Philosophy of Science 49 (3):355-379 (1982)

Authors
John L. Bell
University of Western Ontario
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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DOI 10.1086/289066
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References found in this work BETA

Two Dogmas of Empiricism.Willard V. O. Quine - 1951 - Philosophical Review 60 (1):20–43.
Two Dogmas of Empiricism Symposium.W. V. Quine - 1951 - Philosophical Review 60:20.
Elements of Intuitionism.Michael Dummett - 1980 - British Journal for the Philosophy of Science 31 (3):299-301.
Is Quantum Logic Really Logic?Michael R. Gardner - 1971 - Philosophy of Science 38 (4):508-529.
Categories, Toposes and Sets.J. L. Bell - 1982 - Synthese 51 (3):293 - 337.

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Citations of this work BETA

Quantum Logic as a Dynamic Logic.Alexandru Baltag & Sonja Smets - 2011 - Synthese 179 (2):285 - 306.
In Defense of Flip-Flopping.Andrew M. Bailey & Amy Seymour - 2021 - Synthese 199 (5-6):13907-13924.
The Philosophy of Alternative Logics.Andrew Aberdein & Stephen Read - 2009 - In Leila Haaparanta (ed.), The Development of Modern Logic. Oxford University Press. pp. 613-723.
Quantum Logic and the Classical Propositional Calculus.Othman Qasim Malhas - 1987 - Journal of Symbolic Logic 52 (3):834-841.

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