Probability as a theory dependent concept

D Atkinson*, J Peijnenburg

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

It is argued that probability should be defined implicitly by the distributions of possible measurement values characteristic of a theory. These distributions are tested by, but not defined in terms of, relative frequencies of occurrences of events of a specified kind. The adoption of an a priori probability in an empirical investigation constitutes part of the formulation of a theory. In particular, an assumption of equiprobability in a given situation is merely one hypothesis inter alia, which can be tested, like any other assumption. Probability in relation to some theories - for example quantum mechanics - need not satisfy the Kolmogorov axioms. To illustrate how two theories about the same system can generate quite different probability concepts, and not just different probabilistic predictions, a team game for three players is described. If only classical methods are allowed, a 75% success rate at best can be achieved. Nevertheless, a quantum strategy exists that gives a 100% probability of winning.

Original languageEnglish
Pages (from-to)307-328
Number of pages22
JournalSynthese
Volume118
Issue number3
DOIs
Publication statusPublished - 1999

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