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Quantum Logic and Meaning

Published online by Cambridge University Press:  21 March 2022

Geoffrey Hellman
Geoffrey Hellman*
Affiliation:
Indiana University
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Extract

In concluding their major survey, “Quantum Logics,” Greechie and Gudder (1975) listed four outstanding directions for future research, the last of which was, “Explain the meaning of the word ‘logic’ in the title of this paper.” Broadly speaking, there are two radically different points of view on this. There is the view that, taken strictly, ‘logic’ is a misnomer: quantum logic studies certain algebraic structures naturally arising from the formal, apparatus of quantum theory, structures which may afford insights into quantum physics, on a number of levels, but which do not in any way involve giving up or replacing classical logical laws. (Cf., e.g., Jauch (1968, p. 77).) In contrast, there is the view that the non-Boolean structures arising from the Hilbert space formalism should be taken as giving rise to a genuine non-classical logic, in conflict with classical logic, but appropriate to the description of quantum mechanical reality.

Type
Part IX. Quantum Logic and Quantum Mathematics
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1980 , Issue 2: Volume Two: Symposia and Invited Papers 1980 , 1980 , pp. 493 - 511
Copyright
Copyright © 1981 by the Philosophy of Science Association

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Footnotes

1

This material is in part based upon work supported by the National Science Foundation under Grant No. SES-7924874. I am grateful to Linda : Wessels, J. Michael Dunn, J. Alberto Coffa, David Malament, and Richard Healey for helpful discussion on the issues of this paper, and to Bas van Fraassen, Nuel Belnap, and Hilary Putnam for thought-provoking correspondence .

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