General-linguistic datasets that have become available in recent years promise to enable new progress toward a theory of general grammar. A barrier to success is the incompatibility between the inductive, externalist approach that is natural for exploiting the datasets and the deductive, mentalist philosophy that is currently dominant within linguistics. I argue that the externalist philosophy is viable and that there are reasons to consider it preferable. I argue that the mainstream approach is in some cases unnecessarily concerned with psychological reality, and in other cases too quick to reject required subtheories on the grounds that they belong to “language processing” rather than linguistics, with the result that current grammars give systematically inaccurate answers to questions of the linguistic status of sentences. I suggest that the inductive development of general grammar is already being carried out (though not in those terms) in the field of natural language processing, and that linguistic participation in the effort would be of benefit to both fields.