Gnosticism and Inexact Knowledge

Gnostic consequentialism holds that a belief is rational just in case it is sufficiently likely to constitute knowledge. I show that this view makes implausible dynamic predictions when combined with the most influential models of the “inexact knowledge” we have in cases involving imprecise measurement or repeated chance processes. These models, built on the idea that such knowledge requires a margin for error, allow that one can have “improbable knowledge,” that is, that one can know something even though it is unlikely (given one's evidence, or given how one's belief was formed) that one knows it. I show that the problems can be alleviated by rejecting this idea, but that this may force us to deny that inexact knowledge requires a margin for error. I leave open how we should respond to this dilemma.