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The Probabilistic Argument for a Non-Classical Logic of Quantum Mechanics

Published online by Cambridge University Press:  14 March 2022

Patrick Suppes
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Abstract

The aim of this paper is to state the single most powerful argument for use of a non-classical logic in quantum mechanics. In outline the argument is the following. The working logic of a science is the logic of the events and propositions to which probabilities are assigned. A probability should be assigned to every element of the algebra of events. In the case of quantum mechanics probabilities may be assigned to events but not, without restriction, to the conjunction of two events. The conclusion is that the working logic of quantum mechanics is not classical. The nature of the logic that is appropriate for quantum mechanics is examined.

Type
Research Article
Information
Philosophy of Science , Volume 33 , Issue 1 , March 1966 , pp. 14 - 21
Copyright
Copyright © 1966 by The Philosophy of Science Association

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Footnotes

∗∗

This paper was originally presented at a colloquium in Paris in May, 1964, in honor of the memory of E. W. Beth.

References

[1] Birkhoff, G., & von Neumann, J., “The logic of quantum mechanics,” Annals of Math., 1936, 37, 823–843.CrossRefGoogle Scholar
[2] Kochen, S., & Specker, E. P., “Logical structures arising in quantum theory,” in J. W. Addison, L. Henkin, A. Tarski (Eds.), Theory of Models, Proceedings of the 1963 International Symposium at Berkeley, Amsterdam: North-Holland Publishing Co., 1965, pp. 177–189.Google Scholar
[3] Reichenbach, H., Philosophic foundations of quantum mechanics, University of California Press, Berkeley and Los Angeles, 1944.Google Scholar
[4] Suppes, P., “Probability concepts in quantum mechanics,” Philosophy of Science, 1961, 28, 378–389.CrossRefGoogle Scholar
[5] Suppes, P., “Logics appropriate to empirical theories,” in J. W. Addison, L. Henkin, A. Tarski (Eds.), Theory of Models, Proceedings of the 1963 International Symposium at Berkeley, Amsterdam: North-Holland Publishing Co., 1965, pp. 364–395.Google Scholar
[6] Varadarajan, V. S., “Probability in physics and a theorem on simultaneous observability,” Communications on Pure and Applied Mathematics, 1962, XV, 189–217.CrossRefGoogle Scholar
[7] Wigner, E., “On the quantum correction for thermodynamic equilibrium,” Physical Review, 1932, 40, 749–759.CrossRefGoogle Scholar