Abstract
In this lecture I will present an approach to quantum modal logic which is based on a meta-linguistic interpretation of the modalities and which makes use of a proof-theoretical semantics. The meta-linguistic approach to modalities goes back to Carnap and has been used by several authors. It seems to be very appropriate for the present problem. The language of quantum physics which is used here is based on the material quantum dialog game, which has already successfully been used for establishing the formal object of quantum logic.
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References
P. Mittelstaedt, “Quantum Logic”, D. Reidel Publishing C., Dordrecht, Holland, (1978).
E.W. Stachow, Zur Begründung der Quantenlogik durch die argumentativen orbedingungen einer Wissenschaftssprache, in “Grundlagen der Quantentheorie”, P. Mittelstaedt and J. Pfarr eds., Bibliographisches Institut, Mannheim (1979).
E.W. Stachow, Completeness of quantum logic. Journal of Philosophical Logic 5 (1976), pp. 237–280.
P. Mittelstaedt, The meta-logic of quantum logic, in “Proceedings of the PSA 1978”, P.D. Asquith and I. Hacking eds.. Philosophy of Science Association, East Lansing, Mich. (1978), Vol. 1, p. 249.
G.E. Hughes and M.J. Cresswell, “An Introduction to Modal Logic”, London (1968).
P. Lorenzen and O. Schwemmer, “Konstruktive Logik, Ethik und Wissenschaftstheorie”, Bibliographisches Institut, Mannheim (1977).
P. Mittelstaedt, The modal logic of quantum logic. Journal of Philosophical Logic (1979).
G.W. Leibniz, Theodizee, Part 1, No. 8.
S.A. Kripke, A completeness theorem in modal logic. Journal of Symbolic Logic 24 (1959), pp. 1–14.
P. Mittelstaedt and E.W. Stachow, The principle of the excluded middle in quantum logic. Journal of Philosophical Logic 7 (1978), pp. 181–208.
F.J. Burghardt, “Modale Quantenmetalogik mit dialogischer Begründung”, Dissertation, Universität Köln (1979).
E.W. Stachow, An operational approach to quantum probability, in “Physical Theory as Logico-Operational Structure”, C. Hooker ed., D. Reidel, Dordrecht (1978), pp. 285–321.
E.W. Stachow, Operational quantum probabilities, in “Proceedings of the International Congress on Logic, Methodology and Philosophy of Science”, Hannover (1979).
P. Mittelstaedt, On the applicability of the probability concept to quantum theory, in “Foundations of Probability Theory, Statistical Inference and Statistical Theories of Science, Vol. III”, Harper and Hooker eds., D. Reidel, Dordrecht (1976) pp. 155–167.
J.M. Jauch, The quantum probability caluculus, in “Quantum Mechanics, A Half Century Later”, J. Leite Lopes and M. Paty eds., D. Reidel, Dordrecht (1977), pp. 39–62.
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© 1981 Plenum Press, New York
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Mittelstaedt, P. (1981). The Dialogic Approach to Modalities in the Language of Quantum Physics. In: Beltrametti, E.G., van Fraassen, B.C. (eds) Current Issues in Quantum Logic. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3228-2_17
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DOI: https://doi.org/10.1007/978-1-4613-3228-2_17
Publisher Name: Springer, Boston, MA
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