Counting and the mass/count distinction

This article offers an account of the mass/count distinction and the semantics of count nouns, and argues that it is not based on an atomic/non-atomic nor on a homogeneous/non-homogeneous distinction. I propose that atomicity in the count domain is atomicity relative to a context k, where k is a set of entities that count as atoms (i.e. count as one) in a particular context. Assuming for simplicity Chierchia's (1998a) and Rothstein's (2004) theory of mass nouns, in which they denote atomic Boolean semi-lattices closed under the complete join operation, we define an operation COUNT_k that applies to the mass noun denotation N_mass and derives the count noun 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 the operation applied. So, there is a typal distinction between mass nouns, which are of type <d,t >, and count nouns, which are of type <d×k, t >. The grammatical differences between count and mass nouns follow from this typal distinction. This allows us to encode grammatically the distinction between semantic atomicity, that is, atomicity relative to a context k, and natural atomicity, that is, inherent individuability. We show a number of ways in which this distinction is grammatically relevant.