Number and individuation [electronic resource]
Keywords: Linguistics

This dissertation investigates the semantic foundations of nominal countability. Standard accounts are typically concerned with a binary distinction between countable words (`dog'/`dogs') and non-countable words (`water'). This dissertation examines this issue from the perspective of languages with richer grammatical number systems. I develop a typological generalization that countability is a scalar phenomenon and propose new techniques to formally model these facets of nominal semantics by augmenting standard mereological accounts with topological relations. Languages such as Welsh or Maltese grammatically recognize what I call aggregate nouns--nouns which designate entities that habitually come together, such as insects (ants) or granular substances (sand). These nouns are grammatically distinct from both non-countable nouns and countable nouns with a singular/plural contrast, instead they display a collective/singulative contrast. These grammatical number systems vividly demonstrate how a binary countable/non-countable distinction oversimplifies the typological space. I argue from the data from Welsh and Maltese, and even more complex fieldwork data from the Gur language Dagaare, that countability is a scalar phenomenon. I propose that the morphosyntactic organization of grammatical number systems reflects the semantic organization of noun types according to the degree of individuation of their referents. Nouns of different types are individuated to different degrees and can accordingly be ordered along a scale of individuation: substances < granular aggregates < collectives < individual entities. Noun types which are less individuated are on the lower end of the scale and are cross-linguistically less likely to signal grammatical number, while the converse holds for highly individuated noun types. Understanding morphosyntactic number categories in light of a scale of individuation avoids the difficulties binary accounts face, since languages may divide up the scale of individuation into any number of classes and at different points. For instance, languages with a collective/singulative recognize a grammatical number category corresponding to the middle region of the scale. At the same time, the proposal provides a predictive framework for how grammatical number systems are organized: the contrasts being made are common across languages, and, as a corollary, the endpoints of the scale (substances and individual entities) are predicted to be stable across languages. I show that this view of countability also answers many of the standard criticisms of accounts where a noun's meaning determines its grammatical behavior with respect to number marking. I explore the implications of this broader typological view for formal semantic treatments of countability. Standard mereological accounts turn out to be not sufficiently expressive to model the aggregate nouns nor the grammatical number systems which distinguish them. I enrich the standard mereology framework with topological connection relations, resulting in the more expressive ``mereotopology". Through using different connection relations, this framework is able to represent aggregate nouns and the ways in which entities may come together. Consequently, this framework is able to deliver analyses of particular grammatical number systems, such as Welsh. In addition, this more expressive framework resolves several recalcitrant problems noted for many treatments of countability, such as the ``minimal parts" problem discussed in relation to nouns such as `sand' or `furniture' which, while non-countable, still have minimal pieces.