Extensionality in natural language quantification: the case of many and few

Abstract

This paper presents an extensional account of manyand few that explains data that have previously motivated intensional analyses of these quantifiers (cf. Fernando and Kamp, Proceedings of semantics and linguistic theory, 1996; Lappin, Linguist Philos, 23(6):599–620, 2000). The key insight is that their semantic arguments are themselves set intersections: the restrictor is the intersection of the predicates denoted by the N’ or the V’ and the restricted universe, U, and the scope is the intersection of the N’ and V’. Following Cohen (J Semant, 16:43–65, 1999 ; Nat Lang Semant, 9:41–67, 2001), I assume that the universe consists of the union of alternatives to the nominal and verbal predicates, where an alternative to a property ψ is one that shares a pragmatic presupposition with ψ, and a pragmatic presupposition is one that is selected by context from a set of potential presuppositions associated with the sentence. A many/few-quantified sentence is then true iff the proportion of the scope to the restrictor is greater/less than some threshold, n. In addition to explaining various problematic cases from the literature, the analysis shows how the readings of a many/few-quantified sentence (proportional, reverse, focus-affected, and cardinal) can be derived from the same syntactico-semantic structure, it being unnecessary to claim lexical or structural ambiguity. The analysis also provides strong support for the idea that natural language quantification is always purely extensional.