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A piece of folklore enjoys some currency among philosophical Bayesians, according to which Bayesian agents who, intuitively speaking, spread their credence over the entire space of available hypotheses are certain to converge to the truth. The goals of the current discussion are to show that that kernel of truth in this folklore is in some ways fairly small and to argue that Bayesian convergence-to-the-truth results are a liability for Bayesianism as an account of rationality since they render a certain sort of arrogance rationally mandatory.
For helpful conversations and suggestions, thanks to Bob Geroch, Alistair Isaac, Jim Joyce, Sarah Moss, Laura Ruetsche, and two anonymous referees. This article owes a great deal to the approaches of Earman (1992, chap. 9) and Kelly (1996, chap. 13). For all those readers out there who are fans of both Stefan Banach and Sir Thomas Malory, n. 13 is for you.