Abstract
It is generally agreed that quantum mechanics (QM) constitutes a revolutionary physical theory, and it has been suggested that the revolutionary character of QM penetrates even to the level of logic. This suggestion stems from at least two sources. First of all, there are the various foundational approaches to QM which propose to formulate quantum theory on the basis of ‘quantum logic’.1 This approach to the postulational foundations of QM originates with the seminal work of Birkhoff and von Neumann (1936), which is based on the Hilbert space formulation of quantum theory expounded by von Neumann in his classic treatise (1932) on the mathematical foundations of QM. A parallel and closely related treatment of QM was proposed by Martin Strauss (1937–38) and developed primarily by Kochen and Specker (see, e.g., 1967). Together these approaches comprise what may be called mainstream (or conventional) quantum logic.2 Secondly, there are a number of nonmainstream quantum logics which have been proposed,3 most notably perhaps by Hans Reichenbach. In his treatise on the philosophical foundations of QM (1944, henceforth PhF), Reichenbach proposed a three-valued truth-functional logic as a means of dealing with certain conceptual tensions arising in the quantum mechanical description of the world.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Birkhoff, G. and von Neumann, J.: 1936, ‘The Logic of Quantum Mechanics’, Ann. Math. 37, 823–43.
Bohr, N.: 1948, ‘On the Notions of Causality and Complementarity’, Dialectica 2, 312–19.
Bub, J.: 1973, ‘On the Completeness of Quantum Mechanics’, in C. A. Hooker (ed.), Contemporary Research in the Foundations and Philosophy of Quantum Theory, D. Reidel, Dordrecht.
Bub, J.: 1974, The Interpretation of Quantum Mechanics, D. Reidel, Dordrecht.
Bub, J. and Demopoulos, W.: 1974b, ‘The Interpretation of Quantum Mechanics’, in R. Cohen and M. Wartofsky (eds.), Boston Studies in the Philosophy of Science, Vol. 13, D. Reidel, Dordrecht.
Demopoulos, W.: 1976, ‘The Possibility Structure of Physical Systems’, in W. Harper and C. A. Hooker (eds.), Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, Vol. 3, D. Reidel, Dordrecht, pp. 55–80.
Destouches-Fevrier, P.: 1951, Structure des Theories Physiques, Paris, 1951.
Fine, A.: 1973, “Probability and the Interpretation of Quantum Mechanics’, British J. Philos. Sci. 24, 1–37.
Fine, A.: 1974, ‘On the Completeness of Quantum Mechanics’, Synthese 29, 257–89. Reprinted in P. A. Suppes (ed.), Logic and Probability in Quantum Mechanics, D. Reidel, Dordrecht, 1976, pp. 249–81.
Gardner, M.: 1972, ‘Two Deviant Logics for Quantum Theory: Bohr and Reichenbach’, British J. Philos. Sci. 23, 89–109.
Haack, S.: 1974, Deviant Logic, Cambridge Press, Cambridge.
Hardegree, G. M.: 1974, ‘The Conditional in Quantum Logic’, Synthese 29, 63–80, reprinted in P. A. Suppes (ed.), Logic and Probability in Quantum Mechanics, D. Reidel, Dordrecht, 1976, pp. 55–72.
Hardegree, G. M., 1975, ‘Stalnaker Conditionals and Quantum Logic’, J. Philos. Logic 4, 399–421.
Hardegree, G. M.: 1976a, ‘The Conditional in Abstract and Concrete Quantum Logic’, in C. A. Hooker (ed.), The Logico-Algebraic Approach to Quantum Mechanics, Vol. 2, D. Reidel, Dordrecht, in press.
Hardegree, G. M.: 1976b, ‘Relative Compatibility in Conventional Quantum Mechanics’, Foundations of Physics, in press.
Hardegree, G. M.: 1976c, ‘The Modal Interpretation of Quantum Mechanics’, Proceedings of the Fifth Bienial Meeting of the Philosophy of Science Association.
Hardegree, G. M.: 1976d, ‘Semantics and the Interpretation of Quantum Mechanics. Part I’, unpublished ms.
Hempel. C. G.: 1945, ‘Review of Reichenbach’s Philosophic Foundations of Quantum Mechanics’, J. Symbolic Logic 10, 97–100.
Hempel, C. G.: 1970, ‘On the “Standard Conception” of Scientific Theories’, in M. Radner and S. Winokur (eds.), Minnesota Studies in the Philosophy of Science, Minnesota Press, Minneapolis.
Hooker, C. A. (ed.): 1975, The Logico-Algebraic Approach to Quantum Mechanics, Vol. 1: Historical Evolution, D. Reidel, Dordrecht.
Hooker, C. A. and van Fraassen, B. C.: 1976, ‘A Semantic Analysis of Niels Bohr’s Philosophy of Quantum Theory’, in W. L. Harper and C. A. Hooker (eds.), Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, Vol. 3, D. Reidel, Dordrecht, pp. 221–241.
Jammer, M.: 1974, The Philosophy of Quantum Mechanics, Wiley, New York.
Jauch, J. M.: 1968, Foundations of Quantum Mechanics, Addison-Wesley, New York.
Jauch, J. M.: 1974, ‘The Quantum Probability Calculus’, Synthese 29, 131–154, reprinted
P. A. Suppes (ed.), Logic and Probability in Quantum Mechanics, D. Reidel, Dordrecht, 1976, pp. 123–46.
Kochen, S. and Specker, E. P.: 1967, ‘The Problem of Hidden Variables in Quantum Mechanics’, J. Math. Mech. 17, 59–87.
Lambert, K.: 1969, ‘Logical Truth and Microphysics’, in K. Lambert (ed.), The Logical Way of Doing Things, Yale Press, New Haven.
Lewis, D.: 1970, ‘General Semantics’, Synthese 22, 18–67.
Mackey, G. W.: 1963, Mathematical Foundations of Quantum Mechanics, Benjamin, New York.
Montague, R.: 1968, ‘Pragmatics’ in R. Klibansky (ed.), Contemporary Philosophy: A Survey, 102–22, La Nuova Italia Editrice, Florence, reprinted in R. H. Thomason ( 1974 ).
Montague, R.: 1970, ‘Pragmatics and Intensional Logic’, Synthese 22, 68–94.
Nilson, D. R.: ‘Hans Reichenbach on the Logic of Quantum Mechanics’, Synthese 34, 313–360.
Pauli, W.: 1964, ‘Reviewing Study of Hans Reichenbach’s Philosophic Foundations of Quantum Mechanics, in Collected Scientific Papers, Vol. 2 (ed. by R. Kronig and V. Weisskopf), Interscience, New York.
Piron, C.: 1964, ‘Axiomatique Quantique’, Helv. Phys. Acta 37, 439–68.
Piron, C.: 1972, ‘Survey of General Quantum Physics’, Found. Phys. 2, 287–314.
Reichenbach, H.: 1944, Philosophic Foundations of Quantum Mechanics, Univ. of California Press, Berkeley.
Reichenbach, H.: 1947, Elements of Symbolic Logic, Free Press, New York.
Rescher, N.: 1969, Many-Valued Logic, McGraw-Hill, New York.
Sneed, J.: 1971, The Logical Structure of Mathematical Physics, D. Reidel, Dordrecht.
Stein, H.: 1972, ‘On the Conceptual Structure of Quantum Mechanics’, in R. G. Colodny (ed.), Paradigms and Paradoxes, Pittsburgh Press, Pittsburgh.
Strauss, M.: 1937–38, ‘Mathematics as Logical Syntax — a Method to Formalize the Language of a Physical Theory’, Erkenntnis 1, 147–53.
Suppe, F.: 1967, Meaning and Use of Models in Mathematics and the Exact Sciences, Doctoral Dissertation, Department of Philosophy, University of Michigan.
Suppe, F.: 1972, ‘Theories, Their Formulations, and the Operational Imperative’, Synthese 25, 129–64.
Suppes, P. A.: 1967, ‘What is a Scientific Theory?’, in S. Morgenbesser (ed.), Philosophy of Science Today, Basic Books, New York.
Thomason, R. H.: 1973, ‘Philosophy and Formal Semantics’, in H. Leblanc (ed.), Truth, Syntax and Modality, North-Holland, Amsterdam.
Thomason, R. H.: (ed.), 1974, Formal Philosophy: Selected Papers of Richard Montague, Yale Press, New Haven
van Fraassen, B. C.: 1970, ‘On the Extension of Beth’s Semantics of Physical Theories’, Philos. Sci. 37, 325–39.
van Fraassen, B. C.: 1968, ‘Presupposition, Implication, and Self-Reference’, J. Philos. 65, 136–52.
van Fraassen, B. C.: 1969, ‘Presuppositions, Supervaluations, and Free Logic’, in K. Lambert (ed.), The Logical Way of Doing Things, Yale Press, New Haven
van Fraassen, B. C.: 1973, ‘Semantic Analysis of Quantum Logic’, in C. A. Hooker (ed.), Contemporary Research in the Foundations and Philosophy of Quantum Theory, D. Reidel, Dordrecht.
van Fraassen, B. C.: 1974, ‘The Ladyrinth of Quantum Logics’, in R. Cohen and M. Wartofsky (eds.), Boston Studies in the Philosophy of Science, Vol. 13, D. Reidel, Dordrecht.
Varadarajan, V. S: 1968, Geometry of Quantum Theory (two vols.), Van Nostrand, Princeton.
von Neumann, J.: 1932, The Mathematical Foundations of Quantum Mechanics (tr. by R. T. Beyer), Princeton Press, 1955 (originally published 1932)
von Weizsäcker, C. F.: 1955, ‘Komplementaritat und Logik’, Naturwissenschaften 42, 521–29 and 545–55
Weyl, H.: 1940, ‘The Ghost of Modality’, in M. Farber (ed.), Philosophical Essays in Memory of Edmund Husserl, Harvard Press, Cambridge.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1977 D. Reidel Publishing Company, Dordrecht, Holland
About this chapter
Cite this chapter
Hardegree, G.M. (1977). Reichenbach and the Logic of Quantum Mechanics. In: Salmon, W.C. (eds) Hans Reichenbach: Logical Empiricist. Synthese Library, vol 132. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9404-1_17
Download citation
DOI: https://doi.org/10.1007/978-94-009-9404-1_17
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-9406-5
Online ISBN: 978-94-009-9404-1
eBook Packages: Springer Book Archive