Abstract

Chapter 13 turns to _diachronic_ constraints on the rational probability function—constraints that the thinker’s _past_ beliefs impose on which probability functions can be in the set that represents the opinions of the “evaluating angel”. Some philosophers—such as Brian Hedden—object that the idea of such diachronic constraints is inconsistent with internalism about rationality. These objections are answered here. It seems clear that the past continues to exert an influence over the present. This lingering influence of the thinker’s past beliefs will be referred to as the “doxastic shadow” that those past beliefs cast into the present. The angel will be guided by this shadow in the following way: first, she will find the “shadow priors”—the probability functions that, of all those that meet all the synchronic constraints, are _closest_ to this doxastic shadow. Then the probability functions that constitute the angel’s opinions are those that result from _conditionalizing_ these shadow priors on the facts that are “given” to the thinker now. This chapter ends with a proposal about what explains why this view of diachronic rationality is correct.