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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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III. Do We Need to Reform the Old T-Scheme?

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IIIDo We Need to Reform the Old T-Scheme?

Read 2010 almost verbatim reproduces Read 2008. I was invited to make comments about the later paper (see Woleński 2008). In what follows I shall partly repeat my earlier critical comments about Read’s interpretation of the T-scheme, while also adding new remarks and improving the old ones; some of the additions are inspired by other contributors participating in Rahman, Tulenheimo, Genot 2008, including Stephen Read’s replies in this volume (see Read 2008a) as well as the previous discussion in Discusiones Filosóficas (see Miller 2010, Read 2011, Sandu 2010).

At first, let me remind Leśniewski-Tarski’s diagnosis of the Liar paradox. They pointed out (see Tarski 1944) that the derivation of the paradox uses: (I) self-referential sentences asserting semantic properties; (II) the T-scheme, and (III) classical, that is, bivalent logic. Hence, we can conceive three strategies in order to solve the paradox: (i) to exclude self-referentiality; (ii) to reject or modify the T-scheme; (iii) to change logic. It would be mistaken to maintain that there is a solution free of costs or some artificialities. It concerns Tarski who choose (i), Kripke (and many other logicians) who opted for (ii) (Sandu makes several remarks about this way out), and Read who tries to reform the T-scheme. More precisely, Read argues that the old (Tarskian) T-scheme is inaccurate and proposes its modification. I would like to show that Read’s reading of Tarski is incorrect and that his (Read’s) leads...

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