A unified semantics for distributive and non-distributive universal quantifiers across languages.

Universal quantifiers differ in whether they are restricted to distributive interpretations, like English , or permit non-distributive interpretations, like English . This interpretational difference is traditionally captured by positing two unrelated lexical entries for distributive and non-distributive quantification. But this lexical approach does not explain why distributivity correlates with number: cross-linguistically, distributive universal quantifiers typically take singular complements, while non-distributive quantifiers consistently take plural complements. We derive this correlation by proposing a single lexical meaning for the universal quantifier, which derives a non-distributive interpretation if the restrictor predicate is closed under sum, but a distributive interpretation if it is quantized. Support comes from languages in which the same lexical item expresses distributive or non-distributive quantification depending on the number of the complement. For languages like English that have different expressions for non-distributive and distributive quantification, we propose that the distributive forms contain an additional morphosyntactic element that is semantically restricted to combine with a predicate of atomic individuals. This is motivated by the fact that in several languages, the distributive form is structurally more complex than the non-distributive form and sometimes even contains it transparently. We further show that in such languages, there are empirical advantages to taking the choice between distributive and non-distributive quantifier forms to be driven by semantic properties of the restrictor predicate, rather than morphosyntactic number.