No CrossRef data available.
Article contents
Only if ‘Acrobatic Logic’ is Non-Boolean
Published online by Cambridge University Press: 28 February 2022
Extract
The purpose of this paper is to defend ‘quantum logic’ against a vigorous attack of J.H. McGrath (1978). The case is serious, as he allegedly discredits quantum propositional logic showing it unmotivated and useless. The object of his criticism is the procedure of “taking a well-known theory and distilling its logic” (Finkelstein 1969), or “reading off quantum logic from quantum mechanics” (McGrath 1978). This procedure is indeed the corner stone of the quantum logic philosophy, so if it were be “discredited in a most general way” and shown to be “fundamentally misconceived” (McGrath 1978) then the idea of quantum logic has broken down. I am going to show, on the contrary, that McGrath's account of the ‘reading off’ procedure is not sufficiently precise resulting in the failure of his ‘acrobatic’ counterexample.
- Type
- Part IX. The Cat Paradox and Quantum Logic
- Information
- Copyright
- Copyright © 1980 by the Philosophy of Science Association
Footnotes
1
The first draft of this paper has been written during my stay at the Institute of Physics of the Cologne University. I am greatly indebted to Professor P. Mittelstaedt and Dr. E.-W. Stachow for their warm hospitality and stimulating discussions, as well to the Alexander von Humboldt Foundation for a financial support.
References
Birkhoff, Garret and von Neumann, John (1936). “The Logic of Quantum Mechanics.” Annals of Mathematics 37: 823–843.CrossRefGoogle Scholar
Bugajski, Slawomir (1980). “The Inner Language of Operational Quantum Mechanics.” To appear in proceedings of the Workshop on Quantum Logic held at the Ettore Majorana Centre for Scientific Culture, Erice-Trapani ( Sicily ), 2-9 December 1979. Edited by Beltrametti, E. New York: Plenum Press.Google Scholar
Dalla Chiara, Maria L. (1977). “Quantum Logic and Physical Modalities.” Journal of Philosophical Logic 6: 391–404.CrossRefGoogle Scholar
Finkelstein, David (1969). “Matter, Space and Logic.” In Proceedings of the Boston Colloquium for the Philosophy of Science, 1966/1968. (Boston Studies in the Philosophy of Science, Vol. 5.) Edited by Cohen, R.S. and Wartofsky, M.. Dordrecht: D. Reidel Publishing Co. Pages 199–215.Google Scholar
Goldblatt, R.I. (1974). “Semantic Analysis of Orthologic.” Journal of Philosophical Logic 3: 19–35.CrossRefGoogle Scholar
Jauch, Josef M. (1968). Foundations of Quantum Mechanics. Reading, Mass.: Addison-Wesley.Google Scholar
Kalmbach, Gudrun. (1974). “Orthomodular Logic.” Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik 20: 395–406.CrossRefGoogle Scholar
Mackey, George W. (1963). The Mathematical Foundations of Quantum Mechanics. (Mathematical Physics Monograph Series.) New York: W.A. Benjamin, Inc.Google Scholar
McGrath, J.H. (1978). “Only if Quanta Had Logic.” In PSA 1978, Vol. 1. Edited by Asquith, P.D. and Hacking, Ian. East Lansing, Mich.: Philosophy of Science Association. Pages 268–276.Google Scholar
Mielnik, Bogdan. (1969). “Theory of Filters.” Communications in Mathematical Physics 15: 1–46.CrossRefGoogle Scholar
Mittelstaedt, Peter. (1978a). Quantum Logic. Dordrecht: D. Reidel Publishing Co.CrossRefGoogle Scholar
Mittelstaedt, Peter. (1978b). “The Metalogic of Quantum Logic.” In PSA 1978. Vol. 1. Edited by Asquith, P.D. and Hacking, Ian. East Lansing, Mich: Philosophy of Science Association. Pages 249–256.Google Scholar
Stachow, Ernst-Walter. (1980). “On the Logical Foundations of Quantum Mechanics.” International Journal of Theoretical Physics. Forthcoming.CrossRefGoogle Scholar
van Fraassen, Bas C. (1971). Formal Semantics and Logic. New York: The Macmillan Company.Google Scholar
van Fraassen, Bas C. (1973). “Semantic Analysis of Quantum Logic.” In Contemporary Research in the Foundations and Philosophy of Quantum Theory. (University of Western Ontario Series in Philosophy of Science, Vol. 2.) Edited by Hooker, C.A. Dordrecht: D. Reidel Publishing Co. Pages 80–113.Google Scholar