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Objective Bayesian Calibration and the Problem of Non-convex Evidence

Jon Williamson's Objective Bayesian Epistemology relies upon a calibration norm to constrain credal probability by both quantitative and qualitative evidence. One role of the calibration norm is to ensure that evidence works to constrain a convex set of probability functions. This essay brings into focus a problem for Williamson's theory when qualitative evidence specifies non-convex constraints. 1 Formal Preliminaries 2 A Definition without a Procedure 3 Independence and Epistemic Relevance 4 Conclusion 1 Formal Preliminaries 2 A Definition without a Procedure 3 Independence and Epistemic Relevance 4 Conclusion