Standards for Modest Bayesian Credences

In response to G.Belot’s (2013) criticism that Bayesian theory is epistemologically immodest, we argue that his analysis is misguided. The topological conditions that we understand underpin his criticisms of familiar results about asymptotic Bayesian conditioning are self-defeating. They require extreme a priori credences regarding, e.g., the limiting behavior of observed relative frequencies. Instead, we offer a rival explication of Bayesian modesty: Rival scientific opinions should be responsive to new facts as a way to resolve their disputes. Using a result of Blackwell and Dubins (1962), we explain how amenability to new evidence may serve as the basis for resolving conflicts among Bayesian investigators. When the new evidence fails to achieve a resolution, that failure can identify epistemologically immodest Bayesian credal states. Also we assess A. Elga’s (2016) rebuttal to Belot’s analysis. He focuses attention on the role that the assumption of countable additivity plays in Belot’s criticism of asymptotic Bayesian learning.