Incremental quantification and the dynamics of pair-list phenomena

Abstract

Distributive universals are unique among natural language quantifiers 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 readings not previously recognized as such, and internal readings of comparative adjectives as two sides of the same coin; they are both side effects of incremental 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.

A pragmatic explanation of the mei-dou co-occurrence in Mandarin

“…In English only genuine distributive universals license sentence-internal readings of singular different (Carlson 1987 ; Brasoveanu 2011 ; Bumford 2015 ). We observe in Mandarin these readings are easily found with mei - dou but are hard to obtain with definite- dou , and thus the former but not the latter make good candidates for true universals.…”

“…Second, sentence-internal readings of singular different involve quantifier/distributivity-internal anaphora, in the sense that the distributive universal could introduce two discourse referents within its nuclear scope (Brasoveanu 2011 ; Bumford 2015 ), the values of which are needed for the evaluation of a sentence-internal singular different . Internal interpretations of certain comparatives also belong to this category and are only permitted when under a distributive universal (Beck 2000 ; Brasoveanu 2011 ; Bumford 2015 ). This is again true in Mandarin.…”

“…Indeed, singular different according to Brasoveanu ( 2011 ) is a distributivity-dependent item and can be used to reveal the nature of the distributivity it is associated with. Without going into the technical details of modeling different varieties of distributivity/quantification (see Brasoveanu 2011 and Bumford 2015 for implementations in dynamic semantics), the contrast suggests that mei but not dou contributes the kind of universal quantification/distributivity English every conveys, and thus is the prime candidate for universal quantifier in Mandarin.…”

Where is the destructive update problem?

“…A related approach replaces assignments with sequences of individuals, updated via a monotonic operation like sequence extension, as in (11), where 'e y' is the sequence e extended with the individual y. Proposals along these lines have been discussed by Vermeulen (1993Vermeulen ( , 1995, Dekker (1994), Groenendijk, Stokhof & Veltman (1996), Bittner (2001), van Eijck (2001), de Groote (2006, Nouwen (2007), Brasoveanu (2007), Charlow (2014, Bumford (2015), Nouwen et al (2016), and others. 3 λe.…”

Than clauses as embedded questions

“…A than-clause-internal quantifier can make a matrix-clause quantifier quantificationally dependent, as in (7). 2 A than-clauseinternal universal can also license a "sentence-internal" reading of different in the matrix subject, as in (8), a reading that is available only in the scope of a distributive universal (for discussion, see Bumford 2015). This scopal behavior falls out naturally from entanglement theories, but not from encapsulation theories.…”