Chapter 12 The Case of Logic: Łukasiewicz-Prior’s Discussion on Logic

In: Formal and Informal Methods in Philosophy
Zuzana Rybaříková
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Although mathematical logic is considered a precise tool for solving philosophical issues, it has its own drawbacks. This paper illustrates one of these possible issues by drawing on the example of two philosophers, Jan L. Łukasiewicz and Arthur N. Prior. The two shared many similar views, as well as the conviction that mathematical logic should be used in philosophy. In addition, both were interested in the history of philosophy and both tried to deny determinism and formulate claims to support future contingency. For a certain time, Prior even adopted Łukasiewicz’s system of many-valued logic and was a defender of it. However, after developing his system of temporal logic Prior was more reserved towards Łukasiewicz’s system and formulated several objections to it. While Prior was, in his later works, a proponent of intensional logic and nominalism, Łukasiewicz insisted that any decent system of modal logic had to be extensional. There are also hints that Łukasiewicz may have adopted a Platonist position, even though Łukasiewicz himself was not willing to discuss these philosophical questions in his work. In contrast, Prior was a nominalist. As a result, they postulated divergent systems of logic for solving similar philosophical issues.

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