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Probability as a Theory Dependent Concept

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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Atkinson, D., Peijnenburg, J. Probability as a Theory Dependent Concept. Synthese 118, 307–328 (1999). https://doi.org/10.1023/A:1005242414754

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  • DOI: https://doi.org/10.1023/A:1005242414754

Keywords

  • Relative Frequency
  • Winning Strategy
  • Stochastic Theory
  • Spin Measurement
  • Quantum Game