Towards a new theory of confirmation
type: Item
instance of: scholarly article
title: Towards a new theory of confirmation
zbMATH Open document ID: 0611.03006
DOI: 10.1007/BF02761402
author: Moshe Koppel
published in: Israel Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 03B48
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 60A05
zbMATH DE Number: 3987251
zbMATH Keywords: hierarchies of infinite binary sequences
zbMATH Keywords: probability
zbMATH Keywords: amount of confirmation
zbMATH Keywords: hypothesis confirmation
zbMATH Keywords: Carnap's logical and empirical criteria for determining probabilities
MaRDI profile type: Publication
cites work: Toward a mathematical theory of inductive inference
cites work: Q5799632
cites work: Q4697038
cites work: The definition of random sequences
cites work: A formal theory of inductive inference. Part I
full work available at URL: https://doi.org/10.1007/bf02761402
OpenAlex ID: W1999584335
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description: scientific article; zbMATH DE number 3987251