Hinge epistemology and Bayesianism are two prominent approaches in contemporary epistemology, but the relationship between these approaches has not been systematically studied. This paper formalizes the central commitments of hinge epistemology in a Bayesian framework and argues for the following two theses: (1) many of the types of claims that are treated as paradigmatic hinges in the hinge epistemology literature, such as the claim that there exists an external world of physical objects, are not capable of enabling rational inquiry, even (...) though this is typically regarded as a central property of hinges; (2) the standard Bayesian story of how rational inquiry proceeds is incorrect or at best incomplete. (shrink)