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Is Quantum Logic Really Logic?

Published online by Cambridge University Press:  14 March 2022

Michael R. Gardner
Michael R. Gardner*
Affiliation:
Harvard University
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Extract

Putnam and Finkelstein have proposed the abandonment of distributivity in the logic of quantum theory. This change results from defining the connectives, not truth-functionally, but in terms of a certain empirical ordering of propositions. Putnam has argued that the use of this ordering (“implication”) to govern proofs resolves certain paradoxes. But his resolutions are faulty; and in any case, the paradoxes may be resolved with no changes in logic. There is therefore no reason to regard the partially ordered set of propositions as a logic—i.e. as embodying a criterion for soundness of proofs. Its role in quantum theory ought to be understood in an entirely different way.

Type
Research Article
Information
Philosophy of Science , Volume 38 , Issue 4 , December 1971 , pp. 508 - 529
Copyright
Copyright © 1971 by The Philosophy of Science Association

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Footnotes

†

Present address: Dept. of Philosophy, Mount Holyoke College, South Hadley, Ma. This paper is based upon part of a Ph.D. dissertation, Harvard University, 1971. I wish to acknowledge helpful conversations with Jeffrey Bub, Imre Lakatos, Sir Karl Popper, Hilary Putnam, Abner Shimony, and Lawrence Sklar.

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