Synthese

, Volume 118, Issue 3, pp 307–328 | Cite as

Probability as a Theory Dependent Concept

  • David Atkinson
  • Jeanne Peijnenburg

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.

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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • David Atkinson
    • 1
  • Jeanne Peijnenburg
    • 1
  1. 1.University of GroningenThe Netherlands

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