Discerning fermionsMuller, F.A.Saunders, Simonhttp://dspace.library.uu.nl/handle/1874/32636enjournalArticleOxford University Press20080007-0882We demonstrate that the quantum-mechanical description of composite physical systems
of an arbitrary number of similar fermions in all their admissible states, mixed or
pure, for all finite-dimensional Hilbert spaces, is not in conflict with Leibniz’s Principle
of the Identity of Indiscernibles (PII). We discern the fermions by means of physically
meaningful, permutation-invariant categorical relations, i.e. relations independent of
the quantum-mechanical probabilities. If, indeed, probabilistic relations are permitted as
well, we argue that similar bosons can also be discerned in all their admissible states; but
their categorical discernibility turns out to be a state-dependent matter. In all demonstrated
cases of discernibility, the fermions and the bosons are discerned (i) with only
minimal assumptions on the interpretation of quantum mechanics; (ii) without appealing
to metaphysical notions, such as Scotusian haecceitas, Lockean substrata, Postian
transcendental individuality or Adamsian primitive thisness; and (iii) without revising
the general framework of classical elementary predicate logic and standard set theory,
thus without revising standard mathematics. This confutes: (a) the currently dominant
view that, provided (i) and (ii), the quantum-mechanical description of such composite
physical systems always conflicts with PII; and (b) that if PII can be saved at all, the only
way to do it is by adopting one or other of the thick metaphysical notions mentioned
above. Among the most general and influential arguments for the currently dominant
view are those due to Schr¨odinger, Margenau, Cortes, Dalla Chiara, Di Francia, Redhead,
French,Teller, Butterfield, Giuntini, Mittelstaedt, Castellani, Krause and Huggett.
We review them succinctly and critically as well as related arguments by van Fraassen
and Massimi.The British journal for the philosophy of scienceOxford University Press
2008
0007-0882
URN:NBN:NL:UI:10-1874-32636
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