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On Jan Łukasiewicz’s many-valued logic and his criticism of determinism. (English) Zbl 1274.03012

Summary: The article deals with Jan Łukasiewicz’s thesis that the truth or falsity of some propositions about the future – future contingents – entails determinism. According to Łukasiewicz, determinism could be avoided by rejecting the classical logic (two-valued logic) and replacing it with many-valued logic (three-valued logic). Łukasiewicz’s position is taken under scrutiny from the point of view of Susan Haack’s thesis that the truth values of future contingents do not entail any determinism. I argue in the paper that Haack’s view is incorrect because it does not take into account all premises accepted by Łukasiewicz. The most important of them concerns the semantics of future verbs. Łukasiewicz, as I try to show, assumes the so-called Peircean semantics and not the Ockhamist one. Next, I try to argue that it is possible to preserve the validity of Łukasiewicz’s reasoning which led him to the three-valued logic by taking into account his assumptions regarding the meaning of future verbs. In the last part of my paper, I point out that three-valued logic proposed by Łukasiewicz has some flaws and, therefore, one needs to look for another solution of the problem of future contingents.

MSC:

03A05 Philosophical and critical aspects of logic and foundations
03B50 Many-valued logic
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