Kenny Easwaran (Irvine)

Greaves and Wallace (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 (2013b); Nielsen (2022)) relax finiteness, while others (Carr (2021); Gallow (2021); Isaacs and 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 σ-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.