A familiar defense of Personalist or Subjective Bayesian theory is that, under a variety of sufficient conditions, asymptotically – with increasing shared evidence – almost surely, each non-extreme, countably additive Bayesian opinion, when updated by conditionalization, converges to certainty that is veridical about the truth/falsity of hypotheses of interest. Then, with probability 1 over possible evidential histories, personal probabilities track the truth. In this note we examine varieties of failures of these asymptotics. In an extreme case, conditional probabilities are deceptive when they converge to certainty for a false hypothesis. We establish that proposals for so-called “modest” credences, offered by Elga (2016) and by Nielsen and Stewart (2019) in response to a concern about Bayesian orgulity raised by Belot (2013), instead support deceptive credences. We argue that deceptive credences are not modest, but for a reason different than Belot adduces.

Ruobin Gong,
Joseph B. Kadane,
Mark J. Schervish,
Teddy Seidenfeld,
Rafael B. Stern