Vagueness, Overlap, and Countability1

We propose a novel semantic analysis of the mass/count distinction, within a new framework combining the theory of mereology with Probabilistic Type Theory with Records, Prob-TTR (Cooper et al. 2014)). While the notions akin to VAGUENESS (Chierchia 2010) and OVERLAP (Landman 2011) are needed to ground this distinction, neither on its own is sufficient to accommodate the whole range of data, especially the puzzling intraand crosslinguistic variation in count vs. mass encoding. This variation becomes tractable, if we generally treat the grammatical differences between mass and count nouns as following from the interaction of two notions: namely, VAGUENESS sharpened in terms of graded (probabilistic) type judgements, and DISJOINTNESS relative to a probability threshold. As a result, in the form-denotation mappings, this leads us to a novel semantic classification of nouns into four classes. The mass/count distinction is a bipartite grammatical distinction manifested in the standard diagnostics like a direct combination with numerals, the indefinite article and quantifiers like every, much, among others.