Explanationist constraints on rational degrees of belief

In this paper I counter Alexander Bird's claim that Bayesian probabilities ought to be informed by explanatory considerations.Bird (2022) invokes an argument of Michael Huemer to conclude that inductive inference requires explanatory constraints on prior probabilities.I suggest that this argument is unsuccessful, on account of its appeal to David Lewis' Principal Principle.Bird goes on to interpret the probabilities in Bayes' theorem other than the prior as a measure of how well a hypothesis explains the evidence.I show that this interpretation faces a new version of the old evidence problem.1 This paper adopts the standard conventions that P is an epistemic probability function, i.e., a function that represents an agent's rational degrees of belief, ( | ) denotes conditional probability, is total evidence and is some hypothesis of interest.The negation of a proposition A will be denoted by .'Prior' probabilities are probabilities assigned before the evidence is obtained.(|) is the 'posterior' probability of , i.e., the probability of in the light of evidence .