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Logic, Quantum Logic and Empiricism

Published online by Cambridge University Press:  01 April 2022

John Bell and
Michael Hallett
John Bell
Affiliation:
Department of Mathematics, Department of Philosophy, London School of Economics
Michael Hallett
Affiliation:
Department of Mathematics, Department of Philosophy, London School of Economics
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Abstract

This paper treats some of the issues raised by Putnam's discussion of, and claims for, quantum logic, specifically: that its proposal is a response to experimental difficulties; that it is a reasonable replacement for classical logic because its connectives retain their classical meanings, and because it can be derived as a logic of tests. We argue that the first claim is wrong (1), and that while conjunction and disjunction can be considered to retain their classical meanings, negation crucially does not. The argument is conducted via a thorough analysis of how the meet, join and complementation operations are defined in the relevant logical structures, respectively Boolean- and ortholattices (3). Since Putnam wishes to reinstate a realist interpretation of quantum mechanics, we ask how quantum logic can be a logic of realism. We show that it certainly cannot be a logic of bivalence realism (i.e., of truth and falsity), although it is consistent with some form of ontological realism (4). Finally, we show that while a reasonable explication of the idealized notion of test yields interesting mathematical structure, it by no means yields the rich ortholattice structure which Putnam (following Finkelstein) seeks.

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Type
Research Article
Information
Philosophy of Science , Volume 49 , Issue 3 , September 1982, pp. 355 - 379
Copyright
Copyright © Philosophy of Science Association 1982

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