David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
British Journal for the Philosophy of Science 37 (1):83-99 (1986)
The idea of a 'logic of quantum mechanics' or quantum logic was originally suggested by Birkhoff and von Neumann in their pioneering paper . Since that time there has been much argument about whether, or in what sense, quantum 'logic' can be actually considered a true logic (see, e.g. Bell and Hallett , Dummett , Gardner ) and, if so, how it is to be distinguished from classical logic. In this paper I put forward a simple and natural semantical framework for quantum logic which reveals its difference from classical logic in a strikingly intuitive way, viz. through the fact that quantum logic admits (suitably formulated versions of) the characteristic quantum-mechanical notions of superposition and incompatibility of attributes. That is, precisely the features that distinguish quantum from classical physics also serve, within this framework, to distinguish quantum from classical logic. Some light is shed on the question of whether quantum logic is a genuine logical system by introducing a natural entailment relation for quantum-logical formulas with the implication symbol. The novelty is that, although implication behaves as it should (i.e. the 'deduction theorem' holds), the order of introduction of premises is significant. The fact that a reasonable entailment relation can be formulated for quantum logic supports the view that it is a genuine logical system and not merely an algebraic formalism
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Patrick Suppes (1966). The Probabilistic Argument for a Non-Classical Logic of Quantum Mechanics. Philosophy of Science 33 (1/2):14-21.
Claudio Garola (1992). Truth Versus Testability in Quantum Logic. Erkenntnis 37 (2):197 - 222.
J. Michael Dunn (1980). Quantum Mathematics. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:512 - 531.
Michael Dickson (2001). Quantum Logic is Alive ∧ (It is True ∨ It is False). Proceedings of the Philosophy of Science Association 2001 (3):S274 - S287.
R. I. G. Hughes (1980). Quantum Logic and the Interpretation of Quantum Mechanics. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:55 - 67.
Allen Stairs (1983). Quantum Logic, Realism, and Value Definiteness. Philosophy of Science 50 (4):578-602.
James H. McGrath (1978). Only If Quanta Had Logic. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1978:268 - 275.
Peter Gibbins (1987). Particles and Paradoxes: The Limits of Quantum Logic. Cambridge University Press.
Sonja Smets (2006). From Intuitionistic Logic to Dynamic Operational Quantum Logic. Poznan Studies in the Philosophy of the Sciences and the Humanities 91 (1):257-275.
Added to index2009-01-28
Total downloads76 ( #26,977 of 1,696,808 )
Recent downloads (6 months)13 ( #46,960 of 1,696,808 )
How can I increase my downloads?