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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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XVIII. The Paradox of Analycity and Related Issues

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XVIIIThe Paradox of Analycity and Related Issues

Assume that a sentence (I prefer to speak about sentences as bearers of logical properties. By definition, sentences are syntactically well-formed as well as equipped with meaning and thereby intelligible as far as their understanding is taken into account;) A is analytic or is an analytical (A ∈ AN) under any substantial definition of analyticity (by the adjective ‘substantial’ I mean here: one of the definition of the concept of analyticity occurring in standard philosophical or/and logical discussions on this topic). Generally speaking, such a definition falls under the following scheme:

   (*) A ∈ AN if and only C(A),

where the letter C refers to a condition to be satisfied by an analytical. For instance, C can state ‘is true in virtue of meanings’, ‘is a tautology’, ‘is true in all possible worlds’, ‘it is true on the base of rules of a given language’, ‘is derivable solely on the basis of logic and definitions’, ‘its negation is contradictory’, etc. (see Woleński 2004d for an extensive survey of various attempts to define the concept of analytic sentence from Kant to the end of the 20th century). However, no particular understanding of analyticity is presupposed in my further discussions, except claims captured by the conditions (1) and (2) formulated in the next section.

In order to make things more explicit, I assume two statements, namely:

   (1)   A is analytic and true if and only if...

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