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Aristote au xixe siècle

Denis Thouard

L'Aristote logique

Reply to Prof. Sharples

Jan Wolenski

Texte intégral

Bibliothèque du Centre de Recherche Philologique, Lille.

1Prof. Sharples is perfectly right that there is very much to say about the Sea Battle problem. I would like only to add that Łukasiewicz refers to De Interpretatione and the Sea Battle Problem several times. He does it (a) in «On Determinism» (the Rector speech in 1922), published in Polish in 1961, Eng. tr. by Z. Jordan in S. MacCall (ed.), Polish Logic, Oxford, Clarendon Press, 1967, p. 19-39 and in J. Łukasiewicz, Selected Works, Amsterdam, North-Holland, 1970, p. 110-128, see p. 36, p. 125, respectively; (b) in «Philosophische Bemerkungen zu mehrwertigen Systemen des Aussagenkalkül», Comptes rendus de la Société des Sciences et de Lettres de Varsovie, Cl. III 23 (1930), p. 51-77, Eng. tr. by H. Weber in S. MacCall (ed.), loc. cit., 40-65 and in J. Łukasiewicz, Selected Works, loc. cit, p. 152-178, see p. 63-64, respectively; (c) in «Geneza logiki wielowartosvciowej» (The Genesis of Many-Valued Logic), Nauka Polska 24 (1939), p. 215-223, repr. in J. Łukasiewicz, Logika i metafizyka (Logic and Metaphysics), Warszawa, Wydział Filozofii i Socjologii Uniwersytetu Warszawskiego, 1998, p. 241-245, see p. 217, 243, respectively; (d) in his book Aristotle’s Syllogistic from the Point of View of Modern Formal Logic (2nd edition), p. 152, 155, 175, 178, 207-208. The passages (a) - (c) give strong evidence that Łukasiewicz was inspired by De Interpretatione in his way to many-valued logic. The places mentioned in (d) contain nothing about many-valued logic, but discusses the issue of the contingency and necessity of sentences about future contingent events. This is not surprising because Łukasiewicz rejected his earlier view that the third value could helps us in the interpretation of future contingencies.

2As far as the matter concerns many-valued logic two problems must be sharply distinguished. One concerns formal questions and various applications of many-valued formalisms in theoretical and practical matters, for instance (I give concrete illustrations in brackets), computes science (fuzzy reasonings), mathematics (many-valued topology) or technology (synthesis of electric circuits). From thus point of view, many-valued logic is a fully legitimate variety of formal systems; see S. Gottwald, A Treatise on Many-Valued Logic, Baldock, Research Studies Press, 2001; M. Fitting and E. Orlowska (eds.), Beyond Two: Theory and Applications of Multiple-Valued Logic, Heidelberg, Physica-Verlag, apringer-Verlag Company, 2003 for extensive surveys. Another problem concerns the question of an intuitive interpretation, in particular, of philosophical assumptions (see books by Haack, Malinowski, Rescher, Rosser and Turquette, and Zinoviev quoted in note 11 of my paper. A striking case was raised by Ferdinand Gonseth. Assume that a sentence p is valued by ½ (the third value). So the value of ¬ p is also ½. According to Łukasiewicz matrix for conjunction, the value of p ^ ¬ p = ½, although we are inclined to think about the formula p ^ ¬ pas a contradiction and thereby always false. Another objection to Łukasiewicz points out that he confuses truth and truth at the time t, that is, simultaneously operates with two semantic valuations.

3Perhaps it is important to recall that, according to Łukasiewicz, all logical functions on sentences have to be extensional, that is, the valued of compound sentences are uniquely determined by the values of their atomic components. Hence, the expression «it is possible that p » should be a truth-function of p. It is easy to prove that no functor of two-valued logic can be interpreted as truth-functional possibility. This was the main motivation of Łukasiewicz for introducing three-valued logic as a tool for logical analysis of possibility. Personally I think that two-valued logic is sufficient but that is another matter. However, I do not agree that epistemic interpretations of many-valued logic are better than Łukasiewicz’s own attempts. In particular, they are also plagued by the Gonseth problem.

4I agree that there are several problems of how the interpretation of Aristotle’s concept of truth should be give. Polish philosophers principally referred to Metaphysics 1011b. It is true that Aquinas formulated his definition as a comment to this passage. My original text obscured this point and I am indebted to Prof. Sharples for pointing that out. However, many contemporary scholars see 1027b as the key passage and argue that it is the main intuition expressed by Aristotle (quite recently, L.M. De Rijk, Aristotle. Semantics and Ontology, v. 2, Leiden, Brill, 2002, p. 142-147). I am inclined to think that there is no possibility to interpret 1011b as the correspondence definition of truth. On the other hand, 1027b is more promising in this respect, because one can say that it suggests a parallelism between the linguistic bond and the metaphysical bond.

5As far as the matter concerns Polish Aristotelianism I agree that Aristotle inspired philosophers in different ways. I simply want to stress that no other philosopher of the past influenced Polish philosophy so much as the Stagirite did. Yet this influence was completely different in the case of Neo-Thomism. Of many possible links between Aristotle and Poles, I stress once more that Polish philosophers considered him as the first logical philosopher.

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