Published online by Cambridge University Press: 10 August 2017
I discuss the role of religious experience in Richard Swinburne's probabilistic case for theism. Swinburne draws on his principle of credulity to argue that, if in addition to other evidence we consider that many people have theistic religious experiences, theism comes out as more probable than not. However, on many plausible probability assignments for the relevant non-experiential evidence, the conditional probability of theism already converges towards 1. Moreover, an argument analogous to a general Bayesian argument against phenomenal conservatism suggests that, after we take account of evidence from religious experience, the probability of theism cannot be greater than the prior probability that the best rival hypothesis is false. I conclude that these observations are compatible with what Swinburne would call ‘weak rational belief’ in theism and that such weak belief can be strong enough for rational faith.