Abstract

This paper introduces Richard Montague's theory of determiner phrases to the philosophically oriented readers who are familiar with Russell's traditional treatment. Determiner phrases include not only quantifier phrases in the narrow sense, such as every man, some woman, and nothing, but also DP conjunctions such as Adam and Betty and Adam or Betty, and even proper names such as Adam and Betty. Montague treats all determiner phrases as belonging to type t, i.e., the type of functions from properties of individuals to truth values. This paper also introduces the simply typed lambda-calculus for the explication of Montague's theory. Two major problems with Montague's theory, one more philosophical and the other more linguistic, are discussed.