Forthcoming in Noûs. Penultimate version. Credal dilemmas

Formal epistemologists traditionally model rational states of partial belief with probability measures, functions that map each proposition to a single real number. But many have recently rejected this model as excessively precise. Sometimes your evidence for a certain claim is unspecific. And many have argued that the rational response to unspecific evidence is to have credences that are imprecise, represented not by a single probability measure but by a set of measures.2 However, fans of imprecise credences face a formidable challenge, namely providing a decision theory that protects agents who follow it from forgoing sure money. Agents with imprecise credences seem doomed to act irrationally when faced with diachronic decision problems, where they are called to make decisions at earlier and later times.3 In this paper, I aim to respond to this challenge on behalf of imprecise credence fans. In fact, we have subtle and variegated intuitions about what actions are rational in various diachronic cases. Once we appreciate the complexity of these intuitions, we can see that diachronic cases are in fact evidence for the claim that agents have imprecise credences. In §1, I briefly make the case for accepting that agents have imprecise credences. In §2, I explain the case against imprecise credences in more detail. In §3, I investigate our intuitions about norms governing agents who act as though they are torn between different precise credal states. These agents face credal dilemmas, epistemic analogs of moral dilemmas. I argue that recognizing the strong similarities between moral and credal dilemmas is a desideratum for any theory of