Labels for Non-Individuals?
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Quasi-set theory is a first-order theory without identity, which allows us to cope with non-individuals in a sense. A weaker equivalence relation called “indistinguishability” is an extension of identity in the sense that if x is identical to y then x and y are indistinguishable, although the reciprocal is not always valid. The interesting point is that quasi-set theory provides us with a useful mathematical background for dealing with collections of indistinguishable elementary quantum particles. In the present paper, however, we show that even in quasi-set theory it is possible to label objects that are considered as non-individuals. This is the first paper of a series that will be dedicated to the philosophical and physical implications of our main mathematical result presented here.
Key words:quasi-sets non-individuality labels quantum mechanics
- 1.1. Adams, R., ‘Primitive thisness and primitive identity,’ J. Phil. 76, 5–26 (1979).Google Scholar
- 2.2. Da Costa, N. C. A., and R. Chuaqui, ‘On Suppes' set theoretical predicates,’ Erkenntnis 29, 95–112 (1988).Google Scholar
- 5.5. Dalla Chiara, M. L., and G. Toraldo di Francia, ‘Individuals, kinds and names in physics’, in G. Corsi et al., eds., Bridging the Gap: Philosophy, Mathematics, Physics, pp. 261–283 (Kluwer Academic, Dordrecht, 1993).Google Scholar
- 6.6. French, S., ‘Identity and individuality in quantum theory,’ The Stanford Encyclopedia of Philosophy, Edward N. Zalta, ed., URL = http://plato.stanford.edu/entries/qt-idind/ (2004).Google Scholar
- 11.11. Manin, Yu. I., ‘Problems of present day mathematics I: Foundations,’ in Browder, F. E., ed., Mathematical Problems Arising from Hilbert Problems, Proceedings of Symposia in Pure Mathematics XXVIII (AMS, Providence, 1976), pp. 36–36.Google Scholar
- 14.14. Sakurai, J. J., Modern Quantum Mechanics (Addison-Wesley, Reading, 1994).Google Scholar