Advertisement

The Labyrinth of Quantum Logics

  • Bas C. Van Fraassen
Chapter
Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 13)

Abstract

The conceptual structure of the new quantum theory is in some respects so different from that of classical physics that it has from the very beginning suggested radical departures in philosophy and logic. Specifically, a number of writers have considered non-standard systems of logic in connection with quantum mechanics (see bibliography). Two main directions may be discerned, initiated by Reichenbach, and by Birkhoff and von Neumann. The aim of the present paper is first to present a unified exposition of the main systems found in the literature, and second to discuss and evaluate the main logical and philosophical theses and arguments which have concerned the subject of quantum logic.

Keywords

Hilbert Space Quantum Theory Projective Operator Physical Theory Semantic Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. [2]
    Beth, E. W., ‘Analyse Semantique des Theories Physiques’, Synthese 7 (1948–49) 206–207.Google Scholar
  2. [2]
    Beth, E. W., Mathematical Thought D. Reidei Publ. Co., Dordrecht-Holland, 1966.Google Scholar
  3. [3]
    Beth, E. W., Naturphilosophie Noorduijn, Gorinchem, 1948.Google Scholar
  4. [4]
    Beth, E. W., ‘Semantics of Physical Theories’, Synthese 12 (1960), 172–175.CrossRefGoogle Scholar
  5. [5]
    Beth, E. W., ‘Towards an Up-to-date Philosophy of the Natural Sciences’, Metho-dos 1 (1949), 178–185.Google Scholar
  6. [6]
    Birkhoff, G., ‘Lattices in Applied Mathematics’, American Mathematical Society Proc. of Symposia in Pure Mathematics 2 (1961), 155–184.Google Scholar
  7. [7]
    Birkhoff, G. and von Neumann, J., ‘The Logic of Quantum Mechanics’, Annals of Mathematics 37 (1936), 823–843.CrossRefGoogle Scholar
  8. [8]
    Destouches, J-L., ‘Les Principes de la Mécanique Générale’, Actualités Scienti-fiques et Industrielles 140 (1934).Google Scholar
  9. [9]
    Destouches, J.-L., ‘Le Role des Espaces Abstraits en Physique Nouvelle’, Actualités Scientifiques et Industrielles 223 (1935).Google Scholar
  10. [10]
    Emch, G. and Jauch, J. M., ‘Structures logiques et mathematiques en physique quantique’, Dialectica 19 (1965), 259–279.CrossRefGoogle Scholar
  11. [11]
    Février, P., ‘Logical Structure of Physical Theories’ in L. Henkin et al. (eds.), The Axiomatic Method North-Holland Publ. Co., Amsterdam, Holland, 1959, pp. 376–389.CrossRefGoogle Scholar
  12. [12]
    Février, P., ‘Les relations d’incertitude de Heisenberg et la logique’, Comptes Rendus de l Académie des Sciences 204 (1937), 481–483.Google Scholar
  13. [13]
    Feyerabend, P., ‘Reichenbach’s Interpretation of Quantum Mechanics’, Philosophical Studies 9 (1958), 49–59.CrossRefGoogle Scholar
  14. [14]
    Fuchs, W. R., ‘Ansatze zu einer Quantenlogik’, Theoria 30 (1964), 137–140.Google Scholar
  15. [15]
    Green, N. S., Matrix Mechanics Noordhoff, Groningen, 1965.Google Scholar
  16. [16]
    Halmos, P. R., Introduction to Hilbert Space Chelsea, New York, 1957.Google Scholar
  17. [17]
    Jordan, P., ‘Quantenlogik und das Kommutative Gesetz’, in L. Henkin et al. (eds.), The Axiomatic Method North-Holland Publ. Co., Amsterdam, Holland, 1959, pp. 365–375.CrossRefGoogle Scholar
  18. [18]
    Kochen, S. and Specker, E. P., ‘Logical Structures Arising in Quantum Theory. in J. W. Addison et al. (eds.), The Theory of Models North-Holland Publ. Co., Amsterdam, Holland 1965, pp. 177–189.Google Scholar
  19. [19]
    Lambert, K., ‘Logic and Microphysics’, in K. Lambert (ed.), The Logical Way of Doing Things Yale University Press, New Haven, 1969, pp. 93–117.Google Scholar
  20. [20]
    Ludwig, G., Die Grundlagen der Quantenmechanik Springer-Verlag, Berlin, 1954.Google Scholar
  21. [21]
    Mackey, G. W., The Mathematical Foundations of Quantum Mechanics Benjamin, New York, 1963.Google Scholar
  22. [22]
    McKinsey, J. C. C. and Suppes, P., Review of P. Destouches-Février, ‘La Structure des Theories Physiques’, Journal of Symbolic Logic 19 (1954), 52–55.CrossRefGoogle Scholar
  23. [23]
    Mandi, F., Quantum Mechanics Academic Press, New York, 1957.Google Scholar
  24. [24]
    Putman, H., ‘Three-Valued Logic’, Philosophical Studies 8 (1957), 73–80.CrossRefGoogle Scholar
  25. [25]
    Quine, W. V. O., From a Logical Point of View Harper and Row, New York, 1963.Google Scholar
  26. [26]
    Reichenbach, H., Philosophic Foundations of Quantum Mechanics University of California Press, Berkeley, 1944.Google Scholar
  27. Strauss, M., ‘Mathematics as Logical Syntax — a Method to Formalize the Language of a Physical Theory’, Erkenntnis 7 (1937–38), 147–153.Google Scholar
  28. [28]
    Suppes, P., ‘Logics Appropriate to Empirical Theories’, in J. W. Addison et al. (eds.), The Theory of Models North-Holland Publ. Co., Amsterdam, Holland, 1965, pp. 364–375.Google Scholar
  29. [28]
    Suppes, P., ‘The Probabilistic Argument for a Non-Classical Logic in Quantum Mechanics’, Philosophy of Science 33 (1966), 14–21.CrossRefGoogle Scholar
  30. [30]
    Suppes, M., ‘Probability Concepts in Quantum Mechanics’, Philosophy of Science 28 (1961), 378–389.CrossRefGoogle Scholar
  31. [31]
    Temple, C., The General Principles of Quantum Theory Methuen, London, 1961.Google Scholar
  32. [32]
    van Fraassen, B. C., ‘Meaning Relations Among Predicates’, Nous 1 (1967), 161–179.CrossRefGoogle Scholar
  33. [33]
    van Fraassen, B. C., ‘Presupposition, Implication, and Self-Reference’, Journal of Philosophy 65 (1968), 136–152.CrossRefGoogle Scholar
  34. [34]
    van Fraassen B. C, ‘Presuppositions, Supervaluations, and Free Logic’, in K. Lambert (ed.), The Logical Way of Doing Things Yale University Press, New Haven 1969, pp. 67–91.Google Scholar
  35. [35]
    van Fraassen, B. C., ‘Singular Terms, Truth-Value Gaps, and Free Logic’, Journal of Philosophy 63 (1966), 481–495.CrossRefGoogle Scholar
  36. [36]
    Varadarajan, V. S., ‘Probability in Physics and a Theorem on Simultaneous Observability’, Comm. Pure Appl. Math. 15 (1962), 189–217.CrossRefGoogle Scholar
  37. [37]
    von Neumann, J., Mathematical Foundations of Quantum Mechanics (tr. by R. T. Beyer), Princeton University Press, Princeton, 1955.Google Scholar
  38. [38]
    von Neumann, J., ‘Quantum Logics’, unpublished; reviewed by A. H. Taub in John von Neumann, Collected Works (vol. 4, pp. 195–197), Macmillan, New York, 1962.Google Scholar
  39. [39]
    Weyl, H., ‘The Ghost of Modality’, in M. Farber (ed.), Philosophical Essays in Memory of Edmund Husserl Harvard University Press, Cambridge, Mass., 1940, pp. 278–303.Google Scholar
  40. [40]
    Weyl, H., The Theory of Groups and Quantum Mechanics Dover, New York, 1950.Google Scholar
  41. [41]
    Zadeh, L. A. and Desoer, C. A., Linear System Theory: The State Space Approach McGraw-Hill, New York, 1963.Google Scholar
  42. [42]
    Zierler, N., ‘Axioms for Non-Relativistic Quantum Mechanics’, Pacific Jounal of Mathematics 11 (1961), 1151–1169.Google Scholar
  43. [43]
    Zierler, N. and Schlesinger, M., ‘Boolean Embeddings of Orthomodular Sets and Quantum Logic’, Duke Math. Journal 32 (1965), 251–262.CrossRefGoogle Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1974

Authors and Affiliations

  • Bas C. Van Fraassen
    • 1
  1. 1.Univresity of TorontoCanada

Personalised recommendations