The Mereological Structure of Distributivity: A Case Study of Binominal Each

Binominal each is known to exhibit selectional requirements on the noun phrase that immediately precedes it. The goal of this paper is to reduce these selectional requirements to a single requirement of monotonic growth of measurement in relation to the ‘size’ of distributivity. More concretely, it is argued that binominal each imposes a constraint on the functional dependencies arising from distributive quantification, requiring that the measurement of its host grows monotonically with the number of values being distributively quantified. To make constraints on dependencies formally explicit, I devise a version of dynamic plural logic with features from van den Berg (1996) and Brasoveanu (2008, 2013) to semantically represent dependencies arising from evaluating distributive quantification. The use of a dynamic logic, coupled with a delayed evaluation mechanism in terms of higher order meaning (Cresti 1995, de Swart 2000, Charlow, to appear), allows the constraint to act as an output context constraint on distributive quantification, which mirrors the use of output constraints pioneered by Farkas (1997, 2002b) and and further developed in Brasoveanu (2013), Henderson (2014) and Kuhn (2017).