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 well-formed or is not, though infinitely many distinct sequences are each well-formed. 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.
In order to give an intuitive sense of the conception which I believe ought to replace it, let me quote the remark sometimes made by hail-fellow-well-met types: “There are no strangers, only friends I haven’t met yet” – that is, rather than the world being divided into two sorts of people with respect to our mutual relationships, namely friends and strangers, inherently all people are of the same friendly sort, though in a finite lifetime one has the chance to establish this only for a subset of them. Whether or not this is a good way of thinking about human beings, I believe it is a good way of thinking about word-sequences.
The point of view I am arguing against was put forward (for the first time, so far as I know) almost fifty years ago, by Noam Chomsky in Syntactic Structures:
The fundamental aim in the linguistic analysis of a language L is to separate the grammatical sequences which are the sentences of L from the ungrammatical sequences which are not sentences of L and to study the structure of the grammatical sequences. (Chomsky 1957: 13)
After this principle was stated in 1957, it quickly became central to much of what happened in theoretical linguistics, and it continues to be so. With respect to the recent period, I am not in a...