Wenmackers and Romeijn [38] formalize ideas going back to Shimony [33] and Putnam [28] into an open-minded Bayesian inductive logic, that can dynamically incorporate statistical hypotheses proposed in the course of the learning process. In this paper, we show that Wenmackers and Romeijn’s proposal does not preserve the classical Bayesian consistency guarantee of merger with the true hypothesis. We diagnose the problem, and offer a forward-looking open-minded Bayesians that does preserve a version of this guarantee.

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The Review of Symbolic Logic
Machine Learning

Sterkenburg, T., & de Heide, R. (2021). On the truth-convergence of open-minded Bayesianism. The Review of Symbolic Logic, 15(1), 1–37. doi:10.1017/S1755020321000022