I've been thinking about whether a Bayesian can make sense of the concept of pro tanto epistemic reasons. The idea is that p gives us a reason to believe q, though in the light of our full evidence it may no longer support q. In other words, the idea is that p is pro tanto evidence for q there is a reduced set of evidence relative to which p supports q.
But on a Bayesian picture it can't be just any reduced set of evidence, or else we have too many pro tanto reasons. Let p be the proposition that the sky looks blue and q be the proposition that the sky is red. Let r be some exceedingly unlikely fact, say the fact that when I asked random.org to generate a sequence of 16 random bytes, it generated 52 e2 57 4d 6d 16 c9 dd 12 9e b4 63 27 7e 86 53. Then I believe that (p&~r)→q, where the conditional is material. I believe it, because I believe the antecedent to be false. But if my background consists only of (p&~r)→q, then given reasonable priors p strongly supports q.
So what we want, I think, is to say that p is pro tanto evidence for q provided that there is a privileged reduced set of evidence relative to which p supports q. But what reduced sets of evidence are privileged? There is only one such set that stares one in the face: the empty set. So, the suggestion is: p is pro tanto evidence for q if and only if p supports q relative to an empty background, i.e., according to the absolute priors.
This, I think, offers a way to make some progress on the problem of priors. If we have independent sufficient conditions for something to be a pro tanto reason, then we have a constraint on our absolute priors, namely that if p is pro tanto evidence for q, then P(p & q) > P(p)P(q).
Could we have some such independent sufficient conditions for pro tanto reasons? I think so. For instance, around here, Trent Dougherty has been pushing phenomenal conservatism, which can be taken to be the view that seemings are pro tanto reasons for their contents. If the above Bayesian account of pro tanto reasons is correct, then this puts a constraint on prior probabilities, and that's a good thing.