Countability: Individuation and Context

Much of the recent countability research agrees on the idea that a satisfactory account of individuation in terms of what counts as “one” unit for counting is highly relevant for characterizing a semantics of the mass/count distinction. (What counts as “one” is not necessarily a formal atom in a Boolean algebra or a natural unit associated with natural kinds like cat.) Taking the most parsimonious stance, our main question is: If we have a full-fledged formal theory of individuation (what counts as “one”), what data would still remain to be explained for a formal theory of the mass/count distinction? Would classical mereology be sufficient to cover such data? And, if not, what minimal extensions would be required to classical mereology to do so? We conclude that, minimally, two dimensions of context sensitivity are needed to enrich a mereological semantics of count nouns denotations. The first kind of context sensitivity enables counting operations to apply by removing overlap from an overlapping set of individuated entities. The second kind of context sensitivity allows us to motivate how a set of individuated entities can sometimes be taken as a counts as “one” despite not being a formal atom or a natural unit associated with a natural kind.