A categorical view of nouns in their semantical roles

Abstract

Prototypical CNs and MNsAll 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 ofCns is "dog" and of MNs is "matter" (in the sense of physical stulf). One syntactic difference is that CNs take the plural ('dogs') whereas MNs do not. Other syntactic dis¬ tinctions 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 Jespersen (1924, p. 198).Languages differ in morphology, agreement rules and phrase structure, so one does not expect to find in every natural languages a count/mass distinction with the same linguistic correlates as in English. While many European languages are like English in this connection, not all are. Irish and Latin, for example, lack the ¡definite article, and so one cannot distintiguish CNs from MNs in those languages by the possibility or impossibility of adding the inde¬ finite article to the noun. If we inquire what guides linguists to the decision that there are a count/ mass distinction in languages, the answer cannot simply be grammar. Grammar varies greatly from language to language. Something other than grammar must be contributing to the decision. We submit that the type of reference for prototypical words plays a major role. We think that across variations in grammar there is a semantic uniformity in the interpretation of at least such prototypical nouns as the counterparts of dog and matter and that this semantic uni¬ formity is a good guide to the relevant grammatical facts in each language. We propose to exploit the semantic uniformity as far as possible.This To discuss reports from these subcommittees, a committee of the whole C' is created. This new committee differs from C because the minutes will record all the transactions of C but omit those of C'. This shows that conceptually, C' is different from C. We regard C and C' as "for¬ mal' sups of A and B, a notion to be clarified in a forthcoming paper Besides these examples there are others such as quantity of matter which are important when dealing with functors among the categories of the nominal theory.We interpret the nominal theory as follows: CNs are interpreted as situated sets (or kinds), namely, families of subsets of a given set indexed by situations. A subset indexed by a situation consists of all the members of the given set which are constituent of that situation. Situations are assumed to be pre-ordered by the relation of'having more information' (not to be confused with temporal order), and hence there are obvious connections between the subsets of the family. Morphisms between CNs are interpreted as situated maps, i.e., set-theoretical maps pre¬ serving the relation of constituents of a situation into members of another set which are cons¬ tituents of the same situ...