Discerning Fermions

Abstract
We 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 Schrodinger, 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
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DOI 10.1093/bjps/axn027
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References found in this work BETA
Quantum Physics and the Identity of Indiscernibles.Steven French & Michael Redhead - 1988 - British Journal for the Philosophy of Science 39 (2):233-246.
Particle Labels and the Theory of Indistinguishable Particles in Quantum Mechanics.Michael Redhead & Paul Teller - 1992 - British Journal for the Philosophy of Science 43 (2):201-218.
Exclusion Principle and the Identity of Indiscernibles: A Response to Margenau's Argument.Michela Massimi - 2001 - British Journal for the Philosophy of Science 52 (2):303--30.

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Citations of this work BETA
Remarks on the Theory of Quasi-Sets.Steven French & Décio Krause - 2010 - Studia Logica 95 (1/2):101 - 124.
The Structural Metaphysics of Quantum Theory and General Relativity.Vincent Lam & Michael Esfeld - 2012 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 43 (2):243-258.

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