Discerning "indistinguishable" quantum systems

Abstract: In a series of papers, Simon Saunders, Fred Muller and Michael Seevinck have collectively argued, against the philosophy of quantum mechanics folklore, that some non-trivial version of Leibniz's principle of the identity of indiscernibles is upheld in quantum mechanics. They argue that all particles -- fermions, paraparticles, anyons, even bosons -- may be weakly discerned by some physical relation. Here I show that their arguments make illegitimate appeal to non-symmetric, i.e. permutation-non-invariant, quantities, and that therefore their conclusions do not go through. However, I show that alternative, symmetric quantities may be found to do the required work. I conclude that the Saunders-Muller-Seevinck heterodoxy can be saved after all.