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Induction and the rule of succession through a possibilistic inferential model lens

Aug 2026 · 0 citations · 55 references
Mathematics

Abstract

Induction is the process by which empirical evidence is transformed to knowledge. Hume famously argued---and Popper and others agree---that there can be no logical justification for induction. A weaker form of induction, due to Bayes, expresses the aforementioned knowledge in terms of probabilities, and we review some well-known and not-so-well-known criticisms of the Bayesian solution. We then investigate the relatively new possibilistic inferential model (IM) framework, showing that, in addition to the IM's strong, statistical reliability guarantees that it uniquely enjoys, it is safe from those criticisms that damage the Bayesian foundations. For illustration, we reconsider the classical sunrise problem and compare our proposed solution with Laplace's famous rule of succession.

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