I discuss a contemporary solution to the dynamic problem of old evidence (POE), as proposed by Sprenger. Sprenger’s solution combines the Garber–Jeffrey–Niiniluoto (GJN) approach with Howson’s suggestion of counterfactually removing the old evidence from scientists’ belief systems. I argue that in the dynamic POE, the challenge is to explain how an insight under beliefs in which the old evidence E is known increased the credence of a scientific hypothesis. Therefore, Sprenger’s counterfactual solution, in which E has been artificially removed, does not resolve the problem. I consider several potential responses.

This paper investigates the question of how subjective probability should relate to binary belief. We propose new distance minimization methods, and develop epistemic decision-theoretic accounts. Both approaches can be shown to get “close” to the truth: the first one by getting “close” to a given probability, and the second by getting expectedly “close” to the truth. More specifically, we study distance minimization with a refined notion of Bregman divergence and expected utility maximization with strict proper scores. Our main results reveal that the two ways to get “close” to the truth can coincide.

This note presents a short reply to Henderson’s critical discussion of Schurz’s approach to the problem of induction based on the optimality of meta-induction. Henderson objects that the meta-inductive a posteriori justification of object-induction rests on a certain premise—namely, an approximation condition—that she reveals as untenable. I reply that Henderson’s approximation condition is indeed too strong to be plausible, but it is not needed by the meta-inductive approach; a much weaker and highly plausible approximation condition is sufficient.