Pride and Probability

Abstract Bayesian agents, argues Belot (2013), are orgulous: they believe in inductive success even when guaranteed to fail on a topologically typical collection of data streams. Here we shed light on how pervasive this phenomenon is. We identify several classes of inductive problems for which Bayesian convergence to the truth is topologically typical. However, we also show that, for all sufficiently complex classes, there are inductive problems for which convergence is topologically atypical. Lastly, we identify specific topologically typical collections of data streams, observing which guarantees convergence to the truth across all problems from certain natural classes of effective inductive problems.