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Logic and Its Philosophy

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Jan Woleński

This collection of essays examines logic and its philosophy. The author investigates the nature of logic not only by describing its properties but also by showing philosophical applications of logical concepts and structures. He evaluates what logic is and analyzes among other aspects the relations of logic and language, the status of identity, bivalence, proof, truth, constructivism, and metamathematics. With examples concerning the application of logic to philosophy, he also covers semantic loops, the epistemic discourse, the normative discourse, paradoxes, properties of truth, truth-making as well as theology, being and logical determinism. The author concludes with a philosophical reflection on nothingness and its modelling.

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XVII. Formal and Informal Aspects of the Semantic Theory of Truth

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XVIIFormal and Informal Aspects of the Semantic Theory of Truth44

Tarski’s semantic theory of truth (STT, for brevity) is usually considered as belonging to metalogic or metamathematics understood as including proof-theory (syntax) and model-theory (formal semantics). This qualification justifies a frequent opinion on STT as a formal theory or definition. The title of Tarski 1933, namely The Concept of Truth in Formalized Languages, additionally supports such a view.45 However, a problem appears immediately, when we confront ‘formal’ in ‘STT as a formal theory’ with the list of meanings of this adjective and its contrasts (the second member in every following pair):46 (a) formal as configuration of elements, structure, form vs. matter, shape, etc.; (b) formal vs. substantial (form vs. content); (c) formal vs. material; (d) formal vs. informal; (e) formal as computable vs. non-computable; (f) formal (effective, finitary, etc.) vs. non-finitary; (g) formal as logical vs. extralogical; (h) formal as syntactic vs. semantic; (i) formal as extensional vs intensional; (j) formal as compositional vs. non-compositional; (k) formal as logical plus mathematical vs. empirical; (l) formal as analytic vs. synthetic; (m) formal as in ‘formal language’ vs ordinary (informal); (n) formale vs. sachlich (as in phenomenology). Of course, (a) – (n) are not mutually exclusive and overlap at several points.

Clearly, (a) has no relevance to STT. Other oppositions can be implemented to this theory. In order to see it, let me extract several ingredients of STT. The ← 195 | 196 → following list, without pretending to be complete,...

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