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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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XIV. Truth-Makers and Convention T

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XIVTruth-Makers and Convention T

Since Convention T is a very important ingredient of the semantic theory of truth, every comparison of Tarski’s construction with other approaches to the concept of truth must, sooner or later, discuss the equivalence:

   (1)   S is true if and only if A*,

where A is a sentence in an interpreted (this qualification is important, because is dispenses us with worries whether propositions or sentences function as bearers of truth) language L, S is a name of this sentence and the symbol A* refers to embedding, for example, via translation, of A into a metalanguage ML. Convention T requires that any materially correct truth-definition Df logically entails every instance of (1), that is, the specialization of this scheme for an arbitrary sentence of L; such concrete equivalences are called T–sentences, T–biconditionals or T–equivalences. Note that T–sentences something more than usual material equivalences, because we have that Df B, for any B being an instance of (1) (see Woleński 2008 for a discussion of this problem). According to Tarski, (1) does not constitute a truth-definition, although it can be considered as a partial one. Take the content of the sentence A as the set of all its consequences, formally Cont(A) = Cn({A}). Clearly, Cont(Df) > B. In fact, the content of Df exceeds the collection (rather rather the content) of all instantiations of (1), because truth-definitions usually contain elements (expressions) which do not occur...

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