Many epistemologists call themselves ‘fallibilists’. But many philosophers of language hold that the meaning of epistemic usages of ‘possible’ ensures a close knowledge- possibility link : a subject’s utterance of ‘it’s possible that not-p’ is true only if the subject does not know that p. This seems to suggest that whatever the core insight behind fallibilism is, it can’t be that a subject could have knowledge which is, for them, possibly false. I argue that, on the contrary, subjects can have such possibly false knowledge. My ultimate aim, then, is to vindicate a very robust form of fallibilism. Uniquely, however, the account I offer does this while also allowing that concessive knowledge attributions – sentences of the form “I know that ...