Counting and the Mass/Count Distinction

This paper offers an account of the semantics of count nous. I show that neither the atomic/nonatomic distinction nor the homogeneous/non-homogeneous distinction is sufficient to explain the semantic contrast between mass and count nouns, since there are mass nouns which are atomic, and there are count nouns which are homogeneous. Starting from a version of Chierchia's 1998a account of the semantics of mass nouns under which the mass and count domains are atomic, I show that the denotation of singular count nouns is derived via a measure operation which picks out sets of non-overlapping entities which count as one by a recoverable unit of measurement. These entities I call 'semantic atoms'. Since the choice of unit of measurement may be context dependent, the denotation of a count noun may be context dependent too. Grammatical operations, including, but not restricted to, counting require access to sets of semantic atoms, thus count nouns but not mass nouns can be directly modified by numerals. A third relevant notion of atomicity, to be distinguished from both formal and semantic atomicity, is natural atomicity. This is a (gradable) property of predicates which denote entities which (usually) come in inherently individuable units. The derivation of count nouns may make use of natural atomic structure, but this is not necessary. As Barner and Snedeker 2005 show, mass nouns as well as count nouns may be naturally atomic.