An Objective Justification of Bayesianism I: Measuring Inaccuracy

One of the fundamental problems of epistemology is to say when the evidence in an agent's possession justies the beliefs she holds. In this paper and its sequel, we defend the Bayesian solution to this problem by appealing to the following fundamental norm: ACCURACY An epistemic agent ought to minimize the inaccuracy of her partial beliefs. In this paper, we make this norm mathematically precise in various ways. We describe three epistemic dilemmas that an agent might face if she attempts to follow Accuracy, and we show that the only inaccuracy measures that do not give rise to such dilemmas are the quadratic inaccuracy measures. In the sequel, we derive the main tenets of Bayesianism from the relevant mathematical versions of Accuracy to which this characterization of the legitimate inaccuracy measures gives rise, but we also show that unless the requirement of Rigidity is imposed from the start, Jerey conditionalization has to be replaced by a different method of update in order for Accuracy to be satisfied.