Both bosons and fermions satisfy a strong version of Leibniz’s Principle of the Identity of Indiscernibles (PII), and so are ontologically on a par with respect to the PII. This holds for non-entangled, non-product states and for physically entangled states—as it has been established in previous work. In this paper, the Leibniz strategy is completed by including the (bosonic) symmetric product states. A new understanding of Pauli’s Exclusion Principle is provided, which distinguishes bosons from fermions in a peculiar ontological way. Finally, the program as a whole is defended against substantial objections.
Both bosons and fermions satisfy a strong version of Leibniz’s Principle of the Identity of Indiscernibles (PII), and so are ontologically on a par with respect to the PII. This holds for non-entangled, non-product states and for physically entangled states—as it has been established in previous work. In this paper, the Leibniz strategy is completed by including the (bosonic) symmetric product states. A new understanding of Pauli’s Exclusion Principle is provided, which distinguishes bosons from fermions in a peculiar ontological way. Finally, the program as a whole is defended against substantial objections.
This paper concerns the question of whether Pauli's Exclusion Principle (EP) vindicates the contingent truth of Leibniz's Principle of the Identity of Indiscernibles (PII) for fermions as H. Weyl first suggested with the nomenclature ‘Pauli–Leibniz principle’. This claim has been challenged by a time‐honoured argument, originally due to H. Margenau and further articulated and champione by other authors. According to this argument, the Exclusion Principle—far from vindicating Leibniz's principle—would refute it, since the same reduced state, viz. an improper mixture, can be assigned as a separate state to each fermion of a composite system in antisymmetric state. As a result, the two fermions do have the same monadic state‐dependent properties and hence are indiscernibles. PII would then be refuted in its strong version (viz. for monadic properties). I shall argue that a misleading assumption underlies Margenau's argument: in the case of two fermions in antisymmetric state, no separate states should be invoked since the states of the two particles are entangled and the improper mixture—assigned to each fermion by reduction—cannot be taken as an ontologically separate state nor consequently as encoding monadic properties. I shall then conclude that the notion of monadic properties together with the strong version of PII are inapplicable to fermions in antisymmetric state and this undercuts Margenau's argument.
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. 1. Introduction: The Currently Dominant View1.1. Weyl on Leibniz's principle1.2. Intermezzo: Terminology and Leibnizian principles1.3. The rise of the currently dominant view1.4. Overview2. Elements of Quantum Mechanics2.1. Physical states and physical magnitudes2.2. Composite physical systems of similar particles2.3. Fermions and bosons2.4. Physical properties2.5. Varieties of quantum mechanics3. Analysis of Arguments3.1. Analysis of the Standard Argument3.2. Van Fraassen's analysis3.3. Massimi's analysis4. The Logic of Identity and Discernibility4.1. The language of quantum mechanics4.2. Identity of physical systems4.3. Indiscernibility of physical systems4.4. Some kinds of discernibility5. Discerning Elementary Particles5.1. Preamble5.2. Fermions5.3. Bosons6. Concluding Discussion
The Principle of the Identity of Indiscernibles (PII) is one of the most debatably discussed subjects in the philosophy of quantum physics. Gen- erally, the discussions focus on the domain of the predicate variables involved in the standard formulation of the principle, with versions where the properties are restricted in several ways. We argue that if we restrict the domain of properties, as happens with Henkin semantics for second- order language, we have no more PII, but only a weaker form of indistin- guishability. In quantum physics, we claim that under the non-individuals interpretation, which accepts that the standard notion of identity does not apply to quantum entities, PII fails not because of the properties, but due to the lack of sense of the notion of identity involved in the principle.
Introduction In sections 6 and 7 of their paper in this volume, French and Rickles raise the question of the logical relations between the indistinguishability postulate (IP) and the various senses in which particles might fail to be individuals. In section 6 they refer to the convincing arguments of French and Redhead (1988) and of Butterfield (1993) that IP does not logically entail non-individuality, understood several ways – even though, as all seem to concede, there is something perverse about taking bosons and fermions to be individuals. Going the other way, the possibility of IP violating ‘quons’ (Greenberg, 1991) shows that if non-individuality is taken to mean the absence of continuous distinguishing trajectories, characteristic of standard quantum mechanics (QM), then non-individuality does not entail IP. Nor, as French and Rickles point out, do substance or haecceity views of individuality. But what if we conceive of individuality in terms of the Principle of the Identity of Indiscernibles (PII)? First, French and Redhead (1988) and Butterfield (1993) have given theorems showing that bosons and fermions violate PII, while the former have also demonstrated violations of PII in the case of a certain paraparticle state. But these cases, as I will explain (and as French and Rickles point out), cover just a very few of the possible kinds of quantum particles, and so for each kind the question arises as to whether it violates PII.
We maximally extend the quantum-mechanical results of Muller and Saunders (2008) establishing the ‘weak discernibility’ of an arbitrary number of similar fermions in finite-dimensional Hilbert spaces. This confutes the currently dominant view that (A) the quantum-mechanical description of similar particles conflicts with Leibniz's Principle of the Identity of Indiscernibles (PII); and that (B) the only way to save PII is by adopting some heavy metaphysical notion such as Scotusian haecceitas or Adamsian primitive thisness. We take sides with Muller and Saunders (2008) against this currently dominant view, which has been expounded and defended by many.