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Logical Foundations for Modal Interpretations of Quantum Mechanics

Published online by Cambridge University Press:  01 April 2022

Michael Dickson*
Affiliation:
Indiana University

Abstract

This paper proposes a logic, motivated by modal interpretations, in which every quantum mechanics propositions has a truth-value. This logic is completely classical, hence violates the conditions of the Kochen-Specker theorem. It is shown how the violation occurs, and it is argued that this violation is a natural and acceptable consequence of modal interpretations. It is shown that despite its classicality, the proposed logic is empirically indistinguishable from quantum logic.

Type
Modal Interpretations of Quantum Theory
Copyright
Copyright © Philosophy of Science Association 1996

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Footnotes

Thanks to Guido Bacciagaluppi, Rob Clifton, Michael Friedman, and an anonymous referee for helpful comments.

Department of History and Philosophy of Science, 130 Goodbody Hall, Indiana University, Bloomington, IN 47405-2401.

References

Bacciagaluppi, G. and Hemmo, M. (1996), ‘Modal Interpretations, Decoherence, and Measurements’, Studies in History and Philosophy of Modern Physics, forthcoming.CrossRefGoogle Scholar
Bell, J. and Clifton, R. (1995), ‘QuasiBoolean Algebras and Simultaneously Definite Properties in Quantum Mechanics’, International Journal of Theoretical Physics 34: 24092422.CrossRefGoogle Scholar
Dickson, M. (1995a), ‘Faux-Boolean Algebras, Classical Probability, and Determinism’, Foundations of Physics Letters 8: 231242.CrossRefGoogle Scholar
Dickson, M. (1995b), ‘Faux-Boolean Algebras and Classical Models’, Foundations of Physics Letters 8: 401415.CrossRefGoogle Scholar
Dickson, M. (1996), ‘On the Plurality of Dynamics: Transition Probabilities and Modal Interpretations’, forthcoming in R. Healey and G. Hellman (eds.), Minnesota Studies in the Philosophy of Science.Google Scholar
Fevrier, P. (1937), ‘Les Relations d'Incertitude de Heisenberg et la Logique’, Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences 204: 481483.Google Scholar
Friedman, M., and Putnam, H. (1978), ‘Quantum Logic, Conditional Probability, and Interference’, Dialectica 32: 305315.CrossRefGoogle Scholar
Kochen, S. and Specker, E. (1967), On the Problem of Hidden Variables in Quantum Mechanics’, Journal of Mathematics and Mechanics 17: 5967.Google Scholar
Putnam, H. (1957), ‘Three-Valued Logic’, Philosophical Studies 8: 7380.CrossRefGoogle Scholar
Reichenbach, H. (1944), Philosophic Foundations of Quantum Mechanics. Los Angeles: University of California Press.Google Scholar
Van Fraassen, B. (1991), Quantum Mechanics: An Empiricist View. Oxford: Clarendon Press.CrossRefGoogle Scholar