Monday, November 16 at 2 PM in AP&M 4301.
Split scope and summative existentials: Two faces of bare quantification
It is generally thought that quantificational expressions in natural language are relational: a quantificational determine (for example) composes first with an expression (its “restriction”) that defines its domain of quantification, and second with an expression (its “scope”) that defines the condition that the relevant quantity of objects in its domain of quantification must satisfy. Szabo (2011), however, argues that natural language includes “bare” quantifiers: expressions that combine directly with their scope, and do not have restrictions, like the quantifiers of predicate logic. In this talk, I present two semantic analyses of numerals and related quantity expressions as bare quantifiers, a “Fregean” semantics as second-order properties of individuals, and a “de-Fregean” semantics as second-order properties of degrees. I show that the latter denotation provides an account of “split-scope” phenomena like (1), while the former is required to account for the interpretation of “summative existentials” in (2).
(1) They sought no friends amongst the neighbors, despising them all.
(= It is false that they tried to find friends among the neighbors.)
(2) If they are thrown into the air, there can be three results: head-head, head-tail, tail-tail.
(= Three things are such that they are possible results.)
I conclude with some speculations about how the two bare quantifier denotations for numerals (and their kin) can be derived from a single, more basic denotation.