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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References found in this work BETA
Steven French & Michael Redhead (1988). Quantum Physics and the Identity of Indiscernibles. British Journal for the Philosophy of Science 39 (2):233-246.
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Similar books and articles
F. A. Muller & Simon Saunders (2008). Discerning Fermions. British Journal for the Philosophy of Science 59 (3):499-548.
N. Huggett & J. Norton (2014). Weak Discernibility for Quanta, the Right Way. British Journal for the Philosophy of Science 65 (1):39-58.
Steven French & Michael Redhead (1988). Quantum Physics and the Identity of Indiscernibles. British Journal for the Philosophy of Science 39 (2):233-246.
Simon Saunders (2003). Physics and Leibniz's Principles. In Katherine Brading & Elena Castellani (eds.), Symmetries in Physics: Philosophical Reflections. Cambridge University Press. 289--307.
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