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The Metalogic of Quantum Logic

Published online by Cambridge University Press:  28 February 2022

Peter Mittelstaedt
Peter Mittelstaedt*
Affiliation:
Institut für Theoretische Physik der Universität zu Köln, Germany
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Extract

In order to establish the object language of quantum physics, we begin with a quantum mechanical system S (atom, nucleus, elementary particle) and consider propositions A,B,… about this system S which can be proved or disproved by measuring processes. These propositions will be called elementary propositions. We will assume here that elementary propositions are value definite, i.e.,there always exists an experimental testing procedure which decides between truth and falsity of the respective proposition.

The logical connectives A ∧ B (A and B), A ∨ B (A or B), A → B (A then B) and ┐ A (not A) will be defined by means of dialogs. A dialog is a formalized kind of discussion between two participants, the proponent P who asserts a certain proposition and the opponent 0 who attempts to refute it.

Type
Part VII. Quantum Logic
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1978 , Issue 1: Volume One: Contributed Papers 1978 , 1978 , pp. 249 - 256
Copyright
Copyright © 1978 by the Philosophy of Science Association

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References

Hughes, G.E. and Cresswell, M.J. An Introduction of Modal Logic. London: Methuen and Co., Ltd., 1968.Google Scholar
Mittelstaedt, P. “Quantenlogik.” Fortschritte der Physik 9(1961): 106–147.CrossRefGoogle Scholar
Mittelstaedt, P. Philosophical Problems of Modern Physics. (trans.) Riemer, W. and revised R. Cohen. (Boston Studies in the Philosophy of Science, Volume XVIII). Dordrecht: D. Reidel, 1976. (Translated from the 4th edition of Philosophische Probleme Der Modernen Physik.)CrossRefGoogle Scholar
Mittelstaedt, P. “Quantum Logic.” In Problems in the Foundations of Physics. (Proceedings of the International School of Physics “Enrico Fermi”, Varenna (1977) Course LXVII). Forthcoming.Google Scholar
Mittelstaedt, P. “The Modal Logic of Quantum Logic.” Journal of Philosophical Logic (forthcoming).Google Scholar
Mittelstaedt, P. and Stachow, E.W. “The Principle of Excluded Middle in Quantum Logic.” Journal of Philosophical Logic 7(1978): 181–208.CrossRefGoogle Scholar
Stachow, E.W. “The Completeness of Quantum Logic’ Journal of Philosophical Logic 5(1976): 237–279.CrossRefGoogle Scholar