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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- Greenberger, D.M., M. A. Horne, and A. Zeilinger: 1989, 'Going beyond Bell's Theorem', in M. Kafatos (ed.), Bell's Theorem, Quantum Theory, and Conceptions of the Universe, Kluwer, Dordrecht, 73-76.Google Scholar
- Hájek, A.: 1997, ' “Mises Redux”-Redux: Fifteen Arguments Against Finite Frequentism', Erkenntnis 45, 209-227.Google Scholar
- Kolmogorov, A.: 1933, Grundbegriffe der Wahrscheinlichkeitsrechnung, Springer, Berlin.Google Scholar
- Miller: D.: 1994, Critical Rationalism, A Restatement and Defence, Open Court, Chicago.Google Scholar
- Particle Data Group: 1992, 'Review of Particle Properties', Physical Review D45, I.1-XI.8.Google Scholar
- Skyrms, B.: 1991, 'Stability and Chance', in W. Spohn, B. C. van Fraassen and B. Skyrms (eds.), Existence and Explanation, Kluwer, Dordrecht, 149-163.Google Scholar
- Vaidman, L.: 1998, 'Variations on the Theme of the Greenberger-Horne-Zeilinger Proof', internet URL-http://babbage.sissa.it/form/quant-ph/9808022.Google Scholar