Foundations of Physics

, Volume 44, Issue 12, pp 1269–1288 | Cite as

Separability and Non-Individuality: Is It Possible to Conciliate (At Least A Form Of) Einstein’s Realism with Quantum Mechanics?

  • Décio Krause
  • Jonas R. B. Arenhart


In this paper we argue that physical theories, including quantum mechanics, refer to some kind of ‘objects’, even if only implicitly. We raise questions about the logico-mathematical apparatuses commonly employed in such theories, bringing to light some metaphysical presuppositions underlying such apparatuses. We point out to some incongruities in the discourse holding that quantum objects would be entities of some ‘new kind’ while still adhering to the logico-mathematical framework we use to deal with classical objects. The use of such apparatus would hinder us from being in complete agreement with the ontological novelties the theories of quanta seem to advance. Thus, we join those who try to investigate a ‘logic of quantum mechanics’, but from a different point of view: looking for a formal foundation for a supposed new ontology. As a consequence of this move, we can revisit Einstein’s ideas on physical reality and propose that, by considering a new kind of object traditionally termed ‘non-individuals’, it is possible to sustain that they still obey some of Einstein’s conditions for ‘physical realities’, so that it will be possible to talk of a ‘principle of separability’ in a sense which is not in complete disagreement with quantum mechanics. So, Einstein’s departure from quantum mechanics might be softened at least concerning a form of his realism, which sees separated physical objects as distinct ‘physical realities’.


Quantum objects Non-individuality Separability  Quasi-sets Extensional ontology 


  1. 1.
    Arenhart, J.R.B.: Many entities, no identity. Synthese 187(2), 801–812 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Arenhart, J.R.B., Krause, D.: Quantifiers and the foundations of quasi-set theory. Principia 13(3), 251–68 (2009)CrossRefGoogle Scholar
  3. 3.
    Arenhart, J.R.B., Krause, D.: Why non-individuality? A discussion on individuality, identity, and cardinality in the quantum context. Erkenntnis 79, 1–18 (2014)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Auyang, S.Y.: How is Quantum Field Theory Possible?. Oxford University Press, New York (1995)Google Scholar
  5. 5.
    Browder, F.E. (ed.): Mathematical Problems Arising from Hilbert Problems, Proceedings of Symposia in Pure Mathematics, vol. XXVIII. American Mathematical Society, Providence (1976)Google Scholar
  6. 6.
    da Costa, N.C.A.: Ensaio Sobre os Fundamentos da Lógica, São Paulo, Hucitec/EdUSP (2nd. ed. Hucitec 1994) (1980)Google Scholar
  7. 7.
    da Costa, N.C.A., Krause, D.: Complementarity and paraconsistency. In: Rahman, S., Symons, J., Gabbay, D.M., van Bendegem, J.-P. (eds.) Logic, Epistemology, and the Unity of Science, pp. 557–568. Springer-Verlag, Berlin (2004)CrossRefGoogle Scholar
  8. 8.
    Dalla Chiara, M.L., Toraldo di Francia, G.: Individuals, kinds and names in physics. In: Corsi, G., et al. (eds.) Bridging the Gap: Philosophy, Mathematics, Physics, pp. 261–283. Kluwer Ac. Press, Dordrecht (1993)Google Scholar
  9. 9.
    Dalla Chiara, M.L., Giuntini, R., Greechie, R.: Reasoning in Quantum Theory: Sharp and Unsharp Quantum Logics. Kluwer Academic Publishers, Alphen aan den Rijn (2004)CrossRefGoogle Scholar
  10. 10.
    d’Espagnat, B.: The quantum theory and reality. Sci. Am. 241(5), 158–181 (1979)CrossRefGoogle Scholar
  11. 11.
    Esfeld, M.: Quantum entanglement and a metaphysics of relations. Stud. Hist. Philos. Modern Phys. 35(4), 601–617 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Faye, J.: Copenhagen Interpretation of Quantum Mechanics, The Stanford Encyclopedia of Philosophy (Fall 2008 Edition), Edward N. Zalta (ed.), (2008)
  13. 13.
    French, S., Krause, D.: Quantum Vagueness. Erkenntnis 59, 97–124 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    French, S., Krause, D.: Identity in Physics: a Historical, Philosophical and Formal Analysis. Oxford University Press, Oxford (2006)CrossRefGoogle Scholar
  15. 15.
    French, S., Ladyman, J.: Remodelling Structural Realism: Quantum Physics and the Metaphysics of Structure. Synthese 136, 31–56 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Ghirardi, G.: Sneaking a Look at God’s Cards: Unraveling the Mysteries of Quantum Mechanics. Princeton University Press, Princeton and oxford (2005)Google Scholar
  17. 17.
    Glashow, S.L.: Does quantum field theory need a foundation? In: Cao, T.Y. (ed.) Conceptual Foundations of Quantum Field Theory, pp. 74–88. Cambridge University Press, Cambridge (1999)Google Scholar
  18. 18.
    Howard, D.A.: Einstein on locality and separalility. Stud. Hist. Philos. Sci. 16, 171–201 (1985)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Howard, D.A.: ‘Einstein’s Philosophy of Science’, The Stanford Encyclopedia of Philosophy (Spring 2004 Edition), Edward N. Zalta (ed.), at (2004)
  20. 20.
    Krause, D.: On a quasi-set theory. Notre Dame J. Form. Log. 33, 402–411 (1992)CrossRefzbMATHGoogle Scholar
  21. 21.
    Krause, D.: Why quasi-sets? Bol. Soc. Paran. Mat. 20(1/2), 73–92 (2002)zbMATHGoogle Scholar
  22. 22.
    Ladyman, J., Ross, D.: Every Thing Must Go: Metaphysics Naturalized. Oxford University Press, Oxford (2007)CrossRefGoogle Scholar
  23. 23.
    Lam, V.: Entities without intrinsic physical identities. Erkenntnis (2014). doi: 10.1007/s10670-014-9601-5
  24. 24.
    Ludwig, G.: Foundations of Quantum Mechanics, I. Springer-Verlag, Berlin (1983)CrossRefzbMATHGoogle Scholar
  25. 25.
    Manin, YuI: Mathematical problems I: foundations. In: Browder, F.E. (ed.) Mathematical Problems Arising from Hilbert Problems, Proceedings of Symposia in Pure Mathematics, vol. XXVIII, p. 36. American Mathematical Society, Providence (1976)Google Scholar
  26. 26.
    Maudlin, T.: The Metaphysics within Physics. Oxford University Press, Oxford (2007)CrossRefGoogle Scholar
  27. 27.
    Mittelstaedt, P.: Quantum physics and classical physics—in the light of quantum logic. Int. J. Theor. Phys. 44(7), 771–781 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  28. 28.
    Muller, F.A.: Withering away, weakly. Synthese 180(2), 223–233 (2011)CrossRefGoogle Scholar
  29. 29.
    Paty, M.: Personal communication by e-mail. (2005)Google Scholar
  30. 30.
    Redhead, M., Teller, P.: Particles, particle labels, and quanta: the toll of unacknowledged metaphysics. Found. Phys. 21, 43–62 (1991)ADSCrossRefMathSciNetGoogle Scholar
  31. 31.
    Schrödinger, E.: Science and Humanism. Cambridge University Press, Cambridge (1952)Google Scholar
  32. 32.
    Schrödinger, E.: ‘What is an Elementary Particle?’, reprinted in Castellani, E. (ed.), Interpreting Bodies: Classical and Quantum Objects in Modern Physics, Princeton Un. Press, Princeton, p. 197–210 (1998)Google Scholar
  33. 33.
    Thompson, I.J.: Philosophy of Nature and Quantum Reality, (2003)
  34. 34.
    Toraldo di Francia, G.: What is a physical object? Scientia 113, 57–65 (1978)Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of PhilosophyFederal University of Santa CatarinaFlorianópolisBrazil

Personalised recommendations