Abstract
This paper considers some ways in which quantum particles may be thought of as “vague objects” in the context of a naturalistic approach to metaphysics. It is optimistic about making some connections with the mainstream vague objects literature, for example, E. J. Lowe’s “referential indeterminacy with an ontic source”. Going further, in particular, connecting that literature with the “nonindividuals” approach of Steven French and Décio Krause is more problematic, and indeed there are grounds for skepticism about the metaphysical basis of nonindividuality even from a naturalistic perspective. Nevertheless, the general idea is defended against a charge of a priori incoherence, and some lines are sketched along which it might be elaborated.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The account in question has to be a very particular one, after all: quantum mechanics apparently involves worldly indeterminacy; that is an interpretative problem for quantum mechanics to be solved either by giving a philosophical account of worldly indeterminacy or by coming up with another interpretation of quantum mechanics. Amongst interpretations of quantum mechanics that do require an understanding of worldly indeterminacy, some involve the particular kind of indeterminacy that Skow argues refutes the Barnes-Williams model, and some do not. At this point, why reject the Barnes-Williams model instead of concluding that those particular interpretations of quantum mechanics are indeed impossible?
- 2.
Thanks for an anonymous referee for pointing this out, and for suggesting defences of quasi-set theory on which this section is based.
References
Akiba, K. (2004). Vagueness in the world. Noûs, 38(3), 407–429.
Albert, D. (1992). Quantum mechanics and experience. Cambridge: Harvard University Press.
Arenhart, J. R. B. (2012a). Many entities, no identity. Synthese, 187(2), 801–812.
Arenhart, J. R B. (2012b). Finite cardinals in quasi-set theory. Studia Logica, 100(3), 437–452.
Arenhart, J. R. B. (2011). A discussion on finite quasi-cardinals in quasi-set theory. Foundations of Physics, 41(8), 1338–1354.
Arenhart, J. R. B., & Krause, D. (2009). Quantifiers and the foundations of quasi-set theory. Principia, 13(3), 251–268.
Barnes, E., & Williams, J. R. G. (2011). A theory of metaphysical indeterminacy. Oxford Studies in Metaphysics, 6, 103–148.
Darby, G. (2010). Quantum mechanics and metaphysical indeterminacy. Australasian Journal of Philosophy, 88(2), 227–245.
Domenech, G., & Holik, F. (2007). A discussion on particle number and quantum indistinguishability. Foundations of Physics, 37(6), 855–878.
Domenech, G., Holik, F., & Krause, D. (2008). Q-spaces and the foundations of quantum mechanics. Foundations of Physics, 38(11), 969–994.
Dummett, M. (1996). Does quantification involve identity? In The seas of language. Oxford: Oxford University Press.
Evans, G. (1978). Can there be vague objects. Analysis, 38(4), p. 208.
French, S. (1995). Hacking away at the identity of indiscernibles: Possible worlds and Einstein’s principle of equivalence. The Journal of Philosophy, 92(9), 455–466.
French, S., & Krause, D. (1995). Vague identity and quantum non-individuality. Analysis, 55(1), 20–26.
French, S., & Krause, D. (2010). Remarks on the theory of quasi-sets. Studia Logica, 95, 101–124.
French, S., & Krause, D. (2003). Quantum vagueness. Erkenntnis, 59(1), 97–124.
French, S., & Krause, D. (2006). Identity in physics. Oxford: Oxford University Press.
French, S., & McKenzie, K. (2012). Thinking outside the (tool)box: Towards a more productive engagement between metaphysics and philosophy of physics. European Journal of Analytic Philosophy, 8, 42–59.
Hawley, K. (1998). Indeterminism and indeterminacy. Analysis, 58(2), 101–106.
Krause, D., Sant’Anna, A. S., & Sartorelli, A. (2005). On the concept of identity in Zermelo-Fraenkel-like axioms and its relationship with quantum statistics. Logique et Analyse, 48(189–92), 231–260.
Ladyman, J., Ross, D., Spurrett, D., Collier, J. G. (2007). Every thing must go (Metaphysics naturalized). Oxford: Oxford University Press.
Lawvere, F. W., & McLarty, C. (2005). An elementary theory of the category of sets (long version with commentary). Theory and Applications of Categories, 12, 1–35.
Lewis, D. (1986). On the plurality of worlds. Oxford: Blackwell.
Lewis, D. (1988). Vague identity: Evans misunderstood. Analysis, 48(3), 128–130.
Lowe, E. J. (1997). Reply to Noonan on vague identity. Analysis, 57(1), 88–91.
Lowe, E. J. (1998). The possibility of metaphysics. Oxford: Clarendon.
Lowe, E. J. (1994). Vague identity and quantum indeterminacy. Analysis, 54(2), 110–114.
Lowe, E. J. (1999). Vague identity and quantum indeterminacy: Further reflections. Analysis, 59(4), 328–330.
Lowe, E. J. (2001). Ontic indeterminacy of identity unscathed. Analysis, 61(271), 241–245.
Machover, M. (1996). Set theory, logic and their limitations. Cambridge: Cambridge University Press.
Maudlin, T. (2005). The tale of quantum logic. In Y. Ben-Menahem (Ed.), Hilary Putnam (pp. 156–187). Cambridge: Cambridge University Press.
Noonan, H. W. (1995). EJ Lowe on vague identity and quantum indeterminacy. Analysis, 55(1), 14–19.
Noonan, H. W. (2004). Are there vague objects? Analysis, 64(2), 131–134.
Odrowaz-Sypniewska, J. (2001). Quantum indiscernibility without vague identity. Analysis, 61(1), 65–69.
Pelletier, F. J. (2006). The not-so-strange modal logic of indeterminacy. Logique et Analyse, 27(108), 415–422.
Redhead, M., & Teller, P. (1992). Particle labels and the theory of indistinguishable particles in quantum mechanics. The British Journal for the Philosophy of Science, 43(2), 201–218.
Sainsbury, R. M. (1989). What is a vague object? Analysis, 49(3), 99–103.
Skow, B. (2010). Deep metaphysical indeterminacy. The Philosophical Quarterly, 60, 851–858.
Smith, N. J. J. (2008). Why sense cannot be made of vague identity. Noûs, 42(1), 1–16.
Stanford, K., Humphreys, P., Hawley, K., Ladyman, J., & Ross, D. (2010). Symposium review of Ladyman and Ross. Metascience, 19(2), 161–185.
Williams, J. R. G. (2008a). Ontic vagueness and metaphysical indeterminacy. Philosophy Compass, 3(4), 763–788.
Williams, J. R. G. (2008b). Multiple actualities and ontically vague identity. The Philosophical Quarterly, 58(230), 134–154.
Acknowledgements
I would like to thank Ken Akiba and Ali Abasnezhad for putting together the volume and to Ken, Ali and an anonymous referee for comments on the paper. For discussion of the ideas involved, thanks to David Corfield, Steven French, Décio Krause, Jonathan Lowe and Robbie Williams.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Darby, G. (2014). Vague Objects in Quantum Mechanics?. In: Akiba, K., Abasnezhad, A. (eds) Vague Objects and Vague Identity. Logic, Epistemology, and the Unity of Science, vol 33. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7978-5_4
Download citation
DOI: https://doi.org/10.1007/978-94-007-7978-5_4
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-7977-8
Online ISBN: 978-94-007-7978-5
eBook Packages: Humanities, Social Sciences and LawPhilosophy and Religion (R0)