Abstract: Diachronic Dutch book arguments seem to support both conditionalization and Bas van Fraassen’s Reflection principle. But the Reflection principle is vulnerable to numerous counterexamples. This essay addresses two questions: first, under what circumstances should an agent obey Reflection, and second, should the counterexamples to Reflection make us doubt the Dutch book for conditionalization? In response to the first question, this essay formulates a new ‘Qualified Reflection’ principle, which states that an agent should obey Reflection only if he or she is certain that he or she will conditionalize on veridical evidence in the future. Qualified Reflection follows from the probability calculus together with a few idealizing assumptions. The essay then formulates a ‘Distorted Reflection’ principle that approximates Reflection even in cases where the agent is not quite certain that he or she will conditionalize on veridical evidence. In response to the second question, the essay argues that contrary to a common misconception, not all Dutch books dramatize incoherence – some dramatize a less blameworthy sort of epistemic frailty that the essay calls ‘self-doubt’. The distinction between Dutch books that dramatize incoherence and those that dramatize self-doubt cross-cuts the distinction between synchronic and diachronic Dutch books. The essay explains why the Dutch book for conditionalization reveals true incoherence, whereas the Dutch book for Reflection reveals only self-doubt.
Comment: Appropriate for a graduate level philosophy of probability or formal philosophy seminar. It's a useful adjunct to other readings on the reflection principle which has been recently much discussed.