The Laplace-Jaynes approach to induction

An approach to induction is presented, based on the idea of analysing the context of a given problem into ‘circumstances’. This approach, fully Bayesian in form and meaning, provides a complement or in some cases an alternative to that based on de Finetti’s representation theorem and on the notion of infinite exchangeability. In particular, it gives an alternative interpretation of those formulae that apparently involve ‘unknown probabilities’ or ‘propensities’. Various advantages and applications of the presented approach are discussed, especially in comparison to that based on exchangeability. Generalisations are also discussed. PACS numbers: 02.50.Cw,02.50.Tt,01.70.+w MSC numbers: 03B48,60G09,60A05 Note, to head off a common misconception, that this is in no way to introduce a “probability of a probability”. It is simply convenient to index our hypotheses by parameters [. . . ] chosen to be numerically equal to the probabilities assigned by those hypotheses; this avoids a doubling of our notation. We could easily restate everything so that the misconception could not arise; it would only be rather clumsy notationally and tedious verbally. E. T. J, Monkeys, kangaroos, and N [1], p. 12 1 Dramatis personae, notatio, atque philosophia We continue here our exploration of the notion of ‘circumstance’ and of its applications in plausibility theory. Through this notion we shall here approach no less than