Richard Montague (1930-1971) was an American logician. A student of Alfred Tarski, Montague made important contributions to set theory and model theory.

Contributions to natural language semantics

He is best known for his groundbreaking work in linguistics: his introduction of type theory and generalized quantifiers achieved for natural language semantics the same what Gottlob Frege had achieved almost a century earlier for the quantification theory of formal languages.

In fact, whereas Frege saw the surface position of quantifiers as a logical defect of natural languages which had to be amended for his Begriffsschrift, the powerful techniques of lambda calculus employed by Montague permitted to interpret quantifiers in situ as well, leading to a theory of linguistic interpretation, called Montague grammar, of a mathematical precision and elegance.

By restricting the analysis to language fragments, Montague overcome obstacles like the semantic paradoxes that prevented his teacher Tarski from applying model-theoretic methods to natural languages.