Bayesian epistemology and epistemic conditionals: On the status of the export-import laws

Abstract

Contemporary epistemology requires a reconciliation between probabilistic measures and qualitative notions of belief. A unified Bayesian framework addresses this by postulating conditional probability as the sole primitive, employing two-place probability functions to circumvent the limitations of Kolmogorovian axioms, particularly regarding zero-probability antecedents. By deriving belief and belief change from these functions through a system of nested cores, a paradox-free refinement of the Adams hypothesis emerges. In this setting, the acceptability of conditionals is grounded in conditional credence, leading to a characterization of conditional inference where the Export-Import law is a robust and necessary commitment. This law, frequently rejected in possible-worlds semantics and non-probabilistic epistemic models, is a fundamental feature of probability-based belief change in countable spaces. Such a framework demonstrates that unified probabilism entails specific structural requirements for the logic of conditionals, successfully bridging quantitative measures with traditional epistemological requirements regarding belief consistency and revision. – AI-generated abstract.