Knowledge is standardly taken to be belief that is both true and justified (and perhaps meets other conditions as well). Timothy Williamson rejects the standard epistemology for its inability to solve the Gettier problem. the moral of this failure, he argues, is that knowledge does not factor into a combination that includes a mental state (belief) and an external condition (truth), but is itself a type of mental state. Knowledge is, according to his preferred account, the most general factive mental state. I argue, however, that Gettier cases pose a serious problem for Williamson's epistemology: in these cases, the subject may have a factive mental state that fails to be cognitive. Hence, knowledge cannot be the most general factive mental state.