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Foundations of Physics

, Volume 30, Issue 10, pp 1587–1604 | Cite as

Leibniz's Principle, Physics, and the Language of Physics

  • Elena Castellani
  • Peter Mittelstaedt
Article

Abstract

This paper is concerned with the problem of the validity of Leibniz's principle of the identity of indiscernibles in physics. After briefly surveying how the question is currently discussed in recent literature and which is the actual meaning of the principle for what concerns physics, we address the question of the physical validity of Leibniz's principle in terms of the existence of a sufficient number of naming predicates in the formal language of physics. This approach allows us to obtain in a formal way the result that a principle of the identity of indiscernibles can be justified in the domain of classical physics, while this is not the case in the domain of quantum physics.

Keywords

Recent Literature Formal Language Classical Physic Actual Meaning Concern Physic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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REFERENCES

  1. Y. Aharonov and D. Albert, “Is the usual notion of time evolution adequate for quantum- mechanical systems?” I-II, Phys. Rev. D 29, I: 223–227, II: 228-234 (1984).Google Scholar
  2. R. L. Barnette, “Does quantum mechanics disprove the principle of the identity of indiscernibles,” Phil. Sci. 45, 466–470 (1978).Google Scholar
  3. E. G. Beltrametti and G. Cassinelli, The Logic of Quantum Mechanics (Addison-Wesley, Reading, Massachusetts, 1981).Google Scholar
  4. C. Brown, Leibniz and Strawson. A New Essay in Descriptive Metaphysics (Philosophia, München, 1990).Google Scholar
  5. P. Busch and P. Mittelstaedt, “The problem of objectification in quantum mechanics,” Found. Phys. 21, 889–904 (1991).Google Scholar
  6. J. Butterfield, “Interpretation and identity in quantum theory,” Studies in History and Philosophy of Science 24, 443–476 (1993).Google Scholar
  7. H. Castaneda, “Leibniz's 1686 views on individual substances, existence, and relations,” J. Phil. 72, 687–690 (1975).Google Scholar
  8. E. Castellani, “Galilean particles: An example of constitution of objects,” in Interpreting Bodies: Classical and Quantum Objects in Modern Physics, E. Castellani, ed. (Princeton University Press, Princeton, 1998).Google Scholar
  9. F. Chernoff, “Leibniz's principle of the identity of indiscernibles,” The Philosophical Quartely 31, 126–138 (1981).Google Scholar
  10. A. Cortes, “Leibniz’ principle of the identity of indiscernibles: A false principle,” Phil. Sci. 43, 491–505 (1976).Google Scholar
  11. N. C. A. da Costa, S. French, and D. Krause, “The Schrödinger problem,” in Erwin Schrödinger: Philosophy and the Birth of Quantum Mechanics, M. Bitbol and O. Darrigol, eds. (Éditions Frontières, Paris, 1992).Google Scholar
  12. M. L. Dalla Chiara and G. Toraldo di Francia, “Individuals, kinds and names in physics,” in Logica e Filosofia della Scienza oggi, E. Agazzi and M. Mondadori, eds. (Clueb, Bologna, 1983).Google Scholar
  13. M. L. Dalla Chiara, “Names and descriptions in quantum logic,” in Recent Developments in Quantum Logic, P. Mittelstaedt and E. W. Stachow, eds. (Bibliographishes Institut, Mannheim, 1985).Google Scholar
  14. M. L. Dalla Chiara, R. Giuntini, and D. Krause, “Quasiset theories for microobjects: A comparison,” in Interpreting Bodies, E. Castellani, ed. (Princeton University Press, Princeton, 1998).Google Scholar
  15. D. Dieks, “Quantum statistics, identical particles and correlations,” Synthese 82, 127–155 (1990).Google Scholar
  16. L. Frankel, “Leibniz's principle of identity of indiscernibles,” Studia leibnitiana 13, 192–211 (1981).Google Scholar
  17. S. French, “Identity and individuality in classical and quantum physics,” Australasian J. Phil. 67, 432–446 (1989a).Google Scholar
  18. S. French, “Individuality, supervenience and Bell's theorem,” Phil. Studies 55, 1–22 (1989b).Google Scholar
  19. S. French, “Why the principle of the identity of indiscernibles is not contingently true either,” Synthese 78, 141–166 (1989c).Google Scholar
  20. S. French and M. Redhead, “Quantum physics and the identity of indiscernibles,” Brit. J. Phil. Sci. 39, 233–246 (1988).Google Scholar
  21. S. French, “On the withering away of physical objects,” in Interpreting Bodies, E. Castellani, ed. (Princeton University Press, Princeton, 1998).Google Scholar
  22. S. French and D. Krause, “A formal framework for quantum non-individuality,” Synthese 102, 195–214 (1995).Google Scholar
  23. A. Ginsberg, “Quantum theory and identity of indiscernibles revisited,” Phil. Sci. 48, 487–491 (1981).Google Scholar
  24. R. Giuntini, “Quantum logic and Lindenbaum property,” Studia Logica 46, 17–35 (1987).Google Scholar
  25. R. Giuntini and P. Mittelstaedt, “The Leibniz principle in quantum logic,” Internat. J. Theoret. Phys. 28, 159–168 (1989).Google Scholar
  26. R. C. Hoy, “Inquiry, intrinsic properties, and the identity of indiscernibles,” Synthese 61, 275–297 (1984).Google Scholar
  27. N. Huggett, “Identity, quantum mechanics and common sense,” The Monist 80, 118–139 (1997).Google Scholar
  28. H. Ishiguro, Leibniz's Philosophy of Logic and Language (Cambridge University Press, Cambridge, 1990).Google Scholar
  29. D. Krause, “On a quasi-set theory,” Notre Dame Journal of Formal Logic 33, 402–411 (1992).Google Scholar
  30. K. Lorenz, “Die Begründung des principium identitatis indiscernibilium,” Studia Leibnitiana, Supplementa Vol. III, 149–159 (1969).Google Scholar
  31. A. Kastler, “On the historical development of the indistinguishability concept for micro-particles,” in Old and New Questions in Physics, Cosmology, Philosophy, and Theoretical Biology, A. van der Merwe, ed. (Plenum, New York, 1983).Google Scholar
  32. H. Margenau, “The exclusion principle and its philosophical importance,” Phil. Sci. 11, 187–208 (1944).Google Scholar
  33. H. Margenau, The Nature of Physical Reality (McGraw-Hill, New York, 1950).Google Scholar
  34. P. Mittelstaedt, “Constituting, naming and identity in quantum logic,” in Recent Developments in Quantum Logic, P. Mittelstaedt and E. W. Stachow, eds. (Bibliographishes Institut, Mannheim, 1985).Google Scholar
  35. P. Mittelstaedt, “Constitution of objects in classical mechanics and in quantum mechanics,” Internat. J. Theoret. Phys. 34, 1615–1626 (1995).Google Scholar
  36. H. Post, “Individuality and physics,” The Listener 70, 534–537 (1963).Google Scholar
  37. M. Redhead and P. Teller, “Particles, particle labels, and quanta: The toll of unacknowledged metaphysics,” Found. Phys. 21, 43–62 (1991).Google Scholar
  38. M. Readhead and P. Teller, “Particle labels and the theory of indistinguishable particles in quantum mechanics,” Brit. J. Phil. Sci. 43, 201–218 (1992).Google Scholar
  39. H. Reichenbach, “The genidentity of quantum particles,” in The Direction of Time (University of California Press, Berkeley, 1956).Google Scholar
  40. Y. Shadmi, “Teaching the exclusion principle with philosophical flavor,” Am. J. Phys. 48, 844–848 (1978).Google Scholar
  41. P. Teller, “Quantum physics, the identity of indiscernibles, and some unanswered questions,” Phil. Sci. 50, 309–319 (1983).Google Scholar
  42. P. Teller, An Interpretive Introduction to Quantum Field Theory (Princeton University Press, Princeton, 1995).Google Scholar
  43. P. Teller, “Quantum mechanics and haecceities,” in Interpreting Bodies, E. Castellani, ed. (Princeton University Press, Princeton, 1998).Google Scholar
  44. B. van Fraassen, “Probabilities and the problem of individuation” (presented at the American Philosophical Association in 1960), in Probabilities, Problems and Paradoxes, S. Luckenbach, ed. (Dickenson, Encino, California, 1972).Google Scholar
  45. B. C. van Fraassen, “The problem of indistinguishable particles,” in Science and Reality: Recent Work in the Philosophy of Science, J. T. Cushing, C. F. Delaney, and G. M. Gutting, eds. (University of Notre Dame Press, Notre Dame, 1984).Google Scholar
  46. B. C. van Fraassen, Quantum Mechanics: An Empiricist View (Clarendon, Oxford, 1991).Google Scholar
  47. H. Weyl, Philosophy of Mathematics and Natural Science (Princeton University Press, Princeton, 1949).Google Scholar

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Elena Castellani
    • 1
  • Peter Mittelstaedt
    • 2
  1. 1.Department of PhilosophyUniversity of FlorenceItaly
  2. 2.Institute for Theoretical PhysicsUniversity of CologneGermany

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