Foundations of Physics

, Volume 44, Issue 12, pp 1246–1257 | Cite as

Quantum Mechanics: Ontology Without Individuals

  • Newton da Costa
  • Olimpia Lombardi


The purpose of the present paper is to consider the traditional interpretive problems of quantum mechanics from the viewpoint of a modal ontology of properties. In particular, we will try to delineate a quantum ontology that (i) is modal, because describes the structure of the realm of possibility, and (ii) lacks the ontological category of individual. The final goal is to supply an adequate account of quantum non-individuality on the basis of this ontology.


Modal ontology Non-individuality Indistinguishability 



The authors want to thank Décio Krause for his organization of the Workshop “Logical Quantum Structures” in the context of the 4th World Congress and School on Universal Logic, and also the attendants to the workshop for their constructive comments to the oral version of this work. This paper was partially supported by grants of the Buenos Aires University (UBA), the National Research Council (CONICET) and the National Research Agency (FONCYT) of Argentina.


  1. 1.
    Lombardi, O., Castagnino, M.: A modal-Hamiltonian interpretation of quantum mechanics. Stud. Hist. Philos. Mod. Phys. 39, 380–443 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Lombardi, O., Castagnino, M., Ardenghi, J.S.: The modal-Hamiltonian interpretation and the Galilean covariance of quantum mechanics. Stud. Hist. Philos. Mod. Phys. 41, 93–103 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Ardenghi, J.S., Lombardi, O.: The modal-Hamiltonian interpretation of quantum mechanics as a kind of ‘atomic’ interpretation. Phys. Res. Int. 2011, 379–604 (2011)CrossRefGoogle Scholar
  4. 4.
    da Costa, N., Lombardi, O., Lastiri, M.: A modal ontology of properties for quantum mechanics. Synthese 190, 3671–3693 (2013)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Dieks, D., Vermaas, P. (eds.): The Modal Interpretation of Quantum Mechanics. Kluwer Academic Publishers, Dordrecht (1998)zbMATHGoogle Scholar
  6. 6.
    Lombardi, O., Dieks, D.: Modal interpretations of quantum mechanics. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (Fall 2012 Edition). (2012)
  7. 7.
    van Fraassen, B.C.: A formal approach to the philosophy of science. In: Colodny, R. (ed.) Paradigms and Paradoxes: The Philosophical Challenge of the Quantum Domain, pp. 303–366. University of Pittsburgh Press, Pittsburgh (1972)Google Scholar
  8. 8.
    van Fraassen, B.C.: The Einstein–Podolsky–Rosen paradox. Synthese 29, 291–309 (1974)CrossRefGoogle Scholar
  9. 9.
    Kochen, S., Specker, E.: The problem of hidden variables in quantum mechanics. J. Math. Mech. 17, 59–87 (1967)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Suárez, M.: Quantum selections, propensities and the problem of measurement. Br. J. Philos. Sci. 55, 219–255 (2004)CrossRefzbMATHGoogle Scholar
  11. 11.
    Suárez, M. (ed.): Probabilities, Causes, and Propensities in Physics (Synthese Library). Springer, Dordrecht (2011)Google Scholar
  12. 12.
    Teller, P.: Quantum mechanics and haecceities. In: Castellani, E. (ed.) Interpreting Bodies: Classical and Quantum Objects in Modern Physics, pp. 114–141. Princeton University Press, Princeton (1998)Google Scholar
  13. 13.
    Maudlin, T.: Part and whole in quantum mechanics. In: Castellani, E. (ed.) Interpreting Bodies: Classical and Quantum Objects in Modern Physics, pp. 46–60. Princeton University Press, Princeton (1998)Google 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.
    van Cleve, J.: Three versions of the bundle theory. Philos. Stud. 47, 95–107 (1985)CrossRefGoogle Scholar
  16. 16.
    Loux, M.: Metaphysics: A Contemporary Introduction. Routledge, London (1998)CrossRefGoogle Scholar
  17. 17.
    Benacerraf, P.: What numbers could not be? Philos. Rev. 74, 47–73 (1965)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Shapiro, S.: Philosophy of Mathematics: Structure and Ontology. Oxford University Press, New York (1997)zbMATHGoogle Scholar
  19. 19.
    Keränen, J.: The identity problem for realist structuralism. Philos. Math. 9, 308–330 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    Narvaja, M., Córdoba, M., Lombardi, O.: Different domains, the same problems. In: Pintuck, S., Reynolds, C. (eds.) Philosophy of Science, pp. 67–87. Nova Science Publishers, New York (2012)Google Scholar
  21. 21.
    Sebastião e Silva, J.: Sugli automorfismi di un sistema matematico qualunque. Comment. Pontif. Acad. Sci. IX, 91–116 (1945)Google Scholar
  22. 22.
    Da Costa, N., Rodrigues, A.: Definability and invariance. Studia Logica 86, 1–30 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  23. 23.
    Krause, D., Coelho, A.M.N.: Identity, indiscernibility, and philosophical claims. Axiomathes 15, 191–210 (2005)CrossRefGoogle Scholar
  24. 24.
    Saunders, S.: Physics and Leibniz’s principles. In: Brading, K., Castellani, E. (eds.) Symmetries in Physics: Philosophical Reflections, pp. 289–307. Cambridge University Press, Cambridge (2003)CrossRefGoogle Scholar
  25. 25.
    Muller, F.A., Saunders, S.: Discerning fermions. Br. J. Philos. Sci. 59, 499–548 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  26. 26.
    Muller, F.A., Seevinck, M.: Discerning elementary particles. Philos. Sci. 76, 179–200 (2009)CrossRefMathSciNetGoogle Scholar
  27. 27.
    Dieks, D., Versteegh, M.: Identical quantum particles and weak discernibility. Found. Phys. 38, 923–934 (2008)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  28. 28.
    Castagnino, M., Lombardi, O., Lara, L.: The global arrow of time as a geometrical property of the universe. Found. Phys. 33, 877–912 (2003)CrossRefMathSciNetGoogle Scholar
  29. 29.
    Castagnino, M., Lombardi, O.: The global non-entropic arrow of time: from global geometrical asymmetry to local energy flow. Synthese 169, 1–25 (2009)CrossRefzbMATHGoogle Scholar
  30. 30.
    Dieks, D., Lubberdink, A.: How classical particles emerge from the quantum world. Found. Phys. 41, 1051–1064 (2011)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  31. 31.
    Da Costa, N., Krause, D.: Schrödinger logics. Studia Logica 53, 533–550 (1994)Google Scholar
  32. 32.
    Da Costa, N., Krause, D.: An intensional Schrödinger logic. Notre Dame J. Form. Logic 38, 179–194 (1997)CrossRefzbMATHGoogle Scholar
  33. 33.
    Da Costa, N., Krause, D.: Set-theoretical models for quantum systems. In: dalla Chiara, M.L., Giuntini, M.L., Laudisa, F. (eds.) Language, Quantum, Music, pp. 114–141. Kluwer, Dordrecht (1999)Google Scholar
  34. 34.
    Krause, D.: On a quasi-set theory. Notre Dame J. Form. Logic 33, 402–411 (1992)CrossRefzbMATHGoogle Scholar
  35. 35.
    da Costa, N., French, S., Krause, D.: The Schrödinger problem. In: Bitbol, M., Darrigol, O. (eds.) Erwin Schrödinger: Philosophy and the Birth of Quantum Mechanics, pp. 445–460. Editions Frontiè res, Paris (1992)Google Scholar
  36. 36.
    dalla Chiara, M.L., Toraldo di Francia, G.: Individuals, kinds and names in physics. In: Corsi, G., dalla Chiara, M.L., Ghirardi, G.C. (eds.) Bridging the Gap: Philosophy, Mathematics and Physics, pp. 261–283. Kluwer, Dordrecht (1993)Google Scholar
  37. 37.
    dalla Chiara, M.L., Toraldo di Francia, G.: Identity questions from quantum theory. In: Gavroglu, K., Stachel, J., Wartofski, M.W. (eds.) Physics, Philosophy and the Scientific Community, pp. 39–46. Kluwer, Dordrecht (1995)Google Scholar
  38. 38.
    Worrall, J.: Structural realism: the best of both worlds? Dialectica 43, 99–124 (1989)CrossRefGoogle Scholar
  39. 39.
    Ladyman, J.: What is structural realism? Stud. Hist. Philos. Sci. 29, 409–424 (1998)CrossRefGoogle Scholar
  40. 40.
    French, S., Ladyman, J.: Remodelling structural realism: quantum physics and the metaphysics of structure. Synthese 136, 31–56 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  41. 41.
    French, S.: Structure as a weapon of the realist. Proc. Aristot. Soc. 106, 167–185 (2006)CrossRefGoogle Scholar
  42. 42.
    French, S., Ladyman, J.: In defence of ontic structural realism. In: Bokulich, A., Bokulich, P. (eds.) Scientific Structuralism. Boston Studies in the Philosophy and History of Science, pp. 25–42. Springer, Dordrecht (2011)Google Scholar
  43. 43.
    French, S., Ladyman, J.: The dissolution of objects: a reply to Cao. Synthese 136, 73–77 (2003)CrossRefzbMATHMathSciNetGoogle Scholar

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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.CONICET - Facultad de Ciencias Exactas y NaturalesUniversity of Buenos AiresBuenos AiresArgentina

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