A piece of folklore enjoys some currency among philosophical Bayesians, according to which Bayesian agents that, intuitively speaking, spread their credence over the entire space of available hypotheses are certain to converge to the truth. The goals of the present discussion are to show 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. (shrink)

Brian Skyrms (1987, 1990, 1993, 1997) has discussed the role of dynamic coherence arguments in the theory of personal or subjective probability. In particular, Skryms (1997) both reviews and discusses the utility of martingale arguments in establishing the convergence of beliefs within the context of radical probabilism. The classical martingale converence theorem, however, assumes the countable additivity of the underlying probability measure; an assumption rejected by some subjectivists such as Bruno de Finetti (see, e.g., de Finetti 1930 and 1972). This (...) brief note has a very modest goal: to briefly consider the extent to which Skyrms’s argument can be extended to the finitely additive case. (shrink)