Are the grammatical sentences of a language a recursive set?

Many believe that the grammatical sentences of a natural language are a recursive set. In this paper I argue that the commonly adduced grounds for this belief are inconclusive, if not simply unsound. Neither the native speaker's ability to classify sentences nor his ability to comprehend them requires it. Nor is there at present any reason to think that decidability has any bearing on first-language acquisition. I conclude that there are at present no compelling theoretical grounds for requiring that transformational grammars enumerate only recursive sets. Hence, the fact that proposed transformational grammars do not satisfy this requirement does not, as some have claimed, represent a shortcoming in current theory.