Weakly Intuitionistic Quantum Logic
- Ronnie Hermens
- … show all 1 hide
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
In this article von Neumann’s proposal that in quantum mechanics projections can be seen as propositions is followed. However, the quantum logic derived by Birkhoff and von Neumann is rejected due to the failure of the law of distributivity. The options for constructing a distributive logic while adhering to von Neumann’s proposal are investigated. This is done by rejecting the converse of the proposal, namely, that propositions can always be seen as projections. The result is a weakly Heyting algebra for describing the language of quantum mechanics.
- Birkhoff, G., and J. von Neumann, The logic of quantum mechanics, Annals of Mathematics 37(4):823–843, 1936. Reprinted in , pp. 1–26.
- Bruns, G., Lakser, H. (1970) Injective hulls of semilattices. Canadian Mathematical Bulletin 13: pp. 115-118 CrossRef
- Celani, S., Jansana, R. (2005) Bounded distributive lattices with strict implication. Mathematical Logic Quarterly 51: pp. 219-246 CrossRef
- Coecke, B., Quantum logic in intuitionistic perspective, Studia Logica 70(3):411–440, 2002.
- Coecke, B., and S. Smets, The Sasaki hook is not a [static] implicative connective but induces a backward [in time] dynamic one that assigns causes, International Journal of Theoretical Physics 43(7/8):1705–1736, 2004.
- Dummett, M., Is logic empirical?, in H.D. Lewis (ed.), Contemporary British Philosophy Volume IV, George Allen and Unwin, London, 1976.
- Heisenberg, W., Über den anschauliche Inhalt der quantentheoretischen Kinematik und Mechanik, Zeitschrift für Physik 43:172–198, 1927.
- Hermens, R., Quantum mechanics: from realism to intuitionism, Master’s thesis available at http://philsci-archive.pitt.edu/id/eprint/5021, 2010.
- Hooker, C.A., The Logico-Algebraic Approach to Quantum Mechanics, Volume I, D. Reidel, Boston, 1975.
- Kochen, S., and E.P. Specker, The problem of hidden variables in quantum mechanics, Journal of Mathematics and Mechanics 17:59–67, 1967. Reprinted in , pp. 293–328.
- Stairs, A. (1983) Quantum logic, realism, and value definiteness. Philosophy of Science 50: pp. 578-602 CrossRef
- von Neumann, J., Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, 1955. Translated from the German by R.T. Beyer. Original title: Mathematische Grundlagen der Quantenmechanik, 1932.
- Weakly Intuitionistic Quantum Logic
Volume 101, Issue 5 , pp 901-913
- Cover Date
- Print ISSN
- Online ISSN
- Springer Netherlands
- Additional Links
- Quantum logic
- Intuitionistic logic
- Weakly Heyting algebras
- Ronnie Hermens (1)
- Author Affiliations
- 1. Department of Theoretical Philosophy, University of Groningen, Oude Boteringestraat 52, Groningen, The Netherlands