Philosophers who have taken an interest in linguistics have generally been prepared to accept linguists' assumptions about the potential usefulness of generative grammars in explaining human grammatical competence. Rather than follow the radical opponents of formal linguistics, who object to the whole idea formalized syntactic description, philosophers of linguistics debate specific controversial points (tacit knowledge; rule-following; the relation of language and mind) while accepting the presupposition that generative theorizing is reasonable as an account of linguistic phenomena. This talk focuses on some of the fundamental predictions that any generative theory inevitably entails, and argues that those entailments are often problematic -- for explicit structural description, cross-linguistic structural comparability, grammaticality judgments, language acquisition, linguistic diversity, fragment intelligibility, error tolerance, sentence production, and utterance processing. I outline and discuss a radically different alternative mode of formalizing syntactic theories which yields more plausible theoretical claims about human languages.