Imprecise Evidence without Imprecise Credences

A traditional theory of uncertainty says that beliefs come in degrees. Degrees of belief (“credences”) have real number values between  and , where  conventionally represents certain belief,  represents certain disbelief, and values in between represent degrees of uncertainty. We have elegant, well-understood normative theories for credences: norms for how credences should hang together at a time, how they should change in response to new evidence, and how they should influence our preferences. Many have argued, against the traditional theory, that rational subjects have imprecise credences. Instead of sharp, real number values like ., rational agents have credences that are spread out over multiple real numbers, e.g. intervals like [., .]. ere are descriptive and normative versions of the view. e descriptive (psychological) version argues that humans’ cognitive capacities don’t allow for infinitely sharp credences. In creatures like us, there’s no genuine psychological difference between having credence . and credence .. So we are better represented with imprecise credences.1 e normative (epistemic) version argues that even idealized agents without our cognitive limitations shouldn’t have sharp credences. Epistemic rationality sometimes demands imprecise credences.2 is paper concerns the latter view. e former view seems to me correct, as a matter of psychological fact. Creatures like us are probably better represented by some imprecise credence model or other. But this doesn’t tell us much about epistemology. Epistemic theories of imprecise credences say that, for evidential reasons, it can be irrational to have precise credences. ese theories typically represent ideal rationality in ways that go far beyond human cognitive capacities. is paper concerns, instead, the nature of epistemic norms.3 Does rationality require imprecise credences? Manyhold that it does: imprecise evidence requires correspondingly