The Dialogic Approach to Modalities in the Language of Quantum Physics

  • Peter Mittelstaedt


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.


Modal Logic Object Language Quantum Logic Quantum Probability Scientific Language 
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  1. 1.
    P. Mittelstaedt, “Quantum Logic”, D. Reidel Publishing C., Dordrecht, Holland, (1978).MATHCrossRefGoogle Scholar
  2. 2.
    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).Google Scholar
  3. 3.
    E.W. Stachow, Completeness of quantum logic. Journal of Philosophical Logic 5 (1976), pp. 237–280.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    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.Google Scholar
  5. 5.
    G.E. Hughes and M.J. Cresswell, “An Introduction to Modal Logic”, London (1968).Google Scholar
  6. 6.
    P. Lorenzen and O. Schwemmer, “Konstruktive Logik, Ethik und Wissenschaftstheorie”, Bibliographisches Institut, Mannheim (1977).Google Scholar
  7. 7.
    P. Mittelstaedt, The modal logic of quantum logic. Journal of Philosophical Logic (1979).Google Scholar
  8. 8.
    G.W. Leibniz, Theodizee, Part 1, No. 8.Google Scholar
  9. 9.
    S.A. Kripke, A completeness theorem in modal logic. Journal of Symbolic Logic 24 (1959), pp. 1–14.MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    P. Mittelstaedt and E.W. Stachow, The principle of the excluded middle in quantum logic. Journal of Philosophical Logic 7 (1978), pp. 181–208.MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    F.J. Burghardt, “Modale Quantenmetalogik mit dialogischer Begründung”, Dissertation, Universität Köln (1979).Google Scholar
  12. 12.
    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.Google Scholar
  13. 13.
    E.W. Stachow, Operational quantum probabilities, in “Proceedings of the International Congress on Logic, Methodology and Philosophy of Science”, Hannover (1979).Google Scholar
  14. 14.
    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.Google Scholar
  15. 15.
    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.CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1981

Authors and Affiliations

  • Peter Mittelstaedt
    • 1
  1. 1.Institut für Theoretische Physik der Universität zu KölnKöln 41Germany

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