James is polite and punctual (and useless): A Bayesian formalisation of faint praise

“Damned by faint praise” is the phenomenon whereby weak positive information leads to a negative change in belief. This seemingly conflicts with normative Bayesian predictions, which prescribe that positive information should only exert a positive change in belief. We argue that the negative belief change is due to an inference from critical missing evidence; that is, an implicit argument from ignorance. Such an inference is readily incorporated within a version of Bayes’ theorem incorporating the concept of epistemic closure. This reformalisation provides a general theoretical framework for the phenomenon that clearly outlines those conditions under which it should be observed, and its conceptual relationship with other argumentation phenomena.