Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T22:57:25.143Z Has data issue: false hasContentIssue false

Quantum Logic Is Alive ∧ (It Is True v It Is False)

Published online by Cambridge University Press:  01 April 2022

Michael Dickson*
Affiliation:
Indiana University
*
Send requests for reprints to the author, Department of History and Philosophy of Science, 130 Goodbody Hall, Indiana University, Bloomington, IN 47405; email: midickso@indiana.edu.

Abstract

Is the quantum-logic interpretation dead? Its near total absence from current discussions about the interpretation of quantum theory suggests so. While mathematical work on quantum logic continues largely unabated, interest in the quantum-logic interpretation seems to be almost nil, at least in Anglo-American philosophy of physics.

This paper has the immodest purpose of changing that fact. I shall argue that while the quantum-logic interpretation faces challenges, it remains a live option. The usual objections either miss the mark, or admit a reasonable answer, or fail to decide the issue conclusively.

Type
Quantum Mechanics
Copyright
Copyright © Philosophy of Science Association 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

This paper owes a great deal to numerous conversations that I have had with Michael Friedman. I am also indebted to Matt Frank for some useful correspondence. (Any errors are due to them.)⊥

References

Demopoulos, W. (1976), “The Possibility Structures of Physical Systems”, in Harper, W. L. and Hooker, C. A. (eds.), Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science. Dordrecht: D. Reidel, 5580.10.1007/978-94-010-1438-0_4CrossRefGoogle Scholar
Dickson, M. (1996), “Logical Foundations for Modal Interpretations”, PSA 1996, Vol. 1. East Lansing, MI: Philosophy of Science Association, 322329.Google Scholar
Dickson, M. (1998), Quantum Chance and Nonlocality. Cambridge: Cambridge University Press.10.1017/CBO9780511524738CrossRefGoogle Scholar
Dummett, M. (1976), “Is Logic Empirical?”, in Lewis, H. (ed.), Contemporary British Philosophy. London: Allen and Unwin, 4568.Google Scholar
Dunn, M. (1980), “Quantum Mathematics”, PSA 1980, Vol. 2. East Lansing, MI: Philosophy of Science Association, 512531.Google Scholar
Dunn, M. (1993), “Star and Perp: Two Treatments of Negation”, in Tomberlin, J. (ed.), Philosophical Perspectives: Language and Logic, Vol. 7. Atascadero: Ridgeview Press.Google Scholar
Finkelstein, D. (1962), “The Logic of Quantum Physics”, Transactions of the New York Academy of Sciences 25 (2): 621637.10.1111/j.2164-0947.1963.tb01483.xCrossRefGoogle Scholar
Finkelstein, D. (1969), “Matter, Space, and Logic”, in Wartofsky, M. and Cohen, R. (eds.), Boston Studies in the Philosophy of Science, Vol. 5. New York: Humanities Press, 199215.10.1007/978-94-010-3381-7_4CrossRefGoogle Scholar
Friedman, M. and Putnam, H. (1978), “Quantum Logic, Conditional Probability, and Interference”, Dialectica 32:305315.10.1111/j.1746-8361.1978.tb01319.xCrossRefGoogle Scholar
Gibbons, P. (1987), Particles and Paradoxes: The Limits of Quantum Logic. Cambridge: Cambridge University Press.10.1017/CBO9780511570674CrossRefGoogle Scholar
Hardegee, G. (1979), “The Conditional in Abstract and Concrete Quantum Logic”, in Hooker 1979, Vol. 2, 49108.Google Scholar
Hooker, C. A. (ed.) (1975, 1979), The Logico-Algebraic Approach to Quantum Mechanics, Vols. 1, 2. Dordrecht: D. Reidel.10.1007/978-94-010-1795-4CrossRefGoogle Scholar
Isham, C. (1994), “Quantum Logic and the Histories Approach to Quantum Theory”, Journal of Mathematical Physics 35:21572185.10.1063/1.530544CrossRefGoogle Scholar
Isham, C., Linden, N., Savvidou, K., and Schreckenberg, S. (1998), “Continuous Time and Consistent Histories”, Journal of Mathematical Physics 39:18181834.10.1063/1.532265CrossRefGoogle Scholar
Omnès, R. (1994), The Interpretation of Quantum Mechanics. Princeton: Princeton University Press.10.1515/9780691187433CrossRefGoogle Scholar
Ptàk, P. and Pulmanova, S. (1991), Orthomodular Structures as Quantum Logics. Dordrecht: Kluwer.Google Scholar
Putnam, H. (1969), “Is Logic Empirical?”, in Cohen, R. and Wartofsky, M. (eds.), Boston Studies in the Philosophy of Science, Vol. 5. Dordrecht: D. Reidel, 181206.10.1007/978-94-010-3381-7_5CrossRefGoogle Scholar
Solèr, M.P. (1995), “Characterization of Hilbert Spaces by Orthomodular Spaces”, Comunications in Algebra 23:219243.10.1080/00927879508825218CrossRefGoogle Scholar
von Neumann, J. (1939), “On Infinite Direct Products”, Compositio Math 6:177.Google Scholar