Affirming the explanandum.

The article focuses on the relationship between affirming the consequent (AC), abductive inference, and Bayesian reasoning, providing a Bayesian framework to evaluate when abductive inference is normatively justified. Affirming the consequent is an inferential pattern where one infers the antecedent from the consequent of a conditional statement, which is deductively invalid but can be plausible in certain contexts. The author shows that abductive inference—inferring a hypothesis that explains observed evidence—is structurally similar to AC and can be understood as "affirming the explanandum" (AE) within Bayesian probability theory. The analysis demonstrates that abductive inference is rationally warranted when learning the explanandum increases the probability of the explanans sufficiently, especially when the explanandum is learned with certainty or high probability and the hypothesis strongly explains the evidence. This Bayesian characterization clarifies under which conditions abduction aligns with Bayesian updating and supports the integration of inference to the best explanation (IBE) into Bayesian epistemology.