Binominal each measures distributivity

Jess H.-K. Law, Rutgers


Binominal each, alongside distributive numerals, has been argued to exhibit an ‘association-with-distributivity’ effect (Champollion 2015, Kuhn 2015, 2017, see also Balusu 2005, Henderson 2014, Cable 2014). In this paper, I show that analyses along these lines fall short of two empirical generalizations established for binominal each, namely, Counting Quantifier Constraint (Safir and Stowell 1988, Sutton 1993, Szabolcsi 2010) and Extensive Measurement Constraint (Zhang 2013).

  1. Counting Quantifier Constraint
  1. The boys read two books each.
  2. *The boys read the/those books each.
  3. *The boys read books each.
  1. Extensive Measurement Constraint
  1. The angles are 60 degrees each.
  2. *The coffees are 60 degrees each.

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 distributivity. Concretely, it is argued to impose a monotonicity constraint that the measure function provided by its host should track the internal structure of this functional dependency. 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 of its host.

To implement the monotonicity constraint in a compositional manner, a version of dynamic plural logic is offered 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).