Abstract
Several attempts have been made in recent years to understand the theoretical foundations of quantum mechanics via axiomatization and model construction. While the philosophical and physical significance of these efforts remains largely unclear, they have produced some highly interesting methodological and formal problems. Many of these, especially the ones concerning the understanding of observables, states, and ‘logics’, are insidious and probably will bother philosophers and (mathematical) physicists for a long time.
It is a pleasure to record here my indebtedness to Patrick Suppes for numerous instructive conversations on ‘quantum algebras’ and for his great interest in this work. Thanks are also due to Terrence Fine, Richard Jeffrey, and Joseph Sneed for many stimulating discussions concerning the foundations of probability.
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References
Birkhoff, G. and von Neumann, J., The Logic of Quantum Mechanics, Annals of Mathematics 37 (1936), 823–843.
Bub, J., ‘On the Completeness of Quantum Mechanics’, in C. A. Hooker (ed.), Contemporary Research in the Foundations and Philosophy of Quantum Theory, Reidel, Dordrecht, Holland, 1973.
De Luca, A. and Termini, S., ‘Algebraic Properties of Fuzzy Sets’, Journal of Mathematical Analysis and Applications 40 (1972), 373–386.
Finch, P. D., ‘On the Structure of Quantum Logic’, Journal of Symbolic Logic 34 (1969), 275–282.
Greechie, R. J. and Gudder, S., ‘Quantum Logics’, in C. A. Hooker (ed.), Contemporary Research in the Foundations and Philosophy of Quantum Theory, Reidel, Dordrecht, Holland, 1973.
Gudder, S., ‘Axiomatic Quantum Mechanics and Generalized Probability Theory’, in A. T. B. Bharucha-Reid (ed.), Probabilistic Methods in Applied Mathematics, Vol. 2, Academic Press, New York, 1970.
Kan, D., ‘Functors Involving c. s. s. Complexes’, Transactions of the American Mathematical Society 87 (1958), 330–346.
Kochen, S. and Specker, E. P., ‘Logical Structures Arising in Quantum Theory’, in J. W. Addison, L. Henkin, and A. Tarski (eds.), The Theory of Models: Proceedings of the 1963 International Symposium at Berkeley, North-Holland, Amsterdam, 1965.
Maczynski, M. J., ‘Quantum Families of Boolean Algebras’, Bulletin de l’Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques et Physiques 18 (1970), 93–95.
Scheibe, E., The Logical Analysis of Quantum Mechanics, Pergamon Press, New York, 1973.
Sikorski, R., ‘On the Inducing of Homomorphisms by Mappings’, Fundamenta Mathematicae 36 (1949), 7–22.
Sneed, J. D., The Logical Structure of Mathematical Physics, Reidel, Dordrecht, Holland, 1971.
Suppes, P., ‘The Probabilistic Argument for a Non-Classical Logic of Quantum Mechanics’, Philosophy of Science 33 (1966), 14–21.
Varadarajan, V., Geometry of Quantum Mechanics, Vol. 1, Van Nostrand, Princeton, New Jersey, 1968.
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Domotor, Z. (1976). The Probability Structure of Quantum-Mechanical Systems. In: Suppes, P. (eds) Logic and Probability in Quantum Mechanics. Synthese Library, vol 78. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9466-5_8
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DOI: https://doi.org/10.1007/978-94-010-9466-5_8
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