Abstract
The present work, which is a sequel to ‘Reichenbach and the Logic of Quantum Mechanics’ (this volume; henceforth referred to as Part I), endeavors to place Reichenbach’s proposed quantum logic RQL within the context of his overall interpretation of quantum mechanics (QM). Although it is argued in Part I that Reichenbach intended RQL to provide an alternative logico-linguistic framework for the formulation of the quantum theory, in the present work we interpret RQL as being entirely on a par with mainstream quantum logic (MQL). In particular, we regard RQL as pertaining, not to the theory formulation language TL(QM), but rather exclusively to the elementary (observation) language RL(QM), which is obtained from the elementary language OL(QM), associated with MQL, by adding a variety of three-valued truth-functional connectives. Also, like Part I, the present work is essentially comparative in nature, the purpose being to analyze Reichenbach’s interpretation of QM in the light of more recently proposed interpretations. We take the chief themes of Reichenbach’s interpretation to include the following: the distinction between phenomena and interphenomena; the distinction between exhaustive and restrictive interpretations of QM; the Principle of equivalent descriptions; the proposal of a non-bivalent semantics for the observation language of QM.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abbott, J. C., 1967, ‘Semi-Boolean Algebra’, Matematicki Vesnik 4, 177–98.
Abbott, J. C., 1969, Sets, Lattices, and Boolean Algebras, Allyn and Bacon, Boston.
Belnap, N. D., Jr., 1970, ‘Conditional Assertion and Restricted Quantification’, Nous 4, 1–12.
Birkhoff, G., and von Neumann, J., 1936, ‘The Logic of Quantum Mechanics’, Annals of Mathematics 37, 823–43.
Bub, J., 1974, The Interpretation of Quantum Mechanics, D. Reidel, Dordrecht, Holland.
Bub, J., 1976, ‘Randomness and Locality in Quantum Mechanics’, in P. A. Suppes, ed. (1976), 397–420.
Demopoulos, W., 1976, ‘The Possibility Structure of Physical Systems’, in W. Harper and C. A. Hooker, eds. (1976) Vol. III, 55–80.
Dunn, J. M., 1975, ‘Axiomatizing Belnap’s Conditional Assertion’, Journal of Philosophical Logic 4, 383–97.
Finch, P. D., 1969, ‘On the Structure of Quantum Logic’, Journal of Symbolic Locic 34, 275–82.
Finch, P. D., 1976, ‘Quantum Mechanical Physical Quantities as Random Variables’, in W. Harper and C. A. Hooker, eds. (1976), Vol. III, 81–103.
Fine, A., 1973, ‘Probability and the Interpretation of Quantum Mechanics’, British Journal for the Philosophy of Science 24, 1–37.
Fine, A., 1974, ‘On the Completeness of Quantum Mechanics’, Synthese 29, 257–289, reprinted in Suppes, ed. (1976), 249–281.
Foulis, D. J., 1960, ‘Baer *-Semigroups’, Proceedings of the American Mathematical Society 11, 648–54.
Foulis, D. J., and Randall, C. H., 1972, ‘Operational Statistics, I. Basic Concepts’, Journal of Mathematical Physics 13, 1667–75.
Foulis, D. J., and Randall, C. H., 1974, ‘Empirical Logic and Quantum Mechanics’, Synthese 29, 81–111, reprinted in Suppes, ed. (1976), 73–103.
Gleason, A. M., 1957, ‘Measures on the Closed Subspaces of Hilbert Space’, Journal of Mathematics and Mechanics 6, 885–93.
Greechie, R. J., and Gudder, S. P., 1973, ‘Quantum Logics’, in C. A. Hooker, ed. (1973), 143–173.
Gudder, S. P., 1972, ‘Partial Algebraic Structures Associated with Orthomodular Posets’, Pacific Journal of Mathematics 41, 717–30.
Hardegree, G. M., 1974, ‘The Conditional in Quantum Logic’, Synthese 29, 63–80, reprinted in Suppes, ed. (1976), 55–72.
Hardegree, G. M., ‘Stalnaker Conditionals and Quantum Logic’, Journal of Philosophical Logic 4, 399–421.
Hardegree, G. M., 1976, ‘The Modal Interpretation of Quantum Mechanics’, Proceedings of the Fifth Biennial Meeting of the Philosophy of Science Association, October, 1976, Chicago.
Hardegree, G. M., 1977, ‘Relative Compatibility in Conventional Quantum Mechanics’, Foundations of Physics 7, 495–510.
Hardegree, G. M., 1978, ‘The Conditional in Abstract and Concrete Quantum Logic’, in C. A. Hooker (ed.), The Logico-Algebraic Approach to Quantum Mechanics, Vol. II, D. Reidel, Dordrecht, Holland, 49–108.
Harper, W. L., and Hooker, C. A. (eds.), 1976, Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, D. Reidel, Dordrecht, Holland.
Hooker, C. A. (ed.), 1973, Contemporary Research in the Foundations and Philosophy of Quantum Theory, D. Reidel, Dordrecht, Holland.
Hooker, C. A. (ed.), 1975, The Logico-Algebraic Approach to Quantum Mechanics, Volume I: Historical Evolution, D. Reidel, Dordrecht, Holland.
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 (1976), Vol. 3, 221–241.
Jauch, J. M., 1968, Foundations of Quantum Mechanics, Addison-Wesley, New York.
Kochen, S., and Specker, E. P., 1967, ‘The Problem of Hidden Variables in Quantum Mechanics’, Journal of Mathematics and Mechanics 17, 59–87.
Kolmogorov, A. N., 1933, Foundations of the Theory of Probability (tr. Nathan Morrison), Chelsea Publishing Co., New York, 1950 (orig. 1933).
Lambert, Karel, 1969, ‘Logical Truth and Microphysics’ in Lambert, K. (ed.) The Logical Way of Doing Things, Yale University Press, New Haven.
Lewis, D., 1973, Counterfactuals, Harvard University Press, Cambridge, Mass.
Mackey, G. W., 1963, Mathematical Foundations of Quantum Mechanics, Benjamin, New York.
Nagel, E., 1945, ‘Review of Hans Reichenbach’s Philosophic Foundations of Quantum Mechanics’, Journal of Philosophy 42, 437–44.
Piron, C., 1964, ‘Axiomatique Quantique’, Helvetica Physica Acta 37, 339–68.
Pool, J. C. T., 1968, ‘Baer *-Semigroups and the Logic of Quantum Mechanics’, Communications in Mathematical Physics 9, 118–41.
Popper, K. R., 1957, ‘The Propensity Interpretation of the Calculus of Probability, and the Quantum Theory’, in S. Kürner (ed.), 1957, Observation and Interpretation in Philosophy of Physics, Butterworth, London, 65–70.
Popper, K.R., 1959, ‘The Propensity Interpretation of Probability’, British Journal for the Philsophy of Science 10, 25–2.
Randall, C. H., and Foulis, D. J., 1973, ‘Operational Statistics, II. Manuals of Operations and their Logics’, Journal of Mathematical Physics 14, 1472–80.
Randall, C. H., and Foulis, D. J., 1976, ‘A Mathematical Setting for Inductive Reasoning’, in W. Harper and C. A Hooker (1976) Vol III., 169–205.
Randall, C. H., and Foulis, D. J., 1978, ‘The Operational Approach to Quantum Mechanics’, in C. A. Hooker (ed.), Physics as a Logico-Operational Structure, D. Reidel, Dordrecht, Holland, in press.
Reichenbach, H., 1944, Philosophic Foundations of Quantum Mechanics, University of California Press, Los Angeles.
Reichenbach, H., 1946, ‘Reply to Ernest Nagel’s Criticism of my View on Quantum Mechanics’, Journal of Philosophy 43, 239–47.
Reichenbach, H., 1948 ‘The Principle of Anomaly in Quantum Mechanics’, Dialectica 2, 337–350.
Reichenbach, H., 1956, The Direction of Time, University of California Press, Berkeley.
Sneed, J. D., 1970, ‘Quantum Mechanics and Classical Probability Theory’, Synthese 21, 34–64.
Stalnaker, R. C., 1968, ‘A Theory of Conditionals’, in N. Rescher (ed.), Studies in Logical Theory, Blackwell, Oxford.
Stalnaker, R. C., 1970, ‘Probability and Conditionals’, Philosophy of Science 37, 68–80.
Stalnaker, R., and Thomason, R., 1970, ‘A Semantic Analysis of Conditional Logic’, Theoria 36, 23–42.
Stein, H., 1972, ‘On the Conceptual Structure of Quantum Mechanics’, in R. G. Colodny (ed.), Paradigms and Paradoxes, Pittsburgh Series in the Philosophy of Science, Vol. 5, University of Pittsburgh Press, Pittsburgh, 367–438.
Suppes, P. A. (ed.) (1976), Logic and Probability in Quantum Mechanics, D. Reidel, Dordrecht, Holland.
van Fraassen, B. C., 1966, ‘Singular Terms, Truth-Value Gaps, and Free Logic’, Journal of Philosophy 63, 481–95.
van Fraassen, B. C., 1969, ‘Presuppositions, Supervaluations, and Free Logic’, in K. Lambert (ed.), The Logical Way of Doing Things, Yale University Press, New Haven, 67–91.
van Fraassen, B. C., 1971, Formal Semantics and Logic, Macmillan, New York.
van Fraassen, B. C., 1973, ‘Semantic Analysis of Quantum Logic’, in C. A. Hooker (1973).
van Fraassen, B. C., 1974, ‘Hidden Variables in Conditional Logic’, Theoria 40, 176–90.
van Fraassen, B. C., 1975, ‘Incomplete Assertion and Belnap Connectives’, in Hockney, Harper, Freed (eds. ), Contemporary Research in Philosophical Logic and Linguistic Semantics, D. Reidel, Dordrecht, Holland, 43–70.
van Fraassen, B. C., 1976, ‘Probabilities of Conditionals’, in W. Harper and C. A. Hooker (1976), Vol. 1, 261–301.
Vardarajan, V. S., 1962, ‘Probability in Physics and a Theorem on Simultaneous Observability’, Communications in Pure and Applied Mathematics 15, 189–217.
Varadarajan, V. S., 1968, Geometry of Quantum Theory, Vol. I, Van Nostrand, Princeton.
von Neumann, J., 1932, The Mathematical Foundations of Quantum Mechanics (tr. Robert T. Beyer), Princeton University Press, Princeton, 1955. (orig. 1932)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1979 D. Reidel Publishing Company, Dordrecht, Holland
About this chapter
Cite this chapter
Hardegree, G.M. (1979). Reichenbach and the Interpretation 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_18
Download citation
DOI: https://doi.org/10.1007/978-94-009-9404-1_18
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-9406-5
Online ISBN: 978-94-009-9404-1
eBook Packages: Springer Book Archive