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Aristote au xixe siècle

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Denis Thouard

L'Aristote logique

Comments on Professor Wolenski’s paper

Robert Sharples

Texte intégral

  • 1 I also think that they held, and were interpreting Aristotle correctly in holding, that this indete (...)
  • 2 First, apparently, by N. Rescher, Studies in the History of Arabic Logic, Pittsburgh 1963, 46; cf. (...)
  • 3 C. Strang, ‘Aristotle and the Sea Battle’, Mind 69 (1960) 447-465.

11. I would like to thank Professor Wolenski for his paper, which has provided illuminating insights into the history of the study of Aristotle in Poland and its influence on philosophical activity there in general. I want to raise two particular issues, before ending with a final general question. The first issue concerns the Sea-Battle Paradox and Łukasiewicz’ many-valued logic. Professor Wolenski makes two points that seem to me particularly significant here. The first is that this was a distinct development in the context of, but distinct from, Łukasiewicz’ earlier discussion of the principle of non-contradiction in Aristotle, and the second is that Łukasiewicz thought that Aristotle himself had doubts about the principle of bivalence, and hence changed his label for many-valued logic from «non-Aristotelian» to «non-Chrysippean». This is not the appropriate occasion for a full discussion of the problem of Aristotle’s own position concerning the Sea-Battle paradox; I will only say that it seems to me that Ammonius and Boethius came closest in suggesting that one of a pair of contradictory propositions concerning a future contingent event is true, and the other false, but in such a way that it is not determinate which is which1. The question that is relevant for us here is whether such a view in fact (whatever Ammonius, Boethius, and indeed Aristotle thought) collapses into what has commonly been labelled the «Non-Standard Interpretation» of the Sea-Battle paradox2, according to which the point at issue does not relate to truth at all; statements about future contingents are, on this view, either true or false, simpliciter, depending on the actual outcome even though it has not happened yet, and what changes after the event is only that it then becomes necessarily true (in a sense of «necessary» which we might dispute, but which Aristotle certainly recognises). From this perspective the issue does not in fact have to do with truth at all, only with necessity; and such solutions as Ammonius’ and Boethius’ distinction between determinate and indeterminate truth, or Strang’s distinction between the truth of «strong future tenses» and that of «weak future tenses»3, are from this perspective not in fact points about truth itself at all.

  • 4 Łukasiewicz, art. cit., 41.
  • 5 art. cit., 61.
  • 6 art. cit., 52.
  • 7 J. Łukasiewicz, ‘On Determinism’, in McCall, op. cit., 18-39, at 37.

2The relevance of this point is that similar doubts have been raised about Łukasiewicz’ own position. He himself referred to his enquiry into many-valued logics as based in a study of modal propositions, while stressing (and this is relevant to the general theme of Professor Wolenski’s paper) that he meant this to refer to necessity and possibility in an Aristotelian and medieval, rather than a Kantian sense4; and he also suggested that logics with more than three values could be interpreted in terms of probability5. On the other hand, in the same paper he explicitly linked two-valued logic to bivalence of the true and the false, in a way that at least suggests (though it need not require) that three-valued logic involves a different view of truth and falsity6; and he elsewhere referred explicitly to three-valued logic as involving a third truth-value7.

  • 8 C.A. Baylis, ‘Are some propositions neither true nor false?’, Philosophy of Science 3 (1936) 156-16 (...)
  • 9 C. Salomaa, ‘On Many-Valued Systems of Logic’, Ajatus 22 (1959), 115-159.

3Critics, as I have indicated, have taken a different view. For example, Baylis in 19368 argued that Łukasiewicz’ many-valued logics were not directly relevant to the principle of bivalence (every proposition is either true or false) but rather provided a useful instrument for contexts, such as epistemological ones, in which a classification of propositions into more than two types was appropriate; similarly Salomaa in 19599, noting that (120) «it seems more plausible to interpret [Łukasiewicz’s] truth-values through epistemic concepts... ‘verified’ ‘falsified’ and ‘undecided’. If this is done then the set consisting of ‘true’ and ‘false’ is replaced by a set consisting of the three epistemic concepts. This does not necessarily mean rejection of the law of the excluded middle, but only indicates that the latter set is more useful than the former». Professor Wolenski has shown how Łukasiewicz himself rejected the epistemological turn; there thus seems a certain irony in these reactions to his discoveries claiming that they in fact related to knowledge rather than truth.

 

  • 10 Cf. p. 6 (Twardowski) and p. 12 of Professor Wolenski’s paper. (In the latter he notes, in the cont (...)
  • 11 The notion of truth in the E 4 passage clearly goes back to Plato’s Sophist 263d.

42. The second issue I would like to raise is that of the correspondence theory of truth. Professor Wolenski has indicated how the correspondence theory of truth was rejected if understood as involving the notion of the composition of presentations10. In this connection he cites (p. 13) two passages from Aristotle’s Metaphysics. The first, from Γ 7 1011b27-28, simply defines truth and falsity in terms of saying that what is, is (truth) and saying that what is, is not (falsity; I omit the other two permutations for the sake of brevity). The second, from E 4 1027b18-23, introduces the notions of combination and separation, so that truth is making an assertion when the subject and predicate are in fact combined, falsehood making one when they are not (again, I omit the other two permutations for the sake of brevity)11. Professor Wolenski goes on to say that the passage from Γ was found acceptable but that from E was not, and in this connection refers to Twardowski as rejecting Thomas Aquinas’ theory of truth in the adaequatio formula. But the adaequatio formula as Professor Wolenski cites it contains no explicit reference to composition or separation; it seems in fact parallel to the passage from Γ rather than to that from E.

5Moreover, Aristotle himself in Θ 10, after developing (at 1051b2-17) the account in terms of composition and separation found in E 4, goes on at 1051b17ff. to consider what account is to be given of truth and falsity in the case of incomposites, and to conclude that it must be in terms of knowledge and its absence. One cannot be deceived (or «wrong») about an incomposite; either one speaks about it correctly, or else one fails to apprehend it at all. For Aristotle himself, therefore, it seems that the significant contrast is between the account in E 4, repeated in Θ 10, and the account concerned with incomposites in the latter chapter.

 

63. This leads on to my third, general question. In his conclusion Professor Wolenski says (p. 14) that we have to do not with «a Polish Aristotelianism» but with «a tradition in philosophy inspired by Aristotle». That formulation made me wonder in general what we might mean by saying that a philosopher or a tradition has been inspired by Aristotle. For example (and this list is neither intended as exhaustive nor composed of mutually exclusive items); we might mean that the philosopher or philosophers in question take particular Aristotelian texts as the starting-point of their discussions or enquiries, at least in the sense that their work is inspired by the problems the texts raise. Or we might mean that there is something distinctively Aristotelian about the methods of enquiry and discussion that they use. Or again we might mean that Aristotle’s work has in a general way contributed to their philosophical agenda. There is room, I think, for a general enquiry about the different ways in which Aristotle has inspired philosophers; more immediately, I wondered how one might characterise the particular cases with which Professor Wolenski in his paper has been concerned.

Notes

1 I also think that they held, and were interpreting Aristotle correctly in holding, that this indeterminate status is essentially time-dependent and changes after the event Łukasiewicz refers to the interpretation of Ammonius and Boethius, but without suggesting that there is anything to support it in Aristotle’s actual text (J. Łukasiewicz, ‘Philosophical Remarks on Many-Valued Systems of Propositional Logic’, in S. McCall, ed. Polish Logic 1920-1939, Oxford 1967, 40-65, at 64); I think that it can in fact be seen as warranted by 19a29 and 19a36-38. (Cf. D. Frede, ‘The Sea-Battle reconsidered: a defence of the traditional interpretation’, Oxford Studies in Ancient Philosophy 3 (1985) 31-88, at 76.)

2 First, apparently, by N. Rescher, Studies in the History of Arabic Logic, Pittsburgh 1963, 46; cf. G. Seel, ed., Ammonius and the Sea-Battle, Berlin: De Gruyter, 2001 [Peripatoi, 18]), 18 n. 9. V.R. McKim, ‘Fatalism and the Future: Aristotle’ s Way Out’, Review of Metaphysics 25 (1972) 80-111.

3 C. Strang, ‘Aristotle and the Sea Battle’, Mind 69 (1960) 447-465.

4 Łukasiewicz, art. cit., 41.

5 art. cit., 61.

6 art. cit., 52.

7 J. Łukasiewicz, ‘On Determinism’, in McCall, op. cit., 18-39, at 37.

8 C.A. Baylis, ‘Are some propositions neither true nor false?’, Philosophy of Science 3 (1936) 156-166.

9 C. Salomaa, ‘On Many-Valued Systems of Logic’, Ajatus 22 (1959), 115-159.

10 Cf. p. 6 (Twardowski) and p. 12 of Professor Wolenski’s paper. (In the latter he notes, in the context of a general rejection of correspondence theories of truth, that the term «correspondence» was none the less used «as a convenient abbreviation»).

11 The notion of truth in the E 4 passage clearly goes back to Plato’s Sophist 263d.

Auteur

Professeur au King’s College de Londres.

© Presses universitaires du Septentrion, 2005

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