For two ideally rational agents, does learning a finite amount of shared evidence necessitate
agreement? No. But does it at least guard against belief polarization, the case in which their …

Strict frequentism defines probability as the limiting relative frequency in an infinite
sequence. What if the limit does not exist? We present a broader theory, which is applicable …

In recent publications we have drawn attention to the fact that if the dynamics of a model is
structurally unstable, then the presence of structural model error places in-principle limits on …

This dissertation bridges the theory of algorithmic randomness—a branch of computability
theory—and the foundations of inductive learning. Algorithmic randomness provides a …

Bayesian agents, argues Belot, 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 …

This essay has two aims. The first is to correct an increasingly popular way of
misunderstanding Belot's (2013) Orgulity Argument. The Orgulity Argument charges …

Abstract Bayesians since Savage ([1972]) have appealed to asymptotic results to counter
charges of excessive subjectivity. Their claim is that objectionable differences in prior …

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 …

Merging of opinions results underwrite Bayesian rejoinders to complaints about the
subjective nature of personal probability. Such results establish that sufficiently similar priors …

This last point was brought home by Gordon Belot in his critique of Bayesian epistemology.
2 Belot uses the staple example of flipping a coin infinitely often. A famous result in standard …