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Counting the Particles: Entity and Identity in the Philosophy of Physics

  • Francesco Berto EMAIL logo
From the journal Metaphysica


I would like to attack a certain view: the view that the concept of identity can fail to apply to some things although, for some positive integer n, we have n of them. The idea of entities without self-identity is seriously entertained in the philosophy of quantum mechanics (QM). It is so pervasive that it has been labelled the Received View (French and Krause 2006. Identity in Physics: A Historical, Philosophical, and Formal Analysis. Oxford: Oxford UP: 105). I introduce the Received View in Section 1. In Section 2 I explain what I mean by “entity” (synonymously, by “object” and “thing”), and I argue that supporters of the Received View should agree with my characterization of the corresponding notion of entity (object, thing). I also explain what I mean by “identity”, and I show that supporters of the Received View agree with my characterization of that notion. In Section 3 I argue that the concept of identity, so characterized, is one with the concept of oneness. Thus, it cannot but apply to what belongs to a collection with n elements, n being a positive integer. In Section 4 I add some considerations on the primitiveness of identity or unity and the status of the Identity of Indiscernibles. In Section 5 I address the problem of how reference to indiscernible objects with identity can be achieved.


Various parts of the work were presented between 2015 and 2016 at the Philosophy of Mathematics seminar of the IHPST (University Paris 1-Pantheon Sorbonne), at the 7th Workshop of the MetaMetaPhysical Club, University of Rotterdam, and at the IMERA – Institute for Advanced Study in Marseille. Thanks to the audiences for their comments and remarks. Special thanks go to Andrew Arana, Guido Bacciagaluppi, Alfio Bonanno, Otàvio Bueno, Claudio Calosi, Vincenzo Fano, Federico Faroldi, Fausto Fraisopi, Cristian Mariani, Fred Muller, Fabrice Pataut, and Francesca Poggiolesi.


Adams, R. 1979. “Primitive Thisness and Primitive Identity.” Journal of Philosophy 76:5–26.10.2307/2025812Search in Google Scholar

Aristotle. The Complete Works (edited by J. Barnes). Princeton: Princeton University Press.Search in Google Scholar

Auyang, S.Y. 1995. How Is Quantum Field Theory Possible? New York: Oxford UP.Search in Google Scholar

Baker, R.L. 1997. “Why Constitution Is Not Identity.” Journal of Philosophy 94:599–621.10.2307/2564596Search in Google Scholar

Bencivenga, E. 2002. “Free Logics.” In Handbook of Philosophical Logic, 2nd, Vol. 5, edited by Gabbay, and Guenthner, 147–196. Dordrecht: Springer.10.1007/978-94-017-0458-8_3Search in Google Scholar

Berto, F., and M. Plebani. 2015. Ontology and Metaontology. A Contemporary Guide. London: Bloomsbury.Search in Google Scholar

Black, M. 1952. “The Identity of Indiscernibles.” Mind 61:153–164.10.1093/mind/LXI.242.153Search in Google Scholar

Breckenridge, W., and O. Magidor. 2012. “Arbitrary Reference.” Philosophical Studies 158:377–400.10.1007/s11098-010-9676-zSearch in Google Scholar

Bueno, O. 2014. “Why Identity Is Fundamental.” American Philosophical Quarterly 51:325–332.Search in Google Scholar

Casullo, A. 1984. “The Contingent Identity of Particulars and Universals.” Mind 123:527–554.10.1093/mind/XCIII.372.527Search in Google Scholar

Cortes, A. 1976. “Leibniz’s Principle of the Identity of Indiscernibles: A False Principle.” Philosophy of Science 43:491–505.10.1086/288707Search in Google Scholar

Curtis, B., and H. Noonan. 2014. “Identity.” In The Stanford Encyclopedia of Philosophy. Stanford, CA. in Google Scholar

Dalla Chiara, M.L., and G. Toraldo Di Francia. 1993. “Individuals, Kinds and Names in Physics.” In Bridging the Gap: Philosophy, Mathematics, Physics, edited by Corsi, et al., 261–283. Dordrecht: Kluwer.10.1007/978-94-011-2496-6_13Search in Google Scholar

Deutsch, H. 1998. “Identity and General Similarity.” In Philosophical Perspectives, Vol. 12, edited by Tomberlin, 117–199. Atascadero, CA: Ridgeview.10.1111/0029-4624.32.s12.8Search in Google Scholar

Dirac, P.A.M. 1926. “On the Theory of Quantum Mechanics.” Proceedings of the Royal Society A112:661–677.10.1098/rspa.1926.0133Search in Google Scholar

Domenech, G., and F. Holik. 2007. “A Discussion of Particle Number and Quantum Indistinguishability.” Foundations of Physics 37:855–878.10.1007/s10701-007-9129-5Search in Google Scholar

Dorato, M., and M. Morganti. 2013. “Grades of Individuality. A Pluralistic View of Identity in Quantum Mechanics and in the Sciences.” Philosophical Studies 163:591–610.10.1007/s11098-011-9833-zSearch in Google Scholar

Evans, G. 1978. “Can There Be Vague Objects?.” Analysis 38:208.10.1093/analys/38.4.208Search in Google Scholar

Fine, K. 1982. “The Problem of Non-Existents, I: Internalism.” Topoi 1:97–140.10.1007/BF00157548Search in Google Scholar

Fine, K. 2000. “A Counter-Example to Locke’s Thesis.” The Monist 83:357–361.10.5840/monist200083315Search in Google Scholar

Fine, K. 2009. “The Question of Ontology.” In Metametaphysics, edited by Chalmers, Manley and Wasserman, 157–177. Oxford: Clarendon Press.Search in Google Scholar

Forrest, P. 2010. “The Identity of Indiscernibles.” In The Stanford Encyclopedia of Philosophy. Stanford, CA. in Google Scholar

Frege, G. 1884. Die Grundlagen Der Arithmetik. Hamburg: Felix Meiner Verlag. tr. The Foundations of Arithmetic, Oxford: Blackwell 1950.Search in Google Scholar

French, S. 1995. “Hacking Away at the Identity of Indiscernibles.” The Journal of Philosophy 92:455–466.10.2307/2940853Search in Google Scholar

French, S., and D. Krause. 2006. Identity in Physics: A Historical, Philosophical, and Formal Analysis. Oxford: Oxford UP.10.1093/0199278245.001.0001Search in Google Scholar

Geach, P. 1967. “Identity.” Review Ofmetaphysics 21:3–12.Search in Google Scholar

Greenberg, O.W., and A.M.L. Messiah. 1964. “Symmetrization Postulate and Its Experimental Foundation.” Physical Review 136B:1155–1167.10.1103/PhysRev.136.B248Search in Google Scholar

Haack, S. 1978. Philosophy of Logics. Cambridge: Cambridge UP.10.1017/CBO9780511812866Search in Google Scholar

Hacking, I. 1975. “The Identity of Indiscernibles.” Journal of Philosophy 72:249–256.10.2307/2024896Search in Google Scholar

Heidegger, M. 1957. Identity and Difference. New York: Harper & Row.Search in Google Scholar

Hesse, M. 1970. Models and Analogies in Science. Notre Dame: University of Notre Dame Press.Search in Google Scholar

Jantzen, B.C. 2011. “No Two Entities Without Identity.” Synthèse 181:433–450.10.1007/s11229-010-9717-3Search in Google Scholar

Kearns, S., and O. Magidor. 2012. “Semantic Sovereignty.” Philosophy and Phenomenological Research 85:322–350.10.1111/j.1933-1592.2012.00624.xSearch in Google Scholar

Kripke, S. 1972. “Naming and Necessity.” In Semantics of Natural Language, edited by Davidson and Harman, 253–355 and 762–9. Dordrecht: Reidel. 2nd expanded ed., Oxford: Blackwell, 1980.10.1007/978-94-010-2557-7_9Search in Google Scholar

Ladyman, J., and D. Ross. 2007. Every Thing Must Go. Metaphysics Naturalized. Oxford: Oxford UP.10.1093/acprof:oso/9780199276196.001.0001Search in Google Scholar

Langton, R., and D. Lewis. 1998. “Defining ‘Intrinsic’.” In Papers in Metaphysics and Epistemology, edited by Lewis, 116–132. Cambridge: Cambridge UP.10.1017/CBO9780511625343.007Search in Google Scholar

Lewis, D. 1983. “Extrinsic Properties.” Philosophical Studies 44:197–200.10.1017/CBO9780511625343.006Search in Google Scholar

Lewis, D. 1986. On the Plurality of Worlds. Oxford: Blackwell.Search in Google Scholar

Massimi, M. 2001. “Exclusion Principle and the Identity of Indiscernibles.” British Journal for the Philosophy of Science 52:303–330.10.1093/bjps/52.2.303Search in Google Scholar

Muller, F.A. 2015. “The Rise of Relationals.” Mind 124:201–237.10.1093/mind/fzu175Search in Google Scholar

Muller, F.A., and S. Saunders. 2008. “Discerning Fermions.” British Journal for the Philosophy of Science 59:499–508.10.1093/bjps/axn027Search in Google Scholar

Priest, G. 2014. One. Being an Investigation into the Unity of Reality and of Its Parts, Including the Singular Object Which Is Nothingness. Oxford: Oxford UP.10.1093/acprof:oso/9780199688258.001.0001Search in Google Scholar

Quine, W.V.O. 1975. “On the Individuation of Attributes.” In The Logical Enterprise, eds Anderson, Barcan and Martin. New Haven, CN: Yale UP.Search in Google Scholar

Reichenbach, H. [1956], “The Genidentity of Quantum Particles”, repr, in Castellani (ed.) [1998], Interpreting Bodies. Classical and Quantum Objects in Modern Physics, Princeton, NJ: Princeton UP: 61-72.10.1515/9780691222042-007Search in Google Scholar

Saunders, S. 2003. “Physics and Leibniz’s Principles.” In Symmetries in Physics: Philosophical Reflections, edited by Brading and Castellani, 289–308. Cambridge: Cambridge UP.10.1017/CBO9780511535369.017Search in Google Scholar

Saunders, S. 2006. “Are Quantum Particles Objects.” Analysis 66:52–63.10.1093/analys/66.1.52Search in Google Scholar

Schrödinger, E. 1964. My View of the World. Cambridge: Cambridge UP.Search in Google Scholar

Schrödinger, E. 1996. Nature and the Greeks and Science and Humanism. Cambridge: Cambridge UP.10.1017/CBO9781139878333Search in Google Scholar

Teller, P. 1995. An Interpretative Introduction to Quantum Field Theory. Princeton: Princeton UP.10.1515/9780691216294Search in Google Scholar

Thomson, J.J. 1998. “The Statue and the Clay.” Noûs 32:149–173.10.1111/0029-4624.00094Search in Google Scholar

Toraldo Di Francia, G. 1978. “What Is a Physical Object?” Scientia 113:57–65.Search in Google Scholar

Van Fraassen, B. 1989. Laws and Symmetry. Oxford: Oxford UP.10.1093/0198248601.001.0001Search in Google Scholar

Van Fraassen, B. 1998. “The Problem of Indistinguishable Particles.” In Interpreting Bodies. Classical and Quantum Objects in Modern Physics, edited by Castellani, 73–92. Princeton, NJ: Princeton UP.10.1515/9780691222042-008Search in Google Scholar

Van Inwagen, P. 1990. Material Beings. Ithaca, NY: Cornell University Press.Search in Google Scholar

Van Inwagen, P. 2002. “The Number of Things.” Philosophical Issues 12:176–196.10.1111/j.1758-2237.2002.tb00066.xSearch in Google Scholar

Varzi, A. 2000. “Mereological Commitments.” Dialectica 54:283–305.10.1111/j.1746-8361.2000.tb00286.xSearch in Google Scholar

Weyl, H. 1931. The Theory of Groups and Quantum Mechanics. London: Methuen & Co.Search in Google Scholar

Wiggins, D. 2001. Sameness and Substance Renewed. Cambridge: Cambridge UP.10.1017/CBO9780511612756Search in Google Scholar

Williamson, T. 1990. Identity and Discrimination. Oxford: Blackwell.Search in Google Scholar

Williamson, T. 2007. The Philosophy of Philosophy. Oxford: Blackwell.10.1002/9780470696675Search in Google Scholar

Published Online: 2017-3-18
Published in Print: 2017-4-1

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