The Principle of Credulity: 'It is basic to human knowledge of the world that we believe things are as they seem to be in the absence of positive evidence to the contrary' [Swinburne 1996: 133]. This underlies the Evidential Problem of Evil, which goes roughly like this: ‘There appears to be a lot of suffering, both animal and human, that does not result in an equal or greater utility. So there's probably some pointless suffering. As God's existence precludes pointless suffering, (...) theism is implausible.’ CORNEA is the principle that observation O raises hypothesis H's probability only if O is more probable given H than it is given not-H. Theists sometimes maintain that apparently pointless suffering is just as likely given theism as atheism (I support this claim by appealing to a Lewisian account of the relevant counterfactuals). Given CORNEA, therefore, what we see of suffering does not make theism unlikely. I maintain that a consequence of so deploying CORNEA is that CORNEA and the Principle of Credulity are incompatible. We are left with a skeptical paradox. CORNEA is a consequence of Bayes’s Theorem, I argue; but it is incompatible with a presupposition of empirical science, namely, that appearances create epistemic warrant, ceteris paribus. External-world probability skepticism follows. I treat the paradox as real. First, I offer an account of how we strike a balance in practice between CORNEA, on the one hand, and the Principle of Credulity and the scientific enterprise on the other. Second, I try to resolve the paradox outright by rejecting the Principle of Credulity and maintaining that the scientific project remains well motivated even allowing probability skepticism. On either response to the paradox, the Evidential Problem of Evil continues to have serious, but defeasible, force against theism. (shrink)