A New Semantics for Number

Abstract

Research on the semantics of number has been strongly influenced by the distribution of overt number morphology in English.As is well know, number can be expressed on nouns and on verbs in English.In example (1), overt plural morphology is present in both places.(1) The books-[PL] were-[PL] lying on the table.All research on plurality has assumed the the [Pl]-feature on the noun is interpreted in some way.Bennett (1974) was the first to propose a semantics of number along these line, and this assumption has been adopted by all subsequent research.Furthermore most research has followed Bennett to assume that the [Pl]-feature on the verb remains uninterpreted in English, and is a reflex of syntactic agreement with the subject. 1 A contemporary version of Bennett's proposal (e.g.Chierchia 1998b, Schwarzschild 1996) assigns to the singular noun book a set of individuals as its extension, while the extension of the plural noun books includes groups of these individuals (and, for Schwarzschild, atomic individuals, as well).These denotations are illustrated in ( 2): 2 (2) a. [[book]] = {a, b, c} b. [[books]] = {a⊕b⊕c, a⊕b, a⊕c, . . .}