An Epistemic Puzzle About Knowledge and Rational Credence

ABSTRACT I present some puzzling cases regarding knowledge and its relation to rational credence. They seem to entail a failure of an apparently correct principle: (a) if S knows P, then the epistemic justification S has for believing Not-P is not greater than her epistemic justification for believing P. The cases at issue involve the following two conflicting facts, relative to a given subject S and a proposition P in a determinate context. Firstly, some people have a very strong intuition that: (b) S has perceptual knowledge of P. Secondly, all of us, when reflecting on the relevant data, have a very strong intuition for this other thesis: (c) the epistemic justification S has for believing Not-P is much greater than her epistemic justification for believing P. The cases seem to be instances of the base-rate fallacy, so that—apparently—the subject would be irrational if she believed proposition P. My main aim here is to present the puzzle. But, I also provide a solution for it that preserves thesis (b) without renouncing Bayesian epistemology, which is the basis for thesis (c).