Abstract
The Weak Principle of the Identity of Indiscernibles (weak PII), states that numerically distinct items must be discernible by a symmetrical and irreflexive relation. Recently, some authors have proposed that weak PII holds in non relativistic quantum mechanics, contradicting a long tradition claiming PII to be simply false in that theory. The question that arises then is: are relations allowed in the scope of PII? In this paper, we propose that quantum mechanics does not help us in deciding matters concerning that problem, since that is a metaphysical problem rather than a quantum mechanical one. We argue further that weak PII is unmotivated on metaphysical grounds. We examine three metaphysical theses (bundle theory, counting, empiricism) that may provide reasons for one to sustain PII, and we conclude that weak PII gets no independent motivation from them.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Throughout this work, we shall employ the term ‘quantum particles’ as a synonym for ‘quantum entities’. No special connotation of ‘particles’ is being assumed, and we employ that term only to avoid terminological monotony.
Obviously, we are not claiming that quantum non-individuality was perceived to be only a consequence of the failure of PII in quantum mechanics. Other individuation principles such as bare particulars should fail as well, but whether that really happens is another discussion; see the next paragraph.
Sometimes monadic properties are described as those that may be cashed in terms of a first-order predicate that does not allow reference to other particulars, but most of the times this kind of qualification is not even mentioned.
As an anonymous referee has pointed out, the dispute concerning the status of weak PII may not only be seen as a metaphysical problem, but also as matter concerning the choice of an appropriate quantum logic. Logics such as a modified Lukasiewicz, LMn-logic algebras in a quantum topos may help us providing an appropriate framework for the discussion of weak PII and related problems. Interesting as it is, we shall not address that kind of approach to the problem here, but we point the reader to the relevant literature, see Brown et al. (2007), Baianu et al. (2007, 2010).
That idea will be discussed again when we deal with the relation between PII and empiricism.
Rodriguez-Pereyra (2004) has proposed a version of bundle theory that does not rely on PII; indeed, it is compatible with the failure of PII. His attack concentrates on the precise understanding of the ontological constitution thesis. That does no harm to our proposal, since we are considering the link between PII and bundle theory, that is, our point concerns those versions of bundle theory that need PII. If there are versions of bundle theory that survive even in case PII is false, then, worse yet for PII; that fact only adds more weight to our thesis that PII is unmotivated.
The precise definition of a pure property is a little tricky, but we shall not concern ourselves with that point here. The idea is that those properties are analyzed in terms of relations with other particulars. See the discussion in Adams (1979).
Once again, recall Rodriguez-Pereyra (2004). His version of the bundle theory, as we mentioned before, adds only more doubts on the very relevance of PII.
There is a possible defense for PII in those lines claiming that there is in fact only one object available, but we shall not concern ourselves with that here, since our main aim here is to analyze weak discernibility. Hawley criticizes that kind of strategy in Hawley (2009).
References
Adams R (1979) Primitive thisness and primitive identity. J Philos 76:5–26
Baianu IC, Brown R, Glazebrook JF (2007) A non-abelian, categorical ontology of spacetimes and quantum gravity. Axiomathes 17:353–408
Baianu IC, Georgescu G, Glazebrook JF, Brown R (2010) Lucasiewicz-Moisil many-valued logic algebra of highly-complex systems. BRAIN 1:1–11
Black M (1952) The Identity of Indiscernibles. Mind 61:153–164
Brown R, Glazebrook JF, Baianu IC (2007) A conceptual construction of complexity levels theory in spacetime categorical ontology: non-abelian algebraic topology, many-valued logics and dynamic systems. Axiomathes 17:409–493
Domenech G, Holik F (2007) A discussion on particle number and quantum indistinguishability. Found Phys 37(6):855–878
French S (1995) Hacking away at the Identity of Indiscernibles: possible worlds and einstein’s principle of equivalence. J Philos 92(9):455–466
French S (1998) On the withering away of physical objects. In: Castellani E (eds) Interpreting bodies: classical and quantum objects in modern physics, Princeton University Press, Princeton, pp 93–113
French S (2011) Metaphysical underdetermination: why worry. Synthese 180(2):205–221
French S, Krause D (2006) Identity in physics: a historical, philosophical, and formal analysis. Oxford University Press, Oxford
Hawley K (2009) Identity and indiscernibility. Mind 118:101–119
Jantzen BC (2011) No two entities without identity. Synthese 181(3):433–450
King P (2000) The problem of individuation in the middle ages. Theoria 66:159–184
Krause D (2010) Logical aspects of quantum (non-)individuality. Found Sci 15:79–94
Ladyman J, Ross D, Spurret D, Collier J (2007) Everything must go: metaphysics naturalized. Oxford University Press, Oxford
Ladyman J, Bigaj T (2010) The principle of the Identity of Indiscernibles and quantum mechanics. Philos Sci 77:117–136
Lowe EJ (1997) Objects and identity criteria. In: Hale B, Wright C (eds) A companion to the philosophy of language, Blackwell, Oxford, pp 613–633
Muller FA (2011) Withering away, weakly. Synthese 180(2):223–233
Muller FA, Saunders S (2008) Discerning fermions. Br J Philos Sci 59:499–548
Muller FA, Seevinck MP (2009) Discerning elementary particles. Philos Sci 76(2):179–200
Redhead MLG, Teller P (1992) Quantum physics and the Identity of Indiscernibles. Br J Philos Sci 43:201–218
Rodriguez-Pereyra G (2004) The bundle theory is compatible with distinct but indiscernible particulars. Analysis 64(1):72–81
Russell B (1940) An inquiry into meaning and truth. George Allen and Unwin LTD, London
Saunders S (2003) Physics and Leibniz’s principles. In: Brading K, Castellani E (eds) Symmetries in physics: philosophical reflections, Cambridge University Press, Cambridge, pp 289–307
Saunders S (2006) Are quantum particles objects. Analysis 66:52–63
Steiner M (2005) Mathematics—application and applicability. In: Shapiro S (eds) The Oxford handbook of philosophy of mathematics and logic, Oxford University Press, Oxford, pp 625–650
van Fraassen B (1980) The scientific image. Clarendon Press, Oxford
van Fraassen B (1991) Quantum mechanics: an empiricist view. Clarendon Press, Oxford
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Arenhart, J.R.B. Weak Discernibility in Quantum Mechanics: Does It Save PII?. Axiomathes 23, 461–484 (2013). https://doi.org/10.1007/s10516-012-9188-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10516-012-9188-x