Incremental quantification and the dynamics of pair-list phenomena

Abstract

Distributive universals are unique among natural language quanti-fiers in the following three ways: (i) matrix interrogatives that contain them accept pair-list answers; (ii) indefinites and disjunctions in their scope may assume arbitrary functional readings; and (iii) they permit sentence-internal interpretations of a wide range of comparative adjectives, like new and different. Because other quantifiers in the same environments do not give rise to these interpretations, the constructions provide a window into the semantic processes that underlie quantificational distributivity. In fact, both pair-list and internal readings have been independently argued to expose some of the compositional clockwork behind universal quantification, but the mechanisms they have been taken to reveal are entirely distinct. In contrast, I propose to explain pair-list phenomena, including a class of functional read-ings not previously recognized as such, and internal readings of comparative adjectives as two sides of the same coin; they are both side effects of incre-mental quantification. To make this precise, I analyze distributive universal quantifiers in terms of iterated, incremental update, in effect generalizing the sequential conjunction operator of standard dynamic semantics. I argue that this approach captures the tight empirical connection between pair-lists and internal adjectives, and at the same time provides a simpler and more robust account of the data than the specialized alternatives.