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CANADIAN JOURNAL OF PHILOSOPHY, Volume 16 Number 3 September 1986 pp 359 370. Aristotle on the, Principleof Non Contradiction, S MARC COHEN. University of Washington, Seattle WA 98195, Not the least among the many puzzling features of the fourth book of. Aristotle s Metaphysics is his discussion of the Principle of Non. Contradiction hereafter PNC Even leaving aside the obvious difficul. ty of determining what his arguments succeed in showing about PNC we. face the more fundamental problem of figuring out what he takes them to. show For he proceeds in such a way as to suggest that he is not always. completely clear about what he is up to, Aristotle seems to be offering arguments in support of PNC Yet to do. so would be to try to demonstrate something he considers in. demonstrable to prove a first principle to treat an ultimate explanans as. also an explanandum and to try to explain it These maneuvers fly in. the face of the teachings of the Organon which allow no room for a. demonstration or proof apodeixis of PNC, S Marc Cohen.
Yet PNC like any other first principle can indeed must be known. to be true It is not sufficient for a first principle merely to be believed or. accepted or assumed For the Posterior Analytics tells us that the. premises of a demonstration must be better known than its conclusion. But if to be known is just to be the conclusion of a demonstrative. syllogism the doctrine of the Posterior Analytics would seem to be in. trouble For if all knowledge were demonstrative a knowable first prin. ciple would have to be a demonstrable first principle There would thus. appear to be a collision between the knowability and the unprovability. of first principles, Aristotle s solution in the Posterior Analytics is to distinguish be. tween episteme scientific knowledge and nous intuitive intellect First. principles such as PNC are not objects of scientific knowledge since. they are not demonstrable but are still known since they are grasped. However unsatisfying we may find this appeal to the deus ex machina. of nous we must grant I think that the Posterior Analytics offers a. coherent even if ultimately indefensible account of the knowability of. first principles But this account does not seem to mesh at all well with. Aristotle s procedure in Metaphysics V where there is no mention of the. role of nous as a faculty which grasps first principles Rather we are. given an elenctic demonstration of PNC or so it would seem Indeed. we are provided with this demonstration by the discipline of First. Philosophy a general science of which there is no mention and for. which there seems to be no room in the Organon, There would thus seem to be an inconsistency between the Posterior. Analytics and Metaphysics f on the epistemic status of first principles. such as PNC and the commentators have not missed it T H Irwin1sees. the Metaphysics as rejecting several key ideas developed earlier in the. Organon Lukasiewicz2 is apparently prepared to find an inconsistency. within Metaphysics f itself on the grounds that Aristotle there first. states that PNC is unprovable and then attempts to prove it. Alan Code disagrees with both Irwin and Lukasiewicz Consider his. dispute with Irwin On Irwin s account the Metaphysics agrees with the. Organon in holding that PNC is beyond demonstration but disagrees. 1 Aristotle s Discovery of Metaphysics Review of Metaphysics 31 1977 210 29. 2 Aristotle on the Law of Contradiction in Barnes Schofield and Sorabji eds. Articles on Aristotle vol 3 Metaphysics London Duckworth 1979 50 62. Aristotle on the Principleof Non Contradiction, with it in allowingthereto be a kindof scientificknowledge episteme of. thingsthat are beyond demonstration This branchof knowledgeis not. one of the Organons departmentalsciences whose methods are. demonstrative but the generalscienceof FirstPhilosophy the study of. being qua being First Philosophy s method is not demonstration. apodeixis but elenctic demonstration Clearly then elenctic. demonstrationcannot be viewed as a species of demonstration and Ir. win does not so view it Rather it is a kind of dialecticalargument pro. ceeding in a refutationalmanner against an interlocutorwhose will. ingnessto debatehas alreadybeen secured One might take this to be a. point of agreementbetween the two works since dialectic indeed a. dialecticaltreatmentof first principles is part of the Organons scheme. But Irwin notes that dialectic in the Organondepends on beliefs and. hence is not episteme nd ic n It can point us in the directionof first. principles but it cannot prove them So since the Organonholds that. dialecticdoes not produce knowledgeand the Metaphysicsholds that. elenctic demonstration dialectic does produce knowledge the. Metaphysicsdoes after all contradictthe Organonon this point. AlthoughCode scase againstIrwinis elaborateand arguedin detail. its core is relativelysimple Irwin saccounttakesMetaphysicsYto be at. temptingto establish by means of elencticdemonstration the truthof. PNC And this is what Code disputes Accordingto him what Aristotle. is up to in MetaphysicsV is to prove certainthings about PNC rather. than to prove elencticallyor in any other way PNC itself What Aris. totle wants to prove about PNC is that it is thefirmestprincipleof all. By this he seems to mean that PNC is indubitable Everyonebelieves. PNC Aristotle is maintaining indeed no one is even capable of. disbelievingit To use an older terminology what Aristotleattemptsto. prove is not that PNC is true but that it is a Law of Thought. It cannotbe disputedthatAristotle saim at least some of the time is. directed toward the indubitability of PNC The argument of V 3. 1005b22 34 thatPNC is the firmestof all principlescertainlyis aimedat. indubitabilityratherthan at truth For Aristotle is very clear that this. argumentuses PNC in establishingits conclusion and he is equallyclear. that its conclusionis not PNC but ratherthe propositionthat PNC is the. firmestof all principles f 4 1006a4 5 So the argumentof V3 is not an. attemptto prove PNC The fact that the conclusionof this argumenten. tails that PNC is truedoes not show as Code quitecorrectlypoints out. that the argumentcan be construedas a proof of PNC A proof that q. as opposed to a merelysound argumentwith q as a conclusion must. have as a premisethe why of q And thereis no why of PNC PNC as. S Marc Cohen, it turns out is the why of its own indubitability PNC itself is the princi. ple which explains why PNC is a Law of Thought, The argument of f 3 thus becomes absolutely central for Code since.
it is one of the few places where Aristotle is clearly trying to establish. something about PNC rather than arguing for PNC itself But as Code. also notes the argument of f 3 precedes the introduction at the beginn. ing of f 4 of the notion of an elenctic demonstration And for Code s. conciliatory effort to be successful it is the elenctic demonstrations of f. 4 not just the contrariety argument of f 3 that must be plausibly con. strued as supporting the indubitability of PNC I have some doubts. about this Code also flirts with the idea that the general science of being. qua being to which these elenctic arguments belong may be plausibly. construed as conforming to the model of the departmental sciences pro. posed in the Posterior Analytics I have some doubts about this as well. There are by Kirwan scount 3 seven of these elenctic demonstrations. in f 4 Aristotle precedes them with some introductory remarks about his. intentions Some people he says assert i that it is possible for the same. thing to be and not to be and ii that it is possible to believe this. 1005b35 1006a2 These people presumably dispute both PNC itself. and the claim that PNC is indubitable After conceding that we cannot. give a demonstration 1006a9 Aristotle proposes to counter these op. ponents elenctically and in that way to demonstrate this to be impossi. ble 1006al2 But what does this refer to Presumably what the op. ponents have asserted to be possible But they have asserted two things. to be possible so by demonstrating this to be impossible Aristotle might. mean to demonstrate any of the following, b The indubitability of PNC. c The conjunction of a and b, Apparently we will have to look at the arguments themselves to see. what Aristotle s intentions are, 3 Aristotle s Metaphysics Books V A and E Oxford Clarendon Press 1971. 93 105 W D Ross Aristotle s Metaphysics vol 1 Oxford Clarendon Press. 1924 265 8 likewise finds seven proofs in V4 although his divisions of the text. differ slightly from Kirwan s In the present discussion I follow Kirwan s divi. Aristotle on the Principle of Non Contradiction, The conclusions of the arguments in those cases in which the conclu. sions are plainly stated are as follows, 1 It could not be that everything was so and so and not so and.
so 1006a30 31, 2 a It is not possible that it should be simultaneously true to say. that the same thing is a man and is not a man 1006b33 34. 2 c It is impossible to predicate contradictories simultaneously. 5 There can be no such thing as simultaneously asserting and de. nying the same thing truly 1008a36 bl, 6 Nobody is actually in that condition sc believing that things. both are and are not in a certain state neither those who state. this thesis nor anybody else 1008bl2 13, Of these five conclusions only one argument 6 is clearly the in. dubitability thesis Two are plainly not 1 and 2 a and two can only. be tortured into statements of the indubitability thesis by taking. predicate to mean believe 2 c and construing asserting and denying. as believing and disbelieving 5 But how plausible is such a construal. in a context in which Aristotle explicitly says that people may not believe. the things they say 1005b25 26, I doubt that Code wishes to indulge in such tortuous reconstruals. Nor do I think he would admit that Aristotle has in f 4 lost sight of his. quarry For Code seems willing to concede that the elenctic demonstra. tions are aimed at refutfing somebody who asserts that PNC is false. 356 He even concedes that the conclusion of the elenctic argument is. supposed to be PNC 356 Nevertheless he says Aristotle is not ad. dressing himself to an audience that needs to be convinced of its truth. 356 On this showing Aristotle s method of refuting those who deny. PNC is to offer arguments whose conclusion is PNC but his purpose in. doing this is to explain to someone who already accepts PNC why he. must accept it That is Aristotle offers arguments whose conclusion is. PNC in order to establish that PNC is indubitable, The peculiarity of this procedure is somewhat masked by one of.
Code s formulations of it Aristotle he says in showing why I must ac. cept PNC is not giving me a reason for accepting it He is giving. me a reason why it must be the case that I accept it 356. There is a clear sense in which one who gives me an argument whose. conclusion is q is giving me a reason why I must accept q i e why I. S Marc Cohen, should acceptit But that is the sensein which mustaccept means have. been given a compellingreason for accepting and it is not the sense. which Code requires He requiresthat I must acceptq here means as a. matterof logicalnecessity I do not should acceptq Butit is less easy. to see how an argumentwhose conclusionis q can be used to establish. that I mustaccept q in that sense, One may thereforehave some reservationswhetherAristotlein f 4 is. so clearlyfocused on the indubitabilityof PNC as Code has suggested. Still Code s suggestionis appealing Aristotle sgeneral strategy is to. point out that one who deniesPNC is at least committedto the possibili. ty of saying something i e to the possibilityof significantspeech and. to arguethat in orderto have significantspeech PNC mustbe accepted. Butthereis an importantambiguityin this claim Who mustacceptPNC. in order for a speaker sspeech to be significant The speaker We. theorists Aristotle s discussion seems to vacillate between these. possibilities Certainly we cannot describe the speaker sspeech as. significantunlesswe think that thereis somethingthat he does mean as. opposed to variousother thingsthat he does not Our theory of signifi. cant speechwould disintegrateif it violated PNC But must the speaker. also acceptPNC If he does not he will be in no positionto say what it is. that he meansas opposed to what it is that he doesn tmean But that is. just to say that if he does not acceptPNC he cannot formulatean ade. quate theory of his own linguisticsuccess And it remainsto be shown. that he cannot be successfulas a speakerunless he is successfulas a. This point is worth furtherinvestigation for if it can be resolved we. may be able to construethe conclusionsof the elencticargumentsas the. opponent scommitments and hence as second orderstatementseven. though they are put forward as first orderstatements In this way. althoughPNC itselfwould be the ostensibleconclusionof some of these. arguments we may read Aristotleas saying in effect therefore as my. opponentplainly assumes PNC must be true The parenthetical as my. opponentplainlyassumes is omittedpresumablybecauseit is an implicit. operatorgoverningall of the statementsin the elencticdemonstration. My inclinationto agree with Code about Aristotle saims in f 4 is. CANADIAN JOURNAL OF PHILOSOPHY Volume 16 Number 3 September 1986 pp 359 370 Aristotle on the Principle of Non Contradiction S MARC COHEN University of Washington Seattle WA 98195 U S A Not the least among the many puzzling features of the fourth book of Aristotle s Metaphysics is his discussion of the Principle of Non Contradiction hereafter PNC Even leaving aside the obvious

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