Is there anything characteristic about the meaning of a count noun?

In English, some common nouns, like "cat", can be used in the singular and in the plural, while others, like "wate"r, are invariable. Moreover, nouns like "cat" can be employed with numerals like "one" and "two" and determiners like "a", "many" and "few", but neither with "much" nor "little". On the contrary, nouns like "milk" can be used with determiners like "much" and "little", but neither with "a", "one" nor "many". These two types of nouns constitute two morphosyntactic sub-classes of English common nouns; cf. for instance Gillon (1992). They have been respectively called count nouns and mass nouns. In many languages, notably Romance and Germanic languages, one can similarly identify two morphosyntactic subclasses of common nouns, nouns of one class admitting singular and plural number, and nouns of the other being invariable in grammatical number. The question we want to address in this paper is one in lexical semantics: Is there anything characteristic about the meaning of a count noun?