Grammar without Grammaticality

A key intellectual advance in 20th-century linguistics lay in the realization that a typical human language allows the construction not just of a very large number of distinct utterances but actually of infinitely many distinct utterances. However, although languages came to be seen as non-finite systems in that respect, they were seen as bounded systems: any particular sequence of words, it was and is supposed, either is wellformed or is not, though infinitely many distinct sequences are each wellformed. I believe that the concept of “ungrammatical” or “ill-formed” word-sequences is a delusion, based on a false conception of the kind of thing a human language is.