Article PDF
Avoid common mistakes on your manuscript.
Bibliography
Bergmann, G., ‘The Logic of Quanta’, American J. of Physics 15 (1947) 497–508.
Beth, E. W., ‘Analyse sémantique des théories physiques’, Synthese 7 (1948–9) 206–207.
Beth, E. W., ‘Towards an Up-to-Date Philosophy of Natural Sciences’, Methodos 1 (1949) 178–185.
Beth, E. W., ‘Semantics of Physical Theories’, Synthese 12 (1960) 172–175.
Beth, E. W., Mathematical Thought, D. Reidel, Dordrecht, 1966.
Birkhoff, G., Lattice Theory, 2nd ed., Amer. Math. Soc., Providence, R. I., 1948.
Birkhoff, G. and J. von Neumann, ‘The Logic of Quantum Mechanics’, Annals of Math. 37 (1936) 823–843.
Bunge, M., Quantum Theory and Reality, vol 2, Springer-Verlag, Berlin 1967.
Destouches, J., ‘Les principles de la mécanique générale’ Actualités scientifiques et industrielles 140, 1934.
Destouches, J., ‘Intervention d'une logique modalité dans une théorie physique’, Synthese 7 (1948–9) 411–417.
Destouches-Février, P., ‘Les relations d'incertitude de Heisenberg et la logique’, Comptes Rendus de l'Academie des Sciences, 204 (1937) 481–483.
Destouches-Février, P., ‘Logique et théories physiques’, Synthese 7 (1948–9) 400–410.
Destouches-Février, P., La structure des théories physiques, Paris 1951.
Destouches-Février, P., ‘La logique des propositions experimentales’, in Applications scientifiques de la logique mathématique, Paris, 1954, pp. 115–118.
Destouches-Février, P., ‘Logical Structures of Physical Théories’, in Axiomatic Method (ed. by L. Henkin, P. Suppes, and A. Tarski), North-Holland Publ. Co., Amsterdam, 1959, pp. 376–389.
Dirac, P. A. M., ‘The Quantum Algebra’, Proc. Camb. Philos. Soc. 23 (1926) 412–418.
Emch, G. and J. M. Jauch, ‘Structures logiques et mathématiques en physique quantique’, Dialectica 19 (1965) 259–79.
Falk, G., ‘Axiomatics as a Method for the Formation of Physical Theories’, Z. Phys. 130 (1951) 51.
Feyerabend, P., ‘Reichenbach's Interpretation of Quantum Mechanics’, Philos. Studies 9 (1958) 49–59.
Feyerabend, P., ‘Bemerkungen zur Verwendung nicht-klassischer Logiken in Quantentheorie’, in Deskription, Analytizität, und Existenz (ed. by. P. Weingartner), Salzburg 1966, pp. 351–359.
Fine, A., ‘Logic, Probability and Quantum Theory’, Philos. of Sci. 35 (1968) 101–111.
Finkelstein, D., ‘The Logic of Quantum Physics’, Trans. New York Acad. Sci., 2 Ser. 2, 25 (1962–3), 621–637.
Finkelstein, D., ‘The Physics of Logic’, Internat. Centre for Theor. Phys., Trieste, Report IC/68/35, 631–637.
Finkelstein, D., ‘Matter, Space and Logic’, in Boston Studies in the Philosophy of Science, vol. V (ed. by R. S. Cohen and M. Wartofsky), D. Reidel, Dordrecht, 1969, pp. 199–215.
Van Fraasen, Bas, ‘Meaning Relation among Predicates’, Nous 1 (1967) 161–179.
Van Fraasen, Bas, ‘Presuppositions and Supervaluations and Free Logic’, in The Logical Way of Doing Things (ed. by K. Lambert), New Haven, Yale University Press, 1969.
Van Fraasen, Bas, ‘The Labyrinth of Quantum Logics’, paper read at the Bienniel Meeting of the Philosophy of Science Association, Pittsburgh, October 1968.
Van Fraasen, Bas, ‘Presupposition, Implication and Self-reference’, Jour. of Philos. 65 (1968) 136–152.
Van Fraasen, Bas, ‘Singular Terms, Truth-value Gaps and Free Logic’, Jour. of Philos. 63 (1966) 481–495.
Fuchs, W. R., ‘Ansätze zu einer Quantenlogik’, Theoria 30 (1964) 137–140.
Gudder, S., ‘Systems of Observables in Axiomatic Quantum Mechanics’, J. Math. Phys. 8 (1967) 2109.
Guenin, M., ‘Axiomatic Foundations of Quantum Theories’, J. Math. Phys. 7 (1966) 271.
Hack, M., ‘Relation Between Measurement Theory and Symbolic Logic’, Nuovo Cimento 54B (1968) 147.
Hubner, K., ‘Über den Begriff der Quantenlogik’, Sprache in techn. Zeitalter, 1964, 725–734.
Jauch, J. M., ‘Systems of Observables in Quantum Mechanics’, Helv. Phys. Acta 33 (1960) 711–726.
Jauch, J. M., ‘The Problem of Measurement in Quantum Mechanics’, Helv. Phys. Acta 37 (1964) 293–316.
Jauch, J. M., Foundations of Quantum Mechanics, Addison-Wesley, New York, 1968.
Jauch, J. M., and C. Piron, ‘Can Hidden Variables Be Excluded in Quantum Mechanics?’, Helv. Phys. Acta. 36 (1963) 827–837.
Jordan, P., ‘On the Axiomatic Foundation for Quantum Mechanics’, Z. Phys. 133 (1952) 21.
Jordan, P., ‘Quantenlogik und das kommutative Gesetz’, in The Axiomatic Method (ed. by L. Henkin, P. Suppes, and A. Tarski), North-Holland Publ. Co., Amsterdam, 1959, pp. 365–375.
Kakutani, S. and G. Mackey, ‘Ring and Lattice Characterizations of Complex Hilbert Space’, Bull. Amer. Math. Soc. 52 (1946) 727–733.
Kochen, S. and E. P. Specker, ‘Logical Structures Arising in Quantum Theory’, in The Theory of Models (ed. by J. W. Addison et al.), North-Holland, Publ. Co., Amsterdam, 1965, pp. 177–189.
Kunsemüller, H., ‘Zur Axiomatik der Quantenlogik’, Philos. Nat. 8 (1964) 363–376.
Ludwig, G., Die Grundlagen der Quantenmechanik, Springer-Verlag, Berlin, 1954.
Ludwig, G., ‘Axiomatic Quantum Statistics of Macroscopic Systems’, in Teorie ergodiche (ed. by P. Caldirola), Academic Press, New York, 1961, pp. 57–132.
Ludwig, G., ‘Versuch einer axiomatischen Grundlegung der Quantenmechanik und allgemeinerer physikalischer Theorien’, Zeit. Phys. 181 (1964) 233–260.
Ludwig, G., ‘An Axiomatic Foundation of Quantum Mechanics on a Non-Subjective Basis’, in Quantum Theory and Reality (ed. by M. Bunge), Springer-Verlag, Berlin, 1967, pp. 98–104.
Mackey, G., ‘Quantum Mechanics and Hilbert Space’, Amer. Math. Monthly 64 (1957) 45–57.
Mackey, G., The Mathematical Foundations of Quantum Mechanics, Benjamin, Inc., New York, 1963.
McKinsey, J. C. C. and P. Suppes, ‘Review of P. Destouches-Février's “La Structure des théories physiques”’, Jour. Sym. Logic. 19 (1954) 52–55.
Margenau, H., ‘Application of Many-Valued Systems of Logic to Physics’, Phil. Sci. 1 (1933) 118.
Margenau, H., ‘Probability, Many-Valued Logics, and Physics’, Phil. Sci. 6 (1939) 65.
Miller, M., ‘The Logic of Indeterminacy in Quantum Mechanics’, Ph.D. Thesis, Brown University (1961).
Mittelstaedt. P., ‘Untersuchungen zur Quantenlogik’, Sitzungsber. Bayr. Akad. Wiss. Math.-Nat. Kl. (1959), 321–386.
Mittelstaedt, P., ‘Über die Gültigkeit der Logik in der Natur’, Naturwiss. 47 (1960) 385–391.
Mittelstaedt, P., ‘Quantenlogik’, Forthschr. Phys. 9 (1961) 106–147.
Mittelstaedt, P., Philosophische Probleme der modernen Physik, 2nd ed., Bibliographisches Institut, Mannheim, 1966.
Müller, H., ‘Merkwertige Logik und Quantenphysik’, Phys. Bl. 10 (1954) 151–157.
Von Neumann, J., Mathematical Foundations of Quantum Mechanics, Princeton University Press, 1955.
Von Neumann, J., ‘On the Algebraic Generalization of the Quantum Mechanical Formalism’, Part I, in Collected Works of J. von Neumann (ed. by A. H. Taub), vol. III, Oxford 1961, pp. 492–561.
Von Neumann, J., ‘Continuous Geometries with a Transition Probability’, Collected Works of J. von Neuman, (ed. by A. H. Taub), vol. IV, Oxford 1961, pp. 191–194.
Von Neumann, J., ‘Quantum Logics (strict- and probability-logics)’ in Collected Works of J. von Neumann, (ed. by A. H. Taub), vol. IV, Oxford 1961, pp. 195–197.
Piron, C., ‘Axiomatic Quantum Scheme’, Helv. Phys. Acta. 37 (1964) 439.
Popper, K., ‘Birkhoff and von Neumann's Interpretation of Quantum Mechanics’, Nature 219 (1968) 682–685.
Prugovecki, E., ‘An Axiomatic Approach to the Formalism of Quantum Mechanics, I, and II’, J. Math. Phys., 7 (1966) 1054, 1070.
Putnam, H., ‘Three-Valued Logic’, Philos. Studies 8 (1957) 73–80.
Putnam, H., ‘Is Logic Empirical?’, in Boston Studies in the Philosophy of Science, vol. V (ed. by R.S. Cohen and M. Wartofsky), Humanities Press, New York and D. Reidel, Dordrecht, 1969.
Quine, W. V., From a Logical Point of View, Harper and Row, New York, 1963.
Reichenbach, H., Philosophic Foundations of Quantum Mechanics. Berkeley, Calif. 1944.
Reichenbach, H., ‘Über die erkenntnistheoretische Problemlage und den Gebrauch einer dreiwertigen Logik in der Quantenmechanik’, Z. Naturforsch. 6a (1951) 569.
Reichenbach, H., ‘The Logical Foundations of Quantum Mechanics’, Ann. Inst. Poincaré 13 (1953) 109.
Richter, E., ‘Bemerkungen zur Quantenlogik’, Philos. Nat. 8 (1964) 225–231.
Scheibe, S., Die kontingenten Aussagen in der Physik, Athenäum Verlag, Frankfurt, 1964.
Segal, I. E., Mathematical Problems of Relativistic Physics, Amer. Math. Soc. Providence, Rhode Is., 1963.
Sherman, S., ‘On Segal's Postulates for General Quantum Mechanics’, Ann. Math. 64 (1956) 593–601.
Strauss, M., ‘Mathematics as a Logical Syntax — a Method to Formalize the Language of a Physical Theory’, Erkenntnis 7 (1937–38), 147–153.
Suppes, P., ‘Probability Concepts in Quantum Mechanics’, Philos. Sci. 28 (1961) 378–389.
Suppes, P., ‘The Role of Probability in Quantum Mechanics’, in Philosophy of Science: The Delaware Seminar (ed. by B. Baumrin), Wiley, New York, (1962–3), pp. 319–337.
Suppes, P., ‘Logics Appropriate to Empirical Theories’, in Theory of Models (ed. by J. W. Addison, L. Henkin and A. Tarski), North-Holland Publ. Co., Amsterdam, 1965, pp. 364–375.
Suppes, P., ‘The Probabilistic Argument for a Non-classical Logic in Quantum Mechanics’, Philos. Sci. 33 (1966) 14–21.
Toll, J., ‘Causality and the Dispersion Relation: Logical Foundations’, Phys. Rev. 104 (1956) 1760.
Varadarajan, V. S., ‘Probability in Physics and a Theorem on Simultaneous Observability’, Comm. Pure Appl. Math. 15 (1962) 189–217.
Watanabe, M. S., ‘A Model of Mind-Body Relations in Terms of Modular Logic’, Synthese 13 (1961) 261–302, and Boston Studies in the Philosoply of Science, vol. I (ed. by M. Wartofsky), D. Reidel, Dordrecht.
Watanabe, M. S., ‘Conditional Probability in Physics’, Progress of Theor. Phys., Suppl. (1965), 135–160.
Watanabe, M. S., ‘Algebra of Observation’, Progress of Theor. Phys., Suppl., Nos. 37–8 (1966), 305–367.
Watanabe, M. S., Knowing and Guessing, John Wiley, New York, 1969.
Von Weizsäcker, C. F., ‘Komplementarität und Logik’, Naturw. 42 (1955) 521–529; 545–555.
Von Weizsäcker, C. F., E. Scheibe, and G. Süssmann, ‘Komplementarität und Logik: III. Mehrfache Quantelung’, Zeitschr. für Naturforsch. 13a (1958) 705–721.
Author information
Authors and Affiliations
Additional information
The original version of this paper was read at a meeting of the Boston Colloquim for the Philosophy of Science, 21 January 1969 under the title ‘Quantum Logic Does Not Have to Be Non-classical’. The author wishes to thank Professor R. S. Cohen and the President of Boston University for the hospitality he enjoyed at Boston University as Visiting Associate Professor of Physics during which time he wrote this paper. The present version has been much improved due to conversations with Professors R. S. Cohen and A. Shimony of Boston University and especially with my commentator for that occasion, Professor David Finkelstein of Yeshiva University.
Rights and permissions
About this article
Cite this article
Heelan, P. Quantum and classical logic: Their respective roles. Synthese 21, 2–33 (1970). https://doi.org/10.1007/BF00414186
Issue Date:
DOI: https://doi.org/10.1007/BF00414186