International Journal of Theoretical Physics

, Volume 28, Issue 2, pp 159–168 | Cite as

The Leibniz principle in quantum logic

  • Roberto Giuntini
  • Peter Mittelstaedt


The principle of the “identity of indiscernibles” (Leibniz Principle) is investigated within the framework of the formal language of quantum physics, which is given by an orthomodular lattice. We show that the validity of this principle is based on very strong preconditions (concerning the existence of convenient predicates) which are given in the language of classical physics but which cannot be fulfilled in orthomodular quantum logic.


Field Theory Elementary Particle Quantum Field Theory Formal Language Quantum Logic 
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  1. Beltrametti, E., and Cassinelli, G. (1981).The Logic of Quantum Mechanics, Addison-Wesley, Reading, Massachusetts.Google Scholar
  2. Dalla Chiara, M. L. (1985). Some foundational problems in mathematics suggested by physicsSynthese,62, 303–315.Google Scholar
  3. Dalla Chiara, M. L. (1986). Quantum logic, inHandbook of Philosophical Logic D. Gabbay and F. Guenthner, eds., Reidel, Dordrecht, Vol. III, pp. 427–469.Google Scholar
  4. Dalla Chiara, M. L., and Toraldo di Francia, G. (1985). Individuals, kinds and names in physics,Versus,40, 29–50.Google Scholar
  5. Giuntini, R. (1987). Quantum logics and Lindenbaum property,Studia Logica, XLVI (1), 17–35.Google Scholar
  6. Kalmbach, G. (1983).Orthomodular Lattices, Academic Press, London.Google Scholar
  7. Leibniz, G. W. (1875–1890).Philosophische Schriften, C. I. Gerhard, ed., Berlin.Google Scholar
  8. Lorenz, K. (1969). Die Begründung des principium identitatis indiscernibilium, inAkten des internationalen Leibniz-Kongresses, Vol. III,Hannover 1966, Franz Steiner Verlag, Wiesbaden.Google Scholar
  9. Mittelstaedt, P. (1985). Constituting, naming and identity in quantum logic, inRecent Developments in Quantum Logic, P. Mittelstaedt and E. W. Stachow, eds., Bibliographisches Institute, Mannheim.Google Scholar
  10. Mittelstaedt, P. (1986). Naming and identity in quantum logic, inFoundations of Physics, P. Weingartner and G. Dorn, eds., Hölder-Pichler-Tempski, Vienna.Google Scholar
  11. Mittelstaedt, P. (1978).Quantum Logic, Reidel, Dordrecht.Google Scholar
  12. Scott, D. (1969).Advice on modal logic, inPhilosophical Problems in Logic K. Lambert, ed., Reidel, Dordrecht.Google Scholar
  13. Stachow, E. W. (1985). Structures of quantum language for individual systems, inRecent Developments in Quantum Logic, P. Mittelstaedt and E. W. Stachow, eds., Bibliographisches Institut, Mannheim.Google Scholar

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • Roberto Giuntini
    • 1
  • Peter Mittelstaedt
    • 1
  1. 1.University of CologneCologneWest Germany

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