Defeating Objections to Bayesianism by Adopting a Proximal Facts Approach

Abstract

One major line of attack against probabilistic approaches to the philosophy of science has been to argue that certain results of theirs are in conflict with intuitive notions of confirmation. Thus for example, some have suggested not only that the Hempelian raven paradox1 counts against standard, preprobabilistic notions of scientific confirmation but also that it demonstrates a problem with approaches based on confirmation theory: since P(nonblack object being a nonraven|all ravens are black) is 1, it follows from Bayes’s theorem that the observation of a nonblack nonraven constitutes evidence that all ravens are black.2 Those who find the raven paradox persuasive, and who retain their intuition that such an observation does not even slightly confirm the black raven thesis, ought to find this a compelling argument against Bayesianism, for the probabilistic account contradicts the ostensible commonsense intuition. Others see this as a strength of Bayesianism— that Bayesianism accepts the otherwise plausible equivalence condition3 yet also accounts for the fact that we do not hold such observations to significantly confirm the black raven thesis. The reason for this is that the probability of a nonblack object being a nonraven given that not all ravens are black is trivially close to 1, even though it is not 1. This means that the observation— a nonblack nonraven— is to be expected with a high degree of probability regardless of whether all ravens are black. So the increase in the epistemic probability of the black raven thesis is negligible.