Evidentialism, Inertia, and Imprecise Probability

There is growing interest in imprecise probabilities as a means of representing doxastic states like belief and uncertainty. A key question is how we should update these probabilities when we discover new evidence. We can only answer this question with reference to some broader epistemological theses. One in particular that has been utilized in these debates is evidentialism, which claims that our doxastic states should reflect our evidence—and nothing more. Yet, from an evidentialist point of view, there is a problem with the standard way of updating imprecise probabilities, called ‘inertia’: we seem to either underweight almost all types of evidence or else abandon evidentialism.

Thus far, these debates on inertia have mostly focused on updating imprecise probabilities by a version of conditionalization. In contrast, I consider the issue using Kyburg's system of imprecise probability, where conditionalization occurs only as a special case. I provide the first detailed discussion of the circumstances under which Kyburg's system avoids inertia, which I reveal to be very broad. I also argue for its general compatibility with evidentialism. I close with an irenic point: his system and the standard ‘imprecise Bayesianism’ are not entirely rivalrous. At least from the Kyburgian side, there are computational virtues of imprecise Bayesianism that mean it might often be the best way to revise our beliefs as we acquire new evidence.