If knowing requires believing on the basis of evidence that entails what’s believed, we have hardly any knowledge at all. Hence the near-universal acceptance of fallibilism in epistemology: if it's true that "we are all fallibilists now" (Siegel 1997: 164), that's because denying that one can know on the basis of non-entailing evidence1is, it seems, not an option if we're to preserve the very strong appearance that we do know many things (Cohen 1988: 91). Hence the significance of concessive knowledge (...) attributions (CKAs) (Rysiew 2001)—i.e., sentences of the form 'S knows that p, but it's possible that q' (where q entails not-p). To many, utterances of such sentences sound very odd indeed. According to David Lewis (1996: 550), however, such sentences are merely "overt, explicit" statements of fallibilism; if so, their seeming incoherence suggests that, contrary to our everyday epistemic pretensions, "knowledge must be by definition infallible" after all (ibid.: 549). -/- Recently Jason Stanley (2005) has defended fallibilism against the Lewisian worry that overtly fallibilistic speech is incoherent. According yo Stanley, CKAs are not just odd-sounding: in most cases, they are simply false. But this doesn't impugn fallibilism. Insofar as the odd-sounding utterances Lewis cites state the fallibilist idea, the latter portion thereof ('S cannot eliminate a certain possibility in which not-p', e.g.) expresses the idea that the subject's evidence doesn't entail what's (allegedly) known (hence, the negation of any contrary propositions). According to Stanley, however, this is not the best reading of the possibility clauses CKAs contain. On the correct account of the latter, while the sentences Lewis cites are almost always self-contradictory, they don't capture the fallibilist idea after all. Here, we argue that the sentences in question do express precisely the fallibilist idea, but argue that Lewis has nonetheless failed to raise a problem for the latter. In addition, we respond to worries that the resulting view of the semantics of epistemic possibility statements has certain unacceptable consequences. (shrink)