Count nouns, mass nouns and their transformations: a unified category-theoretic semantics

All natural languages seem to distinguish at the semantic level between count nouns (CNs) and mass nouns (MNs). Some natural languages, like English, mark the distinction at the syntactic level. Prototypical of CNs is ‘dog’ and of MNs is ‘matter’ (in the sense of physical stuff, not in the sense of concern or affair). One syntactic difference is that usually CNs take the plural (‘dogs’) whereas MNs do not. Other syntactic distinctions relate to the determiners and quantifiers. One can say a dog, another dog, many dogs, two dogs, etc.; one cannot correctly say *a matter, *another matter, *many matter, *two matter, etc. It seems that the distinction in English grammar was introduced by Otto Jespersen [6, p198].