Degree-of-belief and degree-of-support: Why Bayesians need both notions

Abstract

I argue that Bayesians need two distinct notions of probability. We need the usual degree-of-belief notion that is central to the Bayesian account of rational decision. But Bayesians also need a separate notion of probability that represents the degree to which evidence supports hypotheses. Although degree-of-belief is well suited to the theory of rational decision, Bayesians have tried to apply it to the realm of hypothe- sis confirmation as well. This double duty leads to the problem of old evidence, a problem that, we will see, is much more extensive than usually recognized. I will ar- gue that degree-of-support is distinct from degree-of-belief, that it is not just a kind of counterfactual degree-of-belief, and that it supplements degree-of-belief in a way that resolves the problems of old evidence and provides a richer account of the logic of scientific inference and belief.