The Semantics of Count Nouns

Abstract

We offer an account of the semantics of count nouns based on the observation that for some count nouns, the set of atoms in the denotation of the singular predicate is contextually determined. We derive the denotation of singular count nouns relative to a context k, where k is a set of entities which count as atoms in a particular context. An operation COUNTk applies to the mass noun denotation Nmass and derives the count meaning: a set of ordered pairs <d,k> where d is a member of N ∩ k and k is the context k relative to which d counts as one. Count nouns and mass nouns are thus typally distinct and the grammatical differences between them follow from this. We distinguish between naturally atomic predicates, which denote sets of inherently individuable entities or boolean algebras generated from such sets, and semantically atomic predicates, which denote sets which are atomic relative to a particular context k. This distinction is shown to be orthogonal to the mass count distinction.