Aristotle uses for designating what I have loosely called the 'conditions of application' for a term. For 'a man', these conditions are called 'for something to be a man'. For 'not a man', they are called 'for something to be not a man'. Aristotle's recipe is: throw the term into the dative, and frame it with '-ro ... dvat'. (I am not saying that possession of the recipe is of any particular help in understanding the resulting construction.) My recipe is: make a frame whose left border is 'for something' and whose right border
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is the term (this is supposed to preserve the dative of the Greek), and fill it with 'to be'. In either case, the term, even if it is complex, as is 'not a man', stays in one piece. The result, for 'not a man', is 'for something to be not a man'. Aristotle simply assumes that that result does not differ in import from 'for something not to be a man'. So he simply assumes that having shown (C) false is having shown (C2) false. The other problem (that Aristotle seems to go straight from (P) to (C) and then moves on from (C)) is stickier. But we can get around it, I think, if we are willing to play a little fast with the expression 'so that' in b24. Suppo~e we take Aristotle to be saying that (C) has to follow from (P), so that (Cl) will be so; that is, that (C) is required to preserve the truth of (Cl), where (Cl) is the more direct consequence of (P), and is shown to be in b25-27. The worst that can be said about this suggestion is that Aristotle ought to have been more careful with his conjunctions.34 But the suggestion has the extraordinary merit35 of putting the argument together, in this way: We want to show that 'a man' and 'not a man' don't signify the same thing: we have to close this loophole if the clincher is to have any effect. In explaining the stipulation that 'man' signifies one thing, we said it meant that when we moved from one thing of which it was true to say that it was a man to another, we would find that what it was for the one to be a man was the same as what it was for the other. Now we are dealing with two expressions, 'a man' and 'not a man', and we want to see what it would be like if they signified one and the same thing. Presumably, that would involve it being the same thing for something to be a man as for something to be not a man. The situation would be as it is for 'jacket' and 'coat': the account you'd give when asked what it was for something to be a jacket would be the same as the one you'd give when asked what it was for something to be a coat; cf. here Phys. A2. 185b19ff. But then 'for something to be a man' must signify the same as 'for something not to be a man' (or 'for something to be not a man'), in order to make it the same thing for something to be a man as for it to be not a man. (This last is the 'so that' clause.) Mter all, it couldn'tjust happen that these were the same, as it just happens that the author of The Mystery of Edwin Drood and the author of Hard Times are one and the same. The former identity has to be made of stronger stuff: it has to be guaranteed by the significance of the words. (The spirit of the objection I was outlining in the last section may
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come to haunt this move as well: I want to tum a deaf ear to its thumpings for now.) But we have already shown, as a corollary of all this stipulating, that 'for something to be a man' and 'for something not to be a man' signify different things. So Antiphasis' challenge, whatever it is, founders on the stipulation of unique significance and its purported corollary. He is now in no position to block or even sneer at the clincher. The argument in b22-28 has at least one suppressed premiss: the law of excluded middle, that enables Aristotle to treat 'for something not to be a man' as amounting to 'for something to be not a man'. Despite Aristotle's apparent confidence that Antiphasis could be made to accept this (in 1007b21-22), we may feel discomfort. But then we ought to bear in mind that the arguments we have been considering in this section are, in a way, sealed off from the main line of the refutation: they tum on specific difficulties presented by Antiphasis. If we were not disciples of Antiphasis, we might find the steps of the main line of the refutation independently plausible. And it is not so much that Antiphasis finds those steps independently implausible, as that he quite fails to understand them. In the next chapter, I want to consider why not. V. SUMMARY
So far, we have this. We have (Section I) an argument against Antiphasis. That argument would show that the predicate in any instance of a denial of the law of non-contradiction could not be significant. So it makes a rigid connection between someone's using a word significantly and his obeying the law of non-contradiction. But that connection is too rigid (Section II). The word 'man' has significance in English, and so does the corresponding Danish word; that allows us to understand Kierkegaard, in translation or in the original, when he insists that Christ was both a man and not a man. A weaker connection seems reasonable, namely, that persistent denial of the law of non-contradiction for some predicate tends to remove sense from that predicate. We have (Section III) an objection against Aristotle's argument for the more rigid connection; this objection only goes against that argument,
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and does nothing to upset the law of non-contradiction, and nothing to upset the weaker connection between significance and that law. But we can see that that objection is not Antiphasis', from what Aristotle says to him (Section IV). Antiphasis is inclined to block the argument by making the word 'man' in some way irredeemably ambiguous, and to save his denial of the law of non-contradiction with ideas that, as Aristotle sees it, make 'a man' and 'not a man' coincide in significance. NOTES 1 1006•11-28 contains a good deal of programmatic material on the way the refutation is to be taken (cf. Chapter 1), as well as the initial moves of the refutation. Norman Kretzmann, in an ingenious discussion note on this material (read at Cornell) suggested that the whole passage could be taken as an independent argument. But (cf. Section I below) there are things presupposed from •28 on that can only be found in this passage, so we shall have to extract them anyway. (cr. Chapter I, n. 37 above.) 1 It is not the only difference: the one expression uses a dative, the other an accusative. There is, sometimes in Aristotle, a difference here: cf. Met. Z 6. 1031 b4-6 for a case. But I do not know what the difference is, and, whatever it is, I cannot see that it plays any part here. a There are other ways of breaking up the text. Ross (AM 1. 265, 270 ad 1006b34) and Kirwan (AM 93, 99) take what I am calling 'the first refutation' and 'the appendix to the first refutation' as separate parts of a single argument. So far, they follow Thomas (in Met. n. 611). Here, there is nothing vital to disagree about: I only want to be able to use 1006b34-1007•20 in commenting on the first refutation, and I do not want to make any special comments on that passage. 4 This follows Thomas (in Met. nn. 611, 624) instead of Ross (AM 1. 266) and Kirwan (AM 100), who take what I am calling 'the second refutation' to be a third part of the single argument extending to 1007b18. Here there is just a little more turning on how one cuts the cake than there was inn. 3: cf. Chapter V below. 4a cr. Moraux, 'La joute dialectique', p. 284, n. 4. 4aa cr. Tarski, 'The Semantic Conception of Truth', n. 6. Ackrill (Cat. &De int. 140) suggests that the interchange might not work, for Aristotle, where the sentence formulates a future contingency, but cf. De an. r 6. 4300.27-bS, esp. b4-5, and Frede, Aristote/es und die 'Seesch/acht', pp. 77ff. 4 b I use 'word' to translate "ovo~a", although it is too broad ('yes' wouldn't be an ovo~); but 'name' is a little too narrow (adjectives, too, are 6v6~ta). cr. Robinson, 'The theory of Names in Plato's Craty/us', 221-22 (Revue) or 100-101 (Essays); Ackrill, Cat. & De int.11S ad16•19; Kretzmann, 'Plato on the Correctness of Names', 128 n. 1; Burnyeat, 'The Simple and the Complex in the Theaetetus', S-6 and n. 8 (pp. 23-24). 4o I take 'aTI~ivstv' with 'netouv' rather than with 'Mystv' (•19); this follows Ross and Kirwan's translations: Antiphasis says something that signifies something, taken this way; the other way, he would say that something signified something. But it hardly matters: we are going to have to get him to admit that what he says signifies something by the time we get to •26-28. I think, then, Kirwan's worries (AM 91-92) aren't in point.
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5 The possibility that only a word for something in the category of substance, such as 'man', will do I take up in Chapter V, Section II below. Certainly nothing so far suggests that drastic a limitation. e cr. n. 4c above. Aristotle says in the De int., etc. (cf. Chapter IV, Section II below) that the utterance of a significant word isn't a matter of saying that something is so, or not so; he does not say that uttering '"Man' signifies biped animal" is not a matter of saying that something is so, or not so. Then "18-22 ought to require only the word of Antiphasis, not the concession that it signifies. 7 I pass over the argument of 1006"26-28, in which Aristotle says that we have already got Antiphasis to agree to something "apart from demonstration". This harks back to 1006"5-9, where Aristotle was complaining of Antiphasis' want of education in demanding a proof for everything. In "28, Aristotle goes on to score a point against Antiphasis: "so that not everything is so and not so" (cf., on the text, n. 8 below). I am not counting this as part of the main structure of the refutation, but as an aside. For its force, cf. Chapter IV, Section II below. s The phrase "lb
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'Truth by Convention', in Ways of Paradox, p. 82. a. also Davidson, 'Truth and Meaning', in Davis eta/., p. 7. 15 'Russell's Ontological Development', in Schoenman, pp. 305ff. 18 He seems to have hold of it in Cat. 4, De int. 1, etc., but he loses his grip in, e.g., Met. I:J. 29. Cf. also Geach, 'Aristotle on Conjunctive Propositions'. 17 Word and Object, p. 57. Cf. 'Meaning and Translation', 471 (Fodor and Katz). 18 Lucien Levy-Bruhl, How Natives Think, p. 63; cf. p. 263. The notion goes back at least to Durkheim and Mauss, Primitive Classification, esp. pp. 5-6, 21, 70-71, 73, 85-88. Against it, see, in addition to Quine, Levi-Strauss in Totemism and The Savage Mind, Macintyre, 'Is Understanding Religion Compatible with Believing?', esp. p. 64 (Wilson)=pp. 117-18 (Hick), and Martin Hollis, 'Reason and Ritual', pp. 231ff. 1 9 Word and Object p. 58; cf. 'Meaning and Translation', p. 471 (Fodor and Katz), and Philosophy of Logic, Chapter 6, esp. pp. 80-83. The immunity that logical connectives enjoy from Quine's general skepticism about translation is part and parcel of his view that the 'unit of meaning' is the sentence: cf. 'Carnap and Logical Truth', 387 (Schilpp)=102 (Ways of Paradox), and passim. 2o Engels, Anti-Diihring, p. 132. 21 Word and Object, p. 27. 22 Philosophy of Logic, p. 96. 2s Fr. 83 (Page), =fr. 104 (Edmonds: v. 2, p. 102). I am indebted for this reference to Michael Stokes. a. his One and Many in Presocratic Philosophy p. 123 and n. 57 (p. 308). 24 'M!;a' supplied from the preceding clause (1009"23): notice that there is no feeling here that no one can have such a belief. 25 It is inspired, in part, from recent material: cf. Donnellan, 'Necessity and Criteria'; Putnam, 'It Ain't Necessarily So', and, more directly, 'Explanation and Reference' and 'The Nature of Dialectics', so far unpublished; Kripke, 'Naming and Necessity'. Some of the case comes from my own 'Agreement and Privacy', but I no longer feel right about some of the things in that paper. And cf. Marx and Engels, The German Ideology, Part I, esp. pp. 31, 42-43 (in Selected Works, v. i, pp. 20, 32; in Easton & Guddat, pp. 409, 421-22). 26 If I were Paul Weiss, I might say: I couldn't love him. Cf. 'Love in a Machine Age', pp. 179-80. I agree that that is relevant, but in the context of our argument, it is likely to sound as if it is begging the question. Perhaps the sound is misleading. Cf. also below, n. 27 and text to that note. 27 a. here Putnam, 'Robots: Machines or Artificially Created Life?'. Z8 a. Kirwan, AM94, with whom I am here agreeing in saying that 'infinitely many' isn't really what Aristotle's argument rules out. But I do not see quite what he (or Anscombe, who says similar things in 'Aristotle', p. 39) means when he says that the argument requires "That there be unit significations, like points on a line, not themselves further divisible". He himself points out on the next page that Aristotle is not requiring that the significations be simple entities. The requirement is not that they be indivisible, but that they be distinguishable. 29 It may be that Aristotle's notion of what a word signifies is not that of a sense it bears: cf. Anscombe, 'Aristotle', p. 41, and Chapter V, Section II below. But that difference, if there is one, does not affect the relevance of this example. zoa So also Alexander, in Met. 280.1-2, Kirwan, AM 96. so The sense is close to the English one. Cf. Alexander, in Met. 280. 18ff.; Ross, AMi. 269 ad b15. Kirwan (AM 96) favors the sense of the word in Cat. 1 (things 14
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that share a name under the same definition are synonyms, 1"6-7), but it is hard to make this fit: there are three words involved here, and all have to be true of the same thing. Cf. also Leszl, Logic and Metaphysics in Aristotle, pp. 92-93. a1 Kirwan (AM 96) thinks maybe not, but 1007"4-8 and b18ff. seem to me conclusive. Bla So far, I am following Kirwan, AM 102-03. He does not discuss how to get the conclusion 'all things are one' (except for a sentence: cf. n. 31b). 81b Hampshire believes this: cf. Thought and Action, p. 31. Kirwan may have in mind something similar in AM 96, where he mentions a possible "suppressed assumption that all predicates are connected by a chain of co-predicability". Blc He might have had difficulty putting it into words, given the trouble he has with the notion of identity: cf. N. White, 'Aristotle on Sameness and Oneness'. He does say such things as "things of which the substance, i.e. the essence, is one are themselves one" (Z 13. 1038"14-15), and if that were taken to mean "if some predicate 'F' gives the essence of both a and b, then a=b", its contrapositive would be "if a,Pb, there is no predicate 'F' that gives the essence of both". That may seem close: if a and b have essential predicates, they must have some distinct ones. But I don't think Aristotle's claim in Z 13 ought to be read that way: cf. Albritton, 'Forms of Particular Substances in Aristotle's Metaphysics'; Woods, 'Problems in Metaphysics Z, chapter 13'; and Lesher, 'Aristotle on Form, Substance, and Universals: A Dilemma'. as Kirwan avoids making Aristotle's hand tip by translating this line "And it will not be to be and not to be at the same time", which is deadpan literal. He interprets it (AM 95) as restating J006b13-14, i.e. as meaning, I guess, "to be [a man] and not to be [a man] will not be the same thing". I find this hard, since similar phrasing turns up only three lines below (1006b2J-22) where it means (and is translated by Kirwan as meaning) "It is not possible for the same thing at the same time to be and not to be a man" (and cf. 1005b35-1006•1). asu The example is not altogether apt, since the two senses of 'man' involved are not complementary. But it will do. asa 'x:a-rd -ro 7tPiiJ.Ul': '7tpliyJ.Ul' becomes important here and in the next chapter; it has to be borne in mind that the word doesn't mean 'fact', even if occasionally phrases of Aristotle's involving it can be paraphrased using 'fact': cf. Geach, 'Aristotle on Conjunctive Propositions', in Logic Matters, p. 21. a8 Cf. Kirwan, AM 97. Aristotle is here, as we noted above, going to have to assume the law of excluded middle. Cf. below, p. 63. 84 I am not too happy about this, but it might as well be pointed out that Bonitz' study of '&ens' does nothing to overthrow the suggestion (Aristote/ische Studien III, in the Olms reprint, pp. 202ff.). 8& Contrast Ross' treatment (AMi. 269-70 ad b22-28), or Kirwan's (AM 97).
CHAPTER III
ON ANTIPHASIS' CHARACTER AND UPBRINGING
Aristotle's imaginary interlocutor, Antiphasis, is denying the law of noncontradiction. But a closer look at what Aristotle says about this shows that he is doing something even more extreme than that: he is insisting that the law of non-contradiction fails quite generally. And this general failure Aristotle associates with Protagoreans. This is the theme of Section I below. It turns out, then, that Antiphasis has clouds of reality trailing around him. We hear from Plato of sophists who said things that bear negatively on the law of non-contradiction, and some of these things can be forged into weapons for Antiphasis. This is the theme of Section II below. That section is an attempt to nail down a persistent confusion that leads to one or another negative attitude toward the law of non-contradiction. It is no coincidence that the confusion in que~tion is one that Aristotle is trying to straighten out in r4. We shall tum to this in Chapter IV below. Some of the material introduced in Section II of the present chapter will be pertinent in connection with the first refutation (Chapter IV). Some of it will be pertinent in connection with the second refutation (Chapter V). Some of it just holds the rest together. Consider the view Aristotle takes himself to be attacking in the debate with Antiphasis. In the jargon he uses to describe those debates, what is Antiphasis' thesis? I. ANTIPHASIS' THESIS
We have every right to expect that that thesis is a simple denial that 'the same thing cannot both belong and not belong to the same thing at the same time in the same respect' and so on (r3. 1005b19-22). This is the way Aristotle puts the law of non-contradiction, and it is the law so stated that would be supported by Aristotle's first refutation. But immediately after putting the law to us, he associates its denial
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with Heraclitus (3. 1005b25). And Heraclitus, as Aristotle sees him, was not one to go but half-way: Heraclitus' [account], saying that all things are and are not, seems to make everything true (r7. 1012"24-26). He says that everything is true and everything false; he also says each of these things separately (8. 1012"34-b1; cf. K 6. 1063 b24-25).
So Aristotle's Heraclitus does not say "something or other has some predicate and its contradictory", but something considerably more catastrophic, something on the order of "everything both has and lacks any predicate". Aristotle fairly often and without warning shifts into rebuttals of some more catastrophic thesis like this. 1 He first does it in an aside in the refutation we are dealing with: either at 1006a28 or at 1006a30--31 (depending on which place you read the words) 2 he apparently takes Antiphasis' concession (S) to show that "not everything can be both so and not so". It is odd enough that he takes this to follow from (S), if that is what it is supposed to follow from; this we can put off for later. The point here is that when he says "so not everything can be both so and not so", he is satisfied that he has scored against Antiphasis. So Antiphasis must be prepared to defend something stronger than "something or other has some predicate and its contradictory". Again, in 4. 1007b18-19, he states Antiphasis' thesis as "all contradictions are true of the same thing at the same time" (and cf. 1007a20ff., 1008b31ff.). So here the thesis is not "something or other has some predicate and its contradictory", and it is clear from the following argument that it is not even "something or other has every predicate and its contradictory", but "everything has every predicate and its contradictory". Aristotle once distinguishes a universal breakdown of the law from its breakdown in some cases but not in others. What he says is this (I008a712): Again, either it works that way [i.e., the law breaks down] for everything, and [anything] is both pale and not pale and a being and not a being, and so on for the other assertions and denials [<paueu; tcai a7tO<pauet~]. or lit does] not, but [breaks down] for some and not for others. And if it does not [break down] for all, those [for which it does not] would be agreed. a
That last enigmatic clause is all he says about a limited breakdown of the law. He apparently means that the cases for which the law holds would be cases on which he and Antiphasis agree, so that they can push these
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cases aside, move on into the area of disagreement, and run through arguments relevant to that area. 4 But even here, what Aristotle is plainly thinking of is a general failure of the law for some predicates and not for others: he is not thinking of someone who says "Socrates is both a man and not a man, but Plato, Antisthenes, and the rest are just men, not also not men"; he is thinking of someone who says "anything pale is also not pale, and anything big also not big, but horses and men are simply horses and men, repectively: not also not horses, or not men".5 At the beginning of rs, Aristotle connects Antiphasis' thesis with Protagoreanism. There we can see that the thesis is that the law is generally false, and we get a clue as to the considerations that might lead someone to adopt such a thesis. Aristotle says (1009&.6--15): Protagoras' claim also comes of this same view, and, necessarily, both are either so or not so equally. For if everything that seems true or appears true is true, necessarily everything is true and false at the same time. For many lpeople] hold beliefs opposed to each other, and think that those who do not have the same views as they do think falsely, so that necessarily the same thing is and is not. And if this is so, necessarily everything that seems so is so. For those who think falsely and those who think truly hold views opposed to each other: so if things are actually that way, everybody will think truly.
This is supposed to show that Protagoras' claim, that everything that seems so, is so, is equivalent to the failure of the law of non-contradiction. Consider the components of this alleged equivalence. First, Protagoras' claim is supposed to entail that the law fails. Here Aristotle, as usual, treats 'is true' and 'is so' as equivalent, and 'is false' and 'is not so' similarly. The 'argument works with "Protagoras' claim" in the form "everything that seems true, is true", and later shifts to "everything that seems so, is so". And he takes the law of non-contradiction in the form "nothing is both true and false". This leads to an inessential wrinkle. The argument goes: Everything that seems true, is true. So if it seems to you true that Socrates is a platypus (you're probably being misled by his nose), it is true that Socrates is a platypus. And if it seems to me false that Socrates is a platypus, then it seems to me true that what seems true to you is false; so it is false. So it is both true and false that Socrates is a platypus. It is essential to this argument that we find two people disagreeing over whether Socrates is a platypus. It is not essential that they be conscious of each other's views, although as the argument is put, they are. This is
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the inessential wrinkle. If Aristotle had taken "Protagoras' claim" in the form "everything that seems so, is so", and the law of non-contradiction in a form that did not involve 'true' and 'false', he could have gone from the fact that Socrates seems to you to be a platypus and seems to me not to be a platypus directly to the conclusion that Socrates both is and is not a platypus. I need never have heard of you and your views about Socrates. Still, it is essential that it does seem to someone that Socrates is a platypus, and to someone else that he is not. But then, on the face of it, we can only get from Protagoras' claim to a limited breakdown of the law of non-contradiction. 6 "Many people hold beliefs opposed to each other", Aristotle says, and we can hardly disagree. But we may find it very hard to accept the idea that everyone who thinks something will be matched by somebody who thinks the opposite. (Kirwan asks7 "who believes ... that e.g. Socrates is a warship?". If we find anybody believing that, it is, at the very best, only luck.) On the face of it, then, the most Aristotle can show is that "everything that seems so, is so" entails, with a plausible second premiss (that people sometimes disagree), the failure of the law of non-contradiction in some, perhaps a very great many, cases. If he had been reading Plato's Euthyphro, he might have thought that paradigms were cases in which some sort of evaluative predicate was involved (cf. Euthp. 7b and ff.). If he had been reading the Republic, he might have fastened on cases in which predicates like 'big' and 'little', 'one' and 'many' were involved (cf. VII. 522e and ff.). But if he had been reading either of these, he would have found the predicates that lead to disagreement contrasted with others that do not: 'bigger' and 'smaller' in the Euthyphro (7b-c), 'finger' in the Republic (523c--e). I think there is a way around this limitation in the argument. But we can see that there had better be if we look at the attempted transition from the denial of the law of non-contradiction to "Protagoras' claim". Here Aristotle reverts to formulations of the two theses that rely on "is so" rather than "is true": the mention of truth is only casually related to the argument. It goes: The same thing both is and is not. Normally, we would take it that where you think that Socrates is a platypus, and I that he is not, you think falsely, since what you think to be so is not so, and I truly, since what I think to be so is so. But if Socrates both is and is not a platypus,
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then what I think to be so is so, and what you think to be so is so. So everything that seems so is so. The argument from Protagora~· claim to the failure of the law suffered from the fact that we had no reason to expect disagreement over every claim that anyone might make. If we tum that coin over, we shall find a corresponding defect in this one. For just as we have no reason to think that we shall find disagreement over every claim, so also we have no way of telling in advance where we shall find disagreement. People, for all we know so far, might fall out over any question. So to get from the breakdown of the law of non-contradiction to the claim that whatever anyone takes to be true is true, we need that law to break down everywhere, or for any arbitrary term as predicate. Either that, or we need a specification of the terms for which it breaks down, and some reason to think that we shall only find people taking opposite sides where those terms are involved. In either case, we are dealing, not with a breakdown of the law localized to one or another particular subject, but with some sort of general breakdown of the law. My project is that ofunderstandingAntiphasis' objections to the moves Aristotle makes and Aristotle's replies to them. I am now trying to erect the platform from which Antiphasis makes those objections. The major plank in that platform is that the law of non-contradiction fails pretty drastically. Here we find Aristotle connecting those drastic failures with Protagoreanism. But we cannot, on the face of it, get from Protagoreanism to the general or semi-general failure of the law of non-contradiction. Actually, though, I think we can get from Protagoreanism to a general breakdown of the law. But we have to ask: how might we get to Protagoreanism? II. SOME SOPHISTRY
The question 'how might we motivate Protagoreanism ?' is not here a straight historical one: I am not about to interpret the sophist Protagoras. Nor am I saying that Aristotle's Antiphasis is a stand-in for Protagoras, or for anyone else.s But there is a basket of ideas associated with Protagoras' name in Plato, and reason to think that rummaging in that basket will tum up something helpful. For in Plato, Protagoras' name is associated with a sort of breakdown of the law of non-contradiction. The breakdown is not the one that Antiphasis pictures, but it is related.
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In Plato's Euthydemus (285dff.), Dionysodorus adopts the view that there is no such thing as one person contradicting (d.vttA.&yew) another; Socrates ascribes that view and (or?) the argument for it to "Protagoras and those around him, as well as people still older (o{ clJ.tcpi Ilpco'tay6pav ... Kai o{ tn 1taA.at6'ttpot 286c2-3).9 The argument for it is connected with one that has just shown it impossible ever to say anything false (286al-4; cf. 283e-284c). If, for the moment, we skip the details, we can see the promise in looking into this. Suppose we have shown that it is impossible ever to say anything false. This thesis is used in the Theaetetus (I 66a, c; cf. Sph. 236de, 240bc) 10 in support of Protagoras' view that what seems so to someone is so for him. In the Euthydemus, Dionysodorus' thought is, very roughly, that since for one person to contradict another, one of them would have to be saying something false, and that is impossible, two people cannot contradict each other. Suppose we deny Dionysodorus' conclusion: suppose we insist that people can contradict each other. But suppose we hold on to the claim that it is impossible to say anything false. Then we'd have to conclude that when one person contradicts another, they are both saying the truth. And that is Antiphasis' thesis. It may seem that it is not; it may seem that it falls short in just the way Aristotle's attempt to get that thesis out of "Protagoras' view" fell short in the last section: here, it may seem, we only have the law of non-contradiction breaking down when people actually utter things that contradict things uttered by others. But that is not so, or, at least, not obviously so. We have here caused the law to break down by ruling out the possibility of saying anything false. The breakdown, then, is not restricted to actu;;&lly uttered contradictions; it affects anything anyone could utter. We might, perhaps, have allowed Aristotle a parallel move in the last section: we might have allowed him to read "Protagoras' view" as saying that anything anyone might believe to be so, is so. We would still have had a little trouble: it is hard to see how anyone even might believe that Socrates is the evening star; it is hard to see what believing that would be believing. But there is no difficulty in imagining someone saying that Socrates is the evening star, if saying that can be done by uttering the sentence "Socrates is the evening star". And the Euthydemus demands, I think, no more than uttering the sentence.n
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All this is only a first approximation to Antiphasis' views. To begin with, it is only a first approximation to Dionysodorus' and Euthydemus' views. Let us shelve Antiphasis for a bit and consider these people. In the Euthydemus, the rejection of the possibility of one man contradicting another comes of a composition of confusions. The argument for that rejection is the last of a set of three arguments. The first of those arguments is this. Cleinias, one of the interlocutors, has come to Dionysodorus and Euthydemus to gain wisdom. He is assumed by his friends to be, as things are, ignorant. So, says Dionysodorus, you want him not to be ignorant, which is what he is now; so you want him not to be what he is; so you want him not to be: you want him to be destroyed (283c3-d8).12 Clearly, Dionysodorus has been carried away by Leibniz' law.1a He is, we might say, making the identity of that of which something is true vary with what is true of it. That need not be an error. If it is true of Cleinias that he is ignorant, but not true of Axiochus' only son that he is, Cleinias is not Axiochus' only son. Here there is no error, but there is a danger. For if we are Bradley-minded,l4 we may read this as having the consequence: since Cleinias is ignorant, if he weren't ignorant, he wouldn't be Cleinias. Dionysodorus is, in that sense, Bradleian: he concludes that if Cleinias weren't ignorant, he wouldn't be what he is, that is, there wouldn't be any Cleinias.l5 We might be able to get this to work with predicates other than 'ignorant': we might want to say that since Cleinias is a man, if he weren't a man, he wouldn't exist. This is, of course, no consequence ot Leibniz' law; if it is true at all, it is a consequence of some special feature of the predicate 'man'. Predicates having that special feature have been called 'essential predicates', and that is what I shall call them.l& They have a prominent place in Aristotle, and in particular, in his second refutation of Antiphasis (1007&20ff.). So it is going to be important to see what bearing this argument of Dionysodorus' has on those that follow. We might put the upshot of the argument like this: Dionysodorus makes the identity of what something is true of vary with what is true of it in such a way that everything true of it is essentially true of it. If Cleinias weren't soand-so, whatever the so-and-so, he wouldn't be Cleinias. One of the reasons one might have for saying that some predicates true of Cleinias are essential to him and others are not is that the essential
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ones nail him down through time, through such changes as he undergoes as a result of education, etc. (cf. here Plato, Phd. 102b-103a, esp. 102e4-S, Aristotle's Categories 5. 4&10:ff., and perhaps An. post. A 22. 83&1-21, etc.).l7 Here Dionysodorus rules out changes in Cleinias by making all the predicates true of him essential to him. But it is of some importance to see that it is not only changes in Cleinias that are ruled out. As things are, for those of us who are not convinced by Dionysodorus, we can think what Cleinias would be like now, while he is ignorant, if he were not ignorant. But our ability to think that would be denied us if we followed Dionysodorus: as he sees matters, if we were thinking of anything when we tried to picture Cleinias not being ignorant, it couldn't be Cleinias, who is ignorant. This is the connection between Dionysodorus' argument and the next one, offered by Euthydemus, that destroys false statements. It begins with Euthydemus asking whether someone who says something false does it "by saying the thing his statement is about, or not by saying it" (283e9-284al : 'lt6Ttpov A.tyoVTa TO 'ltpiiyJJ.a 'lttpi oi'> liv 6 Myoc;, Tj, '11 Jl.Tt A.tyoVTa). We stooges are expected to understand this, and fall into its confusion; we respond: he does it by saying the thing his statement is about. Our ability to understand, and our correlated propensity for being confused, is in part dependent on our speaking Greek: there the verb for saying or stating is also a verb for mentioning and talking about, and the noun translated 'thing' ('ltpiiyJJ.a) might also come into English as 'fact' or 'situation'. So when we grant Euthydemus that someone who says something false does it 'by saying the thing his statement is about', we might well be thinking that anyone who says something, false or not, is talking about something, and what he is talking about is what his statement is about. But we might also be thinking that anyone who says something, false or not, is presenting us with a situation, and the truth or falsehood of what he says turns on whether that situation obtains in the world around us. If we were thinking either of these things, it might be innocuous (we might have troubles, if we were thinking the first of these, over the idea that 'there are no unicorns' is about something, and that would no doubt please Euthydemus; but these are not the troubles he primarily wants us to have here). But if we do not keep clear as to which of these two things we are thinking, we are caught.1s For Euthydemus now gets us to live up to our existential commitments:
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he gets us to admit that there must really be a 'thing one's statement is about', distinguishable from anything else there might be (284al-5). And that, he says, makes the statement true (284a5-8). Suppose I say 'Cleinias is wise'. Suppose (ignoring unicorns and bald but non-existent kings) I concede that there is, must be, a 'thing my statement is about'. How much of the sentence is required to identify that 'thing' and distinguish it from everything else? Normally, just looking at the English phrase 'the thing my statement is about', one would say: 'Cleinias' and context. Of course, that does not distinguish what I say when I say that from what you say when you say 'Cleinias is ignorant'. And we can agree with Euthydemus that these two things ought to be distinguished. But we ought to insist that 'Cleinias' and context do not distinguish them because they were not supposed to distinguish them; the distinction is, rather, made by the different things said about Cleinias in that context. But then we ought not to have conceded so readily that someone who says something false does it 'by saying the thing his statement is about'; we ought to have insisted that there were two questions there, and that a commitment to the existence of a thing the statement is about is not a commitment to the existence of a thing of which the statement is true, or to the obtaining of a situation the statement describes. But then we ought to have got off the train of thought still earlier: we ought not to have let Dionysodotus' argument go by a minute ago. For it is true that when I say 'Cleinias is wise' I am envisaging Cleinias wise. He is not; if we are to think rightly of Cleinias, we shall have to think of Cleinias ignorant. But if Dionysodorus had his way, Cleinias wise and Cleinias ignorant would be two different things: it can't even be the same Cleinias that I envisage wise and you ignorant. So distinguishing what I say from what you say carries with it a distinction between what I am talking about and what you are talking about. I am talking about a wise Cleinias, and you about one who is ignorant. We did not make these distinctions at the time, and we are, presumably, too muddled to make them now. Anyway, Ctesippus, the interlocutor with whom we have been identifying, is too muddled to make them, and make them stick. He first tries opting out of his commitment to the existence of the thing that is said; he says that somebody who says something false "doesn't say things that are" (284bl-2). Euthydemus undoes him by arguments now classic, and with which my concern here is, fortunately,
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marginal.l9 Ctesippus then comes close to distinguishing what is said from what it is said about; he says that somebody who says something false says, or talks about, things that are, but not "as they are" (284c7-8). This Euthydemus handles by devious moves with the adverbial "as they are": it emerges that to 'talk about things as they are' one would have to talk hotly about hot things, and so on (284c9-e6). This is of some, but again, marginal, interest: it makes 'telling it like it is' a way of talking; it transfers what was supposed to have been a feature of what somebody says to his saying it. But I want to leave this as it is. Dionysodorus next undertakes the rubbing out of our possibly contradicting him; by now, there is nothing to it. Suppose each of us says something. If we say the same thing, we are not contradicting each other (286a4-7). If neither of us says that thing (if neither of us is talking about that thing), we pass each other by: again, we are not contradicting each other (a7-b3). And if I say one thing (e.g., 'Cleinias is wise', where I am talking about a wise Cleinias) and you something else (e.g., 'Cleinias is not wise', in which what you are talking about is a Cleinias who is not wise), we are still not contradicting each other, for we are talking about different things (b3-5, 6). And, of course, we cannot have it that where one of us is saying something, the other is saying nothing: saying nothing is not saying anything (285e9-286a3, b5-6). Dionysodorus, using arguments that Socrates ascribes to "Protagoras and those around him", concludes that two people cannot contradict each other. Antiphasis says that they can, and they're both right. There is a difference between these two positions, and Aristotle does not, I think, keep this difference firmly in mind. In this he follows Plato. Plato comes close to seeing the distinction. In the Cratylus, Socrates presents Hermogenes with two doctrines, both to be rejected. One is that of Protagoras, that things are for a person as they seem to him (385e-386a, 386c). The other is ascribed to Euthydemus, but it is not what we would expect if we had just been reading the Euthydemus. 20 In the Cratylus, Euthydemus' doctrine is to the effect "that all things belong equally to all at the same time and always (rtiiot 1t1l.v-ra 6J.1oiro~ dvat &.Jla x:ai <'Lei, 386d3-4). Socrates talks as if the doctrines he wants Hermogenes to reject were distinct in that Protagoras' made each thing unique to the one who thinks about it, whereas that ascribed to Euthydemus made each thing possess all attributes simultaneously (386d8-9). 21 Proclus, commenting
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on the passage, locates the distinction here (in Crat. p. 13.10-17). But Socrates goes on to say that once these doctrines have been rejected, it is clear that things have some firm reality [substance] of their own; [they are not] relative to us or due to us, dragged up and down by our fancy, but are fixed in their own right, relative to their own reality, just as is natural (386d9-e4.)22
So Plato apparently takes it that the doctrines have a common consequence: in Proclus' words, "so, taking off from different starting-points, these sophists arrive at the same place" (in Crat. p. 13 .17-18).23 Both end by denying that "things have some firm reality of their own". But applied to the doctrine ascribed to Euthydemus, this is at best impressionistic. That doctrine does not make things "relative to us or due to us, dragged up and down by our fancy": according to that doctrine, any predicate you like is true of any thing you like. So it is like the doctrine ofProtagoras, in that it rules out the possibility of false (subject-predicate) statements, but it is unlike the doctrine of Protagoras, in that it rules that possibility out by making every statement true as a matter of external fact. And when it comes to contradiction, the doctrine of Protagoras would rule out the possibility of our contradicting each other (we would have to be talking about different things when I say 'Cleinias is wise' and you say 'Cleinias is not wise'); that ascribed to Euthydemus would allow us to contradict each other, but make us both right. In the Cratylus, the assimilation of the two positions is in the direction of subjectivism: both are supposed to make things "relative to us or due to us". In the Theaetetus, there may be an assimilation in the other direction. Early in that dialogue, Socrates feels it necessary to buttress Protagoras' subjectivism by a theory according to which everything is in constant change (cf. Tht. 152dff.). Not only does this support look unnecessary, it looks irrelevant or worse: it supports a claim to the effect that the only truth there is relative to speakers or believers with a claim about what is happening in the world independently of those speakers or believers. And Socrates tells us that (183a; cf. Met. r7. 1012&24-26): It turns out, apparently, that if everything is changing, any answer, whatever the question, is equally correct: one could say that it is so, and not so ....
He goes on to suggest that the supporters of the 'theory of flux' might object to that last clause, but not because it makes no reference to those for whom something is so, or not so: rather because it seems to bring the
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flux to a halt; really, we might have to say "becomes so, and not so" 183a6-7; cf. 157a-c). Besides, when it comes to the refutation of Protagoreanism in the Theaetetus (170&ff.), Plato is sometimes accused of working it by suppressing the reference to the speaker or believer in the statement of the doctrine. The doctrine is that what seems so to someone is so for that someone; on the face of it, that qualifying phrase drops out mid-refutation, and, the accusation reads, the refutation depends on its dropping out. 24 I am not altogether convinced that the refuattion cannot be reconstructed, but, as it stands, the accusation is true. The point is that if that reference goes, and nothing is done to disarm the paradox of false statement, we are left with the doctrine ascribed to Euthydemus in the Cratylus: if, when I say 'Cleinias is wise' and you say 'Cleinias is not wise', we are both right, and talking about the same Cleinias (not I about one that exists for me and you about one that exists for you), the law of non-contradiction fails. Aristotle, just once (in r6. 1011 a 17-b3), shows that he is aware of the reference to the believer or speaker in the statement of Protagorean doctrine. He is hardly sympathetic. He says, echoing Plato (Crat. 386de, on p. 69 above): If not everything is relative to something, but some things are also themselves in their own right, not everything that appears is true. For what appears, appears to someone, so that anyone who says that everything that appears is true makes the things that are relative to something. That's why those who seek compulsion in argument and at the same time demand that they maintain a position25 have to be on guard, [and say] that- not what appears is - but what appears [is] for the one to whom it appears and when it appears and as and how [it appears]. If they maintain the position, but don't maintain it that way, it will soon turn out that they are saying contrary things ... (1011•17-25). But, no doubt, this is why it is necessary for those who say this, not out of confusion but for the sake of argument, to say that this is, not true, but true for this (person] (1011 bl-3).
For Aristotle, then, the inclusion of a reference to a speaker or believer is little more than a debater's dodge, not to be taken seriously. Antiphasis is supposed to be defending his position 'for the sake of argument' (cf. p. 17 above), and his position is supposed to be equivalent to Protagoreanism (Section 1), and we now find that those who maintain Protagoreanism 'for the sake of argument' are supposed to be careful to stick in the reference to the speaker or believer. But if Anti-
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phasis had tried to find a place for that reference in the statement of his position, he would not have had that position: he would not have been denying the law of non-contradiction, but denying it application. The situation, summarized, is this. I say 'Cleinias is wise', and you say 'Cleinias is not wise'. jlili ·-~..---·
Before the sophists get to us, we should take it that we were saying contradictory things about the same man, Cleinias, and that one of us was saying something true about him, the other something false. Suppose Cleinias is ignorant. Then what you say about him is true, and what I say about him is false. We encounter three sophists. Each of them has some terribly confusing argument or other to show that no one can say anything false. The first shows us that no one can say anything false. "So," he says, turning to me, "since Cleinias in fact is not wise, when you said 'Cleinias is wise', you were just making noises, doing no more than you would have if you had been beating a bronze pot." This sophist is the Cratylus of the Cratylus (429c-430a). I have not said much about him, and will pretty much continue the silence: he is committed to saying that the law of noncontradiction never applies, because one half of each contradictory pair of sentences is only sound without sense. The second shows us that no one can say anything false. "So," he says, "you must both be right, and so you must be talking about different Cleiniases: each of you has your own, and one is wise, the other not." This, I think, is Dionysodorus, or the Euthydemus of the Euthydemus. He is committed to saying that the law of non-contradiction never applies, because the halves of a purportedly contradictory pair of sentences are about different things. And he is some sort of subjectivist. The third shows us that no one can say anything false. "So," he says, "you must both be right, and you are talking about this same man, Cleinias, so Cleinias must be both wise and not wise. And that works for anything anybody might say about Cleinias, or about anything else. So everything has every predicate and the negation of every predicate." This is the Euthydemus of the Cratylus. And he is Antiphasis. The difference between Antiphasis and the second of the above sophists, who has some claim to be counted as a spokesman for Protagoreanism,
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is due to Aristotle's attitude toward subjectivism: he thinks it hardly worth mentioning. The likeness between Antiphasis and that spokesman for Protagoreanism is that both rule out the possibility of false statements. If we were right a few pages ago, one of the factors involved in ruling that possibility out was a confusion over the identity of what a statement was about: it was made to turn on what the statement said about it. If we look again at what Aristotle says to Antiphasis, I think we will find that it is this confusion Aristotle wants to undo. NOTES 1 The phenomenon is visible in Alexander as well: cf. in Met. 271.27ff., e.g. Lukasiewicz complains about it: 'On the Principle of Contradiction', pp. 499-500. 2 cr. Chapter II n. 8 above. a cr. Chapter VI, n. 16 on 'q>acnc;'. I do not see how Apostle got his translation of the last clause of this passage, aU-12: "And if it does not apply to all, they should have stated the exceptions" (AM p. 63). 4 cr. Kirwan, AM 104. & I imagine Alexander is right (in Met. 294.5-9) in supposing that the predicates exempted from the breakdown of the law, if there were any, would be predicates essential to their subjects: cf. Chapter V, Chapter VI, Section I. s This point is Kirwan's: cf. AM 106. It had virtually been anticipated by Guthrie: cf. History iii. 182 n. 3. 7 AM106. a One candidate, in particular, ought to be mentioned: Antisthenes. Proclus (in Crat. 429d, p. 12. 18-23 [Pasquali] ascribes the straight argument for the impossibility of false belief to him, and says that the distinction missed by him is that between what something is said about and what is said. He says of someone who says something false: "Kai ~t 6 /J:ymv 7tEpi 'ttVo<; /J:yEt, lCUi o{Jxi n /J:yEl" (12. 22-23). It is hard tO fit this with what Aristotle says in Met. 1129. 1024b34 (cf. Caizzi, 'Antistene', 57-58; the passage from Proclus appears in Caizzi's Antisthenis fragmenta as fr. 49). But I have preferred talking about texts in Plato from which an argument can be obtained to attempting to reconstruct Antisthenes, who has become a scholarly football. For one attempt and references to further literature, cf. Guthrie, History iii. 209-11 and index s. v. 'Antisthenes'; and cf. Burnyeat, 'The Material and Sources of Plato's Dream', pp. 108-17. 9 On the translation, cf. Guthrie, History iii. 182 n. 2. If Plato had anyone in particular in mind when he mentioned "people still older", I suppose it was Parmenides: not because Parmenides, in Plato's estimation, failed "in establishing a criterion of truth" (Sprague, Plato: Euthydemus, p. 28, n. 46), but because, in Plato's estimation, the rejection of the possibility of false belief had its roots in Parmenides: cf. Soph. 24ld and ff. (cr. Sprague, Plato's Use of Fallacy. p. 47, n. 23, which suggests this, although it manages to squeeze Heraclitus in, superfluously, as does Guthrie, History, Joe. cit.)
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1° Diogenes Laertius (IX. 53) takes the paradox of false belief quite seriously in reconstructing Protagoras' views, but it seems to play no real part in text-book reconstructions: cf. Guthrie, History iii. 181fT. Contrast Vlastos, 'Introduction' to Plato's Protagoras, pp. xivff. 11 By contrast with Crat. 429d-430a. Soph. 237e is a different, but related, point. 1a cr. Stokes, One anti Many in Presocratic Philosophy, 4-5. 18 •That is, if x=y, and Fx, Fy. Perhaps this is miscalled "Leibniz' Law": cf. Feldman, 'Leibniz and "Leibniz' Law"', and Curley, 'Did Leibniz State Leibniz' Law?'. Cf., for one passage in which Leibniz certainly seems to state it, Lewis, Survey of Symbolic Logic 291 (also in Leibniz, Logical Papers, 122). For comments and clarification, cf. Cartwright, 'Identity and Substitutivity', 119fT. 14 The (bad) argument from Leibniz' Law to the claim that all predicates are essential (all relations are internal) is hard to find in Bradley: cf. Appearance and Reality, Chapter III. It is associated with his name because of Moore, 'External and Internal Relations'. The above is a modified version of Moore, applied to Dionysodorus. 11 There are problems about taking 'Cleinias isn't Cleinias' to amount to 'Cleinias doesn't exist': cf. Kirwan, 'How Strong Are the Objections to Essence?', p. 43. Leibniz apparently so took it: "AB non=AB (seu AB non est res)", §152 of Generales Inquisitiones etc. (but cf. also§ 155). cr. also Mates, 'Leibniz on Possible Worlds', 341, 347-51. 18 cr. Copi, 'Essence and Accident', and Kirwan, 'How Strong Are the Objections to Essence?', 43. 1 7 This motivation is not confined to antiquity: cf. Wiggins, Identity and SpatioTemporal Continuity (passim, but cf. n. 43, p. 72 and refs. there pp. 30ff.); Shoemaker, 'Wiggins on Identity', PR 534-40 or Munitz 109-13; Hirsch, 'Essence and Identity'. 18 I want to stay clear of the Sophist, but the above has a lot to do with the problems Plato there confronts. cr. esp. M. Frede, Priidikation und Existenzaussage, 94-95; Owen, 'Plato on Not-Being', 262-65, and Wiggins, 'Sentence Meaning, Negation, and Plato's Problem of Non-Being'. 19 cr., on this passage in particular, Hintikka. so At least, not on the basis of the passages we were just considering (cf. next note). The confusion of the two doctrines goes back a long ways: cf. Vlastos, 'Introduction' to Plato's Protagoras, part I, n. 26a (pp. xiii-xiv). ll1 Meridier, in Platon: Cratyle (p. 54, n. 2) refers us to Euthd. 294a ff., 296c for Euthydemus' espousal of this doctrine in the Euthd. The point in those passages is a totally different one. I wonder if this is a misprint, and the reference should have been to 284a If., 286c. If so, Meridier would be confusing the two doctrines I want to distinguish. as "are fixed in their own right, relative to their own reality": "Ka9' ai'J'tci x~ 'tt)v ai'J'tci'IV oocrlav liXOV'ta". cr. Tht. 152d, 153e, 157a (Chapter IV, Section II below), and Aristotle, Met. r 6. 1011"17ff. (p. 70 below). 28 "tK 6w.q~6pmv o~v O.px&v 6pJ.I.(hJ.I.SVOl o~ot ot croq~tcnai eic; 'tO ao'to Ka'tal.:fryooow." 24 cr. Vlastos, 'Introduction' to Plato's Protagoras, part I, n. 27 (p. xiv). s& The term is taken from the practice of dialectic: these people are demanding that they be allowed to play the answerer in a dialogue in which they will defend Protagoras' doctrine. cr. "i'Jxtxsw" in Top. 9 3. 158"31, 9. 160b14, 17, 21-22. cr. Moraux, 'La joute dialectique', 282, n. 2.
CHAPTER IV
THE FIRST REFUTATION: THE TREATMENT OF ANTIPHASIS
The main line of the refutation of Antiphasis is a straight argument for an instance of the law of non-contradiction. It is not a limitation in it that its conclusion is only an instance of the law, since the argument is easily generalizable: it can be used against someone who simply denies the law, who says 'it isn't so that the same thing can't both belong and not belong to the same thing at the same time and so on'. But Antiphasis is saying something stronger: that the law breaks down all over the place. It is not essential to the main line of the refutation that he is saying that, since the argument would go against that as well as against less extravagant claims. But his saying the more extravagant thing is central when it comes to the sub-plots of the refutation. There Aristotle tries to get Antiphasis to see the force of the distinction between a term's signifying something and its being true of something: between what is said of Cleinias when it is said that he is wise, and Cleinias, of whom it is said that he is wise. It is Antiphasis' failure to grasp that distinction that leads to his view that the law of non-contradiction fails quite generally. This may seem too charitable to Antiphasis. He is supposed to be taking up Heraclitus' thesis 'for the sake of argument' (5. 1009&21); he is asking to be forced to give up his denial, rather than to be persuaded that he is confused in making it (6. 1011&13-16, 5. 1009&17-18); refutation of him, unlike persuasion of those who deny the law as a result of real confusions (about change), is a matter of shooting at his words, not his thought (5. 1009&18-22: this is supposed to be shallow practice in Top. A 18. 108&18-33, An. post. A 10. 76b24-27; but the distinction is not as far-reaching as one might think: cf. Soph. el. 10, which is directed against it, or against a formulation ofitl). The only motivation Aristotle suggests for his denial is that, in ignorance of analytics, he wants a proof for everything (4. 1006&5-11, 6. 1011&8-13). Aristotle's initial picture, then, is one of Antiphasis saying: what would happen if I denied this? Could you show I was wrong? But that underrates Antiphasis, or, better, it underrates Aristotle him-
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self. Aristotle sees his main point as that of showing what to do with someone who wants a proof for everything, even the law of non-contradiction. But he can't give Antiphasis a proof; there aren't supposed to be any. He suggests a dialogue. In outlining the dialogue, he gives an argument that would (ignoring the reservations in Chapter II, Sections 11-111) come close to doing the job. But, in philosophical conscience, he has to ask where someone might give him trouble in the course of that argument. In asking that, he has to make trouble for himself out of the materials available to him. The materials available, the ones that were in the philosophical air, include those we looked at in the last chapter. Those he uses to construct Antiphasis, who is confused enough not to grant the steps of the main argument without some softening up. So he has to straighten Antiphasis out. At one point he shows a fleeting consciousness that there is a little substance to Antiphasis: in 5. 1009&20--22, he says, of Antiphasis and others who take up his thesis 'for the sake of argument', "the cure for them is a refutation of their argument [or 'position'] [as it is put] in speech and in words". The question now is, how does Aristotle give him the cure? I. ON CONTRADICTION
Antiphasis' thesis is to the effect that some, a lot, or even all 'contradictions' are true. He gives us no method for picking out contradictions. As a preliminary, let us consider this. Since Antiphasis is denying what Aristotle was asserting in r3 when he propounded the law of non-contradiction, we have to suppose that what would count as a contradiction for Aristotle is what would count as one for Antiphasis. A contradiction, Aristotle says, is an assertion paired with its opposite denial, where the denial has (or is) a term denied without homonymy of the same subject of which, in the assertion, it was asserted (De int. 6. 17b33-35; cf. An. post. A 2. 72&13-14).2 This is not the only way of defining 'contradiction' or 'contrary pair'; indeed, it is arguable that it leads to too many complications to be worth it. In De int. 1. 17b29-37, Aristotle allows 'a man is pale' and 'a man is not pale' to count as a contradictory pair. The intended interpretation of these sentences is apparently 'some man or other is pale' and 'some man
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or other is not pale': Aristotle says that both are true, and so concludes that the members of a contradictory pair can have the same truth-value (cf. 8. 18a 10-11 ). This, of course, is not a breakdown of the law of noncontradiction, but it would force Aristotle to modify some of the things he says in r: e.g., "it is impossible for a contradictory pair to be true of the same thing at the same time" (6. 10llbl6-17). The trouble is that in the De interpretatione Aristotle's criteria for 'the same subject' seem to be merely syntactic: of course, they would have to be strengthened to make the claim of r6 true, and strengthening them might prove difficult. Those criteria would have to be strengthened even to make the De interpretatione come out right. He says in 7. 17b27-29 that where the subject is particular, such as 'Socrates', the contradictory pair must diverge in truth-value. This will not be so, though, if all that is demanded is that the name 'Socrates' occur in the subject position in both sentences: there were at least twelve men named 'Socrates' in antiquity. And there is a further difficulty: to make this claim about contradictoties with particular or singular subjects work, Aristotle would presumably have to count 'Socrates is pale' as false and 'Socrates is not pale' as true when there is no Socrates. This is what he does at Cat. 10. 13b27-33. But it is no easy matter to reconcile this with his saying that from 'Homer is a poet' it does not follow that Homer is (if that is what he says: cf. De int. 11. 21 a24-28), and this latter comment goes with a recurrent thought of Aristotle's: "it isn't so that if that which is not is something [e.g., believed in], it is simply" (Soph. el. 25. 180a37-38; cf. 36-37 with 5. 167a1-2, Top. L\1. 121 a22-24, De int. 11. 21 a32-33). a There is, I. think, a way out of this trap, but it is not of central concern now: I have outlined it in an appendix. 4 The general point is that Aristotle might have avoided some of this trouble if he had defined 'contradiction' in terms of a pair of sentences, one of which is the negation of the other. It is plain that he could have handled the distinction, or something like the distinction, between negating a sentence and negating a predicate: he does something like it in Prior Analytics A 46, and the passage (De int. 1. 17b26-33) that leads up to the definition of 'contradiction' pushes in the direction of sentential negation (cf. also Met. r7. 10llb26-27). But this is not his strategy in the De interpretatione or in dealing with Antiphasis. In n, he puts the law of non-contradiction in the form 'the same thing cannot belong and not belong to the same thing': here the
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identity of the subject of which two contradictory things are said (if it is done in two sentences) is going to have to involve more than the mere identity of the grammatical subject of two contradictory predicates. There are two points to be made in connection with this way of understanding 'contradiction'. First, Antiphasis' acceptance of it does not prejudge the issue against him. Dionysodorus had, in effect, made it a requirement for one person's contradicting another that one of them be wrong: since no one can be wrong, no one can contradict anyone. If that were the notion of contradiction operative in r4, Antiphasis would be in trouble. But it is not. Aristotle does show a tendency to build into the notion of a contradiction the idea that there is no middle between contradictories (as in An. post. A 2. 72&13-14, Met. I 4. 1055a38-b2, b8-9, 7. 1057&33-34, Phys. E 3. 227&7-10), and so some tendency to count as contradictory pairs only such sentences as obey logical laws. But this is only a tendency; it does not show up in De interpretatione 6, where 'contradiction' is defined; rather, the laws of logic get separate treatment (cf. 7. 17b23-24, Cat. 10. 13b2-3, e.g.). And as he is willing to entertain a view to the effect that neither member of a contradictory pair is true in De interpretatione 9 (cf. '&.vr{cpaot~' in 19&27, 35, 37), so here he is entertaining a view to the effect that both are true. In short, we can identify contradictory pairs without using the law of non-contradiction to do it, so Antiphasis is not doomed from the start. But, second, this way of taking 'contradiction' rests on a distinction between what is said about something and the something about which it is said: it tells us that the law of non-contradiction would break down where we had two things, one the negation of the other, true of the same thing. And the distinction here is one that will give Antiphasis trouble, if we can get him to accept it. Why should it give him trouble? The denial of the possibility of a false statement rested on a confused view of the way in which words applied to the world. On this view, the function of those strings of words which we would consider sentences, in which claims about the world are formulated, was that of identifying an object; the identity of the object depended on every one of the components of the sentence. If the object identified by the sentence was not there, the sentence
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identified nothing: the sentence signified nothing. And so, given the plain fact that both the sentences 'Cleinias is wise' and 'Cleinias is not wise' make sense, it must be that one of them identifies something that is wise and the other something that is not wise. Antiphasis' idea is that both sentences identify the same thing, and contradict each other; both are true, so the law of non-contradiction goes. But the fact that distinct terms can be predicated of the same thing blocks the idea that the identity of what is being talked about varies with what is said about it. Aristotle makes a point close to this, in passing, in Posterior A.nalytics A 33. The point is not quite the same, in that it has to do with believing rather than saying, and goes against a schematic statement of the paradox (according to which what one purportedly believes when he believes something false, he doesn't really believe). But it is close enough. Aristotle is defending the notion that "there is a true and a false belief of the same thing" (89&24: I use the construction 'belief of something' because the natural alternatives, 'belief in something' and 'belief about something', seem to settle the very ambiguity that Aristotle is here trying to straighten out). He says, in defense of that notion (89&25-28): For that there is a true and a false belief of the same thing, as some people put it, leads them to accept absurd consequences, and among others, [the consequence] that what one believes falsely one does not believe.
This, presumably, is the paradox of false belief: if you believe, falsely, that Cleinias is wise, you have a belief'of' (in) a wise Cleinias; there isn't any such person; so you have a belief 'of' nothing; you have no belief. Aristotle hangs the resolution of this on the word 'same' (89&28-32): But since the same is said in many ways, in a way it is possible [that there should be a true and a false belief of the same thing], and in another way not. For believing truly that the diagonal is commensurable is absurd, but because the diagonal, which is what the beliefs are about, is the same, the beliefs are of the same [thing], but what it would be for each of them to be, in accordance with the statement, is not the same.&
The jargon here makes this sticky, but it seems to come to this: the belief that the diagonal is commensurable with the side of a square and the belief that it is not are beliefs 'of' the same thing in the sense that they are beliefs about the same thing, but what someone who believes the first believes is not the same as what someone who believes the second believes. The first believer believes in a commensurable diagonal, the
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second in one that is not, and a statement of what each believes would show that. 6 This is the distinction we have to get across to Antiphasis: between something talked about and what is said about it. We could say: between subjects and predicates. But in putting it that way we have to bear in mind that the subject is not the word or expression that is the grammatical subject of the sentence uttered: when we say that Cleinias is wise, we are talking about Cleinias, the man. And so also we have to bear in mind that the predicate, what is said of the subject, is not the word or exppression that forms the grammatical predicate of the sentence uttered. If I say 'Cleinias is far away', meaning that he's in New Zealand, say, and you say 'Cleinias is far away', meaning that he isn't very talkative, what I say of Cleinias and what you say of him have to be distinguished both from him and from each other. It is a distinction this strong that Aristotle uses in putting his definition of'contradiction': the subject must be the same, and the predicate affirmed of it cannot be homonymous with the one denied of it. Here 'homonymous' is used, I suppose, as often 7 in Aristotle: things are homonymous where they share a word under different definitions; being in New Zealand and not being very talkative are conditions homonymous with respect to 'far away' (this is pretty rough: we'd have to add into the descriptions of those conditions clauses about our own location, and so on). We could put our problem with Antiphasis by saying: how do we get him to see the point of talk of homonymy in the definition of 'contradiction'? Or by saying: how do we get him to see the force of the distinction we want to draw between subjects and predicates? And part of the answer seems to be: we wait for him to make a blunder that turns on his ignorance. II. UTTERING AND SIGNIFYING
Consider first the stages of the argument that precede Antiphasis' wriggling. He accepts them, but he is not clear as to what he is accepting. Aristotle first gets Antiphasis to say something: he does not, however, require him to say that anything is so, or that it is not so: Antiphasis might take that to be question-begging. Why might Antiphasis take it to be question-begging? If he wants to
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say 'that is both a man and not a man', he ought not to be reluctant to say 'that is a man'. But he plainly is reluctant to say that. In 10073 8ff., his reluctance is acute, and apparently vexing. Aristotle there says that he will be able to get the consequence he wants from Antiphasis ... if he will answer the question. But if when he is asked it simply, he adds in the negations, he isn't answering the question .... Similarly, then, even ifthe same thing is a man and not a man ten thousand times, one ought not to add, in answering the question whether it is a man, that it is at the same time not a man (1Q07a8-10, 16-18).
And at 10083 30-34 Aristotle says: At the same time it is clear that our inquiry with this man is about nothing, for he says nothing. For he says neither 'it's so' nor 'it's not so', but 'it's so as well as not so'; and then he denies both of these, [and says] 'it's neither so nor not so', for if he didn't do that, there would already be something definite.
(On the argument here, cf. 10083 3-7, p. 13 above, and n. 8 below.) What Aristotle is trying to do is get Antiphasis to say something definite: to say that something is, flatly, a man. Antiphasis is seeing any such isolated statement as at least misleading, and perhaps even false. So his position is blurry, and what is blurred is the distinction between 'that is both a man and not a man' and 'that is no more a man than not a man': it is the latter that makes the isolated statement suspect to Antiphasis. Alexander phrases Antiphasis' position as 'nothing is any more one thing than not' (cf. in Met. 274 .7, .25-26, .29-30; 294. 1-2, etc.). And that Aristotle saw it that way is clear from the fact that he supposes Antiphasis would suppose him to be begging the question by asking Antiphasis to make an assertion at the outset (and it is clear from 10083 7-20, esp. 15-22, 27-28, and cf. K 5. 1062&36-b7;8 from 1008b2-10; and from 1008b31-10093 5). This blurring is not intrinsic to the denial of the law of noncontradiction; it is, rather, the product of Antiphasis' heritage. The Protagoreans or Heracliteans of the Theaetetus insist that nothing really is anything (e.g., at 152d, 153e, 157a; cf. 1007b25-29). And Plato himself tended, at least at the time of the Republic, to see the mundane world in Protagorean terms, as a 'world of appearance'. And so he seems to have thought that there was something wrong with saying, flatly, 'Simmias is tall' {Cf. Phd. I 02b8-d2, Tm. 29b3-c3, 49d-50b): really, the many tall things we encounter here below are no less short than tall (Rp. V 479b3-5, 9-10), that is, they are neither (c3-5) or both (b8; cf. Tht. 152d, 154b-155c, 156e-157a).
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It is this blurring that causes Aristotle to treat Antiphasis' view as a bundle of views: it is possible for the same thing to be and not to be (1005b35-1006a3, b21-22); all contradictories are simultaneously true of the same thing (1007b18-19); everything is simultaneously true and false (5. 1009a9, 8. 1012a34-35); everything both is and is not, so everything is true (7. 1012a24-26, 8. 1012a33, b15); everything neither is nor is not, so everything is false (7. 1012&26-28 with 4. 1007b25-26). It is not that Aristotle runs all these together (he distinguishes a couple of them in 7. 1012a24-28); they are run together in the sophistry that stands in back of Antiphasis. We now get him to accept (S), "'Man' signifies something". If it does not, Antiphasis will not even get as far as denying the law of non-contradiction: 'that is both a man and not a man' signifies nothing if 'man' signifies nothing. Admitting this does not commit Antiphasis to very much; in particular, it does not commit him to saying that the word 'man' is ever true of anything. Presumably, Antiphasis is happy about tlus: he has not yet had to say that something or other is a man, and so has not yet been moved from the position we just found him in when we considered (U). Aristotle does stop here to point out that (S) is, by itself, a definite claim, so that Antiphasis has allowed one isolated positive claim, and has budged some (1006&26-28): And again, one who agrees to this has agreed that there is something true apart from demonstration, so that not everything is so and not so.
But this is not the major theme.
We ought to look a little more closely at the way in which (S) is noncommittal on the question whether anything actually is a man: there is a bit of sophistication quietly handed to Antiphasis here. In De interpretatione 4. 16b26-30, Aristotle points out that the existence of a significant word such as 'animal' does not involve there being any animals, and in 3. 16b19-22 he points out that the existence of such significant words as 'recovers' does not involve anything's actually recovering. He thinks that there is a difficulty about asking what something is unless we know that it is (cf. An. post. B I. 89b34-35, 7. 92b4-7), but knows that this is only a difficulty: we can define words like 'triangle' without yet having proved that there are any (cf. An. post. B 10. 93b29-35, 7. 92b19-25, A 2. 72a23-24, 10. 76b35-36).
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The point is that if all this were made explicit, and Antiphasis swallowed it, he would find himself accepting a distinction between applying a term, at which level truth and falsehood emerge, and granting it a sense, which is below that level (cf. Cat. 4. 2&4--10, 10. 13b10-12, De int. 1. 16&918, De an. r6. 43()a26-b6, Met. E 4, a 10, etc.). Aristotle does not stick as firmly as one might like to the idea that words are applied in sentences, which belong in a new syntactic world, but he is in a position to distinguish between a term's being true of something and its being significant, so that it could be true of something (cf. Met. ll. 29. 1024b17-1025&1). The situation here is parallel to the one with the notion of contradiction: Aristotle is working with, but leaving implicit, a distinction that runs against Antiphasis, and Antiphasis is accepting what Aristotle says. The distinction has so far remained below the surface of the dialogue. It begins to show through in the next step but one. III. SIGNIFYING AND DEFINING
We now get Antiphasis to give us one thing that 'man' signifies, in (almostD), and then get him to allow it to signify only that throughout the argument, in (D). It is the latter, with its stipulation of uniquencess, that Aristotle relies on in getting (1), but Antiphasis' troubles over picking one thing that is signified are as much troubles over (almost-D) as they are over (D). For once he has granted (almost-D), he is in no position to object that there is just no saying what the word signifies, and so in no position to block the stipulation that, since biped animal is one thing that 'man' signifies, we can hold the word to that significance. The direct consequence of the stipulation is that in every application of the word 'man' it will have the same significance. If there should be anything of which it is true to say that it is a man, it would be true to say that of it because it is a biped animal. Or, as Aristotle put it at the beginning of the clincher, "necessarily, then, if it is true to say of anything that it is a man, it is a biped animal (for this is what 'man' signified)" (1006b28-30). If (D) gives us this, it is natural that Antiphasis should squirm before conceding (D), and especially natural that he should squirm over the stipulation of uniqueness of significance it incorporates. But if all he can say against it is that 'man' does not signify one thing, but signifies two,
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three, or a dozen different things, then, as Aristotle tells us, his squirming is pointless. For he would have no good reason not to allow us to pick one of those two, three, or a dozen things and have 'man' signify that for the duration of the argument. But what if he doesn't say that? What if he tries to disallow us from picking one of the things signified by 'man' by insisting that 'man' signifies indeterminately many things, so that we can't pick one? Then what he would be saying would be fairly obscure. If he had said: what 'man' signifies is indeterminate, he might have had in mind something like the train of thought we looked at in Chapter II Section 3. But he doesn't say that; Aristotle rather imagines him saying that 'man' signifies indeterminately, or even infinitely, many different things. Really, his qualms are over (almost-D) (but recall that this step was not separated from (D) in what Aristotle said). He is insisting that we cannot say anything that 'man' signifies, so there is no question of picking one thing it signifies. The same allowances that we made in the last section for (S}, that it did not commit Antiphasis to saying that anything was a man, are ones that Aristotle wanted to make for such definitions as (almost-D) or (D). (cf. the passages referred to in connection with (S)}. But he does not make this explicit in talking with Antiphasis; in fact, he is very misleading about it. Consider his way of putting what the stipulation that 'man' signifies one thing comes to (1006&31-34): Again, if 'man' signifies one thing, let this be biped animal. And this is what I call signifying one thing: if this [e.g., biped animal] is a man, then if anything should be a man, this will be for it to be a man.
Suppose we do not have the notion of 'signifying' as opposed to 'being true of'. Then Aristotle's way of getting us to see the difference is this: Socrates is one thing that is a man; a biped animal is one thing that is a man. But the latter we can take to be a single thing that 'man' signifies, since we can say: if a biped animal is a man, then for anything to be a man is for it to be a biped animal. But then the concession (almost-D) is going to look to Antiphasis like a matter of granting that something, namely a biped animal, is a man. (His confusion is the converse of that interlocutors in Socratic dialogues fall into: when asked 'what is the beautiful?', they say things like 'well, a beautiful girl is beautiful'. I shall get back to this in Chapter VI, Section
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I.) And that, as he construes his thesis, is not something he ought to concede while trying to defend it. We might get a better idea of the extent of his disease if we made out a case for him. It is not, as it stands, a case for denying the law of noncontradiction, but a case for saying that there is no way of instantiating the variable in 'if x is a man, then if anything should be a man, it will be [an] x'. So you are never saying anything generally determinate (anything that will carry over from one utterance of the word to the next) when you say something of the form 'this is a man'. To concede that 'man' signifies one thing is to concede that applications of the word 'man' under varying circumstances, to different (hypothetical) individuals, will carry the same significance. But that, Antiphasis might think, cannot be so: if 'man' is true of Socrates, and true of Coriscus, and Socrates and Coriscus are different, then 'man' plainly signifies different things; here, Socrates and Coriscus. And there is no saying, in advance, how many men there are. You yourself, he might say to Aristotle, often comment on the indeterminate or infinite plurality of individuals (cf. Top. B 2. 109b14, Soph. el. 1. 165all-12, An. post. A 24. 86a3-4, Met. B 4. 999a26-27, and perhaps Rhet. A 2. 1356b32-33). And since you are a believer in the eternity of species (you say, e.g. " ... there is always a class of men, of animals, and of plants" in De gen. an. B 1. 731b5-732a2, and recall De an. B 4. 415b6-7 and De gen. et corr. B 11. 338b5-19),9 and since you say in the same breaths that no member of those species is eternal, you are committed to saying that there are infinitely many men in all eternity. So I want to say that 'man' signifies infinitely many things, in that its application to new men gives it new significance, and so that there is nothing to put into the blank in "if anything should be a man, it will be a man because it is _ _ ". I'd like, incidentally (Antiphasis might continue), to point out that in one of the places where you go on about the infinity of individuals, you almost saw the truth. You say (Soph. el. 1. 165a10-13): ... words [or 'names'] and the number of phrases [or 'accounts'] are limited, but things are infinite in number. So it is necessary for the same phrase and the single word to signify more than one thing.
That is nearly what I want to say. But you don't draw the obvious consequence, and I do: if the fact that there are infinitely many things and only
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a finite stock of words or phrases 1o with which to talk about them makes it necessary for some word or phrase to signify more than one thing, it makes it necessary for some word or phrase to signify infinitely many things. For any exhaustive division of an infinite plurality into a finite number of classes will give you at least one infinitely large class. The association of words with things is, on your own view, like that. And we've just seen that, also on your own view, 'man' is a word associated with an infinitely large class. So, again on your view as it emerges from the passage I just quoted, the word 'man' must signify n infinitely many things. And that is precisely what I want to say. We can push Antiphasis' case even farther than this. Besides, he might go on, the men themselves change: they are now pale, later dark; now ignorant, later wise; now crude, later cultured. You've read Theaetetus 158e-160c (cf. 157bc) and Euthydemus 283cd as well as I have, and you know I'm sympathetic toward Protagoreans; they point out, in those passages, that these variations make for different things. Socrates sick isn't the same as Socrates well. Here again we are dealing with variations that are in principle unpredictable (cf. Met. E 2. 1026b3-4, 10273 6-7, 19-26, An. post. A 30-31, 33) and indeterminate or infinite in number (cf. Met. E 2. 1026b7-10, K 8. 10653 24-26, Phys. B 5. 196b27-29, and perhaps Rhet. A 2. 1356b32-33). So when you call Cleinias a man while he's ignorant, 'man' signifies a thing different from what it signifies when you use it of him after he becomes wise. At that rate, it looks as if any new application of the word 'man' will carry a new significance. So Antiphasis concludes that the whole picture, of 'man' signifying one, two, or a dozen things, is ridiculous; he concludes that 'man' signifies infinitely many things, and in a way that precludes our picking one and insisting that repeated occurrences of the word bear that significance. Aristotle's response to this is (1006b6-ll): it is plain that [at that rate] there wouldn't be any argument. For not signifying one thing is signifying nothing, and when words do not signify our dialogue with each other is destroyed, and, really, [so is] dialogue with oneself: for it is not possible to think without thinking one thing, and, if it is possible, one word could be given to this thing.
It is tempting to translate 'A.6yor;' in the first sentence of this as 'discourse' instead of (as above) 'argument'.12 The rest of the passage makes it clear that Aristotle is primarily concerned about his debate with Antiphasis, and is insisting that if Antiphasis were right, he wouldn't be able to parti-
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cipate in it. But the point Aristotle wants to make is more general than this. It had already been made by Plato. After laying out a series of objections to the theory of forms, Parmenides says (Parm. l35b5-c2): But still, Socrates, if somebody who looks at all these [objections] and others of the sort won't allow that there are forms, and won't distinguish a specific form for each single thing, he won't have any place to which to turn his thought, since he isn't allowing that there is an idea, always the same, for each of the things that are, and thus he will demolish our capacity for dialogue.
Aristotle, naturally, did not buy the conclusion that there were forms, but he certainly accepted the idea that our ability to communicate depends on our being able to say the same thing of different things (the 'one over many' argument of Met. A 9. 990b13: cf. Alexander, in Met. 80.8-15) and the correlate idea that our ability to think, to talk to ourselves, depends on our being able to think the same thing about different things (the 'argument from thinking' of Met. A 9. 990b14: cf. Alexander, in Met. 81.25-82.1, and Plato, Parm. 132b3-c8). In On ideas, apparently, Aristotle had said of the first of these that it is clear that this argument does not prove that there are ideas, but it does go to show18 that what is predicated in common is different from the particulars of which it is predicated (Alexander, in Met. 81.7-10).14
And, in general,15 arguments of that sort do not show what they are supposed to, which was that there are ideas, but they do show that there is something separate from particulars and perceptibles. But it doesn't always work out that if there are things separate from particulars they are ideas; for there are, separate from particulars, [things predicated] in common,16 ••• (Alexander, in Met. 79.15-19).17
The distinction here is going to give Aristotle trouble: there are cases for which he will come to doubt whether it can be drawn so cleanly. We shall have to face some of this trouble in Chapter VI. For the moment, the distinction can stand. It blocks a certain conflation of the subject talked about with what is said about it. The conflation here would involve making what is said vary with what it is said about: making the significance of a term vary with each new application (and here the criteria for newness of application are spectacularly permissive). And this conflation would be one to which Antiphasis is prone: if the
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significance of a term varies with its application, so that 'man' signifies different things at different moments, from different points of view, and so on, all depending on what is being called a man, it is difficult to see what could ever make it false to say of something that it is a man. If we add to that that what a term applies to varies with the significance of the term, so that Socrates will be different things depending on the different things you say of him, it is not only hard to see what could ever make it false to say something of him, it is impossible. And then, if we allow that when I say he is a man and you say he is not, we are contradicting each other, we shall find that one and the same thing is different things: here, a man and not a man. We shall have to give up the law of non-contradiction, unless we are prepared to go on, with the Protagoreans, to abandon the idea that we have a common, public world as an arena for disagreement. All this has been an elaboration on 1006&31-32: "Again, if 'man' signifies one thing, let this be biped animal". Aristotle announces in J006bll that he has got the stipulations he wants ("So let the word signify something, and one thing, as we said in the first place", bll-13), and goes on
(bl3-15): Then it is not possible for 'for something to be a man' to signify just what 'for something not to be a man' does, if 'man' not only signifies of one thing, but signifies one thing.
He is here saying, in my paraphrase (cf. Chapter II, p. 33) that the conditions that make it true to say of something that it is a man cannot be the same as those that make it true to say of something that it is not a man. To be more faithful to the text, he says that a description of the one set of conditions cannot signify the same thing as a description of the other set; but later, in the reductio of 1006b22-28, he collapses this into saying that the conditions cannot be the same: cf. especially b25-28. Since we are not here concerned to 'hide the conclusion' (cf. Chapter II, Section IV above), let us work with it in the form: the conditions of application cannot be the same as those for denying the application of 'man'. It is not clear why he bothers with this. The step plays no formal part in the main plot of the refutation. Besides, one would think, if the reductio of b22-28 is all right, so that the idea that these sets of conditions are the same boils down to the suggestion that 'man' and 'not a man' signify the same thing (or that 'Socrates is a man' and 'Socrates is not a man' say the
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same thing), there would be no point in Antiphasis' even trying it out. For if he were to adopt the idea, he would find that 'this is a man and not a man' is no contradiction, but a matter of saying the same thing twice: defending its truth, then, would not be defending the denial of the law of non-contradiction. Is So why waste time on it? In the appendix to this refutation (1006b34-1007&20), Aristotle gives us instructions on what to do if various things go wrong. He is particularly concerned with a strategy for getting Antiphasis to answer a certain question; he says (1007&7-20): there will follow what we said, if he will answer the question. But if when he is asked it simply, he adds in the negations, he isn't answering the question. For nothing stops the same thing being a man and pale and ten thousand other things; nonetheless, when he is asked whether or not it is true that this is a man, he ought to answer with something signifying one thing and not add in that it is pale and big. For it is impossible to run through its accidents, which are infinite; so let him run through all or none. Similarly, then, even if the same thing is a man and not a man ten thousand times, one ought not to add, in answering the question whether it is a man, that it is at the same time not a man, if it is not right to reply as well with the other accidents it has -whatever it is or is not. But if he does that, he won't be having a dialogue with us.
So the question Antiphasis is being petulant about answering is: is it true to say that this is a man, or isn't? (&12), or: isn't this a man? (&17-18). And that is puzzling, since, on the face of it, Aristotle asks that question nowhere in the course of the refutation. In particular, he does not ask it at the beginning of the clincher: there he asks, not whether something is a man, but whether, if something is a man, it doesn't have to be a biped animal. And the possibility that Antiphasis might 'add in the negations' has no relevance to this. Where, then, does Antiphasis have room to 'add in the negations'? Aristotle gets the concession I have labelled '(D)' somewhere in the course of 1006&28-32: First, then, it is clear that so much is true: that the word signifies for this to be or not to be. Again, if 'man' signifies one thing, let this be biped animal.
I am not at all clear as to all the questions Aristotle imagines putting to Antiphasis, nor as to what the order is in which he imagines them being put. But at some point, he has to say: (QD)
Can't we let biped animal be [a] man?
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That the question took this form is plain when Aristotle goes on to spell out the stipulation of uniqueness of significance (&32-34): if this [i.e. biped animal] is [a] man, then if anything should be a man, this will be for it to be a man.
The force of the question (QD) is that of a request for a stipulation as to what 'man' signifies, and Aristotle is going to have to bring out what a stipulation of that sort comes to, in &32-34 and subsequent lines. That is, he is going to have to make it clear that the effect of the answer 'yes, that's a man' (or 'yes, let that be a man') to (QD) is not the same as the effect of a 'yes' answer to the question: (Q)
Can't we let Socrates be a man?
'Yes', in response to the latter, would give us a stipulation as to something that 'man' is true of(or 'signifies of' in the jargon of 1006b14), not one as to something that 'man' signifies. But the distinction between these two effects is precisely the distinction of which Antiphasis is, as yet, innocent. At least, he is ignorant of it at the point at which (QD) is put to him. And Aristotle has already made it plain that Antiphasis would be reluctant to agree to any flat assertion of the form 'this is a man': he is trying to dissolve the determinateness of such assertions by insisting on adding 'and not a man' (notice particularly 1006&18-21). So, not seeing what Aristotle intends in asking (QD), he takes it as no different in structure from (Q), and answers: (A)
Yes, that's a man; and it's not a man.
Aristotle says that we ought here to insist that this isn't answering the question (1007&7-20). Besides, taken as an answer to (QD), with the intended force of that question, it makes 'man' and 'not a man' signify the same thing. So he tries to show, in 1006b13ff., that they can't signify the same thing, if 'man' signifies one thing. We might, alternatively, put more of the responsibility for the confusion on Antiphasis, and have Aristotle ask something less misleading than (QD); we might have him ask: (QDs)
Can't we let 'man' signify biped animal?
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Then Antiphasis' reply would be: (As)
Yes, as long as we bear in mind that that's also not a man.
Either way, we come out with the same confusion: Antiphasis is conflating being true of something with signifying something. (I prefer the first alternative.) Either way, Aristotle goes on to undo the conflation; he says (1006bl318): Then it is not possible for 'for something to be a man' to signify just what 'for something not to be a man' does, if 'man' not only signifies of one thing, but signifies one thing. (For we are not asking that of signifying one thing, [namely, signifying] of one thing, since then even 'educated', 'pale', and 'man' would signify one thing, so that all would be one thing, for they'd be synonyms.)
The only actual argument Aristotle offers for the claim that signifying one thing is distinct from being true of one thing is this one. I have already (Chapter II, Section IV) commented on its structure: part of its force turns on its driving Antiphasis into monism, and if there is anything that Antiphasis is not, he's not a monist. I am not sure we ought to follow Aristotle this far; the argument to monism turned on some rather expensive premisses (the identity of indiscernibles and the 'principle of ubiquitous likeness'). But even an argument that dubious might awaken Antiphasis to the distinction Aristotle wants him to make. For most of us, it would be enough of an argument against the idea that signifying one thing amounted to being true of one thing that the idea made 'educated', 'pale', and 'man' signify one thing. But maybe it wouldn't have been enough for Antiphasis: he, after all, was prepared to deny the law of non-contradiction, and that would keep most of us from discipleship without further dissuasion. One point is worth reiterating, before we leave direct comment on this refutation. Aristotle's prose (in bl3-15) makes it sound as if the distinction between being a man and not being a man followed from the stipulation that 'man' signify one thing. But if we are right, that is not what he is saying. He is saying, in part, that Antiphasis' response rests on a confusion, and that if that confusion is straightened out, he will not be so ready with that response. But there is a little more to it than that: Aristotle goes on to outline how it might be that being a man and not being a man were the same thing. That might happen if 'a man' signified two complementary things
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(1006b19-20: "as if what we call a man others were to call not a man"). But, he says, that only gives the appearance of saving the denial of the law of non-contradiction (b18-19, 20-22): [At that rate], it won't be possible for the same thing to be and not to be [a man] except by a homonymy...• But that isn't the problem- whether it is possible for the same thing at the same time to be and not to be a man [where it's just a matter of] the word- but [where it's a matter of] the thing.
((Alternatively, we might take the opening senten.ce of this to be registering a complaint that Antiphasis' response to (QD) or (QDs), the answer (A) or (As), made men homonymous: 'the same thing' in that sentence would then refer to biped animal, or whatever 'man' signifies. This would fit with the first alternative on pp. 88-89. But, either way, Aristotle is saying by the end of the passage that Antiphasis is only saving the denial of the law of non-contradiction by making 'man' a homonym.) So we need not commit Aristotle to saying that it follows from his stipulation of uniqueness that being a man and not being a man do not coincide. But he has pointed out that failure to recognize the force of that stipulation may lead Antiphasis into unwittingly saying that they do coincide. And, more, he has outlined one situation in which they might coincide, and in that situation the stipulation is not satisfied. Perhaps situations of that sort were the only ones he could think of in which they might coincide. They are the only ones I can think of. So it seems to me fair to leave the burden of thinking of others on Antiphasis. And even if he manages to shoulder that burden, he is going to have to explain to us how making them coincide leaves 'that is a man and not a man' a contradiction. With that out of the way, the clincher is on us. IV. CONCLUSION
To make the refutation work, Aristotle has to get Antiphasis to accept the distinction I have been harping on: between something talked about and what is said about it, between being true of something and signifying something, between 'subjects' and 'predicates'. Antiphasis is Aristotle's creation, I keep saying, and that becomes important now. For the distinction Aristotle makes is one that gives him trouble. That comes into view in the next attack on Antiphasis.
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1 Cf. Poste, Aristotle on Fallacies, pp. 123-24, n. 1; 125-26, n. 9. s The ambiguity preserved in the above, "the denial has (or is) a term denied ... ", is, I think, present in the text of De int. 6: cf. esp. 17,.26-29, and Geach's comment on this in 'Aristotle on Conjunctive Propositions', Logic Matters, p.16; also Anscombe, 'Aristotle', p. 39. It is not that Aristotle never talks about truth or falsehood in connection with full sentences (often in the De int. that seems the best way to take him), but that he is capable of sliding back and forth from talking of a statement's being true to a predicate's being true of something. Since he thought that statements (or sentences) could vary in truth-value over time, the assimilation is even easier. a Thompson, 'On Aristotle's Square of Opposition', suggests reading the passage about Homer to mean: it doesn't follow from 'Homer is a poet' that Homer is a substance (pp. 56-57 in Moravcsik); he thinks it does follow that Homer exists. He then takes De int. 11. 21,.32-33 to say that it doesn't follow from the fact that that which is not is believed in that it is something. I'm not clear how to put these two readings together. Soph. el. 25. 180&37-38, Met. Z 4. 1030&25-26, etc., show that Aristotle's preferred way of stomping out creeping Eleaticism is to say: it doesn't follow from the fact that that which is not is something, e.g., believed in, that it is simply. 4 Appendix II below. Briefly, the idea is this. Aristotle is saying that cancelling the predicate in 'Homer is a poet' is illegitimate (the string 'Homer is' can be taken as a full sentence, and then it is not a part of 'Homer is a poet'). If the sentence were 'Homer is a man', the cancellation would be legitimate (the string 'Homer is' taken as a sentence is a part of the sentence 'Homer is a man'), since Homer is a man in his own right (Ka9' aftt6). & Ross (APPA 601-08 ad •25-28 and •29-32) takes Aristotle to be attacking Antiphasis directly: he supposes the view 'that there is a true and a false belief of the same thing' to be the denial of the law of non-contradiction. Tredennick (Posterior Analytics, Loeb, p. 168, n. a) apparently follows him. It seems to me better to take Aristotle to be saying that although it is possible for there to be a true and a false belief 'of' the same thing, there is room for error if one takes the 'thing' here to be the thing believed (or believed in), and not the thing that the belief is about. The sophists who perpetrate confusion here do not begin by denying the law of non-contradiction and then get the conclusion that there is no such thing as a false belief; they start with the latter, and some of them go on to the former. e This involves playing down the phrase 'what it would be for each of them to be' in 89•32. The phrase is normal Aristotelian jargon for 'essence' (cf. Chapter V, Section I below), and is taken to mean that by Ross and Tredennick here (loc. cit., n. 5): the essence of the diagonal would have to be different if it were commensurable. But that weakens the distinction a good deal: Cleinias would not have to have a different essence if he were wise. And it does not square with a view of Aristotle's covered below in Chapter VI, Section II. So I am taking Aristotle to be saying that what it would be for a commensurable diagonal to be is different from what it would be for an incommensurable diagonal to be: cf. Top. E 4. 133b34-36, and DUring, 'Aristotle's Use of Examples in the Topics', p. 205 (which is almost right). 1 Perhaps not always: cf. Owen, 'A Proof in the xspl tlislilv", p. 295, n. 1 (Allen), Leszl, Logic and Metaphysics, 93. s The passage in K 5 fits better with 1008•27-30 than with 1008•3-7. The latter association is Ross' and Jaeger's (cf. their texts ad locc.); it goes back at least to
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Bonitz (cf. AMp. 459). But Ross' own note ad 1062"36-b7 belies him: the passage in K argues that Antiphasis is committed to saying 'both (p and not-p) and not (p and not-p)', 1008"3-7 that he is committed to saying 'both (p and not-p) and neither p nor not-p'. The former commitment is registered in 1008"27-30. 9 a. Torrey and Felin, 'Was Aristotle an Evolutionist?': after reviewing evidence, they say (p. 15), "Our conclusion is that Aristotle was not, in fact, either a cosmic or a racial evolutionist". One of the most curious of Sarton's many curious pronouncements in A History of Science is his saying of Torrey and Felin's response to their title question "After reviewing all the evidence, they cannot answer yes or no" (i. 535, n. 40). 1o a. p. 44 above. Notice that there is a practical upper bound (although not a least upper bound) on phrase length: a phrase containing 284 words is out of the question. . 11 The most charitable thing to do, for Aristotle, would be to take his premiss to be that there are infinitely many significances, not infinitely many things to talk about: he can't get from the latter to the claim that homonymy is unavoidable without collapsing the distinction between signifying and being true of, as Antiphasis is doing. 111 Cf. Chapter I, n. 52 above. 18 "l>s1KVilva1 Pou1..sta1": Ross, in Select Fragments, translates "tend to show" (p. 127). 14 In Ross, Fragmenta selecta, p. 123; the fragment is not in Rose 8 • 1& The comment is really about the 'arguments from the science', but these have a structure similar to that of the 'one over many' and the 'argument from thinking', and Aristotle clearly thinks the point is a general one. 16 "ta IC01Va". a. Soph. el. 22. 179"8-9. Ross (Select Fragments, p. 125) translates 'universals', but there is another word for those (tci Ka961..ou), even if Aristotle or Alexander plainly means universals (cf. Bonitz, Index 399b29). a. Met. A 9. 992"5, Z. 16. 1040b23, etc.; in Plato, Tht. 208d8, 209a10 (but not 185b8, c5, etc.: here I agree with Diiring, 'Aristotle's Use of Examples in the Topics', p. 205). 17 Ross, Fragmenta selecta, p. 122; Rose 3 , fr. 187 (pp. 149-50). 18 Cf. Kirwan, AM 95.
CHAPTER V
THE SECOND REFUTATION
Aristotle alleges that people like Antiphasis are committed to denying that there is such a thing as substance, or 'what it is to be' (1007&20-33). He then tries to explain what would be wrong with doing that (&33-blS). The only claim this has to being a new refutation is that it brings in an 'ontological scheme' that might be used in getting Antiphasis to concede that 'man' signifies one thing: from there on, the first refutation takes over. The ontological scheme is introduced by rephrasing some of the stages of the first refutation in jargon characteristic of that scheme. The scheme itself is argued for, sketchily, in the second half of this refutation; it will be easier to look at that first. Then we can come back to the first half, where the rephrasing is done. The rephrasing, on the face of it, involves a severe restriction in the scope of the first refutation, and getting clear about this demands a grasp of the scheme: so it is easier to deal with the scheme first. I. ON SUBSTANCES, ESSENCES, AND WHY WE NEED THEM
Aristotle uses the phrase 'substance, or what it is to be' in telling us what Antiphasis must reject (1007&21). Subsequently, he replaces 'what it is to be' with other barbarisms already familiar to us: 'for something to be a man' (cf. 1007&24) or 'just what for something to be a man [is]' (lS7tsp tiv9pro7tcp stvat, a22, 23, 28). These phrases, all of them, are often covered by the translation 'essence' or 'essence of man'. We may as well follow the tradition, at least occasionally. The problems over substances and essences are numerous, notorious, and enormous. It is customary to put off a full explanation of them to another occasion; I am going to follow that custom. There are a few problems that are elementary; others are deep in the abyss that is Metaphysics Book Z. We can get what we need for understanding the second refutation if we tie a rope to the elementary and go only a short way into the abyss.
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When Aristotle says that Antiphasis is committed to rejecting substance, a reader fresh from the Categories might take him to mean that Antiphasis is committed to denying the existence of individuals. He does not mean that, although he thinks that that would be a consequence of what he does mean. He means that Antiphasis is committed to rejecting the claim that there are any predicates essential to anything: the claim that there is anything true of Cleinias, say, such that if it weren't true of Cleinias, Cleinias wouldn't exist. It is worth spending more time on this reader fresh from the Categories. Understanding the merits and defects of his view helps bring out the sense of the argument that forces Antiphasis to accept 'substance, or what it is to be'. In a longer run (Section II} it helps in trying to see whether this refutation implies any restriction in the first one. Finally, the distinctions introduced here have to be squared with that between what a term signifies and what it is true of, and that is difficult (Chapter VI}. So some of the material introduced here is supposed to give a foundation for later questions; the chief question for now is: when Antiphasis destroys substances, what has he destroyed? Aristotle uses the word 'substance' in two distinct types of grammatical environment. 1 One is illustrated by this (Z 2. 1028b9-10}: So it is that we say that the animals and plants and their parts are substancss ... (3t6 -ru Ccfla Kal -rei cputci Kat tci p6pU1 a6tc71v oocrl~ slvaf. cpaJ!SV).
't8
The other is illustrated by this (Z 6. 1031&17-18): For each [thing] seems to be no different from its substance (fKam6v -rs ycip of>K dlAo 3o1C8i slvat tfl~ tautoO oocrl~).
In the latter construction, the word 'substance' carries a dependent genitive: we can ask 'what is the substance of (say) a turnip?'. But when we come to the turnip, it is among the animals and plants and their parts which, 'we' say, just are substances (full stop). A turnip is not, on the face of it, the substance of anything. (Z 6, in suggesting that at least some things are 'no different from their substances', does something by way of collapsing this distinction: I shall say more about this below.) In the second of these constructions, where Aristotle speaks of the substances of things, he identifies a thing's substance with its essence; the second of the two passages above continues (1031&18): "and the essence is said to be the substance of each [thing]" (Kat 'tO Ti T)v dvat ft SKci<nou
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oi>aia; cf. 1031b2-3, 31-32, Z 3. 1028b33-36, 13. 1038b2-3, H 1. 1042&17,
and Z 7. 1032b14). He often changes off between 'substance of .. .' and 'essence of .. .' without comment (cf., in Z, 4. 1029b1-3 with 13-14, 10. 103Sb15-16, 11.1037&21-b7, 13.1038b17with20, 17.1041&27andb6with b8-9). In ~8, he is nearly explicit about this distinction, and about the identification of the substances of things with their essences. He first distinguishes four types of case in which 'substance' is used.2 They are these: (1) The elements (earth, air, water), animals, gods, their parts, and presumablyourtumip,arecalled 'substances'(1017b10-13;cfZ 2.1028b914, De cae/o rt. 298&29-32); "these are all called substance because they are not said of a subject but other things are said of them" (1>13-14: cf. Cat. 5. 2&34-b6, 2b15-17, 37-3&1, Met. Z 3. 1028b33-37, etc.). (2) "In another way, ['substance' is used of] whatever is responsible for [a thing's] being, by being present in such things as are not said of a subject, e.g. the soul [in] an animal" (1017b14-16). (3) 'Substance' is used of things that are present in (1 )-type substances, mark them out as individuals, s and are 'essential' to them in something like4 our original sense: "when [these constituents] are destroyed, the whole [(10-type substance] is destroyed" (1017b17-19). The examples Aristotle gives (without planes, no bodies; without lines, no planes, "as some say"; and without numbers, nothing at all, "some think", bJ9-21) are peculiar, and difficult, but there is no point in stopping over them here. 5 (4) "Again, the what it is to be [or 'essence'], the account of which is a definition, is called the substance of each thing" (1017b2J-23). He closes the chapter by regrouping these into two main types of case: apparently (2)-{4) go into one bag,e and (1) goes into another. The first bag would contain our substances of things, or essences, and the other would contain our substances (full stop). The broad outlines of all this (not the details) are elementary. And it is also elementary that in the second refutation Aristotle is accusing Antiphasis of destroying the substances of things, their essences (cf. 1007&21, a.26), and not, at least in the first instance, of destroying substances (full stop). But my imaginary reader fresh from the Categories, who thought that Aristotle was accusing Antiphasjs of destroying substances (full stop) has
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something going for him: the reason Aristotle takes the accusation he does make as telling is that he thinks that the abolition of the substances of things would be the abolition of substances (full stop). And this is not so elementary. It is here that the danger of going too far into the abyss crops up. I want to sketch the scheme that I take to be surfacing in 1007&26-27, 31-33, and 33-b17 without dealing with every interpretative difficulty, and without giving a full defense of the scheme itself. 7 Aristotle believes that there are certain things on whose existence the existence of everything else depends; these are the substances. Indeed, to say that something is a substance is to say that it is a thing of that sort (cf. Met. r2. 1003b6-IO, Z 1. 1028&13-20, etc.). In the Categories(2.Ib3-6, 4. 1b27-28, 5. 2&11-14) Aristotle picks what a philosopher would call 'individuals' or 'particulars' (men, horses, plants, their parts [for which cf. 7. 8&13-28, b15-16, 20-21]) as primary cases. He picks them because they satisfy something likes the requirement A8 places on its first class of substances: they are the subjects of which other things are predicates (cf. Cat. 5. 2b37-3&1). They are our substances (full stop). But Aristotle also believes that it is possible to answer the question 'what is it?' asked about any of these individuals or particulars and that there are appropriate and inappropriate answers to such questions. For an example, consider Socrates: he is a man, an animal, pale, educated, and so on. While all these things are true of him, only the first two constitute answers to the question 'what is Socrates?' (cf. Cat. 5. 2b29-37, Top. A 9. 103b22). These answers give us, in the Categories, secondary applicants for the title 'substance' ('secondary substances', 5. 2&14, b7, etc.). They get the title for two reasons: one is that they do answer questions of the form 'what is it?' asked about the primary cases of substance (2b29-37), and the other is that by that very fact they come close to satisfying the subject-criterion that picks out the primary cases: since what Socrates is, is a man, whatever predicates are true of Socrates are true of a man (3&1-6; cf. 2bl7-22, 3&9-15: I think Aristotle is confused here). Still, the answers to questions like 'what is Socrates?' only give us derivative cases of substances: if there were no men, the species man would not be, as there is no longer a species of dodos (cf. 2&34-b6: there is something amiss here as well). In the Categories, these answers give us 'secondary substances'; in
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Metaphysics r, Z, and elsewhere, they give us the substances (or essences) of the things about which the questions are asked (there is a difficulty over the phrase 'thing about which the question is asked': we shall encounter it in the next section). There is a difference between the grammatical form of the expression for a 'secondary substance' ('the dodo', 'man'9, '[a] man') and the grammatical form of the expression for the substance of a thing ('for something to be a man'; 'what it is to be a man'). One of Aristotle's doctrines (that of Z 6, that some things are the same as their essences) apparently glosses over this difference in grammatical form. And it is glossed over in the by now too familiar sentence in which Aristotle explains 'signifying one thing' (1006a32-34): And this is what I call signifying one thing: if this [i.e., biped animal] is a man, then if anything should be a man, this will be for it to be a man.
(The last clause unpacks as: 'a biped animal will be for it to be a man', and so the grammatical difference is glossed over.) Grammar is left to take care of itself; Aristotle is now saying that the word'man', which had given us the species as a secondary substance in the Categories, "signifies to be or not to be this" (I006a29-30), that what it signifies is "the substance of something" (I007a25-26), and that "to signify a substance [of something] is [to signify] that for something to be that is not something else" (1007a26-27). In the Categories, what made secondary substances secondary was their dependence on primary ones for their existence. So we should expect the substances of things, under the new regime, to be dependent for their existence on the things of which they are substances. We certainly find him saying that, e.g., in Met. A 9. 991bl-2 ( =M 5. 1079b35-36): Again, it would seem impossible for a substance and that of which it is the substance to exist separately.
He expects this thesis to be anti-Platonic: he goes on to ask (991b2-3, = 1080a1-2), How, then, could the Ideas, which are the substances of things, exist separately?
So here he is expecting the substances of things to be dependent on those things for their existence. But it is not all that easy for Aristotle to save himself from Platonism: the dependence here goes both ways.
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(Once more, I am not going to give a full defense of Aristotle's position; I am not able to. It strikes me as having some truth in it, but I cannot say just what.) The answers to the question 'what is it? give us the substances of the things about which it is asked. And any inventory of the universe worth the time ought to tell us what there is in it. Telling us that Socrates is in it is no help: those of us for whom 'Socrates' could be as easily the name of a man, a star, or a bend in the river still need to know what Socrates is. Telling us that Socrates is pale is no good either: we would still ask 'what is this pale thing, Socrates?' Telling us that he is a man does not prompt the same question: 'what is this man, Socrates?' Under conditions of alienation, we could ask that, and expect to hear, say, 'he's a bricklayer'. But first philosophy, if anything, is exempt from alienation: 'what is this man?' is not a question we ask in inventorying the universe, and, anyway, presupposes the crucial answer for that inventory, 'he's a man'. Besides, Socrates, the man, would still be among us if he weren't a bricklayer, but one of the idle rich. The crucial answer, 'he's a man', gives us his substance, his essence, and to tell us that is to say that for something to be Socrates (or, now, for Socrates to be) is nothing other than for it, or him, to be that. Other things, besides his being a man, serve to distinguish him from other men. These are his 'accidents': 'pale' and 'educated' give us paradigms. They will not do, separately or collectively, for identifying what we are talking about when we say that the universe has Socrates in it. For one thing, there are indefinitely or infinitely many of them (cf. Met. E 2. 1026b7, 430. 1025&24-25, K 8. 1065&24-26), so there is no hope of capturing them all in a sentence (I'4. 1007&14-15) or a science (E 2. 1026b312, etc.). For another, any of them might fail to be true of Socrates without Socrates thereby leaving the universe (cf., e.g., 430. 1025&14-24, Top. A 5. 102b4-14, etc.): indeed, Socrates' career in history will involve many failures and successes of that sort (cf. Cat. 5. 4&10-bJS, Met. A 3. 983b910, etc.). Whatever the merits of these considerations (and we have not done with that question altogether), they leave Aristotle in a small bind. In the Categories, Socrates had been a primary substance. Now he is dependent for his existence on something: if there were no such thing as being a man, there would be no Socrates; Socrates can't exist without being a man. So
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it is not unnatural that Aristotle shows a tendency, especially in Z, to talk as if the essences of what were, originally, his primary substances, were now the primary substances (Z 7. 1032b1-2, 11. 1037&5, b1-5 10, probably11 13. 1038b9-10; cf. I 3. 1054&35-b3). And this is a tendency in the direction of Platonism. Still, he would very much like to save the original scheme: that much is clear, I think, from Z 1-2. And he would like to do it by insisting on the original criterion for substantiality: the substances are the rock-bottom subjects (cf. Z 3, 13. 1038b4-6, 07. 1049&27-36: this involves another difficulty, one that for present purposes can be ignored, over the notion of matter: the introduction of this notion threatens the original scheme from another direction, and a great deal of Z turns on that). So he tries to salvage the original scheme by suggesting, in Z 6, that any scheme whatever, any 'ontology' (the example he uses to illustrate the point, in 6. 1031&28 and ff., is Platonism) will have to recognize a level at which there is no distinction to be drawn between the subjects of which other things are said and whatever it is that has to be true of them if they are to exist at all. At that level, 'each thing is no different from what it is for that thing to be'. It is here that we find the glossing over of grammatical differences we noted a few pages back. To save the original scheme, he would have to show that that level is in fact the one at which we get Socrates, Callias, Bucephalus, and so on: the original primary substances of the Categories. Whether he manages to show that is one of the questions that would take us too far into the abyss. I think that he does, or thinks he does, by the time he gets to H 6. In any case, the use of the example 'Socrates' in r4 shows that there he is operating under the assumption that this is the way things work out. For the rest, the scheme we have been outlining is the one that surfaces in the second refutation. When it surfaces, it does so through some difficult jargon. In 1007&31-33, we find Aristotle saying: For it is by this that substance and accident are distinguished: the pale is an accident of the man because he is pale but not just pale.
'Just pale' is a term of art for Aristotle.12 There is a concise sketch of the overall picture that uses this term, and others that are involved in the second refutation, in Posterior Analytics A 22. 83&24-32. That passage is no paradigm of clarity, but a brief look at it may help us to see a little farther through the jargon.
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He begins it by saying (83&24-25): Again, [terms] that signify a substance, signify that that of which they are predicated is just this, or just a certain this.1a
Here 'this' (my italics) is to be replaced by the term in question, so that we get the following format: where 't' signifies a substance, if xis t, either xis just t, or xis just one or another t. Consider some examples; it will help to put these examples without using the indefinite article, giving us barbarian English in imitation of Aristotle's Greek. 'Man' signifies a substance; so if Socrates is man, either Socrates is just man, or Socrates is just one or another man. Here the latter alternative is the right one. Again, biped animal is man (a biped animal is a man); so either biped animal is just man, or biped animal is just one or another man. Here the former alternative is the right one: these two terms are co-extensive, and we could have worked the example in reverse, taking 'biped animal' as the term signifying a substance, and predicating it of 'man' (or of man). Again, 'animal' signifies a substance, and either Socrates or man comes out as one or another animal: this example Aristotle himself gives us a few lines later. He goes on (83&25-28): but such [terms] as do not signify a substance, but are said of another subject that is not just this or just a certain this, [signify] accidents, as with pale, said of the man.l4
Here 'the man' strikes me as ambiguous between the species and a member of it, say, Socrates. But it does not seem to matter for the overall picture which way it is taken. The examples he now gives do not clarify this issue (83&28-30): For the man is not just pale, or just a certain pale [thing?], but, perhaps, animal; for the man is just animaJ.16
If the above is right (and I cannot see any other way to cash the format in), this last clause would be more precise if it read: 'for the man is just a certain animal'. However that turns out, the general point is that a predicate that gives us the substance of a subject serves to identify that subject, either 'completely' (as with 'biped animal' and 'man', where the former serves to define the latter), 01 by telling us that what that subject is, is an instance of that predicate. It is on this last that the contrast between substance and accident de-
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pends, and that becomes clear by putting together a series of passages. One is 1007&26-27: To signify a substance is [to signify] that for something to be that [or: for that to be] is not something else.
Another is 83&25-28: such [terms] as do not signify a substance, but are said of another subject•.• signify accidents.
Another is 1007&35-b1: an accident always signifies a predicate of a certain subject.
And the last is what is left of the passage from the Posterior Analytics, 83&30-32 (and cf. A4. 73b5-10): Such [terms] as do not signify a substance have to be predicated of a certain subject; there is nothing that is pale which is not something else that is pale.
Socrates may be pale, but what he is is something else: a man. That gives us the subject of which 'pale' gives us an accident. Aristotle alleges that Antiphasis must destroy substance, i.e., essence. That is, he must say that there is nothing that tells us, finally, what we are talking about: all that is true of anything is accidental to it. Aristotle's response is (1007&33-b1): But if all [terms] are said accidentally, there will be no first [term] of which they are said, if an accident always signifies a predicate of a certain subject.
This much is merely a statement of the core of the scheme we have been constructing. He goes on (1007b1): Therefore it is necessary for it to go on infinitely. This is a little puzzling. There are infinitely many, or at least indefinitely many, accidents of any given subject. For any two of them, it is possible to formulate a true claim linking them in a simple sentence; e.g., 'the pale is educated', 'the hot is pale', 'the short is hot', etc.17 If there are infinitely or indefinitely many accidents, there are infinitely or indefinitely many such sentences. But that should not create any problem, even given the essentialist scheme Aristotle has. Besides, these sentences do not set up any order that could
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'go on infinitely' to any vicious effect: their predicates are as good as their subjects; there is no priority of one of these accidents over another, with a third prior to the first, and so on. Actually, that, it emerges, is Aristotle's point. He pictures Antiphasis trying to answer the question 'what is it that is educated?' with 'the pale', and the question 'what is it that is pale?' with 'the hot', and so on. Here we are seeking a certain sort of 'prior' answer: we are trying to find out what it is that is under discussion, and we are getting nowhere. All Antiphasis can do is continue giving us accidents, if not ad infinitum, at least ad nauseam. So the objection against him is not that there is, in fact, a series containing many terms, each prior to the last in that it is a little closer to identifying the rock-bottom subject of which all are true, which series has to be stopped short of infinity. It is, rather, that if we were offered 'the pale' as identification for the educated, 'pale' would have to have that sort of priority over 'educated', and if we were then offered 'the hot' as identification for the pale, 'hot' would have to be prior to 'pale', and so on. And if all there was by way of identification for the subject under discussion was this sort of thing, there would be an infinite, or indefinite, regress. What is wrong with that regress is less its infinity than its construction, for none of these terms is really 'prior' to any other. That this is Aristotle's point emerges when he goes on to say of this (bogus) regress (1007bl-6): But that is impossible; for not more than two [terms] are interwoven. For an accident is not an accident of an accident, unless because both are accidents of the same thing: I mean, e.g., the pale is educated and this is pale, because both are accidents of the man. -But it is not in that way that Socrates is educated, because both are accidents of something else.
'Not more than two [terms] are interwoven': of course, any number of things are true of Socrates, but they all fall into two levels : the ones that identify him, and the ones that don't. It might be that the pale is educated, and that would give us a case describable, but misleadingly, as one in which we had an accident of an accident. But one of these doesn't signify a 'predicate' of the other, its 'subject', in the sense of aJ4-bl: what they are both predicates of is Socrates, the man, their subject. And it is not as if we could start with that subject, and begin heaping its 'predicates' on it, getting longer and longer terms that serve for fuller and fuller identification of Socrates:
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So, since some accidents are said in the latter way, some in the former, such as are said in the latter way (like the pale, of Socrates) cannot go on infinitely upwards, as if there might be some other accident of Socrates the pale: for there is not any one thing that comes out of all [these] (1007b6-10).
I am not going to stop over Aristotle's considerations about 'unity' here; 18 roughly, what he is saying is that for Socrates to be is one thing, perhaps, for him to be a man, but for him to be pale is another: he could exist without being pale. So saying that he is pale is no part of saying what he is. Aristotle closes the refutation with a gathering together of its threads (1()()7bll-18): Really, there will not be any other accident of the pale, such as the educated, for this is no more an accident of that than that is of this; and, at the same time, we have determined that while some terms are accidents in this way, others are like the educated, of Socrates: in cases of the latter sort, the accident is not an accident of an accident, but in cases of the former sort [it is], so that not everything will be said accidentally. So there will be something that signifies [something] as a substance. And if that's so, we've shown that it is impossible to predicate contradictories at the same time.
Now just where have we shown that? How is it that someone who, like Antiphasis, wants to deny the law of non-contradiction will have to deny that there is such a thing as a substance, an essence? II. ANTIPHASIS' COMMITMENTS AS TO ESSENCES
Aristotle's allegation reads (1007&20-23): And those who say this really do away with substance and what it is to be. For it is necessary for them to say that everything is accidental, and that there is no such thing as just what it is for something to be a man or for something to be an animal.
This raises two general problems, at least. First, we had Antiphasis beginning from a line of argument that made all the predicates of a thing essential to it: what something was varied with whatever was true of it; what one was thinking of varied with what one thought of it; what one was talking about varied with what one said about it. And now we have Aristotle saying that he is committed to the opposite. Second, there is a problem about Aristotle's own commitments. On his view, what we should think of as the 'predicates' of a thing come in two boxes: one contains the essential 'predicates' {although here Aristotle would not call them 'predicates'), and the other the accidental ones. Does
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he think that the status of the law of non-contradiction varies depending on which box its predicate is drawn from? Or, short of that, does he think that the workability of the first refutation depends on Antiphasis' picking a predicate from the essential box? This section is concerned with these two problems. They are interrelated. Both of them require consideration of the support Aristotle offers for the allegation that Antiphasis must do away with substance and essence. He first says (1007&23-25): For if there is to be such a thing as just what it is for something to be a man, it won't be for something to be not a man or for something not to be a man; but these are its negations.
But Antiphasis' denial of the law of non-contradiction did not directly commit him to saying that for something to be a man was for something not to be a man, or for something to be not a man. That was something he fell into through failure to grasp a distinction between what a term signified and what it was true of. Aristotle is here assuming that he has already fallen into it. So we are here back within the first refutation. And that becomes clearer when Aristotle goes on to say (1007&25-26): For what it signified was one thing, and this was the substance of something.
Here 'it' probably refers to 'for something to be a man': but Aristotle plainly has in mind the concession labelled (D) in chapter two above, or the stipulation of unique significance that permitted (D). So, again, we are back in the first refutation.Aristotle is not even adding anything to the refutation; he has merely replaced talk of 'for something to be a so-andso' with talk about substance, or what it is to be a so-and-so, and this is merely trading jargons. How far along are we in the refutation? We have plainly got at least as far as the stipulation of uniqueness. And we have got Antiphasis already committed to saying that 'man' and 'not a man' signify the same thing. In the course of the refutation we showed him wrong on that score by getting him to concede that 'for something to be a man' could not signify just what 'for something not to be a man' does (1006b13-14). We were supposed to get him to concede that by beating him with the stipulation that 'man' signifies one thing (cf. 1006bll-13, 14-15), together with some
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persuasion to get him to see the difference between being true of one thing and signifying one thing (blS-18, 1007&1-7). And now we are told this (1007&26-29): And to signify a substance is [to signify] that for something to be that is not something else. But if just what for it to be a man is should be either just what for it to be not a man is, or just what for it not to be a man is, it will be something else, .•••
And there is no new argument here. Antiphasis has conceded that 'man' signifies one thing, that is, he has conceded that we could fill in for the word 'this' in "if this [e.g., biped animal] is a man, then if anything should be a man, this will be for it to be a man" (1006&32-34). Put another way: if a biped animal is a man, then if anything should be a man, for it to be a man is nothing other than for it to be this. And that Aristotle here calls 'signifying a substance'. But Antiphasis has fallen into saying that 'man' and 'not a man' signify the same thing. That is, he has fallen into saying that when we say of Socrates that he is a man, what we are saying about him is just what we should be saying about him if we said he was not a man. But this is not so: for him to be a man is something other than what it would be for him to be not a man, or for him not to be a man. So Antiphasis must be wrong, if 'man' signifies a substance, and he has already conceded that is does. He conceded that when he conceded that it signified one thing. Here, then, 'one thing' seems to be bearing a great deal of weight: the concession that 'man' signifies one thing now looks like more than a ruling out of mere ambiguity. This has to do with a possible restriction in the scope of the first refutation; I shall get back to it shortly. I said that there was no new argument here: that is, if Antiphasis were disposed to identify the significance of 'a man' and 'not a man', and stick by that, we could only revert to the considerations already introduced in the first refutation and in the appendix to it (1006bl5-18, 1007&1-7). We would have to ask him whether he'd say that 'pale' and 'man' signify the same thing, and point out that, if so, he's in danger of making all things one, and if not, he'll have to tell us why he thinks that 'man' and 'not a man' signify the same thing. Aristotle here assumes that these considerations would be effective, ... so that it is necessary for them to say that there is no such account of anything, and everything is accidentally ... (1007•29-31).
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That is, if Antiphasis is to get off the train of the first refutation, he will have to say that it is impossible to pick out any one thing that 'man' signifies: any one thing such that to be a man is to be that, and never to be anything else. Then no predicates signify the substance of anything; they all at best signify accidents, for it is by this that substance and accident are distinguished: the pale is an accident of the man because he is pale but not just pale (1007•31-33).
To signify an accident of a man, as 'pale' does, is to signify something such that to be a man is something other than to be that. So the simplest answer to the first of our two general problems, how an ultra-essentialist like Antiphasis might become committed to ultra-accidentalism, is: by responding as he does to Aristotle in the first refutation. (But we shall find, in Chapter VI, Section I that he might have been stuck with this even apart from the first refutation.) It might be that Antiphasis' ultra-essentialist roots are part of the reason Aristotle wants to point out to him that he has been driven into ultra-accidentalism. But Aristotle says nothing of this, and it would be an excess of zeal on my part to try to make anything of it. The second of our two general problems is nastier: Aristotle seems to be saying that the first refutation worked only because the term Antiphasis picked was 'man', which signified a substance, and thus that a term like 'pale', which signifies an accident, would not have done the trick. This, I think, is not so, but it is a possibility that cannot be brushed aside. So I shall spell it out in more detail. Here I am elaborating on some things said by Miss Anscombe. 1e What difference would there be, on this interpretation, between 'man' and 'pale', that makes the first refutation work for 'man' but not for 'pale'? As we went through that refutation, there was not the slightest hint of any such restriction. To see the relevant difference between 'man' and 'pale', we have to distinguish between Aristotle's notion of 'significance' and our notion of 'sense'. Consider the word 'tall' rather than 'pale': the point is easier to make with this, and it can then be extended to 'pale'. 'Tall' is not, on our present understanding, a word that signifies a substance. So we should have to say that the first refutation does not work for it. In particular, we
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should have to say that it is not a word for which we can pick out a single significance, to hold constant throughout the refutation. And that seems odd, if we understand 'sense' where Aristotle has 'significance', for we could formulate a sense for the word, say, 'above standard height', and fix on that. But the word 'standard' in this formulation shows something about the word 'tall' that distinguishes it from words like 'man'. To say of something that it is tall, or that it is not tall, requires our fixing a standard height. But there is no standard height for things: tall tulips are short by comparison with giraffes, and although giraffes are tall animals, buildings are generally taller. But that does not make giraffes short, nor does the fact that giraffes are tall make tulips short. Perhaps Mount Everest is the tallest thing on earth, but we seem to have no use for a categor) of thingson-earth (much less a category of things in general) that would make us go on from there to saying that men are short things-on-earth. And even if we did, the point would hold: 'that's tall' is not a sentence that stands on its own; understanding it requires some idea as to what sort of thing it is that is being said to be tall - a tulip, a giraffe, a building, or, just possibly, a thing-on-earth. This isn't to say that 'tall' is ambiguous: we have, in 'above standard height', a pretty good characterization of its single sense. It is rather to say that the conditions under which it is true to say of something that it is tall vary with the sorts of thing in question. Aristotle, I bet, would say that they vary with what the things are, with their essences. The interpretation that limits the scope of the first refutation identifies the significance of the term picked with its conditions of application, in that sense. The concession of uniqueness of significance, then, is not one we can expect for a word like 'tall'. A great deal more work would be needed to make it even faintly plausible that this distinguishing feature of the word 'tall' is generalizable over the whole class of accident-words. It covers a great number of the terms that particularly bothered Plato and helped him to set up the theory of forms (cf. Rep. VII 523a ff.).2o It might cover 'pale', if we took 'pale' and 'dark' as terms that locate colors relative to each other, and that seems right: a pale American Beauty (rose) is one thing, a pale man another, and so on. But it is hard to see how we could extend the point to cover 'vermilion', 'octogenarian', 'two cubits long', etc. Aristotle might have assimilated
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these to terms like 'pale' and 'tall' by reciting the formula of Posterior Analytics A 22. 83&32: "there is nothing pale which is not something else that is pale"; there is nothing two cubits long which is not something else that is two cubits long. But the need to specify this something else that is tall, pale, or two cubits long is bound up with the truth-conditions for saying that it is tall or pale, and it is not similarly bound up with the truth-conditions for saying that it is two cubits long. So there would be more work involved in making this, or anything like this, the distinction between substance and accident. But 83&32, 1007&32-33, etc., seem to show that Aristotle was headed in that direction. Then the refutation or refutations are limited to cases in which Antiphasis picks a word for a substance. And, on this interpretation, that means that he is not free to pick any (predicate-) word he chooses: he must pick one of 'man', 'horse', 'battleship', etc. It is not that Aristotle would be limiting the truth of the law of noncontradiction to cases in which these words are involved; r4. 1008&7ff. shows him as unhappy over denying the law with 'pale' for a predicate as over denying it with 'man' for a predicate.21 But he certainly does say that the word Antiphasis picked signified the substance of something. If this involves limiting the scope of the argument, it turns out to be an argument for less than what we expected, and, apparently, less than Aristotle really wants. But, I think, it is not. The trouble with this interpretation comes of supposing that only words like 'man', 'horse', 'battleship', etc.- only a word for what in theCategories was called a 'secondary substance' - can signify the substance of anything. That supposition is a legacy left by my reader in the last section fresh from the Categories. The supposition is false. In Topics Z 12. 149b37 we hear of the substance of justice, and of wisdom. Poetics 6. 1449b22-24 reads: Let's talk about tragedy, pulling together the definition of its substance that emerges from what we've already said.
Physics A2. 21{)&11-13 (cf. 5. 213&10-11) reads: We've stated the considerations on the basis of which it is necessary that there be such a thing as place, and, again, those on the basis of which one might have a problem about its substance.
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In Metaphysics Z 7. 1032b3-5 (cf. 9. 1034a26-31), Aristotle says: For the substance of a privation is the opposite substance, e.g., health [is the substance] of disease, for disease is its absence.
And he says in Top. Z 8. 146b3-4: The substance of everything relative to something is relative to something else, since for each thing relative to something, to be is the same as relating somehow to something.
We hear of the substance of a sense (sight, touch, etc., De an. B 6. 418a25), of male and female (De gen. an. B 1. 73Ib18-20; cf. here Met. I 9), and often of numbers (An. post. B 13. 96a33, 34, bl2, Met. ~30. 1025a30-32, De part. an. A 3. 643a27-31, etc.). But none of these would count as a primary or secondary substance in the Categories. In other words, the notion 'substance of something' (i.e., 'essence of something') can float free of the category of substance. In r7. I012a21-24, Aristotle says of people like Antiphasis (only there they are making trouble over the law of excluded middle) that against all such people the starting point is from a definition. And a definition comes from the fact that it is necessary for them to signify something; for the account of which the word is a sign will be a definition.21
The attack on Antiphasis in r4 has such a starting-point: we get him to give us a definition. A definition is an 'account signifying an essence' (Myoc; 6 -ro -ri i'jv etvat O"I')J.Laivrov, Top. A 5. 101b39, H 3. 153a15-16, 5. 154a31-32; cf. Met. Z 5. 1031bll-12, etc.), or an 'account that reveals the substance' of something (cf. Myoc; -rf\c; oucriac;, Cat. 1. 1a2, 4, 7, 9-10,23 Top. E 2. 130b26, Z 3. 140a34, etc.). This is what Aristotle is after when he is looking for the substance of place, of a tragedy, and so on. And it is what he wants from Antiphasis: a definition corresponding to whatever word he picks, an account of the substance corresponding to whatever word he picks. It may seem that this conflicts with a concession we made in the last section to the reader fresh from the Categories. The point we allowed in his favor was that there is a connection between the substances of things and substances (full stop): the destruction of the former carries with it the destruction of the latter, and part of the argument of r4 turns on that. Doesn't allowing 'substance of' to float free ofsub~tances (full stop), that is, of substances in the category of substance, threaten the entire scheme?
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What is it now that gives priority to an inventory of the universe that tells us that there are men, horses, and battleships in it over one that tells us that there are things pale, tall, and educated in it? A brief review of the scheme answers these questions. We had a rockbottom level of things to talk about; these were the substances (full stop). We had to be able to say what they were; in doing that we would be giving their substances. That tended to confer some priority on their substances: without those substances, they would not exist. But they (the 'substances (full stop)') were supposed to be the things without which nothing else would exist. That difficulty, the suggestion went, Aristotle tried to resolve by saying that the substances of substances were not, in any relevant sense, something 'else': there could be no question of the priority of one of substances (full stop) and their substances over the other, because there was no relevant distinction between them. But there are cases in which the substance of a thing and the thing are relevantly distinct. This happens when we give an accidental specification of something and ask for its essence so specified: when, for example, we are talking about some pale thing, and ask what it is for it to be a pale thing, or by virtue of what it is a pale thing. Then we get this situation (Z 6. 1031b22-28): (As to] What is said accidentally, like the educated or [the] pale, since it signifies two ways, it isn't true to say that it and its essence are the same; for [it signifies] both that of which pale is an accident and the accident, so that it and its essence are in a way the same and in a way not the same: it isn't the same as the man, or the pale man, but it is the same as the affection.
The 'affection' (or 'attribute') by virtue of which a man is pale and the man who is pale are both called 'pale'. The 'affection' isn't the man, but it is the essence of pale: so the essence of pale is the same as the affection and not the same as the man. A pale (thing) isn't the same as its essence so described, but pale is. (This involves taking the 'it' in the last clause of the passage to refer to the essence of pale. I can't see any other way of taking it.) If we filter out the things that are distinguishable from their essences, we filter out pale men, and are left with men and the 'affection' pale. If we can then show that the affection is dependent for its sense or existence on the men and other things that have it, we shall have saved the primacy of men, horses, and (maybe) battleships.
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Fortunately, most of that is another story. Here and now, the chief point is that we are not destroying the scheme outlined in the last section by anything added to it in this one. What happens, then, if the word Antiphasis picks in the first refutation is, not 'man', but 'pale' or 'educated'? Here are two suggestions. First, we noted a few pages ago that a definition that gives the sense of 'tall' would show the dependence of this notion on the selection of a range of things within which something would be tall. And we noted that Aristotle would be inclined to assimilate the behavior of a great many words for accidents to this pattern. So we can imagine him starting from a definition that looks like this: (Dp)
A pale so-and-so is a so-and-so colored more penetratively than is standard for so-and-so's.
(The definition 'penetrative color' or 'color penetrative of sight' comes from Top. r5. 119&30, H 3. 153&38-bl, A 15. 107b28-31, Met. I 7. 1057b810, 18-19). From there he might lead Antiphasis toward a premise for the clincher that looks like this: (lp)
Necessarily, if something is a pale so-and-so, it is a so-and-so colored more penetratively than is standard for so-and-so's.
And that would do it. It would be cumbersome, and Aristotle certainly doesn't come out and tell us about it. (Besides, he had some troubles with contextual definitions: cf. his problems with 'snub' in Met. Z 5 and elsewhere.) It would have the merit of making the need for a specification of a subject-range explicit, and that would go well with the ontological scheme operative in r4 (cf. especially the comments on the priority of some sorts of definition over others in Met. Z 4. 1030&17-27, 29-bl3). But, second (and more plausibly, perhaps), Aristotle has a different way of getting nearly the same effect. The original statement of the law of non-contradiction in r3. 1005bi9-22 is this: It is impossible for the same thing both to belong and not to belong at the same time to the same thing and in the same respect (and let as many other qualifications as are added against logical [or 'dialectical']24 difficulties be added).
Here qualifications such as 'in the same respect' are put in to sidestep dialectical difficulties; in De interpretatione 6. 17&35-37 (cf. EE. B 3.
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1221b4-7) they guard us against 'sophistic troubles' (cf. Plato, Rp. IV. 436b8-9). What troubles or difficulties are these? He tells us of some of them in Sophistici elenchi 5. There he is worried about what a refutation is; he says that it leads to (or is) a conclusion contradictory to the thesis originally being defended. In it the predicate will be denied of whatever the thesis asserted it of "in the same respect, relative to the same thing, in the same way, and at the same time" (167&23-27). He illustrates failure to observe the stipulation that the predicate be relative to the same thing in both thesis and conclusion with a case in which two is double in the thesis and not double in the conclusion: it is double one but not double three (167&29-30). And he illustrates failure to observe the stipulation that the predicate hold in the same respect in both thesis and conclusion with a case in which something is once double and then not double because it is double in length but not double in width. The pattern of non-genuine, sophistic refutation he envisages is this: Thesis: Two is a double. [(Q1} (A1) (Q2) (A2)
Isn't it impossible for the same thing to be both double and not double? Yes.) But two isn't double three: isn't that so? Yes.
Conclusion: So two isn't a double. I have put the sequence (Q1)-(Al} in brackets because, it later emerges, the question may not be explicit; when it is, he recommends refusing to make the concession (26. 181 aS-8): If at the outset this should be asked as well, one ought not to agree that it is impossible for the same thing to be double and not double, but say [that it is possible], only not in the way that it was agreed would be a refutation.
It is not pushing Aristotle too far to take him to mean that the refutation won't work because 'the same thing can't be both double and not double' is not a case of the law of non-contradiction. Suppose Antiphasis, asked to utter a word, uttered 'double'. The behavior of this word is, for present purposes, only a vastly more explicit version of the behavior of 'tall' and 'pale': all, as we are seeing them, require additional material for their application to make sense. So, if
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Aristotle had got 'double' from Antiphasis, he would have to build into the stipulation that 'double' signifies one thing, or maybe stipulate in addition, that 'double' be used throughout the argument in relation to the same thing, in the same respect, and so on. He might ask for this: (Dd)
What is double something in some respect (and so on) exceeds that thing by an amount equal to that thing in that respect (and so on).
(The definition here comes fromTop.Z9. 147&30--31.) This is cumbersome, too. And it does not tie in quite as nicely to the ontological apparatus as does the first suggestion. The refutation works with the least drudgery where Antiphasis picks a word like' man', 'horse', or 'battleship'. But plainly Aristotle could have handled it whatever the word. NOTES 1 Cousin, in 'Aristotle's Doctrine of Substance', makes a good deal out of the distinction. I This strikes me as better than "senses of 'substance'", but its virtue is mostly its vagueness. cr. Hintikka, in 'Aristotle and the Ambiguity of Ambiguity', which softens one's confidence that Aristotle is talking about senses but does not make it clear what he is talking about. I This follows Ross' interpretation of "6pil;ovta 't£ mi 't6li£ 't\ GTIJ.Udvovta", 1017b1718: cf. his n. ad loc., AMi. 310. 4 Not altogether the same as our original sense: Aristotle is here talking about the constituents of a thing, not predicates of it. The need for the distinction is (fairly) clear in An. post. A 4. 73..34-37 (which goes with (3) above) and 73b5-10 (which goes with (1) above). Cf. Ross' note ad 73..37-38 (APPA 520-21) and Bonitz, Aristotelische Studien, pp. 258-62 (Olms reprint). 6 Kirwan's note on this, AM 147-48, is particularly good. e I am not clear why Kirwan (AM 148) thinks that (3) drops out; contrast Ross (AMi. 310 ad 1017b23), whom I am following here. 7 Part of what follows is based on my paper 'On Some of Aristotle's First Thoughts About Substances'; part of it on a projected sequel, 'On Some of Aristotle's Second Thoughts about Substances'. Cf. also White, 'Origins of Aristotle's Essentialism'. a In the Cat., there is an additional clause: substances are neither said of nor in subjects (S. 2..11-14, 3&7-21). This is not directly relevant here. e Aristotle's Greek often has a definite article before 'man' in subject position when (but not only when) the species is in question, as our English has one before 'dodo'. This definite article functions as a quantifier, and Aristotle sometimes comes close to recognizing this where Plato (I think) had very studiously failed to recognize it. But Aristotle has troubles with this insight: cf. Geach, 'History of the Corruptions of Logic', pp. 44-51; 'Nominalism', pp. 289-92 (both references to Logic Matters).
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1o Jaeger brackets b3-4, for no very good reason. u Ross and Jaeger both have '7tpl7rtov' rather than '7tp6>'ttl' in b9 (although Ro!ls indexes the passage under '7tp6>'tT)oo
'tT)' seems a little better attested. _ 12 a. the discussion of the term in Charlton, Aristotle's Physics 1-11, pp. 60--61. 13 "~n 'tel ~v oilaiav aT)Imivov'ta <S7tep SKeivo i\ o7tep SKeiv6 'tt O"T)jlaivet Ka9' o6 KQ'tT)yopei'tat." 14 "oaa oe lll'l oo yap SO"'tlV 6 dv9pro7to~ Oil'tE 07tEp l..eUKOV oil'te 07tEp l..euK6V 'tl, aA.Mi. /;cflov ia~ o7tep yap 1;4'16v SO"'ttV 6 dv9pro7to~." 16 "oaa OS j.11'J OOaiav O"T)jlaiVEl, Oei KQ'tU 'tlVO~ UnOKEljlEVOU KQ'tT)yopeia9at, Kai J.l1'J £lva( 'tl l..eUKOV 0 oo:x; ~'tep6v 'tl ov A.euK6V SO"'tlV." 17 Maybe not: we might run out of words. But this is not the difficulty with which Aristotle is trying to nail Antiphasis. 1s Cf. White, 'Aristotle on Sameness and Oneness'. See also Aristotle's 'earlier' troubles in De int. 5, 8, and 11 (with Ackrill's notes in Cat. and De int.); and the even greater troubles once matter has found its way into the schema, in Met. Z 12 and H6. 19 'Aristotle', pp. 39ff. She goes farther than my elaboration does, since she believes (pp. 41, 44) that 'necessarily' covers only the consequent of the conditional in the premiss for the clincher, (1). She is followed by DUring, Aristote/es, 601-02, but spurned by Leszl, Logic and Metaphysics, p. 112, n. 39, who cites r 5. 1010b18ff. (esp. b25-26). so a. Owen, 'A Proof in the PERI IDEON', 302-09 (in Allen); Strang, 'Plato and the Third Man', 194-98 (in Vlastos). 21 Anscombe hints that he might have limited the law to these cases: cf. 'Aristotle', pp. 43, 44. 22 Here the definition is of 'true': cf. 7. 1011 b25ff. 23 a. the review of positions on what originally stood in the manuscript of the Categories in Simplicius, in Cat. 29. 28-30.15: I am inclined to the now common view that 'A.6yo~ ~~ ooaia;' was in it. Cf. Anton, 'The Aristotelian Doctrine of Homonyma' and 'Ancient Interpretations of Aristotle's Doctrine of Homonyma', and Waitz, Org. i. 269-70. 24 'A.oytKa~·. Cf. Bonitz, AM ii. 187; Waitz, Org. ii. 353-55.
CHAPTER VI
ON SENSE AND ESSENCE
One of the chief themes of this study has been a distinction between (broadly) subjects and the predicates true of them. By way of tying things together, I want to consider that distinction. Plainly there is a difference between Cleinias and what is said of him by someone who says'Cleinias is a man' or 'Cleinias is pale'. Lots of other things besides are men, and lots of other things are pale. What 'man' or 'pale' signifies about Cleinias is, then, distinct from him, or from any of the things of which those predicates are true. This distinction is perfectly general: it will hold for any subject-predicate statement. But it is not the only distinction we need. For an essentialist of Aristotle's sort, there is a distinction between the two predicates, 'man' and 'pale', that are here attached to Cleinias. A predicate like 'pale' could be true of Cleinias, or false of him, whether or not he is in fact pale. A predicate like 'man', if it is true of him, could not be false of him. Cleinias' identity is not threatened by changes in his complexion; it is threatened when his standing as a man is threatened. It turns out that this latter distinction is the one that is needed to handle the sophistic confusions that motivate r4. And that fact has some ununexpected repercussions for Aristotle's own views about sense and essence. I try to clarify these matters in Sections I-II below. Consideration of them leads to a reconsideration of the pattern of objection to the first refutation outlined in Chapter II, Sections III-IV. We use a lot of words as predicates, and I am going to accept Aristotle's root intuition that some of them are and others are not appropriate answers to questions of the form 'what is that?'. But have we any right to expect that this fairly simple fact about the language we speak is founded on a 'metaphysical' fact, e.g., that things have essences, and our privileged predicatewords signify those essences? I think not, and I think that Aristotle shouldn't have thought so, either. This is taken up in Section III below.
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I. SUBJECTS AND PREDICATES; ESSENCES AND ACCIDENTS
Antiphasis' original position, we said, was ultra-essentialism. As Dionysodorus developed that position, it led to a 'suspension' of the law of non-contradiction: a claim to the effect that it never applies, that two people cannot contradict each other, that no statement ever contradicts any other, because purportedly contradictory statements really say, state, are about different things. A lemma to this, or a corollary of it, was that both of two purportedly contradictory statements have to be true: 'Cleinias is wise' presents us with, states, is about a wise Cleinias, and if there were no such Cleinias, it would present us with, state, or be about nothing. And all that is just as true of 'Cleinias is not wise'. As we developed ultra-essentialism for Antiphasis, it led to a denial of the law of non-contradiction. This was because, in addition to giving him the semantics of ultra-essentialism, we had him grant the plain truth that 'Cleinias is wise' and 'Cleinias is not wise' are both about Cleinias. We have him saying that they are about the same thing, and about different things. Either development of the position might lead to ultra-accidentalism about objective reality. Dionysodorus' would lead there fairly deviously. We found Plato paraphrasing this position as one according to which 'nothing is anything in its own right' (Ka9' aO't6: cf. pp. 68-69, 80 above). In the first instance, that has to mean: there are no things independent of an observer or thinker that have any characteristics of their own, about which that observer or thinker might be wrong. But it shades over into meaning something like: anything in the objective world will have to be devoid of characteristics whose loss would carry the thing with it. This is the sense Aristotle would give it; he says: "[what it is for you to be] is what you are in your own right" (8 dpa Ka'ta crau't6v, Met. Z 4. 1029b15-16). For a consistent Protagorean, the only things there are are subjective things, and every characteristic of one of them is essential to it. But if he slips into making claims about things that are objective (and Plato and Aristotle allow that kind of slippage), he will have to say that none of the characteristics of any of those things is essential to it. Antiphasis makes the slip, and his development of the position leads quite directly to ultra-accidentalism: if the opposite of any predicate true
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of Cleinias is also true of him, there is no predicate such that if it were not true of him, he would not exist (cf. Alexander, in Met. 294. 5-9). What is needed to straighten out either of these people is a distinction between what is said about something and what it is said about; and, in particular, what is needed is a distinction of that sort that will allow what is said about something to vary independently of what it is said about. These are different matters, although they are related. I think Aristotle may have had trouble keeping them apart. He inherits the distinction between what is true of something, or what is said of something, and what it is true or said of, from the theory of forms. We can see the beginning of the trouble if we consider a facet of that. Socrates' first historical act, if we are to believe the early dialogues of Plato, was that of showing the world the difference between a predicate true of a plurality of things and the plurality of things of which it is true. He asks Euthyphro 'what is the pious?' (Euthp. Sd1), and Euthyphro answers 'it's what I'm doing now' (5dk2). 1 Socrates duly points out that a lot of other things are pious (6dl-l0): what he is after, Aristotle would say, is the one thing that 'pious' signifies, not one of the many things about which it signifies, or of which it is true. But when Hippias responds to Socrates' question 'what is the beautiful?' (Hipp. maj. 286dl-2, 287d3, d6) with 'it's a beautiful girl' (287e3-4), Socrates combines the retort that there are lots of other beautiful things (288bc) with another: any beautiful girl will be beautiful compared with a pot, or an ape, but ugly compared to a goddess (289ab); so she will both beautiful and ugly, and so not the beautiful (289cd). And this is a different point. To phrase it Aristotle's way, if you say that the beautiful is so-and-so in response to the question 'what is the beautiful?', you are saying that to be beautiful is never anything other than to be so-and-so. The definition 'beautiful girl' fails to meet this requirement in two ways. First, since lots of other things are beautiful, there will have to be cases in which to be beautiful is not to be a beautiful girl. But, second, since any beautiful girl is also ugly, and to be ugly is something other than to be beautiful, it must be that to be a beautiful girl is something other than to be beautiful. It is not that the argument here is a good one. Rather, the point is that even if it were a good one, there would be a crucial difference between
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the two ways in which the definition 'beautiful girl' fails. Generalized, anything that is not co-extensive with the predicate 'beautiful' will fail as a definition in the first way; anything that is not essentially beautiful will fail in the second way. But they are combined here in a single attack on the definition 'beautiful girl': they are combined to show that the beautiful is something other than a beautiful girl. The running together of these two considerations is preserved when Plato gets around to working his reflections on definitions into a metaphysical theory, the'theory of forms' (cf. Phd.14a-c, Rp. V. 476-80: there the second of the two ways for a definition to fail is used to show the distinctness of forms from their mundane participants). The preservation is visible in a wavering on Plato's part as to the range of predicates covered by forms. 2 On the one hand, he acts as if, in the nearly worn-out words of Rp. X. 596a6-7, we customarily posit a form for each of the [groups of] many [things] to which we apply the same word.
This ties to the simple distinction between any predicate and the plurality of things to which it applies. But, on the other hand, Plato sometimes (e.g., in Rp. VII. 523a and ff.) acts as if, when it comes to a predicate like 'finger', there is no need to posit a form: at least, on the question whether something is a finger, it is "as if judging by perception is adequate" (523bl-2; cf. 523c-e), and it is where we get contrary judgements from perception (as with hard and soft, heavy and light, and, presumably, beautiful and ugly: cf. 523e-524c) that thought is 'dragged toward substance' (523a2-3), that is, toward the things that are soft, light, and beautiful essentially, entirely (cf. Rp. V. 477a3), purely (477a7), and in their own rights (cf. Parm. 128e6-129al, 129d5-6). And in the Parmenides, Socrates thinks that mud, hair, and dirt are "just what we see" (130d3-4), and he thinks maybe man, fire, and water are, too (cf. 130cl-4: commentators standardly ignore Socrates' doubts as to whether there are forms for man, fire, and water, turning quickly to Parmenides' allegation that Socrates is too young and afraid of public opinion to admit forms for mud, hair, and dht: but although the explanation might handle the latter cases, it will not cover the doubts about the former). And it is because Simmias is tall, but not tall because he's Simmias, that we need to distinguish between him and tallness in Phaedo 102bc; and we show that he is not tall because
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he is Sim.mias by pointing out that although he is tall by comparison with Socrates, he is short by comparison with Phaedo. If there were anything true of Simmias because he is Simmias, this passage would give us no reason to set up a form for'it. We found in the fragments of On ideas reason to think that Aristotle's distinction between what a term signifies and what it is true of was an inheritance from the theory of forms (p. 86 above). There he was concerned to nail the more general theory to the Platonists. The contrast between a form and its instances based on the idea that a beautiful girl is both beautiful and ugly, whereas the form, the beautiful, is not and cannot be ugly, meets with a fatal accident in the Parmenides, and is suppressed deliberately in the Sophist (cf. esp. 256e-257a) and in thePhilebus (cf. 14c--e). That leaves only arguments like the 'one over many' and the 'argument from thinking' to buttress the theory, and these arguments are general: they work for any predicate. How Plato and his colleagues responded to this is beyond saying (anyway, beyond my saying). But many of Aristotle's points in On ideas (or in Met. A 9: it is from Alexander's commentary on this that our fragments come) tum on his recognition of the fact that these arguments are perfectly general, and do not allow for limitations in the range of predicates for which there are forms. Those arguments (the one over many and its fellows) don't show that there are forms, he says, but that something predicated of a plurality of things is distinct from anything in the plurality. What of essential predicates? Here Aristotle has trouble. Some of the trouble shows through in the fact that Aristotle has a use of the term 'accident' and its cognates that does not contrast at all neatly with 'essence'. Consider the fallacies that he calls 'fallacies dependent on accident'. In Sophistici elenchi 5, he records two sophisms that, I think, Antiphasis, had he ever lived, would have appreciated. The analysis Aristotle offers for these sophisms provides for a sharp distinction between subjects and their predicates. What he says is this (166b28-36): The fallacies that depend on accident occur whenever anything is claimed to belong to the thing and to its accident alike. For since many things are accidental to the same thing, it is not necessary for all the same things to belong to all the predicates and to that of which they are predicated. For example, if Coriscus is different from [a) man, he is different from himself; for he is [a) man. Or: if he is different from Socrates, and Socrates is [a) man, they say that it has been agreed that he is different from [a) man, because it is an accident that that from which he was said to be different is [a] man. a
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To get the upshot of these sophisms, reverse their order. The second is: (a) (b)
Socrates is a man. Coriscus is different from Socrates.
Therefore, (c)
Coriscus is different from a man.
And the first is: (c) (d)
Coriscus is different from a man. Coriscus is a man.
Therefore, (e)
Coriscus is different from himself.
Aristotle wants to reject (a)-(c}. So he cannot be taking the conclusion (c) as 'Coriscus is different from some man or other'; so taken, there would be nothing wrong with the argument. He apparently takes (c) to amount to 'Coriscus is other than a man', 'Coriscus is not a man'. The phrase 'is different from' in {b) could be replaced by 'is not'; perhaps, then, the way to see a fallacy in {a}-(c} is to see it as saying: (a) (b 1)
Socrates is a man. Coriscus is not Socrates.
Therefore, (c1)
Coriscus is not a man.
The analysis Aristotle suggests for the fallacy is what is of interest. He takes 'a man' in (a) to stand for an 'accident' of Socrates (that from which Coriscus was said to be different), and blocks the inference by saying: although the frame 'Coriscus is different from ( )' is true of Socrates, there is no reason why it should be true of an accident of Socrates, such as a man. The argument that runs from (c) to (e) is supposed to get a similar analysis. I take it, then, that in this argument, the interpretation to be given to (c) is one under which it comes out true: what we want to see is why (e) doesn't follow from (c) and (d). Presumably, (c) here comes to
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'Coriscus is different from some man or other'. Then the analysis would be: although (c) tells us that the frame 'Coriscus is different from ( )'is true of a man, (d) only tells us that a man is an accident of Coriscus; so it doesn't follow that 'Coriscus is different from ( )' is true of Coriscus. Obviously, Aristotle would not want to rule out every inference that involves substitution in a sentence-frame.4 I think he ought to have concentrated his attention on what are now called 'quantifiers': (a}-(c) would fail (if the above interpretation of that argument is right) due to an illegitimate generalization, and (c)-(e) would fail due to an illegitimate instantiation. But Aristotle had trouble with quantifiers, 5 and the above analyses do not point toward clarity over them. Many chapters later, he gets around to trying to formulate a principle that will tell us when we can and when we cannot carry out legitimate substitutions in sentenceframes. He does not, in the later passage, return to our two arguments; he fastens on others, e.g. (from Soph. el. 24. 1796 33, 39-bl): suppose your thesis is that you know what's good, and I lay waste to your defences with this: {f) (g)
You don't know what I'm about to ask you. What I'm about to ask you is what's good.
Therefore, (h)
You don't know what's good.
The trouble is supposed to be that the frame 'you don't know ( )' is true of what I'm about to ask you, but (g) only tells us that what I'm about to ask you is an accident of what's good, so that 'you don't know ( )' needn't be true of what's good. Perhaps there is a little more plausibility to this sort of analysis as applied to that argument. But Aristotle is led to the following principle (24.1796 35-bl; cf. Phys. r3. 202bi4-166): It is plain that it isn't necessary in all cases for what is true of the accident to be true of the thing as well; for the same [predicate] is taken to belong only to things that are indistinguishable and one in substance. As for what's good L(f)-(h)], it isn't the same thing for it to be good and for it to be going to be asked about.
Suppose we applied this formula to our illegitimate inferences (a}-(c) and (c)-(e): we would find ourselves forced to say that, in (a), Socrates and a man are distinguishable in substance, and, in (d), Coriscus_and a man are
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distinguishable in substance. So although Aristotle has the notion of the substance of something, its essence, he is comitted to saying that Socrates and a man are distinguishable in essence, that a man is an accident of Socrates. (This use of 'accident' is found elsewhere in Aristotle: cf. especially, in the present connection, Met. A 1. 981&19-20).7 Here, then, the distinction between an accident and that of which it is an accident is as general as the distinction between a predicate and that of which it is a predicate. And both are as general as the distinction Aristotle tries to fasten on to Platonists in On ideas and Met. A 9, between a form and its participants. This is not the picture we had him painting in the last chapter. There, some of the predicates of a thing were essential to it, and some accidental. But this was the way I put it, not the way he does: he is still saying in r4 "anaccidentalwayssignifies a predicate of a certain subject" (1007&34-bl). (He does not outright say that only accidents do that, but the implication is pretty clear from the context.) The fact is that he had trouble separating these two distinctions. And the reason he had trouble is that he wanted to save the criterion for something's being a substance, a 'reality', according to which a substance, a reality, is an ultimate subject for predicates. His attempts to save that criterion involve a certain amount of confusion, and the confusion might have been avoided if he had distinguished his two distinctions. He could have done that in the Categories. There 'secondary substances' (essential predicates) are what we get in answer to the question 'what is that?' asked about primary substances. And there Aristotle says (3. 1bl012): Whenever one thing is predicated of another, as of a subject, all that is said of the predicate will be applied to the subject. s
If 'predicated of', 'said of', and 'applied to' are here merely variant ways of expressing the relation between any predicate (or, perhaps, what the predicate 'signifies') and a subject of which it is true,9 what Aristotle is saying erases the 'fallacy of accident' from the list of fallacies. Even under a more restricted interpretation, according to which 'said of' only holds between species and genera and the things that fall under those species and genera, 10 Aristotle could not square the principle he here propounds with his analyses of (a)-(c) and (c)-(e) as fallacies of accident.
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Either way, he is in a position to make the subject-predicate distinction quite generally: his principle reads 'whenever one thing is said of another .. .'.U In a predication, one thing will be said of another, and that will be so even where the predication counts as an appropriate answer to the question 'what is that?' asked about its subject. For contrast, consider Posterior Analytics A22. 83a24-32 (cf. above, pp. 101-02), or the following passage, from Top. A 9. Aristotle has just been making some difficult points about terms; he goes on to say (103b3539): for each such [term)1 2, if it is said of itself, or if its genus is said of it, [that] signifies what it is; but when it is said of something else, it does not signify what [that] is, but how-big [it is], of-what-sort [it is], or one of the other categories.
Part of Aristotle's inclination toward saying that an essential predication is a matter of saying something of itself is due, no doubt, to the simple intuition that an essential predicate tells you what its subject is, and so had better not be something other than its subject. But part of that inclination has to do with his desire to avoid Platonism. We found him, in On ideas (p. 86 above), conceding that Platonic arguments showed that what was predicated was different from what it was predicated of, and even that they showed that what was predicated was something separate from what it was predicated of. This fits well enough with what sense can be made of his analysis of the trouble that underlies the 'third man' in Soph. el. 22. 13 There he says that the feature of Platonism that gives rise to the 'third man' is not its 'isolating' a common predicable like 'man' or 'educated', bit its additional claim that what is thus isolated signifies a 'this' (179a3-5). Apparently he believed it possible to say that predicates can be made separate from their subjects without committing oneself to the claim that those predicates signify particular things, and so without committing oneself to Platonism. But this is a fuzzy belief, and if Aristotle had it at all, he did not have it always. We find him saying, in Metaphysics M 9. 1086a31-b12, that the root error of the Platonists is their separating Ideas from particulars, and so making them into new particulars (1086a32-35, b6-7). Socrates, in his innocence, was really better off: he didn't separate universals (1086b2-5). But as for the Platonists (1086b7-11), they [took it] as necessary, if there are to be any substances besides perceptible and changing ones, that they be separable; but they had no other candidates [Aristotle
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does: his unmoved mover or movers], and isolated these [substances], the things said universally, in such a way that universals and particulars are virtually the same natures.
(Cf. also B 5. 1003&7-12.) Here, it looks as if 'isolating' universals is already too much; at any rate, making them 'separate' will not do. And in Posterior Analytics A 11. 77&5-9, he says: So it is not necessary, if there is to be a demonstration, that there be forms, or any one thing beside the many, but it is necessary that it be true to say one thing ofmany things, for there wouldn't be a universal if this weren't so, and if there weren't a universal, there wouldn't be a middle [term], and so no demonstration, either. Then there has to be some one and the same thing, non-homonymous and [true] of many things.
I have no idea what to say about the chronology of all this: it may be, for all I know, that it is an expression of simultaneous conflicting intuitions on Aristotle's part. The point is that the distinction between a predicate and its subject is one Aristotle struggles to put in the right words, so as to avoid committing himself to the metaphysics of Platonism. But in some cases, he feels, there is no real problem about distinguishing predicates from their subjects: namely, in cases in which the predicate is accidental to its subject. We found him saying (An. post. A 22. 83&30-32; p. 102 above): Such [terms] as do not signify a substance have to be predicated of a certain subject: there is nothing that is pale without being something else that is pale.
This is courting trouble: we have to say, where we have a pale man, that the man and the pale thing are different. In Aristotle, they are: for the man to be is not for a pale thing to be. They are, I suppose, 'intentionally' distinct; Aristotle would say: they are distinct in being, in form. But that does not bother him, precisely because there is nothing pale that isn't something else that's pale. He goes on (83&32-35): For the forms can be dismissed: they are prattle, and it is not relevant to the present discussion whether they exist, for demonstrations are about [terms] such [as we have been talking about].
So although the man and the pale thing are distinct in being, in that for a man to be is not for a pale thing to be, the common predicable 'pale' gives us nothing that can be separated from things that are pale: for a pale thing to be is for one or another thing (a man, a horse, a battleship) to exist, and to be pale. Let 'paleness' (cf. Cat. 8. 1(}&30, etc.) be the color a man must have if
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he is to be pale. (There are type-distinctions here that Aristotle is not always too careful about.) Something's being pale is then dependent on the existence of paleness. But the existence of the thing that is pale is not dependent on that of paleness: its existence is dependent on its being a man, or a horse, or a battleship, or whatever it is. But now that dependence, if taken along with a general distinction of subjects and predicates, carries with it the threat of Platonism. It is this threat that Aristotle counters by identifying the thing and its essence. What the predicate 'man' signifies is no different from what it is true of. And that leads him into trouble: 'man', after all, is true of a number of things, and signifies just one thing. He tries to face the trouble in Metaphysics Z 13: there he is trying to save the subject-criterion for substantiality, while hanging on to his brand of essentialism. That unpleasant chapter is part of another story. My point here is that Aristotle might have saved himself a lot of trouble by separating his distinctions. He might have said: what an essential predicate signifies is different from what it is true of. But, where what it is true of is an ultimate subject, it and its essence are dependent on each other for their existence. This is complicated to formulate: the essence of man is not dependent for its existence on that of Socrates in particular, or Coriscus in particular: it is dependent for its existence on the existence of men. Paleness is, similarly, dependent for its existence on the existence of pale things. But in the latter case, the relation is asymmetrical; in the former, it is not. That is, those pale things, on whose existence paleness is dependent for its existence, could exist even if paleness did not: they just wouldn't be pale. But men couldn't exist without being men. It is just possible that this is what, in the long run, he wants to make out of such pronouncements as the following (Met. Z II. 1037a33-b4): Each thing and what it is [for it] to be are in some cases the same, as in the case of primary substances, ... 1 4 (I call a substance primary which is not called [whatever it is called] by virtue of one thing's being in another, in a subject, as in matter).
But it would be nice if he had said so more clearly. It would be nice, if only because clarity here is needed for the purposes of the debate with Antiphasis. In r4, he demands that Antiphasis accept a distinction between signifying one thing and signifying about one thing, and the predicate in question is 'man'. He was trying to get Antiphasis to see that that predicate could be applied on different occasions, to different
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things, with the same significance. So he is in no position to say that what it signifies is the same as what it is true of. This goes back right to the beginning of the debate, where he is softening Antiphasis up by saying that his utterance of 'man', and perhaps even his concession that it signifies something, do not commit him to saying that anything is any more a man than not a man. Perhaps he was standing back from his own views about the coalescence of the essence-accident distinction with the subject-predicate distinction, thinking: well, I can hardly expect someone as obstreperous as he is to swallow all that without some strenuous arguing, so I'll just forget about it for now. Or, perhaps, he had not yet got to writing Metaphysics Z. Or, perhaps, he just wasn't thinking. II. ESSENCE AND FALSEHOOD
It was Antiphasis' ultra-essentialism that led him into denying the pos-
sibility of false statement, and from there into denying the law of non· contradiction. Aristotle is not an ultra-essentialist, but he is an essentialist. Should he not, then, have some of the same troubles Antiphasis had over falsehood and contradiction? He does. What he says that bears on this question, he says in presenting one of his more obscure ideas: we shall have to brush by a lot of the obscurity to get anywhere. He says, in Metaphysics 111. l0l7a3J-35 (and cf. E 4, 910): 'To be' and 'is' signify that it is true, and 'not to be' that it is not true but false, in a similar way for an assertion and for a denial, e.g., that there is [an] educated Socrates, that this is true, or that there is [a] not pale Socrates, that it is true; and 'there is not the commensurable diagonal', that it is false.u
This is gruesome English; it is less gruesome Greek. I am, I'm afraid a little inclined to think that Aristotle would have been less disposed to say some of things he does say in this connection if he had spoken English. But we need not spend any time on his idea that there is a use of 'is' in which it signifies the truth of something or other. He wants to say that the truth of a simple subject-predicate sentence consists in the existence of a combination of the subject and the predicate (or of waht the subject
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signifies and what the predicate signifies); its falsehood in the non-existence of such a composite. 'Socrates is educated' is true if and only if educated Socrates exists, or there is educated Socrates. The English is still pretty bad: we at least need an indefinite article to get a semblance of syntax, and even then the result is grating: 'an educated Socrates exists' or 'there is an educated Socrates'. But perhaps we can give in to the idea for the moment: 'Socrates is educated' depends for its truth on the existence of a combination of Socrates and whatever 'educated' signifies. The pattern should remind us of the Euthydemus: it was on an analysis having this pattern that the paradoxes we looked into from that dialogue depended. And that is part of the point. The rest comes through if we look at what Aristotle has to say about cases in which there is no question of a combination or composite of subject and predicate: when we turn to 'simples' or 'non-composites'. He gives no examples of these. At first blush, we might take him to be talking about terms as opposed to propositions, about 'Socrates' and 'pale' instead of about 'Socrates is pale'. 1 5 We might then expect him to say that there simply is no truth or falsehood here: that only comes in at the level of statements, propositions, composites. And that is what he does say about terms, 'things said without combination', as opposed to full sentences in Categories 4. 2&4-10, 10. 13b10-12, and De interpretatione 1. 16&9-18.
But it is not what he says when talking about 'being as truth'. He wants to associate a kind of truth with simples, but rule out falsehood. We might have anticipated this even while we were wedded to the idea that the distinction between simples and composites was that between terms and propositions. For if the truth of 'Socrates is pale' consists in the existence of a combination of, say, Socrates and paleness, the existence of a simple like Socrates ought to give us the truth of 'Socrates exists'. What Aristotle has to say is this (910. 1051b17-26): What is being or not being, truth or falsehood, for incomposites? For [one of these] is not composite, in such a way as to be when it is composed and not to be when it is divided, as with the stick which [is] pale, or the diagonal which [is] incommensurable, and truth and falsehood will not work in a similar way in these and in the previous cases. Rather, just as truth is not the same in these cases, so also being is not the samebut as for truth and falsehood, contact and stating are true (for a statement is not the same as an affirmative predicationl 6), and not to make contact is to be ignorant (for it is not possible to be deceived about what [something] is, except accidentally ... ).
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When Aristotle talks about 'incomposites', then, he is talking about essences, what things are. A little later he says (1051b30-32): Then about such things as are just what something is to be, and are actually, it is not possible to be deceived, but only to think of them or not.
A moment ago, I suggested that the existence of a simple ought to give rise to the truth of an existential statement. But, for Aristotle (cf. Appendix II), an existential statement ('Socrates is') is elliptical for an essential predication ('Socrates is a man'). And that is echoed in 910. 1051 b33-1 052&2): As for being as truth, and not being as falsehood, in the one case there is truth if it is composed, and falsehood if it is not composed; in the other case, if [there is a] being, it is in a certain way, and if it is not in that way, it [just plain] is not. And truth is thinking of these things, but there is no falsehood, only ignorance.
(Cf. E 4. 1027b27-28, De an. r6. 430&26-28, b1-2.) We might put together a part of Aristotle's train of thought17 as follows. The existence of Socrates gives us the truth of 'Socrates is'. But 'Socrates is' is elliptical for 'Socrates is a man'. So the truth of either consists in the existence of Socrates, the man. And Socrates, the man, is no more a composite than Socrates is: the collapsing of the subject-predicate distinction that we were considering in the last section operates here, as well. If Socrates exists, he exists 'in a certain way' : as a man. If he did not exist in that way, he just plain would not exist. Then there is no such thing as falsehood here: you cannot refer to, 'make contact with', or think of Socrates, and say or think that he's a battleship. Thinking about him as a battleship, or talking about him as a battleship, is just not thinking of or talking about Socrates. But this does not commit Aristotle to denying or suspending the law of non-contradiction, for he need not go on to suggest that if you do think of or talk about Socrates as a battleship, you must be thinking of or talking about something else. Presumably, you are just not thinking of or talking about anything. The only options you have in the case of Socrates are to think of him or not, to talk about him or not, to 'make contact' with him or not. Aristotle does allow us to be deceived about what something is 'accidentally' (1051 b26), and it is hard to see what he has in mind.17a Perhaps it is this. Socrates, in his cell, asked Simmias whether he had ever thought
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the equal to be unequal, and Simmias replied without hesitation that he never had (Phd. 74cl-3; cf. Tht. 190b-c).l7b His promptness could hardly have been due to a simple certainty that it had just never occurred to him that the equal might be unequal: he must rather have decided that he never could have thought that the equal was unequal, because if he had, he could not really have been thinking of the equal. So far, the idea is Aristotle's. But he adds to it. Simmias might, after Socrates' death, reminisce, and his memory might fail him. He might think: the form Socrates and I were discussing on that awful day was unequal. Then Aristotle would say: he is in error; the form was the equal, and that (if Plato were right) is essentially equal. Simmias' thought is not really of the form: the equal is unequal; it is of the form: the form Socrates and I were talking about is unequal. But the form Socrates and he were talking about was the equal; it is an accident of the form that they were talking about it; so he is in error about the form accidentally. Similarly, suppose Socrates is standing in the corner wrapped in a sheet. I might think: that thing, wrapped in a sheet, is a hatrack. I would be in error, but my error would not be of the form 'Socrates is a hatrack'. It is an accident of Socrates that he is wrapped in a sheet; my error is in thinking that what is wrapped in the sheet is a hatrack; so my error is only accidentally an error about Socrates. It is this that makes our infallibility about essences no comfort when we face the world and try to understand what there is in it. It is the kind of lack of comfort we get from the realization that if we know something, we can't be wrong about it: that realization is only the realization that if something is false, we'd have to be wrong if we thought we knew it. And that makes the business of knowing no easier. Similarly, Aristotle's view about essences makes it no easier than it ever was to find out what things are. We can identify and reidentify 'unidentified flying objects' without having the faintest notion what they are. Suppose they are tricks of light caused by sunspots. And suppose we think that they are Martian spaceships. Then we are in error. But the kind of error we are in is accidental; we are not thinking: tricks of light are Martian spaceships. We are thinking: those greenish blobs near the horizon are Martian spaceships. And it is an accident of the tricks of light caused by sunspots that they are, or cause, greenish blobs near the horizon. But then the answer to the question 'what are those greenish blobs
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near the horizon?' or 'what are unidentified flying objects?' is not one we can get simply by finding out what 'greenish blob near the horizon' or 'unidentified flying object' means. A definition for the word 'man' is not going to tell us what a man is in anything like this strong a sense. In Metaphysics r, Aristotle seems to ignore this. He doesn't always, though: let us consider what he has to say about definitions. III. WORDS AND ESSENCES
Recall r7. 1012a21-24: against all such people the starting-point is from a definition. And a definition comes from the fact that it is necessary for them to signify something; for the account of which the word is a sign will be a definition.
That committed Antiphasis, in the first refutation, to granting Aristotle a non-trivial necessary truth, the premise for the clincher. And in the second refutation, together with the idea that a definition is an 'account signifying an essence', Aristotle made use of the same train of thought. There, Aristotle was alleging that the only hope Antiphasis had of evading the first refutation was by denying that there were any essences: by denying that there were any single things for the words he uttered to signify. In other words, Aristotle is committed to two things: first, if a word is significant, there is a definition for it; and, second, if a word is significant, there is an essence corresponding to it. In Chapter II, Sections III-IV, we considered a line of thought that would go against the first of these. If the second is merely a rewriting of the first (and that was the way I was interpreting it in talking about the second refutation), the same line of thought might weaken our confidence in it, as well. But Aristotle does not, generally, want to say that there are essences wherever there are significant words, or that an essence is given us by the definition of any significant word. I want to close this study with a consideration of his thoughts on this matter, and how they bear on our refutations. In Posterior Analytics B 10, Aristotle distinguishes among types of definition.1B He begins that chapter by saying (93b29-32): Since a definition is said to be an account of what [something] is, it is plain that one sort of account will be of what a name or other namelike expressionl 9 signifies: e.g., what 'triangle' signifies.
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This is the sort of definition or account we demand of Antiphasis. It is also the sort of definition we might not be able to get if the considerations in Chapter II, Sections III-IV are right. And it is not, for Aristotle, in general true that wherever we have this sort of definition, we have an essence. He had said earlier, in laying out problems some of which this chapter is intended to resolve: It is necessary for someone who knows what a man or anything else of that sort is to know that it is; for no one knows what that which is not is, but, when I speak of a goatstag, [one might know] what the name or the expression signifies; but it is impossible to know what a goat-stag is (B 7. 92b 4-8; cf. 92b17-18, 26-30).
And he plainly means to stick by this argument in solving his problems in B 10 (cf. 93b32-35). Let us call this sort of definition a 'nominal definition'.20 Suppose we have a nominal definition for, say, 'thunder': a noise in the clouds. And suppose we find that there is something to which 'thunder', so defined, applies. "Once we have it that it is, we ask why it is" {93b32; cf. B 1. 89b29-31, etc.), and the answer to that will get us to another sort of definition (B 10. 93b38-94a9): Another [definition of definition] is: a definition is an account that shows why [something] is. So the previous [sort of definition] signifies but does not prove, and this latter sort, plainly, will be, as it were, a proof of what [the thing] is, differing from a proof in arrangement. For there is a difference between saying why it thunders and saying what thunder is: in the first case, one says 'because fire is extinguished in the clouds', but [to] 'what is thunder?', [one would say) 'noise when fire is extinguished in the clouds'. So that the same account is put in a different way: in one way it is a continuous proof, and in the other a definition. Again, there is the definition of thunder: noise in the clouds; and this is the conclusion of the proof of what it is.
We could set out the train of thought here as follows. We begin with a nominal definition for 'thunder': 'thunder' signifies a noise in the clouds. We find that there is a noise in the clouds. So we can take our definition out of the formal mode and put it into the material mode: thunder is a noise in the clouds. That definition (Aristotle means, as always, not the whole defining sentence but the definiens) 21 will appear as the conclusion of a proof that there is such a thing as thunder, and that proof will constitute an explanation, an answer to the question 'why does it thunder?'. A rearrangement of the terms that appear in that proof will give us a new definition for thunder. (cf. also De an. B 2. 413at3-20). As often, Aristotle's syllogistic format muddies the waters. But the
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proof he has in mind looks like this (An. post. B 8. 93b9-12). Its terms are 'cloud', 'noise' (in 93hll-12; 'thunder' in b9), and 'the extinguishing of fire'. Then: (a)
The extinguishing of fire belongs to a cloud
("for fire is extinguished in it", 93hll). (b)
Noise (thunder) belongs to the extinguishing of fire.
(Aristotle says in 93hl2 that the extinguishing of fire is the 'account' of noise, or perhaps thunder: this is pretty loose.) So: (c)
Noise (thunder) belongs to a cloud.
That is, thunder takes place; there is such a thing as thunder. This is messy. We can, I think, capture his intent by rewriting the proof like this: (al) (bl)
Fire is extinguished in the clouds. Noise takes place whenever fire is extinguished.
That's why: (cl)
Noise takes place in the clouds.
We already know that we call the noise that takes place in the clouds 'thunder'. We've now explained why it takes place; that is, why it thunders. So what thunder really is, is the noise that occurs when fire is extinguished in the clouds. And this rearrangement of the terms of our explanation gives us a new definition for thunder. (Cf. also B 8. 933 30ff., Met. H 4. 1044h12-15 on eclipses.) Let us call it a 'real definition'. The terms 'nominal' and 'real definition' are not Aristotle's; they are intended to remind one of Locke. We can develop Aristotle's picture farther by making the comparison with Locke explicit. In the Essay (III. iii. 15), Locke says: 22 .... it may not be amiss to consider the several significations of the word essence. First, Essence may be taken for the very being of anything, whereby it is what it is. And thus the real internal, but generally (in substances) unknown constitution of things, whereon their discoverable qualities depend, may be called their essence....
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Secondly, ... it being evident that things are ranked under names into sorts or species, only as they agree to certain abstract ideas, to which we have annexed those names, the essence of each genus, or sort, comes to be nothing but that abstract idea which the general, or sortal... name stands for .... These two sorts of essences, I suppose, may not unfitly be termed, the one real, the other nominal essence.
The distinction is Aristotle's. It is his 'real definitions' that give us essences: the essence of a thing is an explanatory core, the expression of which is an outline of a deductive argument whose conclusion is what we want explained: why is there thunder, i.e., a noise in the clouds? We want an explanation of its 'discoverable' properties on the basis of its 'previously unknown constitution' (cf. De an. B 2. 413&11-12). Its nominal definition picks it out on the basis of its 'discoverable' properties: so its nominal definition functions as the explanandum. (This, too, has its parallel in Locke: cf. Essay III. iii. 17, vi. 6, IV. vi. 15, etc.) But there are differences between Aristotle and Locke. For one thing (and I think this is less important than it looks), 23 Aristotle is less skeptical than Locke about our ability to get at real essences.24 But the idea 25 that we can get that knowledge in mystic flashes, or through an infallible intellectual intuition, is foreign to him. (Contrast the views of the author of the Platonic Seventh Letter, expressed at 341cd, 344bc.) We saw in the last chapter that Aristotle thought we could not be wrong about essences. But it would be grossly misleading to put this by saying that we are infallible about essences: it is still a lot of work to get right about essences. Similarly, it is, I suppose, not possible to know something that isn't so. And that does nothing to make it any easier to get to know things: if anything, it makes it harder. For another thing, Locke believes that the distinction between a real and a nominal essence breaks down where the word in question stands for a 'simple idea or mode' (cf. esp. III. iv. 3); the distinction really only comes into its own when we are dealing with the name of a substance (III. vi. 3). 26 For Aristotle, too, there is a place at which the distinction does not attach. But it is a different place. In Posterior Analytics B 10, he lists a third variety of definition (94&9-14): And a definition for immediates is an indemonstrable positing of what [the thing] is. So one [sort of] definition is an indemonstrable account of what [a thing] is, one is an argument about what [a thing] is, differing from a proof in syntax (ntci>aet), and a third is the conclusion of a proof of what [a thing] is.
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The previous chapter (B 9) informs us that this new variety of definition is what we get when there is no further explanation ('cause') for the thing or phenomenon or event (there is no word here in Aristotle, only an elided substantive, at best: "For some [things], there is some other cause; for others, not", 93b21: cf. 21-25, 8. 93 3 5-6). We know in advance which cases it is going to be for which we get such definitions. It is as well that we do: he does not outright tell us that in these cases we are dealing with primary, non-composite substances.27 And it is no easy task to relate what Aristotle has to say about syllogistic proofs that explain 'events', like eclipses and thunder, to what he has to say about substances. But in Metaphysics H 4. 1044b8-20, he makes it clear that the first thing to do in dealing with eclipses and thunder is find the substance that undergoes or is a subject for those events: in the case of an eclipse, the moon (and the earth and the sun are going to have to put in an appearance; 1044b10-ll), in the case of thunder, presumably, the clouds. Where we have an event, or a case in which an accident is true of something, we can ask 'why does that happen?' or 'why is that so?', and the question is really of the form 'why does this belong to that?' (Z 17. 1041 3 10-11). But where we are dealing with a primary substance, what we are dealing with is not what it is because one thing belongs to another (cf. Section I above). So here there is no question of the form 'why does this belong to that?', no explanation for the unity of a subject and an attribute, because there is no unity of that sort: a thing that is primary just is its essence (cf. here H 6. 1045b16-23). Or, at least, there is no cause of the right sort: a man exists because of a series of biological events, but the subjects that suffered these events are just more men. So it is in cases such as men, moons, and (perhaps) clouds that the explanatory procedure we outlined (nominal definition, existence claim, material mode version of nominal definition, proof of the existence claim, real definition) breaks down. So, it seems, it is in precisely those cases in which Locke took the distinction to have its home that Aristotle takes it to be an intruder. He might have illustrated (not established) his idea by referring to the (Shorter) OED. Thete, under 'swan', we read: a large web-footed swimming-bird of the genus Cygnus or subfamily Cygninae of the family Anatidae, characterized by a long and gracefully curved neck and a majestic motion when swimming, ••••
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This is not, I think, a 'nominal definition' for the word 'swan': it is not a phrase synonymous with the word 'swan'. It is, rather, an attempt to characterize swans. And this sort of definition is relatively common where what is being defined is (a word for) a 'natural kind'. Very often, for natural kinds, there seems to be no nominal definition available. But if he had made use of this illustration, he would have found himself in trouble. For the clincher in the first refutation, the premise he needs (the 'necessary premise') is itself the registration of a necessary truth: (1)
Necessarily, if anything is a man, it is a biped animal.
Where do we get such necessary truths? Sometimes, perhaps, we get them just by giving a nominal definition: by finding a phrase synonymous with a word (presumably, a phrase that is also more readily understood than the word, if it is to be of any use as a definition). Aristotle might have got the premise for the clincher fairly easily if Antiphasis had picked the word 'bachelor' or the word 'vixen'. Bachelors and vixen are philosophers' pets just because nominal definitions for them are not hard to come by. But often (most of the time, I think), matters are trickier, sa and the force of the refutation depends on Antiphasis' having a free choice. Antiphasis picks 'man'. Aristotle hands him the definition 'biped animal' for it. I don't think that this, or anything in the neighborhood, tells us what the word means. If we got enough of the radiation in the air into our systems, some rather startling mutations might take place. Perhaps, over time, it would get to us all, or, rather, to all our descendents. They might well still call each other 'men'. The meaning of the word would not have changed, even if they were all six-legged. Or, more weakly: I cannot see what point there would be in saying that the meaning of the word had changed. The species would be different, and certainly people (six-legged people) would have to take account of that, if they cared at all about history. But to take account of it, they would not have to say anything about changes in the meaning of the word for the species. Men used to be two-legged; now they are not. (I am not saying that the meanings of words never change: 'presently' means something different in Shakespeare from what it means now. I am only saying that the situation just described doesn't force us to say that
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'man' has changed its sense. At least a part of the reason it does not is that men have a history, and that situation is merely an envisaged extension of it. But it would be wrong to think that whereas doing something presently used to be doing it on the spot, now, that same thing, doing something presently, or its contemporary descendent, takes a little longer. I do not know what conditions are necessary, much less sufficient, for a change of meaning, but this seems to me a relevant difference between the two cases.) If this is so, Antiphasis' concession that 'man' signifies something does not guarantee that there is a nominal definition for it. At any rate, the definition 'biped animal' is not one. 'Human being', I suspect, is, in English. But we can hardly say that the English word 'man' would have meant nothing had English not contained the phrase 'human being'. This was the point of Chapter II, Sections II-III above. Now we can carry it a little farther. If I am right, 'biped animal' is not a good nominal definition for the word 'man'. And, more, there might well be (or might well have been, considering 'human being') no good nominal definition for it. But a definition for the word, a statement of what it signifies, a nominal definition, is the most that Aristotle can demand of Antiphasis in the refutation. We just saw that Aristotle did not extend the distinction between nominal and real definitions to cases such as 'man' or man. But he ought to have seen some distinction of this sort in the neighborhood: not a distinction between two sorts of definitions, perhaps (although that might cover some cases: cf. 'human being' again, which is possibly a good nominal definition for 'man', but singularly unhelpful in resolving any disputes such as the one we had in Chapter II, Section III over Bernie), but at least a distinction between a word's being significant and there being some characterization of what it stands for, privileged, maybe, in its power to explain the behavior of what it stands for, or features of what it stands for, or whatever. He did not; the only distinction that he recognizes that comes close is the one he makes between a definition for 'goat-stag' and one for 'man': a nominal definition (only) in the first case, since there is no behavior of goat-stags, or feature of them, since there are no goatstags; a definition that is both nominal and real, or neither, in the latter case, since the obvious definition, 'biped animal', does not give us a pred-
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icate whose truth of an independent subject leads us to characterize the resulting complex as a man. Let us try saying that 'biped animal' is a stab at a real definition for 'man' or man, simply ignoring Aristotle's failure to draw the distinction here. Would it then support the clincher? Would it, that is, give us a necessary truth? We would then be saying: what a man really is, is a biped animal. The idea is not entirely implausible. If our desire to know what a man is is rooted in a desire to explain other things about men, the answer 'biped animal' has at least a going chance of being a good definition. It is an attempt to fit men into a framework that includes a lot of other animals, and to fit them in along a plane that has a lot to do (especially in Aristotle) with the things they do: in particular, with how they get around. And, with a little imagination, we can see someone thinking that their particular mode of getting around has connections with other things that they do: for example, it frees their hands, but keeps them earthbound (another standard part of Aristotle's definition is 'wingless' or 'terrestrial'), and so on. Suppose such considerations were decisive in favor of the definition 'biped animal'. Would that make it necessary for men to be biped animals? We might defend the idea that it would, if we were careful. 29 Consider what seems to count against it. We might find that, on some island in the central Pacific near a former atomic test site, the mutations I imagined a little while ago had already taken place, and that there were on that island men who were not bipeds. Kripke is even prepared to imagine that we might just have been wrong all along, deceived by tricks of light, say. so This takes some strenuous imagining, but it is less of a strain the less familiar we are with the species in question. Or the future history of all of humanity might be the one I described, with those mutations. The easiest case is the one in which we have been wrong all along: the fact that we might have been wrong no more counts against the necessity of what we were wrong about than the fact that some Greeks thought it possible to trisect an angle with compass and straightedge alone shows that it is not a necessary truth that one can't. Aristotle thought that, when it comes to essences, there is no error: if
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what a man is, is a biped animal, we cannot intelligibly deny it; our purported denial would not be false, but, rather, wouldn't be a denial about anything. I think he is only able to hold on to this view by failing to distinguish between the conditions under which a word makes sense from the conditions under which there is real definition available for what it stands for in the particular case of primary, simple, or immediate entities. If I say 'a man is a biped animal', and I'm wrong, deceived by a trick of light, I'm still using the word 'man' as you would, to mean what you would, and referring to the same things you would be. And Aristotle's failure to see this comes of his failure to distinguish the subject-predicate distinction from the essence accident distinction (cf. Section II above). The other cases, in which there already are or will be men who are not two-legged, might also be treated as a case in which one is just wrong. But that wouldn't go quite far enough. For there is a feature central to these envisaged possibilities: if, as things are here and now, a man is a biped animal, these other men, who are not biped animals, must be seen as descendents of biped animals. That is all that makes it plausible to say that those creatures, so unlike us, are men. If we had merely said: imagine that, on some other planet, or in some other world, there are men who have six legs, we would have had no case at all for calling them men. The case we have for calling them men is that they have a history that connects with biped animals (if that is what men are). The 'explanatory core' remains 'biped animal'. Perhaps what would be necessary is that men, at one time or another, are biped animals. I am not sure of this, by any means. But one thing that might have blocked Aristotle from taking such envisaged histories into account is the fact that neither he, nor Plato before him, was alive to the possibility that history might carry with it very far-reaching changes. On that score, they are centuries apart from us. NOTES There is an element of generality in the rest of Euthyphro's reply that I am glossing over: it is often difficult in Plato to see whether he is talking about an individual instance or a range of instances that fall under the same description. The same is true ofHippias' beautiful girl, below. cr. Gosling, 'Republic, Book V'. 11 cr. Chapter V, n. 20 and Allen, 'The Argument from Opposites in Republic V'. 8 ot ~v oilv napa 'tO cruJ.LIJsiJTIKOc; napaAoytO'J.LOi &tcnv lS'taV 6J,LOiooc; 6'tto0v aeUD9fi 1
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