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Only if Quanta had Logic

Published online by Cambridge University Press:  28 February 2022

James H. McGrath
James H. McGrath*
Affiliation:
Indiana UniversitySouth Bend
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Extract

Perhaps no claim in the philosophy of logic has attracted as much attention in the last decade as one defended by Hilary Putnam: some of the so-called ‘necessary truths’ of logic may turn out to be false for empirical reasons and consequently “logic is, in a certain sense, a natural science.” (p. 216). Putnam and others have attempted to reinforce this position by citing findings from quantum mechanics, findings which are intended to provide empirical reasons leading to the conclusion that particular aspects of classical logic have in fact turned out to be false. In this paper I will challenge one of the major procedures leading to the conclusion that quantum mechanics provides ample reason to revise logic. Quantum mechanics, I will argue, has shown neither that logic is empirical nor that some aspect of classical logic is false.

Type
Part VII. Quantum Logic
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1978 , Issue 1: Volume One: Contributed Papers 1978 , 1978 , pp. 268 - 275
Copyright
Copyright © 1978 by the Philosophy of Science Association

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Footnotes

1

I gratefully acknowledge encouragement and helpful comments from Roger T. Simonds and Bas C. van Fraassen and financial support from the Borden P. Bowne Foundation.

References

Beltrametti, E. G. and Cassinelli, G. “Logical and Mathematical Structures of Quantum Mechanics.” Forthcoming in Il Nuovo Cimento.Google Scholar
Birkhoff, G. and von Neumann, J. “The Logic of Quantum Mechanics.” Annals of Mathematics 37 (1936): 823–843. (As reprinted in [12]. Pages 1-26).CrossRefGoogle Scholar
Finkelstein, D. “The Logic of Quantum Physics.” Transactions of the New York Academy of Sciences 25 (1962): 621–637.CrossRefGoogle Scholar
Finkelstein, D. “Matter, Space and Logic.” In Boston Studies in the Philosophy of Sciences, Vol. 5. Edited by Cohen, R. S. and Wartofsky, M. Dordrecht: Reidel, 1970. Pages 199–215.Google Scholar
Finkelstein, D. “The Physics of Logic.” In Paradigms and Paradoxes. (University of Pittsburgh Series in the Philosophy of Science, Volume 5.) Edited by Colodny, R. Pittsburgh: University of Pittsburgh Press, 1972. Pages 47–66.Google Scholar
Goldstein, Larry. Abstract Algebra. New Jersey: Prentice-Hall, 1973.Google Scholar
Haack, Susan. Deviant Logic. Cambridge: Cambridge University. Press, 1974.Google Scholar
Halmos, Paul. Lectures on Boolean Algebras. London: Van Nostrand Reinhold, 1972.Google Scholar
Heelan, P. “Complementarity, Context Dependence, And Quantum Logic.” Foundations of Physics 1 (1970): 95–110.CrossRefGoogle Scholar
Heelan, P. “Quantum and Classical Logic: Their Respective Roles.” Synthese 21 (1970): 2–33.CrossRefGoogle Scholar
Heelan, P. “The Role of Subjectivity in Natural Sciences.” The Proceedings of the American Catholic Philosophical Association 43 (1969): 187–194.CrossRefGoogle Scholar
Hooker, C. A. (ed.). The Logico-Algebraic Approach to Quantum Mechanics. Dordrecht: Reidel, 1975.CrossRefGoogle Scholar
Mackey, G. The Mathematical Foundations of Quantum Mechanics. New York: Benjamin, 1963.Google Scholar
McGrath, J. Quantum Mechanical Paradoxes and Non-Standard Logics. Unpublished Ph.D. Dissertation, The American University, 1977.Google Scholar
Putnam, H. “Is Logic Empirical?” In Boston Studies in the Philosophy of Science, Vol. 5. Edited by Cohen, R. S. and Wartofsky, M. Dordrecht: Reidel, 1969, Pages 216–241.CrossRefGoogle Scholar