Unreducible N-Ary Quantifiers in Natural Language

Abstract

In part one of this paper I exhibit a variety of English expressions which are naturally interpreted in terms of properly n-ary quantifiers — ones which may be thought of as simultaneously binding 2 or more variables. These contrast with what we call standard natural language quantifiers which bind just one variable. My primary concern here is to show that the interpretations of expressions using n-ary quantifiers are not, in a sense I make precise in section two, reducible to ones using only standard quantifiers. Section two here develops the mathematical techniques necessary to prove unreducibility. Section three returns to informal questions concerning the semantic expressive power of English noun phrases — questions that can be answered in terms of the techniques developed in section two. Section four concludes with a discussion of several problems which remain open and presents some partial results concerning those problems.