Basic Concepts

Abstract

Richard Montague was the first to seriously propose and defend the thesis that the relation between syntax and semantics in a natural language such as English could be viewed as not essentially different from the relation between syntax and semantics in a formal language such as the language of first-order logic. While Montague’s claim was and is a controversial one, both the perspective he offered and the technical apparatus used in developing it have transformed the study of natural language semantics. In this section we focus first on the principle of compositionality and its central role in articulating the relation of semantics to syntax in a formal language. The principle is also known as Frege’s principle, and Montague took himself to be formalizing a basically Fregean viewpoint in adopting it. The second topic of this chapter is the lambda calculus, invented by Alonzo Church in the 1930’s but introduced to linguists mainly through Montague’s work. The lambda calculus has no intrinsic connection to the principle of compositionality, but it has proved to be one of the most important and fruitful tools in the formal semanticist’s toolbox, and without it, it would be much harder to make a plausible case for the compositionality of natural language semantics. For a linguist interested in semantics, we would suggest that a familiarity with the basics of the lambda calculus could be as important as a familiarity with first-order predicate logic.