Formal semantics

Formal semantics is the branch of linguistics and philosophy of language that studies meaning by constructing precise mathematical models of the relationship between linguistic expressions and the world. Its central project is truth-conditional semantics: the idea that to know the meaning of a sentence is to know the conditions under which it would be true. Formal semantics treats natural languages as interpreted formal systems, applying tools from logic — set theory, lambda calculus, type theory, and model theory — to analyze reference, quantification, tense, modality, and compositionality. The tradition descends from Frege and was systematized in the twentieth century by Richard Montague, who showed that the syntax and semantics of English could be given a rigorous algebraic treatment. The claim that natural language is a formal system is not merely a methodological stance; it is the foundational bet that the apparent messiness of language hides an underlying mathematical structure that can be excavated and made explicit.