Greaves, H., & Wallace (Mind, 115(459), 607–632 2006) justify Bayesian conditionalization as the update plan that maximizes expected accuracy, for an agent considering finitely many possibilities, who is about to undergo a learning event where the potential propositions that she might learn form a partition. In recent years, several philosophers have generalized this argument to less idealized circumstances. Some authors (Easwaran, Thought: A Journal of Philosophy, 2(1), 53–61 2013; Nielsen, Statistics & Probability Letters, 185, 109412 2022) relax finiteness, while others (Carr, Synthese, 198(4), 3581–3601 2021; Gallow, Noûs, 55(3), 487–516 2021; Isaacs & Russell, 2022; Schultheis, 2023) relax partitionality. In this paper, we show how to do both at once. We give novel philosophical justifications of the use of \(\sigma \) -algebras in the infinite setting, and argue for a different interpretation of the “signals” in the non-partitional setting. We show that the resulting update plan mitigates some problems that arise when only relaxing finiteness, but not partitionality, such as the Borel-Kolmogorov paradox.
