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Sometimes appearances provide epistemic support that gets undercut later. In an earlier paper I argued that standard Bayesian update rules are at odds with this phenomenon because they are ‘rigid’. Here I generalize and bolster that argument. I first show that the update rules of Dempster–Shafer theory and ranking theory are rigid too, hence also at odds with the defeasibility of appearances. I then rebut three Bayesian attempts to solve the problem. I conclude that defeasible appearances pose a more difficult and pervasive challenge for formal epistemology than is currently thought. 1 The Challenge for Bayesianism 1.1 Updating and experience 1.2 The problem 1.3 Objections 2 The Challenge for Dempster–Shafer Theory 2.1 Background on Dempster–Shafer theory 2.2 The problem for Dempster–Shafer theory 3 The Challenge for Ranking Theory 4 The Appeal to Metacognition 5 The Appeal to Richer Inputs 6 The Appeal to a Generic Underminer 7 Conclusion
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