Abstract

Is knowledge consistent with literally any credence in the relevant proposition, including credence 0? Of course not. But is credence 0 the only credence in p that entails that you don’t know that p? Knowledge entails belief (most epistemologists think), and it’s impossible to believe that p while having credence 0 in p. Is it true that, for every value of ‘x,’ if it’s impossible to know that p while having credence x in p, this is simply because it’s impossible to believe that p while having credence x in p? If so, is it possible to believe that p while having (say) credence 0.4 in p? These questions aren’t standard epistemological fare, at least in part because many epistemologists think their answers are obvious, but they have unanticipated consequences for epistemology. Let ‘improbabilism’ name the thesis that it’s possible to know that p while having a credence in p below 0.5. Improbabilism will strike many epistemologists as absurd, but careful reflection on these questions reveals that, if improbabilism is false, then all of the most plausible theories of knowledge are also false. Or so I argue in this paper. Since improbabilism is widely rejected by epistemologists (at least implicitly), this paper reveals a tension between all of the most plausible theories of knowledge and a widespread assumption in epistemology.