Towards a new theory of confirmation
Any sequence of events can be ''explained'' by any of an infinite number of hypotheses. Popper describes the ''logic of discovery'' as a process of choosing from a hierarchy of hypotheses the first hypothesis which is not at variance with the observed facts. \textit{L. Blum} and \textit{M. Blum} [Inf. Control 28, 125-155 (1975; Zbl 0375.02028)] formalized these hierarchies of hypotheses as hierarchies of infinite binary sequences and imposed on them certain decidability conditions. In this paper we also consider hierarchies of infinite binary sequences but we impose only the most elementary Bayesian considerations. We use the structure of such hierarchies to define ''confirmation''. We then suggest a definition of probability based on the amount of confirmation a particular hypothesis (i.e. pattern) has received. We show that hypothesis confirmation alone is a sound basis for determining probabilities and in particular that Carnap's logical and empirical criteria for determining probabilities are consequences of the confirmation criterion in appropriate limiting cases.
hierarchies of infinite binary sequences
Carnap's logical and empirical criteria for determining probabilities
scientific article; zbMATH DE number 3987251