I develop a general framework with a rationality constraint that shows how coherently to represent and deal with second-order information about one's own judgmental reliability. It is a rejection of and generalization away from the typical Bayesian requirements of unconditional judgmental self-respect and perfect knowledge of one's own beliefs, and is defended by appeal to the Principal Principle. This yields consequences about maintaining unity of the self, about symmetries and asymmetries between the first- and third-person, and a principled way of knowing when to stop second-guessing oneself. Peer disagreement is treated as a special case where one doubts oneself because of news that an intellectual equal disagrees. This framework, and variants of it, imply that the typically stated belief that an equally reliably peer disagrees is incoherent, and thus that pure rationality constraints without further substantive information cannot give an answer as to what to do. The framework also shows that treating both ourselves and others as thermometers in the disagreement situation does not imply the Equal Weight view.

This paper addresses two examples due to Peter Achinstein purporting to show that the positive relevance view of evidence is too strong, that is, that evidence need not raise the probability of what it is evidence for. The first example can work only if it makes a false assumption. The second example fails because what Achinstein claims is evidence is redundant with information we already have. Without these examples Achinstein is left without motivation for his account of evidence, which uses the concept of explanation in addition to that of probability.