On the Proper Treatment of Quantifiers in Montague Semantics

Abstract

The grammatical and semantical theories of the late Richard Montague present us with a most interesting treatment, perhaps the most interesting existing treatment, of certain aspects of the syntax and semantics of natural languages.¹ These theories are not satisfactory in their present form, however, not even if we restrict our attention to those linguistic phenomena that Montague himself primarily wanted to cover, together with certain closely related phenomena. The most central of these seems to be the variety of ways in which quantification is represented in natural languages. This concern is highlighted by the title of Montague’s last published paper, ‘The Proper Treatment of Quantification in Ordinary English’. In my own paper, I shall concentrate on the nature of natural- language quantifiers for the same reasons as Montague. In view of the importance of the problem of treating natural-language quantifiers, it is in order to point out and to discuss a number of shortcomings of Montague semantics in this department. It is of course the very precision and force of Montague’s treatment that lends a special interest to these shortcomings. Just because Montague was so successful in carrying out certain general strategic ideas in the formal theory of language, the shortcomings of his treatment point to general morals in the theory and methodology of linguistics and of the logical analysis of natural language.