Logic and Semantics in the Twentieth Century
Gabriel Sandu, Tuomo Aho · Oxford University Press eBooks · 2009
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.