Logic and semantics in the twentieth century

This chapter explores logical semantics, that is, the structural meaning of logical expressions like connectives (it is not the case that, either or, if ... then), quantifiers (there is, for all, etc.), and modalities (it is necessary that, it is possible that). It focuses on truth-theoretical semantics for formalized languages, a tradition emerging from Carnap's and Tarski's work in the first half of the last century that specifies the meaning of these expressions in terms of the truth-conditions of the sentences in which they occur. It considers Tarski-style definitions of the semantics of a given language in a stronger metalanguage, Tarski's impossibility results, and attempts to overcome them in the post-Tarskian tradition