Binominal each and association with the structure of distributivity
Jess Law
January 2022

Binominal each, alongside distributive numerals, has been argued to exhibit an ‘association- with-distributivity’ effect (Champollion 2015, Kuhn 2015, 2017, see also Henderson 2014). In this paper, I show that analyses along these lines fall short of some empirical general- izations established for binominal each, including Counting Quantifier Constraint (Safir and Stowell 1988, Sutton 1993, Szabolcsi 2010) and Extensive Measurement Constraint (Zhang 2013). Instead, I submit that binominal each does not associate with distributivity, but with the internal structure of distributivity, i.e., the internal, mereological structure of the functional dependency induced by distributive quantification. Concretely, it imposes a monotonicity con- straint that the measure function provided by its host should track the part-whole structure of the functional dependency induced by distributivity. Since monotonic measurement typically tracks the part-whole structure of the object being measured (Schwarzschild 2006,Wellwood 2015), this amounts to saying that binominal each measures distributivity, with help from the measure function contributed by its host. The proposal is couched in a version of dynamic plural logic that resembles the original Dynamic Plural Logic in van den Berg (1996) but also incorporates more recent innovations such as domain plurality and delayed evaluation, found in its cousin logic Plural Compositional DRT (Brasoveanu 2006, 2008, 2013).
Format: [ pdf ]
Reference: lingbuzz/004289
(please use that when you cite this article)
Published in: Journal of Semantics (accepted)
keywords: distributivity, dependent numerals, mereology, dynamic semantics, semantics
previous versions: v1 [October 2018]
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