(I finally have time to reply; sorry for the long delay.)
Eliezer, one can reasonably criticize a belief without needing to give an exact algorithm for always and exactly computing the best possible belief in such situations. Imagine you said P(A) = .3 and P(notA) = .9, and I criticized you for not satisfying P(A)+P(notA) = 1. If you were to demand that I tell you what to believe instead I might suggest you renormalize, and assign P(A) = 3⁄12 and P(notA) = 9⁄12. To that you might reply that those are most certainly not always the best exact numbers to assign. You know of examples where the right thing to do was clearly to assign P(A) = .3 and P(notA) = .7. But surely this would not be a reasonable response to my criticism. Similarly, I can criticize disagreement without offering an exact algorithm which always computes the best way to resolve the disagreement. I would suggest you both moving to a middle belief in the same spirit I might suggest renormalizing when things don’t sum to one, as a demonstration that apparently reasonable options are available.
(I finally have time to reply; sorry for the long delay.)
Eliezer, one can reasonably criticize a belief without needing to give an exact algorithm for always and exactly computing the best possible belief in such situations. Imagine you said P(A) = .3 and P(notA) = .9, and I criticized you for not satisfying P(A)+P(notA) = 1. If you were to demand that I tell you what to believe instead I might suggest you renormalize, and assign P(A) = 3⁄12 and P(notA) = 9⁄12. To that you might reply that those are most certainly not always the best exact numbers to assign. You know of examples where the right thing to do was clearly to assign P(A) = .3 and P(notA) = .7. But surely this would not be a reasonable response to my criticism. Similarly, I can criticize disagreement without offering an exact algorithm which always computes the best way to resolve the disagreement. I would suggest you both moving to a middle belief in the same spirit I might suggest renormalizing when things don’t sum to one, as a demonstration that apparently reasonable options are available.