The basis for any theory of syntactical categories is the linguistic fact that in all natural languages there are strings of (one or more) words which are mutually interchangeable in all well-formed contexts salva beneformatione—that is, with well-formedness (grammaticality, syntactical correctness) being preserved in the interchange—and that there are innumerable other strings which do not stand in this relation. Any theory of semantical categories rests on a similar fact, with well-formed replaced by meaningful or semantically correct, and beneformatione by significatione.

The relation between well formed and meaningful is, in general, complex, and neither term is simply reducible to the other. The English expression "Colorful green ideas sleep furiously" (to use an example given by Noam Chomsky) is, at least prima facie, syntactically well formed. Yet it is semantically meaningless, even though certain meanings can be assigned to it by...