Code-Aristotle's Investigation of a Basic Logical Principle

Canadian Journal of Philosophy

Aristotle's Investigation of a Basic Logical Principle: Which Science Investigates the Principleof Non-Contradiction?Author(s): Alan CodeReviewed work(s):Source: Canadian Journal of Philosophy, Vol. 16, No. 3 (Sep., 1986), pp. 341-357Published by: Canadian Journal of PhilosophyStable URL: http://www.jstor.org/stable/40231475 .Accessed: 14/05/2012 05:50

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CANADIAN JOURNAL OF PHILOSOPHY Volume 16, Number 3, September 1986, pp. 341-358

Aristotle's Investigation of a Basic Logical Principle: Which Science Investigates The

Principle of Non-Contradiction?

ALAN CODE University of California, Berkeley

Berkeley, CA 94720 U.S.A.

Aristotle shares with Plato the attitude that the world, 'the all/ is a kosmos, a well-ordered and beautiful whole which, as such, can be rendered intelligible, or understood, by the intellect. One understands things, generally speaking, by tracing them back to their sources, origins or principles (apxoct) and causes or explanatory factors (atxiat), and seeing in what manner they are related to these principles. We know, or understand, a thing when we grasp 'the why' or cause.1 Consequently,

1 APo. A2, 72b9-12, Bll, 94a20; Ph. Al, 184 alO-15, B3, 194bl7-23; Metaph. Al, 981 a 24-30, A2, 982 b2-4

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understanding is systematic. Some things we understand through themselves - these are the first principles and as such are not understood by tracing them back to causes.2 (The first causes have no causes.) We understand other things by systematically relating them in appropriate ways to what is known through itself. These other things are known through, or by means of, their causes and principles.3

The first principles must be more intelligible and better known than those things of which they are the principles.4 We have knowledge or understanding (7uaTT)|ir)) of something intelligible (yvcopipux;) by relating it in just the right way to principles that are even more intelligible (yvcoptfxcoxepa). Knowledge or understanding in the strict sense (7itaTrj[A7) QLTzyGx;) is demonstrative knowledge (d7io8etxTixri ema-crnxr)), where what is known is necessary and could not possibly be otherwise,5 and to know such things just is to deduce them from those necessarily true first principles that are their causes. We understand such a 'conclusion' only when we see the reason why it is the case and could not possibly not be (the case). As for the first principles, they must be indemonstrable, for they are primary and immediate.6 If a principle is immediate, it must be primary in the sense that there is nothing prior to it in terms of which it is understood or known,7 and hence it cannot itself be deduced from its prior principles or causes. Since demonstration consists in just such a deduction, the principles cannot be demonstrated. We cannot, therefore, give an account of the reason why the principle is true. There simply is no 'why' for the 'why.'8 Since a first principle is known through itself (8t ocuto), and not through other things (8t aXXcov), it has no reason, or reasons, by means of which it is known. If there were a reason for a first principle, then that reason would be prior to the first principle - but nothing is prior to a first principle.

Since ini(5xr\[ir\ requires an account of the 'why,' it follows that a first

2 APr. B16, 64b34-36 with APo. A9, 76al9-20; see also APo. A10, 76b23-24.

3 APr. B16, 64b34-36; cf. APo. A2, 72a30-32 and Ph. Al, 184 al2-14.

4 APo. A2, 71b20-22, b29-30, 72a28-39 (esp. 28-29, 31-32, 36-37, 37-38); B19, 100b9-10; cf. A3, 72b5-6, 20-25.

5 APo. A2, 71b9-bl6

6 APo. A2, 71b20-21, 72a7-8; A3, 72bl8-22 (Also, see A9, 76 al6-17 on the iSioc

principles.)

7 APo. 72a7-8

8 See APo. A9, 76al9-20: ex xcov rcpo-cepcov yap olSev, oxav ix (XT) atTiax&v ei&fj atxiwv.

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principle is not an object of 7110x7^7). 9 However, this is not because the principles are objects of some inferior intellectual state such as belief, but because being even more intelligible than the objects of iiziaT:r\iJLr\, they are objects of a superior intellectual state. The first principles are objects not of ini(Tzr\[i.r\ but of vou

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are counted among 'the things from which' (eij


Being the firmest of all principles, it is the most intelligible (yvcopifxcoTocTYj) - it must be grasped and understood by anybody who is able to understand anything at all. If one is to yucopiCeiv anything, one has to yucoptCeiv this.22 This is perfectly consistent with the account given in the Analytics, and like the latter it rules out the possibility that only the practitioners of a general science of the axioms could know it to be true. The practitioners of the special sciences, since they know things within the confines of their own sciences, must also know this axiom. They do not need any metaphysical argument in order to know that it is true. Fur- thermore, their knowledge of it is not simply 'hypothetical,'23 awaiting certification from above by the student of being who understands its 'why.'24 Although everybody uses it, they do not use it as an hypothesis of any sort. What must be grasped and understood by anybody who understands anything most emphatically is not hypothetical.25

Despite this, Terry Irwin claims that the author of Met . T holds that a metaphysical treatment of PNC can yield knowledge of its truth. His account goes like this.26 The Organon denies the possibility of a science that treats of the axioms, and furthermore holds that the axioms cannot be known scientifically. They are indemonstrable, and hence must be reached dialectically. Dialectic, however, is argument 'according to belief,' and hence leads only to belief, not to knowledge. Recognizing this, Aristotle brings in his deus ex machina - an obscure kind of intellectual grasping called vou$. By way of sharp contrast, in Met. F we find that there is, after all, a general science that investigates the axioms, and that it enables us to obtain knowledge of the axioms without demonstration and without appeal to vou$! This science treats PNC as the conclusion of an elenctic demonstration, and this is a dialectical argument that rests upon premises which are such that the attempt to deny them (in a dialectical context) is self -refuting. Such an argument proceeds not from mere belief, then, but from premises that no rational person can reject, and hence its conclusion counts as knowledge.

22 MetaphS3, 1005bl6-17

23 As W.D. Ross, Aristotle's Metaphysics, Vol. 1 (Oxford: Clarendon Press 1924), 263, states in his note on 1005bl4: 'avurcoGexov is used quite in the Platonic sense of the word,' and not with reference to Aristotle's use of 'u7t60Eai

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Such is the story Irwin tells. However, it badly misdescribes the premises of the elenctic demonstration given in the text of F4. Irwin writes as though the premises of the argument are all beliefs, the denial of which would be self-defeating in live debate - beliefs such as 'the belief that he says and signifies something/ Against this it should be observed that the argument also contains such highly theoretical claims as the premise that 'if anything is a man, then it is what it is to be a man,'27 and this is clearly not (in the relevant sense) a premise that no one can ra- tionally reject. Again, the opponent is said to be committed to the view that everything is an accidental being, and Aristotle then argues that this last is impossible.28 Acceptance of all of this requires buying into quite a bit of Aristotle's semantical and metaphysical theorizing, and one can hardly assume that the opponent is failing to make significant statements if he denies the theses employed in the argument. Surely agreement with the pertinent aspects of Aristotle's essentialism is not a prerequisite of ra- tionality.

In any case, even if the premises did fit Irwin's description, and their rejection were self-defeating, those premises would nonetheless fail to explain why PNC is true, and hence would not yield knowledge of the principle. In general, an elenctic demonstration does not yield knowledge of its conclusion precisely because it need not (and in general does not) pro- ceed from premises that are prior to and explanatory of that conclusion. A demonstration proper, on the other hand, proves its conclusion by means of those prior principles that are explanatory of it, and for that reason does yield knowledge. Since absolutely nothing is prior to PNC, demonstration proper is impossible for it.

One might think that Aristotle holds that any attempt to demonstrate PNC would be question-begging, and for that reason maintains that no proof can be given. This is not, however, the case. An attempted demonstration begs the question if it tries to prove some conclusion by utilizing premises that are proved by means of that very conclusion (and hence are posterior to it), or by utilizing the intended conclusion itself as one of the premises.29 It being the case that PNC is a first principle, it might be thought (Aristotle tells us) that the attempt to prove it will turn out to beg the question.30 However, an attempted proof that made use

27 Metaph.VA, 1006a32-33 28 Metaph.T*, 1007a20-bl8 29 APr. B16, 64b36-65al - though here he in fact characterizes question-begging

only for alleged proofs of propositions that are not first principles. 30 Metaph.Tl, 1006al6-17

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only of other first principles would not seem to be question-begging in Aristotle's sense. Such an attempt would fail for some other reason.

Nonetheless, even if the premises in a valid argument having PNC as a conclusion do not give the reason for that law, we might be able to obtain those premises by eliciting agreement from an interlocutor. If the interlocutor is responsible for the premises, then elenchos, or refutation, will be possible, even though demonstration proper is not.31 An elenchos is a case of a syllogism (a valid one), the conclusion of which is the contradictory of some proposition. Presumably an elenctic demonstration is an elenchos, the conclusion of which is the contradictory of a proposition asserted by the interlocutor, and the premises of which are each ob- tained from that same interlocutor. The premises need not be, and typically are not, prior to and explanatory of the conclusion.32

The elenctic demonstration with which we are concerned starts out by having an opponent signify something (arjuatvetv tl) both to himself and to another,33 and then invokes various metaphysical and semantical theses in order to argue in support of PNC. Basically, the argument is to the effect that acceptance of PNC is required for the possibility of significant thought and speech. An interlocutor who accepts the premises of the argument, and who is then led to acceptance of PNC on the basis of these

31 Metaph.Vl, 1006al7-18

32 J. Lukasiewicz attributes to Aristotle the view that 'an elenchos is an ordinary syllogism differing from a proper proof only in the extrinsic fact that it is used as a means of refutation,' and hence concludes that the distinction between proof and elenctic proof is 'entirely empty' ('Aristotle on the Law of Contradiction,' in J. Barnes, M. Schofield & R. Sorabji, eds., Articles on Aristotle, Vol. 3 [London: Duckworth 1979], 55; originally published as 'Ueber den Satz des Widerspruchs bei Aristotles,' in Bulletin International de I'Academie des Sciences de Cracovie [1910]). His criticism is vitiated by the fact that he does not observe that an elenctic proof, unlike a proof proper, need not explain the conclusion. Lukasiewicz also misconstrues the point, at 1006al5-18, about begging the question. He takes Aristotle to be saying that somebody trying to prove PNC is guilty of begging the question, but that if the opponent commits the fallacy 'an elenchos is possible - and everything is all right.' The point, however, is that the advocate might seem to beg the question if he attempts a proof proper, but if he can elicit

premises from the opponent that can be used to derive PNC, he will then be in a

position to give (not a proof proper but) an elenctic proof. Since in an elenctic

proof neither party is trying to explain the truth of the conclusion, neither will be

committing the fallacy of petitio principii.

33 Metaph.TA, 1006a21

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admissions, has accepted the principle as true, and has done so without a demonstration of its truth from prior principles.34

The purpose of the elenctic demonstration is not to yield the knowledge that or why the principle is true. All knowers know the 'that/ and there is no 'why/ So what is its purpose? To answer this we should consider the nature of the science that investigates the common axioms, and the nature of the investigation itself. A fruitful way to approach this topic is to consider whether the science that investigates substance does or does not conform to the model presented in the Analytics, and whether the science (if such there be) which treats of PNC is or is not the same as the science of substance.35 A host of preliminary questions must be by-passed in order to get to the heart of our present concern. Let us simply assume the idea that if there is a science of substance, then it will be, or be a part of, a general science of being, and let us use 'metaphysics' as a label for the putative science of being. // metaphysics is a science in the way that the other (the departmental) theoretical sciences are sciences (assuming that it is a science at all), then it should be understood as having:

1. A subject matter.36

Aristotle held that to ov is not a generic kind predicable in common of all the things-that-are (xoc ovxoc) - the various kinds of being do not come together to form a highest genus of being of which those kinds are species.37 Nonetheless, the expression 'to 6V can be used to designate or specify a certain sort of subject matter, and in Metaph. Fwe find the term used for the subject matter of metaphysics.38

2. A set of items (both propositions and terms) that hold good of that subject matter.

34 Metaph.Tt, 1006b26-28

35 These questions are in the spirit of Metaph. Bl, 995b6-10 and B2, 996b26-15.

36 This will be a yevo? {APo. A10, 76bll-13) or yevo? ikoxeinevov {APo.A7, 75a41-bl, Metaph. B2, 997a6).

37 See APo.B7, 92bl3-14 where it is said that being is not the ouaia (substance or essence) of anything because it is not a genus. (Also, Metaph. B3, 998b22-27.)

38 Metaph.Yl, 1004b22; cf. T3, 1005b9.

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This breaks down into two major classes:

A. First Principles and Causes.

(i) Propositions: indemonstrable, immediate truths.

(ii) Terms: items belonging in the what it is' of the beings falling within the scope of the genos, and those beings themselves.

B. Non-Principles:

(i) Propositions: non-immediate truths (the 'theorems') about the genos and the beings falling within its scope.

(ii) Terms: items that apply to the beings within the scope of the genos, and to the genos itself, but do not fall under 2. A.(ii). Call these the pathe.39

3. That in respect of which terms apply to the genos.

This is the respect in virtue of which the science in question studies the application of the various terms to their subject matter. Aristotle typically indicates this item by prefacing it with an adverbial 'ff (often translated 'qua'), or using an adverbial phrase constructed from 'xoctoc' plus some name for this item put in the accusative.40

This is, of course, extremely sketchy. A more detailed specification of a science would require a characterization of the set of terms and propositions mentioned under heading 2. We want to know what counts as falling within the scope of a genos, and which propositions, terms and first principles applying to the beings falling within its scope are relevant

39 These include 7ta8r) {APo.AlQ, 76bll-15 - see also hi, 75bl and Metaph. B2, 997a6-7) and various kinds of auptpepTixoxa (75bl).

40 See APo.A* - esp. 73b28-29.

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to that science. Also needed is an analysis of the mode of connection both between principles and theorems, and between primitive and derivative terms. In this paper I can at best scratch the surface, and will here discuss only a few of the many distinctions and topics that Aristotle broaches in this regard.

It is important to see that the third entity, 'that in respect of which/ is absolutely crucial to a specification of which type 2 items fall within the scope of the science in question, for each science treats of only those type 2 items that hold good of their subject matter in some particular respect. Here are some of the relevant ways. An item can hold good of a subject with respect to itself (i.e., with respect to that subject) in at least three fundamental ways:

1: That item is in the xt eaxt of the subject.41 (Examples: both biped and animal hold good of man in respec^ of itself.)

2: That item is such that the subject in question is in its xi eaxt.42 (Examples: the male and the female hold good of animal in

respect2 of itself; man holds good of animal in respect2 of itself.)

3: That item holds good of the subject because of, or on account of ('8td' plus the accusative or articular infinitive), the subject.43 (Examples: being-receptive-of -grammar holds good of man in

respect3 of itself; having-interior-angles-equal-to-two-right- angles belongs to triangle in respect3 of itself.)

Further sub-divisions can be made within these classifications, but for present purposes we may stop here.

What does not hold good of a subject with respectn to itself (n = 1,2) may be called 'accidental/44 and hence items that hold good of something in respect3 of itself are sometimes called xocO' auxoc au[A(k(3r)x6xa, or per se accidents. The per se accidents of a genos are not per se accidents of the species. However, we might say (I am not sure whether Aristotle in fact

41 APo.At, 73a34-bl

42 APo.A*, 73bl-4

43 APo.Al, 73blO-16

44 APo.Al, 73b4-5

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did) that they are per se accidents of the species, but only accidentally (xoctoc au(x(ie[irix6

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difficulty.45 The fact that the subject matter of metaphysics cannot be (in the ordinary sense) a generic kind is not something that distinguishes it from the special sciences, for not all of them investigate some generic kind either. For instance, there is a single departmental science that studies everything that is healthy, and this despite the fact that although there are different kinds of healthy things, these kinds do not come together under a single generic kind. A single science taking for its subject matter this sort of subject matter, healthy things, is nonetheless possible because everything that is healthy is so-called with reference to a single item, with reference to health (7cpo


characterization of different sciences, we can give a rough outline of the difference between a particular and a universal science.

A particular science, intuitively speaking, studies not only what holds good of all of the species or kinds that fall within its subject matter, but also what holds good of any of those kinds. For instance, biology does not study only principles that govern all living things qua living things, but also must treat of the definitions of the particular kinds of animal, and the per se accidents (the 1810c) of each kind of animal. It must treat of the species themselves (items that belong to living thing in

respect2 of itself) and those items that apply to the species in respect3 of itself. A universal science, by way of contrast, will study only what belongs to all of the kinds within its scope.46 Metaphysics, as the general science of being qua being does not investigate what holds good of any particular kind of being qua that particular kind of being. As the general science of being, it studies what holds good of every being in respect of being, but does not treat of what holds good of some particular kind of being as such. Although being for a particular frog is no other than being a frog (its being just is its being a frog), nonetheless the metaphysician does not have to know what holds good of the frog in virtue of its being a frog. The biologist does. Of course, not all biologists actually study the same branches of biology, and not all know the same things, so talk of 'the biologist' is to some extent a fiction. Nonetheless, truths about frogs qua frogs are biological truths, and the study of such truths is part of the study of biology. However, even though the metaphysician is studying the principles and causes of being as such, and for a frog its being just is its being a frog, the metaphysician does not study frogs as frogs. Frog- ology is not a part of metaphysics in the way that it is a part of biology. Furthermore, the principles that hold of being qua being are not part of the subject matter of biology. If something applies to Kermit the frog qua being, then that something does not apply to Kermit qua frog or qua animal (again, despite the fact that his being just is his being a frog).

Still, it would be a mistake to suppose that the only principles that metaphysics investigates are those that hold good of every thing-that-is qua thing that is. This point is very important if we are to have a proper

46 In this sense there is a universal mathematics, distinct from such particular mathematical disciplines as arithmetic, geometry and astronomy (Metaph. El, 1026a25-27; cf. APo.A5, 74al7-25). This studies what belongs to numbers, lengths, etc., but not what belongs to them as such, but rather qua some more

general term (e.g., quantity).

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understanding of the way in which a metaphysician will treat PNC, for I want to argue that Aristotle's metaphysician will have to demonstrate truths about PNC - truths that do not hold ubiquitously.

Aristotle believes that the metaphysician studies both being qua being and the things that hold good of being qua being. To study the former is to study the ubiquitous truths about all beings as such; to study the latter involves a study of the terms that apply to beings as such (e.g., same, other, one), and investigate truths about them. The metaphysician must investigate the xocO' ocuxo 7ia0r| of being (and unity) as such,47 and these do not belong as twcGt) to number as such, or line as such, or fire as such.48 It is the job of the metaphysician both to know what they are and to understand their av[L$t$r\x6x


it is such that nothing is prior to it. In giving this proof, we are entitled to assume that PNC is true. It is clearly not question-begging in Aristotle's sense to assume the truth of PNC in an argument for the claim that PNC is a 'first' unless either (i) that conclusion just is PNC (which it is not), or (ii) that conclusion is prior to and explanatory of PNC (which it is not, for nothing is prior to and explanatory of PNC). In proving of PNC that it is a 'first/ we are indeed proving something that entails PNC itself. If PNC is a first principle, then it is true; it is a first principle; hence it is true. However, adding this argument to a demonstration that PNC is a first principle does not produce a demonstration of PNC itself, for it would not be proceeding from premises that are prior to and explanatory of the conclusion.

Aristotle claims in Metaph. F3 that PNC is the firmest principle of all. This is a claim about PNC - in effect, it is saying of PNC that it has the property of being the firmest first principle of all. Aristotle then goes on to attempt a proof of this claim. A person cannot at one and the same time believe that something is a so-and-so and also believe that it is not so-and-so, for the belief that a thing is a so-and-so is the contrary of the belief that it is not a so-and-so. However, since PNC is true, it is impossible for contraries to hold good simultaneously of the same subject.50 If somebody were to believe at one and the same time both that something is F and that it (the very same thing) is not F, then contraries would be true of the same subject at the same time, for these two beliefs, which are themselves contraries, would simultaneously be true of the person who (allegedly) believed them.

There are, of course, many problems and difficulties with this proof, but they will have to wait. Let us instead focus on what it is that Aristotle thinks it shows. He concludes the passage with the remark that this is the reason (8to) why all who give proofs are ultimately led back to PNC, for it is the apxrj of all the other common axioms as well.51 Furthermore, he began the passage with an indication that he was about to show why PNC is indeed the firmest principle of all.52 Aristotle thinks that he has demonstrated that PNC is the firmest principle, and that he has done so by means of the principle itself.53

50 See Metaph.YZ, 1005b26-28 and r6,1011bl5-22.

51 Metaph.H, 1005b32-4

52 MetaphS3, 1005b22ff

53 Metaph.V4, 1006a3-5

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In Metaph. F4 he tells us that PNC cannot be demonstrated, but can be given a demonstration elenctically - and it is at this point that Aris- totle begins the elenctic demonstration with which we are presently concerned. Although he is showing us a way to refute somebody who asserts that PNC is false, he is not addressing himself to an audience that needs to be convinced of its truth.54 He is presupposing an audience that has already learned its analytics (10005b2-5), and hence already believes that PNC is an indemonstrable, but true, first principle. They have the oti, the fact. A metaphysical argument can give them the Sioti, or reasoned fact.

With such an audience in mind, what purpose could the elenctic refutation serve? Certainly not to refute them. They already believe that everybody knows PNC without proof (if they didn't, they would get sent back to analytical prep school), and they do not have to be persuaded that the law is true, or that they already believe it. For Aristotle's purposes, it does not even matter if his elenctic argument would convince a 'Heraclitean' opponent. I doubt that he expected that one could use this argument to win over a recalcitrant. However, what does matter is this. If Aristotle is (as he thinks) arguing from true premises, then anybody who accepts the premises, and hence would find the argument convinc- ing, would see that belief in PNC is required for significant thought and speech. The conclusion of the elenctic argument is supposed to be PNC, but the premises do not give the reason for that conclusion. The fact that acceptance of PNC is required for significant thought is not the reason why PNC is true. But Aristotle is not trying to show why the principle is true. He is concerned to show why it must be accepted as true. In showing why I must accept it, he is not giving me a reason for accepting it (I must accept it without a reason). He is giving me a reason why it must be the case that I, or anybody else engaged in significant thought or discourse, accept it.

Elenctic demonstration does not provide a metaphysical path leading to knowledge of PNC. The principle is already known by anybody who knows anything, and hence one does not have to be a metaphysician to

54 See Jonathan Lear, Aristotle and Logical Theory (Cambridge: 1980), Chapter 6, 'Proof by refutation,' 99, 113-14. My thinking on the matters discussed in this

paper was greatly assisted by Lear's book.

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know that it is true. However, only the metaphysician knows why it is the case that all engaged in significant thought must accept it.55

Received August, 1984

55 This paper was delivered to the Pacific Division of the American Philosophical Association in March 1984. Montgomery Furth and S. Marc Cohen were the commentators, and their replies are published in this issue. Substantial portions of previous drafts were presented to both the Philosophy and Classics Depart- ments of the University of Texas, Austin, and to the Logic Seminar of the Section on Foundations, Department of Mathematics, University of California, Berkeley. In addition to the members of those audiences, I would like to thank Allan Silverman and Gregory Vlastos for comments and advice. I owe a special debt to H.P. Grice. The central topic of this paper ('Which Science Investigates the Principle of Non-Contradiction?') and the strategy for dealing with it both arose from extended discussion with him concerning the characterization of

metaphysics.

357

Article Contentsp. 341p. 342p. 343p. 344p. 345p. 346p. 347p. 348p. 349p. 350p. 351p. 352p. 353p. 354p. 355p. 356p. 357

Issue Table of ContentsCanadian Journal of Philosophy, Vol. 16, No. 3 (Sep., 1986), pp. 341-574Front MatterAristotle's Investigation of a Basic Logical Principle: Which Science Investigates the Principle of Non-Contradiction? [pp. 341-357]Aristotle on the Principle of Non-Contradiction [pp. 359-370]A Note on Aristotle's Principle of Non-Contradiction [pp. 371-381]Toward a Theory of Coercion [pp. 383-405]Hume's Academic Scepticism: A Reappraisal of His Philosophy of Human Understanding [pp. 407-435]Pascalian Wagering [pp. 437-453]Basic Theistic Belief [pp. 455-464]The Function of Epistemic Justification [pp. 465-492]Justified Belief and Internal Acceptability [pp. 493-502]Relatively Speaking: The Coherence of Anti-Realist Relativism [pp. 503-509]'The Divine Sign Did Not Oppose Me': A Problem in Plato's Apology [pp. 511-526]Critical NoticeReview: untitled [pp. 527-543]Review: untitled [pp. 545-557]Review: untitled [pp. 559-574]

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