'Hume's theorem' concerning miracles

Abstract

A conditional Bayesian framework prioritizing the probability of an event given its testimony provides the most accurate formalization of the logic governing miraculous claims. While alternative interpretations treat the “general maxim” as a non-conditional theorem involving the joint probability of testimony and its falsehood, these approaches fail to align with the textual evidence and focus unnecessarily on the initial probability of the testimony being presented. A simpler formalization—positing that a miracle is probable only if the probability of the event given the testimony exceeds the probability of the testimony being false given its presentation—better captures the intended philosophical result. This interpretation provides both necessary and sufficient conditions for belief, whereas non-conditional alternatives often fail to establish sufficiency. Although this result constitutes a near-tautology within formal probability theory, its significance lies in its capacity to correct for base-rate neglect. Just as individuals frequently overestimate the reliability of diagnostic tests for rare conditions by ignoring low initial probabilities, the assessment of miracles often suffers from a failure to weight antecedent improbability against testimonial evidence. The maxim functions as a cognitive safeguard, ensuring that the immense initial improbability of a miracle is not overshadowed by the perceived reliability of a witness. It serves as a crucial methodological tool for empirical reasoning when confronted with extraordinary claims. – AI-generated abstract.