The strongest version of the principle of the Identity of Indiscernibles states that of necessity, there are no distinct things with all their universals in common (where such putative haecceities as being Aristotle do not count as universals: I use 'universal' rather than 'property' here and in what follows for the simple reason that 'universal' is the term of art that most safely excludes haecceities from its instances). It is commonly supposed that Max Black's famous paper 'The identity of indiscernibles' (...) (2) refutes this thesis. (Armstong's [1], chapter 9 is representative here.) Black argues ([2], p. 156) that it is perfectly possible that there be a world consisting solely of two indiscernible spheres at some distance to each other and that this world constitutes a counterexample to the principle above. The strongest version of the bundle theory of substance claims that of necessity, the substances that make up the world are bundles of universals.1 It is commonly supposed that a consequence of Black's defeat of the principle of the Identity of Indiscernibles is that this bundle theory of substance is mistaken. (Again, Armstong's [1] is representative.) I shall argue that Black's thought experiment does not defeat the bundle theory and that, as a result, the bundle theory can be used to salvage the principle of the Identity of Indiscernibles. (shrink)

Particle indistinguishability has always been considered a purely quantum mechanical concept. In parallel, indistinguishable particles have been thought to be entities that are not properly speaking objects at all. I argue, to the contrary, that the concept can equally be applied to classical particles, and that in either case particles may (with certain exceptions) be counted as objects even though they are indistinguishable. The exceptions are elementary bosons (for example photons).

v. 1. Nominalism and realism.--v. 2. A theory of universals.

In considering the possibility that the fundamental particles of matter might violate Leibniz's Principle, one is confronted with logical proofs that the Principle is a Theorem of Logic. This paper shows that the proof of that theorem is not universal enough to encompass entities that might not be unique, and also strongly suggests that photons, for example, do violate Leibniz's Principle. It also shows that the existence of non-individuals would imply the breakdown of Quine's criterion of ontological commitment.

Saunders has recently claimed that “identical quantum particles” with an anti-symmetric state (fermions) are weakly discernible objects, just like irreflexively related ordinary objects in situations with perfect symmetry (Black’s spheres, for example). Weakly discernible objects have all their qualitative properties in common but nevertheless differ from each other by virtue of (a generalized version of) Leibniz’s principle, since they stand in relations an entity cannot have to itself. This notion of weak discernibility has been criticized as question begging, but we (...) defend and accept it for classical cases likes Black’s spheres. We argue, however, that the quantum mechanical case is different. Here the application of the notion of weak discernibility indeed is question begging and in conflict with standard interpretational ideas. We conclude that the introduction of the conceptual resource of weak discernibility does not change the interpretational status quo in quantum mechanics. (shrink)

Quantum mechanics tells us that states involving indistinguishable fermions must be antisymmetrized. This is often taken to mean that indistinguishable fermions are always entangled. We consider several notions of entanglement and argue that on the best of them, indistinguishable fermions are not always entangled. We also present a simple but unconventional way of representing fermionic states that allows us to maintain a link between entanglement and non-factorizability.