Degrees of Countability: A Mereotopological Approach to the Mass/Count Distinction

Most formal semantic treatments of countability aim to account for a binary count/non-count distinction through the use of mereology, or part-structures. This paper discusses data from Welsh, which possesses three categories of grammatical number, distinguishing a collective/singulative class under which fall entity types such as 'collective aggregates' (swarming insects, vegetation) and 'granular aggregates' (sand). I show that standard mereological accounts turn out not to be sufficiently expressive to account for this broader typological data. I then argue that it is necessary to enrich mereology with connection relations that model ways in which the referents of nouns may come together, resulting in the more expressive mereotopology. I show that this extension leads to faithfully modeling the degrees of countability found in Welsh and overcomes well-known problems for classical mereological accounts, e.g., the "minimal parts" problem.