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
ARISTOTLE'S PROGRAM
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.oaox 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.
26
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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27
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
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(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
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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
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'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 "lbK 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)ootav ll-repov Ka9' &-rtpou KK llcrnv ft 8tUJl&tpoc; crUJlJl&tpoc;, l>tt I(I&Moc;. 1 6 I am not at all sure that 'cpacrtc;' should be translated 'statement', as above. The parallel that comes to mind is De an. r 6. 430b26: cf. Hicks' n. ad foe. (Aristotle: De Anima 524). But Hamlyn ad Joe. fAristotle's De Anima 145) takes the word to mean 'assertion', and emends' 'tcatcicpacrtc;' in b27 to 'O.n6cpacrtc;'. He has no support from the mss. for this. It makes the usage parallel to that in Met. r 4. 1008"9, 34, etc. (and to Plato, Soph. 263e12), but that is the most that can be said for it. Ross (AM ii. 277 ad 1051 b24) takes 'cpcicrtc;' to mean a term as opposed to a proposition or full sentence, and cites De int. 16b27, 17"17 for parallels, but this depends on the interpretation of Aristotle's idea that I am about to reject (cf. also n. l7a below). 17 One part of it that I am leaving out has to do with actuality, potentiality, motion, and, perhaps, unmoved movers: cf. 1051 b28-30, 31, 1052"4-5, etc.
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17a Ross (AM ii. 277-78 ad 1051 b2S) has Aristotle saying that although one can't be wrong in uttering a term as opposed to a sentence, one can be wrong about its analysis. He wants to fit this with 1051 b32-33. But it leaves him with no very good account of Aristotle's saying that although there is no falsehood here, there is truth: cf. AM ii. 275-76 ad 1051 b17-1052"4. 17b a., on the Tht., Ackrill, 'Plato on False Belief: Theaetetus 187-200', pp. 388 -90; McDowell, 'Identity Mistakes', and Williams, 'Referential Opacity and False Belief in the Theaetetus'. 1s I follow Ross (APPA 634-35) in taking it that there are only three types of definition laid out in this chapter. The three are (in my terminology): (1) nominal definitions (93b29-37), (2) real definitions (93b38-94•7), (3) indemonstrable definitions for 'immediates' (94&9-10). The three are summarized in 94•11-14. 94•7-9 I take, with Ross, to refer to (1); contrast Hicks, Aristotle: De Anima, p. 322 ad De an. B 2. 413•14: he messes things up hopelessly by identifying (3) with the definitions that end up as the conclusions of demonstrations (these I am taking to be material mode versions of nominal definitions). I cannot imagine how he could reconcile this with his and Aristotle's saying that the (3)'s are indemonstrable. 19 Following Ross, APPA, p. 635, instead of an alternative parsing which would give as a translation: "one sort of account will be of what a name signifies, or another namelike account". so This is not intended as a translation for 'i..6y~ ... OVOJ.LU't~Tit,;' in b30-31: cf. last note. 21 a. Popper, The Open Society and Its Enemies ii. 288 (n. 30 to Chapter 11); contrast Moravcsik, 'Aristotle's Theory of Categories', p. 130. BB The following comparison with Locke was prompted by Bennett, Locke, Berkeley, Hume, pp. 120-23. Some of the references to the Essay come from him. 18 Popper, The Open Society and Its Enemies ii. 15-16. 24 a. esp. IV. vi. 11-15, and Bennett, Joe. cit., n. 22. 26 Popper's: cf. The Open Society and Its Enemies, Chapter 11 (v. ii pp. 11, 15), nn. 32-33 (pp. 288-89). sa a. Bennett, Locke, Berkeley, Hume, p. 123 on this. 17 But this is standardly the way the text is taken: cf. Ross, APPA, p. 629, p. 623 ad 93b2J. B 7. 92b12-13 would support this if we read 'On' and not '6 'tt' in b13: but cf. Ross APPA, 626-27 ad Joe. as a. Putnam, 'The Analytic and the Synthetic'. se On what follows, cf. Kripke, 'Naming and Necessity'. 80 'Naming and Necessity', pp. 317, 318.
a.
CHAPTER VII
CONCLUSION
Let us start with some truisms. They are foggy truisms, and their fogginess is dangerous. Perhaps we can avoid the dangers. Articulate thinking requires having definite thoughts about definite things; saying something articulate requires saying something definite about something definite. The latter requires words or expressions with relatively clear senses; the former requires something at least analogous. And either of the two requires something more, something like 'ground rules'. When you are thinking through a problem, and find that what you think about it would commit you to a contradiction, you know that something has gone wrong. So one of the 'ground rules' is the law of noncontradiction; presumably others of the simpler laws of logic are among the 'ground rules'. But there is fakery in this way of putting it: articulate thinking and talking are not games we play. It is possible to disobey these rules without ceasing to think or talk articulately. For an example, consider again what Engels says about motion (p. 36 above): 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.
This is wrong, but it is articulate. It is not the ravings of a lunatic, or of a fanatic who wants to reject rationality in the name of an idol. And it is not a chunk of discourse from someone who means something different by one or another of his words from what the rest of us mean by those words. Engels means by those words just what you know perfectly well he means by those words, and he is wrong. One might deny the law of non-contradiction for all sorts of reasons. None that I have seen strike me as good reasons. But neither do I see any reason for saying that there never could be good reason for denying it.
APPENDIX I
De interpretatione 14
Ammonius (in De int. 251.27ff.) suspected that this chapter was either not by Aristotle or a dialectical exercise. The only visible reason for doubting its authenticity is that some of what it says conflicts with things said elsewhere in Aristotle, and that is not much of a reason. So let us take it as genuine (cf. Ackrill, Cat. & De int. p. 153). In any case, the chapter contains some astounding confusions. So either Aristotle is genuinely confused, or Ammonius' second alternative is right, and he is just trying out arguments. For present purposes, it does not matter which alternative we take. The chapter takes up the problem (23a27-30): Whether the affirmation is contrary to the negation or the affirmation to the affirmation - the statement that every man is just contrary to the statement 'no man is just' or 'every man is just' contrary to 'every man is unjust'.
(I am using Ackrill's translation, with very slight modifications.) So we have three statements: (a1) (a2) (a3)
every man is just. no man is just. every man is unjust.
And we want to know which of (a2) or (a3) is contrary to (a1). De int. 7. 17b20-24 had already answered this question: (a2) is the contrary of (a1). So Aristotle undertakes to defeat the thesis that (a3) is contrary to (a1) (cf. 23a33-34, 24b2-6). It is the way he conducts the refutation that is confused, not the conclusion at which he arrives. Immediately after raising the question, he says (23a30-32): Take, for example, 'Callias is just', 'not: Callias is just', 'Callias is unjust'; which of these are contraries?
He is apparently deceived into thinking, or trying to deceive us into thinking, that 'not: Callias is just' is a parallel for (a2). Perhaps we could
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better see the nature of the deception by rewriting (a2) as: (a2')
every man is not just.
Then the claim would be that we can straighten out the relations among (a1), (a2'), and (a3) by straightening out those among (b1) (b2) (b3)
Callias is just. Callias is not just. Callias is unjust.
But the parallel is no good: in De int. 1. 17b26-29, 38-18&3, Aristotle commits himself to the view that (b1) and (b2) are contradictories, and in Cat. 10. 13bl2-25, to the view that (bl) and (b3) are contraries. That is not the way the relations come out here: to get the right result for the (a)'s, he now has to argue that (b2) is the contrary of (bl). It is easy enough to see how he fell into this trap, or how he expected us to fall into it. He is treating 'every man' as a term, like 'Callias', to which the predicables '( ) is just','( ) is not just', and'( ) is unjust' are annexed; that way, the construction of the (a)'s (using (a2')) is parallel to that of the (b)'s. This analysis of the confusion is borne out by the rest of the chapter. We are to get at the structure of the (a)'s by getting at that of the (b)'s. It now emerges that we are going to do that by getting at the structure of the beliefs expressed by the (b)'s (23&32-39): Now if spoken sounds follow things in the mind, and there it is the belief o/the contrary which is contrary (e.g. the belief that every man is just is contrary to the belief 'every man is unjust'), the same must hold also of spoken affirmations. But if it is not the case there that the belief of the contrary is contrary, neither will the affirmation be contrary to the affirmation, but rather the above-mentioned negation. So we must inquire what sort of true belief is contrary to a false belief, the belief of the negation or the belief that the contrary holds.
The principle here, that the logical structures of and relationships among beliefs are parallel to the logical structures of and relationships among statements, might be called the 'principle of expressibility' (after Searle, Speech Acts 19). Plato gets it by simply identifying thought and silent speech (Tht. 189e-190a, Soph. 263d-264b). Aristotle might be seen as defending it in Soph. el. 10.
'DE INTERPRET A TIONE'
14
145
Normally, it is used the other way around: to get at beliefs by straightening out sentences. But Aristotle now wants to get at the sentences by straightening out the beliefs. And this, I think, helps him compound the confusion. For at least two, perhaps all, of the three arguments he is about to offer to show that the belief expressed by (b2) is contrary to the belief expressed by (b1) do not go to show that, but go to show that believing (b2) is contrary to believing (b1): in effect, that one could not believe both, but might believe neither. And this is initially more plausible for believing than it is for stating, for there seems nothing wrong with stating both that Callias is just and that he is not: that, after all, is a paradigm way of contradicting oneself. If those two arguments do go to show that believing (b2) is contrary to believing (b1), they are the ones that bear on r3, for that is the claim we need there. The thesis Aristotle is going to refute he puts in the form 'it is the belief of the contrary which is contrary', and the instance he gives of the thesis he is against is 'the belief that every man is just is contrary to the belief "every man is unjust" '. Here the initial contrariety is in the predicates, 'just' and 'unjust'; we tack those predicates on to the subject 'every man', and say that with respect to the belief expressed by 'every man is just', the belief expressed by 'every man is unjust' is a belief 'of' the contrary. We now ask: is the one belief contrary to the other? The thesis is 'yes'; Aristotle wants to show us that this is wrong. Before he does that, he shifts examples once more (23a39-b2): What I mean is this: there is a true belief about the good, that it is good, another (false) one, that it is not good, and yet another, that it is bad; now which of these is contrary to the true one?...
So now we are going to fiddle with the relations among the beliefs expressed by (c1) (c2) (c3)
the good is good. the good is not good. the good is bad.
This trio shows a triple ambiguity. The statements are singular in grammatical form; that might be taken seriously, so that the statements are all about a single entity called 'the good'. Or they might be taken as
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implicitly general, like 'the llama is a hairy sort of woolly fleecy goat, with an indolent expression and an undulating throat' (Hilaire Belloc, after Wisdom, Logical Constructions, p. 42). That is, {cl) might be taken to mean (very roughly; this reading will not do for sentences of this type in general: cf. Wisdom, op. cit., pp. 43-45) 'everything good is good'. This first ambiguity is one Aristotle makes use of. Down to 24a3, he takes the (c)'s to be about a single entity called 'the good', and so takes what he has to say about the (c)'s to apply to the {b)'s. But he reconstrues the (c)'s in 24aJ-bl by taking 'the good' 'universally' (24a7), and so uses the same example, with the same comments, to illustrate the behavior of the (a)'s. Again, then, he is treating 'every man' as a term on a par with 'Callias'. The second ambiguity is this. He actually phrases the (c)'s in terms of beliefs about the good: 'there is a true belief about the good, that it is good, ... '. Suppose we take him to be talking about a single thing, called 'the good'. Take the belief about it that it is not good. What belief is in question? Is it a belief about something that is good, to the effect that that something is not good? Then perhaps its appropriate expression would be 'knowledge is not good' {the example, and the general question here, come from Ackrill, Cat. & De int., p. 154). Or is it a belief which someone might actually express by saying 'the good is not good', a self-contradictory belief? At least this much is clear: if, in taking the (c)'s as about a single thing called 'the good', Aristotle wants them to illustrate the behavior of the {b)'s, he cannot rely on any peculiarities in the behavior of the (c)'s due to the fact that (cl) is a tautology and (c2) a contradiction, for there is nothing tautologous about 'Callias is just' or contradictory about 'Callias is not just'. So if his argument is to work, it will have to be possible for us to construe the {c)'s as (cl') (c2') (c3')
This (which is good) is good. This {which is good) is not good. This (which is good) is bad.
And that much we can do. But it is not enough to save Aristotle from a variant of the same trap (that of relying on features of the (c)'s not shared by the (b)'s). For there is a third ambiguity.
'DE INTERPRET A TIONE'
14
147
The subject for the (c)'s is 'the good'; take it that it is supposed to give us a single thing, to parallel the (b)'s. Aristotle might have in mind a peculiar sort of thing: a Platonic form, perhaps, which is good 'in its own right', i.e., such that to think of it as not good is really not to think of it (cf. the discussion of these sorts of examples in Chapter VI, Section II below). This may sound very odd, but the first of Aristotle's three arguments, soon to come, seems to turn on taking the (c)'s this way. And, again, the (b)'s cannot be taken that way: Callias is not just 'in his own right'. As a last preliminary, Aristotle tries to soften his opponents' intuition that a belief of the contrary is a contrary belief (23b3-7): (It is false to suppose that contrary beliefs are distinguished by being of contraries. For the belief about the good, that it is good, and the one about the bad, that it is bad, are perhaps the same - and true, whether one belief or more than one. Yet these are contrary things. It is not, then, through being of contraries that beliefs are contrary, but rather through being to the contrary effect.)
This does not add much, beyond confirming our conclusion of a little ways back (p.145) that when Aristotle speaks of a 'belief of the contrary' he means a belief with a contrary predicate. The first argument to show the belief expressed by (c2) contrary to that expressed by (c1) begins with a reiteration of the (c)'s (23b7-9): Now about the good there is the belief that it is good, the belief that it is not good, and the belief that it is something else, something which does not and cannot hold of it.
The last clause ought to arouse our suspicions. If (c3), in saying that the good is bad, says something of the good that cannot hold of it, it is not parallel to (b3) (or, for that matter, to (a3)). And Aristotle could justify the claim that (c3) says something of the good that cannot hold of it only if he took the (c)'s either as the appropriate expressions for the beliefs in question (so that (cl) expresses a tautologous belief, (c2) a contradictory one, and (c3) an impossible one) or as talking about something that is essentially good. He now makes a comment I do not understand in the slightest. He says (23b9-15): (We must not take any of the other beliefs, either to the effect that what does not hold holds or to the effect that what holds does not hold - for there is an indefinite number of both kinds, both of those to the effect that what does not hold holds and
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of those to the effect that what holds does not hold, but only those in which there is deception. And these are from things from which comings-into-being arise. But comings-into-being are from opposites. So also, then, are cases of deceit.)
It just may be that this is a very poor way of saying this (I am expanding on Ackrill, Cat. & De int. 154 ad 23b7): we are not interested in cases
such as 'the good is ugly'; that is wrong, all right, but you could explain to someone what his error was in believing that by telling him: the good isn't ugly, it's good. "'Good' and 'ugly' may be incompatible but they are not opposites" (Ackrill, loc. cit.). That explanation hardly covers the whole passage, though: in particular, it does not explain why Aristotle introduces talk of 'coming-intobeing' here. It just may be that Aristotle is intending to block the interpretation of the (c)'s that makes them about something that is good 'in its own right': he has a view to the effect that where simple entities are concerned (cf. Chapter VI, Section II on this), that do not come into or go out of being (cf. Met. H 5), there can be no deception (cf. Met. 910. 1051 b25-33, 1052a4ff.), apparently because if you think of such a simple entity as the pale (H5. 1044b23) as not pale, you are not deceived about the pale, because you aren't really thinking about that. And the reason you are not is that the pale is pale in its own right: that is what it is, pale; so thinking of it is not pale can't be thinking of it (again, cf. Chapter VI, Section II for more on this obscure doctrine). But if that is what Aristotle thought he was doing, he forgets about it altogether when he finally gets around to giving us the argument (23b15-27): Now the good is both good and not bad, the one in its own right, the other accidentally (for it is accidental to it not to be bad); but the more true belief about anything is the one about what it is in its own right; and if this holds for the true it holds also for the false. Therefore the belief that the good is not good is a false belief about what holds in its own right, while the belief that it is bad is a false belief about what holds accidentally, so that the more false belief about the good would be that of the negation rather than that of the contrary. But it is he who holds the contrary belief who is most deceived with regard to anything, since contraries are among things which differ most with regard to the same thing. If, therefore, one of these is contrary, and the belief of the contradictory is more contrary, clearly this must be the contrary. The belief that the good is bad is complex, for the same person must perhaps suppose that it is not good.
This is either hopelessly obscure or a rotten argument (cf. Ackrilll54--55). I am concerned with only one facet of it: it makes the question 'which
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belief is contrary to which?' turn on the question 'which predicate of the holder of a belief is contrary to which?' Someone who goes wrong about something is in a state contrary to that of someone who is right about it; since contraries are the extreme opposites in any given range of predicates, the man who goes farthest wrong will be in the state contrary to that of the one who is most right. Of course, someone who held no beliefs about the good would be in neither state: this is standard behavior for contraries. That is not intended to be a complete interpretation of the above argument; it is a stripped-down version of it with a goal in mind: that of getting an argument we can use in support of Aristotle's claims in r3: believing that p is contrary to believing that not-p. So even the conclusion of this stripped-down version is not actually the one Aristotle wants in De int. 14: he wants to show that the belief that xis F is contrary to the belief that x is not F. But we knew from the outset (and he shows the same knowledge elsewhere) that he could not really get that conclusion. The second argument he gives us is this (23b27-32): Further, if in other cases also the same must hold, it would seem that we have given the correct account of this one as well. For either everywhere that of the contradiction is the contrary, or nowhere. But in cases where there are no contraries there is still a false belief, the one opposite to the true one; e.g., he who thinks that the man is not a man is deceived. If, therefore, these are contraries, so too elsewhere are the beliefs of the contradiction.
Here we are dealing with a new example: (d 1) (d2)
Callias is a man. Callias is not a man.
And there is no (d3). Notice, first, that this argument does not require anything about Callias being a man in his own right. As it turns out, he is a man in his own right, and (d2) would then give Aristotle trouble if he wanted to stick by it as a case of deception (cf., yet again, Chapter VI, Section IQ. But for all that really counts in this argument, Aristotle could have used a predicate drawn from the category of quantity: these, as well as predicates drawn from the category of substance (Cat. 5. 3b24-27}, do not have contraries (3b27-30, 6. Sbll-6&18). So we might have had: (e1) (e2)
Callias is two cubits long. Callias is not two cubits long.
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The point would be the same: if Callias is two cubits long, someone who thought he was not would still go wrong, and so be in a state contrary to that of someone who was right, and believed what is expressed in (el). So, Aristotle here tries to tell us, (el) (he has (dl)) is expressive of a belief contrary to that expressed in (e2) (or (d2)). In the third and last of his arguments, he comes back to the (c)'s (23b33-35): Further, the belief about the good that it is good and that about the not good that it is not good are alike; and so, too, are the belief about the good that it is not good and that about the not good that it is good.
So (cl) is supposed to be parallel to (fl)
the not good is not good.
And (c2) parallel to (f2)
the not good is good.
The point, it emerges, is supposed to be that if we find that the beliefs expressed by (f2) and (fl) are contrary, so will those expressed by (c2) and (cl) be contrary. And then, so will those expressed by (b2) and (bl) be contrary. Things are getting very tenuous. But, in a way, they are not as tenuous as they were in the last two arguments, for this one does not depend as overtly on the principle of expressibility, and might perhaps have been done by talking about the statements themselves. The mistake is in the parallels just registered. We are now supposed to ask (23b35-36): What belief then is contrary to the true belief about the not good that it is not good?
And we answer that by exhausting the possibilities: we have only a limited range of predicates to choose from, 'bad', 'not bad', and 'good'. But the contrary belief is (23b36-39) Certainly not the one which says that it is bad, for this might sometimes be true at the same time, while a true belief is never contrary to a true one. (There is something good which is not bad, so that it is possible for both to be true at the same time.)
(f3)
the not good is bad.
is not the contrary of (fl): sometimes something that is not good is bad. At least, here we are moving toward the idea that the subject for the (f)'s
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is something characterized as not good, rather than some unique entity that is essentially not good, not good 'in itself'. Nor again is it the belief that it is not bad, for these also might hold at the same time (23 b39-40).
We might pick out something indifferent, neither good nor bad. So we are left with (f2) (23b40-24&1): There remains, then, as contrary to the belief about the not good that it is not good, the belief about the not good that it is good.
But we are left with that only because we are supposed to be convinced that there is a contrary (as opposed to a contradictory) for (fl). The original format for our trios gave us sentences (expressive of beliefs) in which the (I)'s had a predicate, to which the predicate in the (2)'s was contradictory, and to which the predicate in the (3)'s was contrary. Those were the parallels. But when we come to the (f)'s, we are given a trio in which the predicate in (2) contradicts that in (1 ), all right, but the prediate in (3) is not contrary to that in (1), but to that in (2). And there is no good reason to think that any predicate can be found that is contradictory to that in (fl). Nor is there any good reason to think that somewhere, there must be a sentence that expresses a belief contrary to that expressed by (fl) (or by a sentence of the form 'xis not good'). Unless, that is, Aristotle is thinking: there is a state contrary to that of thinking that Callias is not good; there must be, because being right and being wrong are contraries, and somebody could be right in thinking that Callias is not good, so there must be a way of being wrong about that. We are now supposed to have been pushed into conceding that (c2) and (cl) are contrary, read as being about a single thing called 'the good' (24&2-3): Hence, too, the belief about the good that it is not good is contrary to that about the good that it is good.
So now we are convinced about the (b)'s; now we have to reinterpret the (c)'s as models for the behavior of the (a)'s {24&3-bl): Evidently it will make no difference even if we make the affirmation universally. For the universal negative will be contrary; e.g. the belief that none of the goods is good will be contrary to the belief to the effect that every good is good. For if in the belief about the good that it is good 'the good' is taken universally, it is the same as the belief that whatever is good is good. And this is no different from the belief that everything which is good is good. And similarly also in the case of the not good.
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So (cl) now comes to express the belief expressed by (gl)
every good is good;
(c2) first comes to express the belief expressed by (g2')
every good is not good,
and then to express the belief expressed by (g2)
no good is good;
and (c3) comes to express the belief expressed by (g3)
every good is bad.
Now we run these results back through the principle of expressibility, and take the (g)'s as representatives for our original examples, the (a)'s (24bl-5): If then this is how it is with beliefs, and spoken affirmations and negations are symbols of things in the soul, clearly it is the universal negation about the same thing that is contrary to an affirmation; e.g. the contrary of 'every good is good' or 'every man is good' is 'no good is good' or 'no man is good' ....
.
It is to Aristotle's credit that, even with those arguments, he came" out
here with the right conclusion.
APPENDIX II
De interpretatione 11. 21 "25-27
Among too many other things, Aristotle is concerned in De int. 11 with patterns of inference in which the cancellation of a term yields a conclusion: it follows from 'this is a pale man' that this is pale, and that it's a man (21"18-20), but not from 'this is a dead man' that this is a man ("21-24). He says of the uncancelled term in the conclusion that it is used 'simply' (O.JtA.(i')~: as, etc.): an alternative paraphrase might be 'on its own'. Thus if you went (illicitly) from 'Socrates is a good cobbler' to 'Socrates is good', you would be concluding that Socrates is good simply, or that 'good' on its own applies to Socrates (cf. 20b35-36, 21&14-15). We can represent this device (which, I think, is almost purely syntactic) with a linguist's boundary marker: your conclusion would be 'Socrates is good#'. One of his examples in which the inference is apparently supposed to fail is this (21 "25-27): Homer is something, e.g., a poet. Well, is he, therefore, or not? For 'is' is predicated accidentally of Homer; for because he is a poet, not in its own right, 'is' is predicated of Homer.
'In its own right' here is 'Ka9'ao-r6'. It is not a synonym for 'simply': it does not do the same job that the boundary marker does. If it did, Aristotle would be telling us nothing about the relation between (I)
Homer is a poet.
and (2)
Homer is.
that we cannot see already: that 'is' in (I) is not 'is#', but 'is' supplemented by a predicate. And so, in particular, he would be giving us no argument at all to the effect that (2) does not follow from (1). All the patterns of inference here in question are ones in which a conclusion uses a term simply and comes from a premiss in which the term is not used simply, and some of them are valid. '(I); therefore (2)' is a pattern fitting that
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description, and the question is whether it is valid. So it is no good just pointing out that it is of that pattern. Rather, it looks as if Aristotle is saying that (2) does not follow from (1), and giving as a reason for saying that, that in (1), 'is' is not used of Homer in its own right, but accidentally. Presumably, if it were used of Homer in its own right, (2) would follow without a hitch. Presumably, in (2), 'is' is used of Homer in its own right. And it is used simply. First, Aristotle ought not to be saying that (2) does not follow from (1): that conflicts with what he says in Cat. 10. 13b27-33 (cf. p. 76 above), and the latter intuition strikes me as better entrenched in Aristotle. In Met. Z 1. 1028&30-31 he says that "substance is that which is primarily: not that which is something but that which is simply". He seems to mean it (cf. also De gen. et corr. A 3. esp. 317b5-13, Phys. A 7. 1903 32-33). This notion is as murky as the notion of substance itself, but let us take it as implying that (2) could only be true if Homer were a substance. Then he might be saying that (2) does not follow from (1) because it does not follow from (1) that (3)
Homer is a substance.
(This is Thompson's suggestion: cf. Chapter IV, n. 3.) The idea would have to be that 'poet' is not a word for a substance, any more than 'runner', 'boxer', and 'wrestler' are (cf. Cat. 8. I0&34-b5): these words come under the category of quality; a man is a pugihst because he has a certain quality, pugilism, in him. But this, too, must be wrong. Even if a man is only called a poet because he has a certain quality, skill at making verses, it is a man that is called a poet, not a cloud or a cube. So it follows from (1) that (4)
Homer is a man.
And (3) follows from that: 'man' is a word for a substance. The point is a different one: in charity, we can take him to be saymg that (2) does not follow from (1) by simple cancellation of the predicate 'a poet', although 'Socrates is pale#' does follow by simple cancellation of 'a ... man' from 'Socrates is a pale man'. In 20b35-36 and 21&14-15, Aristotle notes that it does not follow from 'Socrates is good# and a cobbler' that Socrates is a good cobbler. The converse point would be that it does not follow from 'Socrates is a good
'DE INTERPRETATIONE'
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cobbler' that 'Socrates is good#'. The reason it does not follow is that 'good' in construction with a noun gets some part of its force from the noun, or, still vaguely, that the conditions under which a phrase of the form good+ NP' applies are not a simple result of concatenating independent conditions for applying 'good' with those for applying the NP. (Cf. Chapter V, Section II and Geach, 'Good and Evil'.) He is thinking that the same holds for 'is' in (1): the 'is' in (1) is different from the 'is' in (2), and even if (2) did follow from (1), it would not do so in the way 'Socrates is pale#' follows from 'Socrates is a pale man'. The 'is' in (1), he says, is not an 'is' "in its own right"; the one in (2) is an 'is' in its own right. "What you are in your own right is your essence", he tells us (Met. Z 4. 1029b15-16; cf. A 18. 1022a25-29). I think he is prepared to go from this to saying that the 'is' in (4) is an 'is' in its own right (cf. Met. A 7: but it would take a lot of argument to show that he is doing that in 1017a22ff. of that chapter). Then the point would be this. (2) contains 'is'. But, faced with it, we are entitled to ask (5)
Homer is what?
So far, it is as if he were seeing 'is#' as elliptical, as we find it in the answer 'Homer is' to the question 'Is Homer a poet?'. (This intuition is, it appears, Austinian: cf. Raphael, 'To Be and Not to Be', p. 57.) But he wants to go a step farther: the range of appropriate answers to questions like (5) is restricted; saying what Homer is is a matter of giving his essence (cf. Chapter V, Section I and, in this connection, Met. H 2. 1042b25-1043a1, and Owen, 'Logic and Metaphysics' p. 165 n. 2; 'Aristotle on the Snares of Ontology' p. 71 n. 1; 'Plato on Not-Being' passim, esp. pp. 265-66). So the answer to (5), properly, is (4). Then the 'is# ' in (2) is elliptical for 'is a man' in (4); the 'is# ' in (2) is an 'is' in its own right, and so is the one in (4); and (2) follows from (4) by simple cancellation of 'a man' but not from (1) by simple cancellation of'a poet'. (In putting Aristotle's point in this way I have adopted a suggestion of Oswaldo Chateaubriand's.)
APPENDIX III
Metaphysics r3. IQ05bll to 4. IQ07bl8 Text and Translation
The text is Ross'; the translation facing is mine. It is intended only for the convenience of readers of this study, who are advised to check it with the Greek, if possible, or with other translations (especially Ross'). A number of mistakes were caught at the eleventh hour by Elizabeth Asmis. The ones that remain are all my own.
1005b The firmest principle of all is one about which it is impossible to be
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mistaken, for necessarily that sort of principle is most knowable (for it is what they don't know that everybody makes mistakes about) and unhypothet cal. For a principle which someone must have if he understands any of the things that are, is not a hypothesis, and what it is necessary for someone to know if he knows anything, it is necessary for him to have when he comes [to class]. So it's clear that this sort of principle is the firmest of all. Next let's say what it is: 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 we might added against dialectical difficulties be added). This, then, is the firmest of all principles, for it fits the definition above. For it is impossible for anyone to believe the same thing both to be and not to be, as some think Heraclitus says. For it isn't necessary that what someone says, he also believes, and if it is not possible for contraries to belong at the same time to the same thing (and let's have the customary qualifications added to this premiss as well), 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 is and is not; for someone who went wrong about this would have contrary beliefs. That's why everyone who proves [anything) comes back to this belief in the end, for it is by nature the principle for all the other axioms also. Chapter 4
35
As we said, there are some who themselves say that it is possible for the
'METAPHYSICS': TEXT AND TRANSLATION
157
PePatO'ta:ttt a· apxT! 7taO'&V 7t&pi ftv ata'Jf&U0'6f\vat aMva'tov· yvroptJ.lOl'ttl'tllV 't& yap avayx:aiOV &{vat 'tTJV 'tOtaU'tttV (7ttpi yap li J.lTJ yvrop{~000'\V a7ta'tc7>V'tat 7ttlV't&~) x:ai avott69&'tOV. ftv yap avayx:aiov ~X&tv 15 'tOV 6'tto0v ~uvt&V'ta 'ttbv oV'troV, 'tOO'to oux fm69&0't~· 8 at yvropi~etv avayx:aiov 'tq'l 6no0v yvropi~ovn, x:ai ilx:&tv ~XOV'ta avayx:atov. O'tt J.18v oov PePatO'ttl'ttt 1) 'tOtaU'tll 7taO'&V apxiJ, af\A.ov· 'tt~ a· EO"ttV aiS'ttt, J.l&'ta 'taO'ta A.tyroJ.l&V. 'to yap au'to liJ.la ottapxetv 't& x:ai J.lTJ f>ttapxetv aMva'toV 'tcp au'tq'lx:ai x:a'ta 'tO au't6 (x:ai oO'a t'iA.A.a ttpoO'atoptO'aiJ.1&9' 20 t'iv, ~O''tOl ttpoO'atroptO'J.lSVa 7tpo~ 'tel~ A.oytx:a~ auO'xepeiac;). aiS'ttt a11 7taO'&V EO"ti PtPatO'ttl'tll 't&V apx&v· ~X&t yap 'tOV &ipttJ.l&vov atoptO'J.16V. U86va'tov yap 6V'ttvo0v 'tau'tov 6ttoA.aJ.1Pavetv etvat x:ai J.lTJ &tvat, x:a9a7t&p 'ttVE~ OlOV'tat A.tyetv 'Hpad&t'tOV. OUlC ~O''tt yap avayx:atov, 25 lin~ A.tyet, 'taO'ta x:ai 6ttoA.aJ.1Pavetv. et M J.lTJ tvatxe'tat liJ.la f>ttapxetv 'tcp au'tq'l 'taVaV'tia (7tpoO'atropi0'9ro 5' 'fJJ.liV x:ai 'taU'tlJ 'tij 7tpO'tclO'&t 'tel etro96'ta), tvaV'tia a• EO''ti M~a a6~1J 1) 'tf\~ avncpaO'ero~, cpavepov on aMva'tOV liJ.la OttoA.aJ.lpavetv 'tOV aO'tOV etvat x:ai J.lTJ &tvat 'tO au't6· 31 liJ.la yap liv ~xot 't~ tvaV'tia~ M~a~ 6 at&'lf&UO'J.l&Vo~ 7t&pi 'tOU'tOU. ato 7ttlV't&~ ot attoaetv6V't&~ et~ 'taU'tllV avayooO'tV EO'Xtl'tllV M~av· cpUO'&t yap UPXTJ x:ai 'ttbV liA.A.rov Q~lOlJ.ltl'tOlV aiS'ttt 7ttlV'tOlV. EiO'i a& 'ttV&~ ot, x:a9attep et7tOJ.l&V, aO'toi 't& tvasxe0'9ai cpaO't 'tO au'to 35
15 l;uvt6vta Ab 16 ilno9east Ab 5] -ro Ab 17 l!xovtt E PsPato-rci'tTI ante O.pxit 1. 18 EJr AJ.l 19 AtyO>J.I.SV JSTr; AtyoJ.I.SV EAb -rs Ab AJ.c: om. EJ Asc.l 21 f EJr AJ.c: tQ> aO'tQ> fntapxsw Ab 27-28 npo8tmpia9o> 1'111tv Ab 29 486va-rov di'U EJr Asc.: d~tU 0.86va-rov A b 31 8tswsuaJ,Ltv~ A b AI.: 8wwsuaciJ.1.Svoc;; EJ 32 oi Ab AI. Asc.c: om. EJ 35 aO'toi -rs codd. Al.l: om. r
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1006a 1 same thing to be and not to be, as well as that they believe that [the same
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thing both is and is not]. Many people take this position, among those [who write] about nature also. But we just now took it that it is impossible 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. Through a lack of education, some ask that even this be proved; for it is a lack of education not to know of what one ought to look for a proof and of what not; for really it is impossible for there to be a proof of everything (for one would go on infinitely, so that in that way there wouldn't be any proof); and if there are some things for which one ought not to look for a proof, they couldn't say what principle they could ask for that is a better candidate [than the principle of non-contradiction]. But even with this, it is possible to prove by way of refutation that it is impossible, if only the one who disputes it will say something; and if he says nothing, it is ridiculous to look for an argument against someone who has no argument, in so far as he has none, for such a person, as such, is like a plant. I mean 'proving by way of refutation' to differ from 'proving' in that [here,] in proving, one might seem to beg the question, but where someone else - a person of this sort - is responsible for this, there will be a refutation, not a proof. The starting-point, in all such cases, is not asking him to say that something is or is not (for this someone might take to be begging the question), but to signify something, both to himself and to someone else; for this is necessary, if he is to say anything. For if he does not [signify something], a person of his sort has no argument, either with himself or with anyone else. But if someone grants this, there will be a proof, for there will already be something definite. But the party responsible isn't the one who does the proving, but the one who puts up with it, for while he does away with argument, he puts up with argument. And again, one who agrees to this has agreed that there is something true apart from proof, so that not everything is so and not so.* "' The words 'so that not everything is so and not so' occur twice: in azg and in a30-31. Ross (and Jaeger) bracket the first occurrence; I am inclined to bracket the second. Such reasons as I have are given in Chapter II, n. 8. I have followed my inclination in the above translation.
'METAPHYSICS': TEXT AND TRANSLATION
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stvat Kai J.1Tt dvat, Kai 01tOAUJ.1~UV&tv OUtC.O~. xprovtat 38 tcp Mycp to6tq> 1toA.A.oi Kai trov 7ttpi ~ ciA.A.' 6 61toJ,18vc.ov· civatprov yap Myov 61toJ,18vet Myov. f-ct 38 6 -coO-co crunc.opftcra~ 0"\l'YK&XWPTtKt -ct ciA.Tt98~ dvat xc.opi~ ci1to3&i~t~ (WO"t'& 001C liv 1tiiV o6-c~ Kai OOX o6"C~ fxot).-7tpOO"Cov J,18v OOV 3fiA.ov
1006a 5-18, cf. K. 1062a 2-5 28-34, cf. 1062a 19-23)
18-1007a 20, cf. 1062a 5-19 (1006b
1006• 2 xptbvtat JAb r, ex xptbvro fecit E 0 : 6.7taad'lV Ab 158 r 8 dmi.vrcov EJ Asc. 0 : 7tQvtCOV Ab 14 J.lll fX&t Ab AI.: 11118£va fx&t ).Jyyov EJr 15 i\1511 A b AI. :i\1511 fcmv Jr: om. E Asc. 16 &n] l>tt 6 EJ 17 liv 861;&t&v att&taOat ante 15taq>£p&tv (1. 16) r attf\aOat Ab dll' ool58 toO r 18 attiou om. Ab 19 oo EJ yp. AI.: ooxi Ab: om. AI. 20 yap om. yp. AI. 21 cU.M] dllci to recc. n om. A b aot~ EJ 23 oiiO' aflt,P EJ 26 ftt .•. 27 d7to8&il;~ Ab AI.: om. EJr Asc. 28 axn& ... fxot Ab Al.l: om. EJr Asc.: cf. 1. 30
•s 7tU1t
p.f38f311K6c;· 'tO yap A8UKOV 'tcp dv9pro7tcp aup.~8P11K8V O'tt san p.tv MUKOc; dA.A.' oox 01t8p A8UK6V. d at 1tclV'ta KU'tcl aup.f3tf311Koc; Mye'tat, o09tv fmat 7tplO'toV 'tO Ka9' oo, d dei 'tO aup.pepllKOc; Ka9' 01tOK8tp.8VOU 'ttVOc; GllP,UtV8t 'tTJV KU'tllYOpiav. QVclYK'Il lf.pa de; dv9 d7tttpov isvat. dA.A.' dMva'tov· o\>38 yap 1tA.eiro aup.7tA.8Kt'tat auoiv· 'tO yap aup.f3ef311Koc; oo aup.f3ef311K6n aup.f3tf311K6c;, d p.l) on dp.q>ro aup.f38f311K8 'taO'tcp, Myro a• o{ov 'tO A.euKov p.oumKov Kai 'tOi>'to MUKOV on dp.q>ro 'tcp dv9pro7tcp aup.~8f311Ktv. dA.A.' oox 6l:roKpa't'llc; p.oumKoc; ofhroc;, on dp.q>ro aup.f38~11K8V &'tspcp 'ttvi. S1td 'toiwv 'tel p.tv oil'troc; 'tel a• SKdvroc; Mye'tat aup.f38~11K6'ta, oaa oil'troc; Mye'tat roc; 'tO MUKOV 'tcp l:roKpa't8t, OOK svasxe'tat d1t8tpa dvat s1ti 'tO dvro, o{ov 'tcp l:roKpa't8t 'tcp A8UKcp E't8p6v 'tt aup.f38~11K6c;· 00 yap yiyve'tai 'tt ~v s~ cl1tclV'tiDV. oMs al) 'tql A8UKcp e'tep6v n fmat aup.~tP11K6c;, otov 'to p.oumK6v· o098v 'tt yap p.iiA.A.ov 'tOi>'to SKdvcp ft SK8ivo 'to(ncp aup.f38P11K8V, Kai lip.a atropta'tat on 'tel p.tv oil'tro aup.f38f311K8 'ta a• «he; 'tO p.oumKov l:roKpa'ttt' oaa a• ofhroc;, oo aup.~t~11K6'tt aup.f38~11K8 aup.f3tf311K6c;, dA.A.' oaa SKdvroc;, {{)a't' oo 7taV'ta KU'tcl aup.~8f311KOc; A8X9flat'tat. ~a'tat dpa 'tt Kai lilc; ooaiav GllP,UiVOV. d at 'tOi>'tO, asaetK'tUt O'tt M6va'tOV lip.a KU't11YOP8ia9at 'tclc; dvnq>aaetc;. 1007b 18-1008& 2, cf. 1062a 23-30
27 af>tQ) -ro EJT AI.: n Ab 28 i\ Ab AI. Asc.c: om. EJT ~11'1 civ9pchmp EJT AI. Asc.c: civ9~ J.11't Ab 29 Ei11 J ii)..).o EJr AI. Asc.: iiUo n Ab AJ.c 31 -rou-rq> ... cruJ.113&13111C6
