Theories in the cognitive science of religion (CSR) are sometimes seen as debunking religious or supernatural beliefs (SBs). To date, arguments have been produced by proponents on both sides, with some claiming that debunking would result and others claiming that it would not. In this paper, I depart from the approach taken by others and offer an approach based in broadly Bayesian methods of updating subjective probability assignments, including classical Bayesian formulas as well as comparative ratios and Jeffrey conditionalization. I (...) argue that debunking may take place, but only if specified conditions are met. One way to show that debunking takes place would be to show that the probability of some CSR theory naturalistically explaining SBs diminishes when it is postulated that SBs have epistemic warrant. Another alternative would be to show that CSR theories are less likely to succeed in explaining the origin of SBs if SBs have warrant than if they lack warrant. It can also be helpful to consider the role played by uncertain and even ineffable judgments. Either way, debunking SBs does not follow simply from CSR but must be considered in light of prior epistemic commitments and the role they play in evaluating probabilities. (shrink)