Formal Semantics

Formal semantics is the project of constructing mathematically precise theories of meaning for natural languages, treating sentences as expressions in logical formalisms whose interpretations are computed compositionally from the interpretations of their parts. The approach was inaugurated by Montague in the 1970s, who showed that substantial fragments of English could be translated into intensional logic and interpreted via possible worlds semantics, and has since become the dominant paradigm in linguistic semantics.

Its central commitment — that meaning is truth-conditions computed by recursive rules — generates precise predictions about scope, quantification, and modality, but struggles with context-dependence, presupposition, and the non-truth-conditional dimensions of meaning that pragmatics and speech act theory address. The tension between formal and pragmatic semantics remains the central unresolved axis in the philosophy of language, and drives the development of dynamic semantics — frameworks in which meaning is modeled as the update of a discourse context rather than as a static truth-value.