Some Afterthoughts and Examples on the Logic of Induction

The aim of Saint-Mont (2020) was to provide a rather general answer to Hume’s problem. To this end, induction was treated within a straightforward formal paradigm, i.e., several connected tiers of abstraction. This note mainly discusses the basic two-tier model and associated examples. It points out that a sound logical solution to the problem of induction boils down to proper accounting, and Bayes’ formula in particular. Generalizations are also possible if one evokes suitable assumptions such as some kind of continuity property. Moreover, the precision added by formal analysis relative to verbal arguments demon- strates that the crucial issue with induction is rather not circularity, but being able to find a suitable general tier that allows for a smooth transition between a less and a more specific situation, avoiding inconsistencies.