Journal Article

Discerning Fermions

F. A. Muller and Simon Saunders

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 59, issue 3, pages 499-548
Published in print September 2008 | ISSN: 0007-0882
Published online September 2008 | e-ISSN: 1464-3537 | DOI:
Discerning Fermions

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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 Schrödinger, 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.

Introduction: The Currently Dominant View 1.1

Weyl on Leibniz's principle


Intermezzo: Terminology and Leibnizian principles


The rise of the currently dominant view



Elements of Quantum Mechanics 2.1

Physical states and physical magnitudes


Composite physical systems of similar particles


Fermions and bosons


Physical properties


Varieties of quantum mechanics

Analysis of Arguments 3.1

Analysis of the Standard Argument


Van Fraassen's analysis


Massimi's analysis

The Logic of Identity and Discernibility 4.1

The language of quantum mechanics


Identity of physical systems


Indiscernibility of physical systems


Some kinds of discernibility

Discerning Elementary Particles 5.1






Concluding Discussion

Journal Article.  18781 words.  Illustrated.

Subjects: Philosophy of Science ; Science and Mathematics

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