Abstract
H. Post's conception of quantal particles as ‘non-individuals’ is set in a formal logico-mathematical framework. By means of this approach certain metaphysical implications of quantum mechanics can be further explored.
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Butterfield, J.: 1992, ‘Review ofQuantum mechanics: anEmpiricist View, by Bas C. van Fraassen’, forthcoming.
da Costa, N. C. A.: 1974, ‘On the Theory of Inconsistent Formal Systems’,Notre Dame Journal of Formal Logic 15, 497–510.
da Costa, N. C. A. and Krause, D.: 1994, ‘Schrödinger Logics’,Studia Logica 53(4).
Cushing, J.: 1991, ‘Quantum Theory and Explanatory Discourse: Endgame for Understanding’,Philosophy of Science 58, 337–58.
Dalla Chiara, M. L. and G. Toraldo di Francia: 1993, ‘Individuals, Kinds and Names in Physics’, in Corsi, G. et al. (eds.),Bridging the Gap: Philosophy, Mathematics and Physics, Kluwer Academic Publishers, Dordrecht, pp. 261–83.
Dalla Chiara, M. L. and G. Toraldo di Francia: 1993a,Identity Questions from Quantum Theory, preprint, University of Florence.
Dalla Chiara, M. L. and D. Krause: 1993,Some Remarks on the Axiomatics and on the Interpretation of Quasi-sets, preprint, University of Florence.
Dirac, P. A. M.: 1958,Principles of Quantum Mechanics, 4th ed., Oxford University Press, Oxford.
Fales, E.: 1979, ‘Relative Essentialism’,British Journal for the Philosophy of Science 30, 349–70.
Fraenkel, A. A.: 1966,Abstract Set Theory, North-Holland, Amsterdam.
French, S.: 1987, ‘First Quantised Paraparticle Theory’,International Journal of Theoretical Physics 26, 1141–63.
French, S.: 1989a, ‘Identity and Individuality in Classical and Quantum Physics’,Australasian Journal of Philosophy 67, 432–46.
French, S.: 1989b, ‘Why the Principle of the Identity of Indiscernibles is not Contingently True Either’,Synthese 78, 141–66.
French, S.: 1989c, ‘Individuality, Supervenience and Bell's Theorem’,Philosophical Studies 55, 1–22.
French, S. and M. Redhead: 1988, ‘Quantum Physics and the Identity of Indiscernibles’,British Journal for the Philosophy of Science 39, 233–46.
Howard, D.: 1989, ‘Holism, Separability and the metaphysical Implications of the Bell Experiments’, in Cushing, J. T. and McMullin, E. (eds.),Philosophical Consequences of Quantum Theory, University of Notre Dame Press, Notre Dame, pp. 224–46.
Hughes, R. I. G.: 1990, ‘Bell's Theorem, Ideology and Structural Explanation’, in Cushing, J. T. and McMullin, E. (eds.),Philosophical Consequences of Quantum Theory, University of Notre Dame Press, Notre Dame, pp. 195–207.
Jauch, J.: 1966,Foundations of Quantum Mechanics, Addison-Wesley, Massachusetts.
Korner, S.: 1969,Fundamental Questions in Philosophy, Penguin Press, Harmondsworth.
Krause, D.: 1990, ‘A ‘Dialetização’ da Teoria Tradicional da Identidade’,Boletim da Sociedade Parananaense de Matemática 11(2), 157–73.
Krause, D.: 1991, ‘Multisets, Quasi-Sets and Weyl's Aggregates’,Journal of Non-Classical Logic 8, 9–39.
Krause, D.: 1992, ‘On a Quasi-Set Theory’,Notre Dame Journal of Formal Logic 33, 402–11.
Landau, L. and E. S. Lifshitz: 1965,Quantum Mechanics, 2nd ed., Pergamon Press, Oxford.
Merzbacher, E.: 1974,Quantum Mechanics, 2nd ed., John Wiley, New York.
Messiah, A. M. L. and O. W. Greenberg: 1964, ‘Symmetrization Postulate and its Experimental Foundation’,Physical Review B136, 248–67.
Post, H.: 1963, ‘Individuality and Physics’,The Listener 70, 534–7.
Post, H.: 1971, ‘Correspondence, Invariance and Heuristics’,Studies in History and Philosophy of Science 2, 213–55.
Quine, W.: 1976, ‘Whither Physical Objects?’, in R. S. Cohen, P. K. Feyerabend and M. W. Wartofsky (eds.),Essays in Memory of Imre Lakatos, D. Reidel, Dordrecht, pp. 497–504.
Quinton, A.: 1973,The Nature of Things, Routledge and Kegan-Paul, London.
Redhead, M.: 1983, ‘Quantum Field Theory for Philosophers’, inProceedings of the 1982 Biennial Meeting of the Philosophy of Science Association, Vol. 2, PSA, East Lansing, pp. 57–99.
Redhead, M. and P. Teller: 1991, ‘Particles, Particle Labels and Quanta: the Toll of Unacknowledged Metaphysics’,Foundations of Physics 21, 43–62.
Redhead, M. and P. Teller: 1992, ‘Particle Labels and the Theory of Indistinguishable Particles in Quantum Mechanics’,British Journal for the Philosophy of Science 43, 201–18.
Schrödinger, E.: 1952,Science and Humanism, Cambridge University Press, Cambridge.
Schrödinger, E.: 1953, ‘What is matter?’,Scientific American 52–7.
Schrödinger, E.: 1957,Science Theory and Man, Allen and Unwin, London.
Shimony, A.: 1989, ‘Search for a Worldview which can Accommodate our Knowledge of Microphysics’, in Cushing, J. T. and McMullin, E. (eds.),Philosophical Consequences of Quantum Theory, University of Notre Dame Press, Notre Dame, pp. 25–37.
Stolt, R. H. and J. R. Taylor: 1970, ‘Correspondence between the First and Second Quantised Theory of Paraparticles’,Nuclear Physics B19, 1–19.
Tarski, A.: 1965,Introduction to Logic and to the Methodology of Deductive Sciences, Oxford University Press, Oxford.
Toraldo di Francia, G.: 1985, ‘Connotation and Denotation in Microphysics’, in Mittelstaed, P. and Stachow, E. V. (eds.),Recent Developments in Quantum Logic, Mannheim, Bibliographisches Institut, pp. 203–14.
Weyl, H.: 1949,Philosophy of Mathematics and Natural Science, Princeton University Press, Princeton.
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The authors would like to thank Prof. Newton C. A. da Costa and the anonymous referee for their comments and suggestions. S. French would also to thank his colleagues at Southeast Missouri State University for their support during the preparation of this work.
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Krause, D., French, S. A formal framework for quantum non-individuality. Synthese 102, 195–214 (1995). https://doi.org/10.1007/BF01063905
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DOI: https://doi.org/10.1007/BF01063905