Logic

Meaning and Necessity

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Rudolf Carnap

1947

Meaning and Necessity: A Study in Semantics and Modal Logic is Carnap's major work in the philosophy of language and the theory of meaning — the work in which he developed the framework of intension and extension, sense and reference, that has shaped analytic philosophy of language ever since. Adapting and extending Frege's distinction between Sinn and Bedeutung, Carnap proposes a method of extension and intension: the extension of a term is its actual referent or truth-value; the intension is the rule or concept that determines the extension in any possible state of the world (any "state-description," in Carnap's terminology). This framework allows Carnap to give a systematic account of modal logic — the logic of necessity and possibility — by interpreting necessity as truth in all state-descriptions and possibility as truth in at least one. The work also develops the concept of L-truth (logical truth) and L-equivalence, providing a purely syntactic and semantic account of analyticity: a sentence is analytic if and only if it holds in every state-description by virtue of the meanings of its terms. Carnap uses this framework to analyse the problem of meaning for psychological and intentional contexts, introducing the notion of intensional contexts (where substitution of co-extensive terms fails). Quine's "Two Dogmas of Empiricism" (1951) directly attacked Carnap's distinction between analytic and synthetic statements, launching one of the central debates of twentieth-century analytic philosophy.