In this paper, I argue that the notion of “best explanation”, as it appears in the Inference to the Best Explanation (IBE), can be defined in terms of explanatory power (EP) (i.e. the best explanation among a set of possible explanations is the one having the highest EP), if we employ a probabilistic measure of EP, which takes into account both the likelihoods and the prior probabilities of the compared explanatory hypotheses. Although the association between the EP of a hypothesis and its likelihood is largely uncontroversial, most of those working on EP do not see an association between EP and the prior probability of an explanatory hypothesis. I provide three examples (two toy examples and one from real scientific practice), in order to show that the role of priors in decisions about the best explanatory hypothesis deserves a serious consideration. I also show that such an explication of “best explanation” allows us to compare IBE and Bayesian confirmation theory (BCT) in terms of the probabilities they assign to two competing hypotheses, and thus to elicit the conditions under which both IBE and BCT lead to the same conclusion and are in this sense compatible.
Bayesian confirmation theory (BCT), Bayesianism, explanatory power, Inference to the Best Explanation (IBE), prior probabilities