 Philosophically, permutation symmetry has given rise to two main sorts of questions. On the one side, seen as a condition of physical indistinguishability of identical particles (i.e. particles of the same kind in the same atomic system), it has motivated a rich debate about the significance of the notions of identity, individuality, and indistinguishability in the quantum domain. Does it mean that the quantum particles are not individuals? Does the existence of entities which are physically indistinguishable although “numerically distinct” (the so-called problem of identical particles) imply that the Leibniz’s Principle of the Identity of Indiscernibles should be regarded as violated in quantum physics? On the other side, what is the theoretical and empirical status of this symmetry principle? Should it be considered as an axiom of quantum mechanics or should it be taken as justified empirically? It is currently taken to explain the nature of fermionic and bosonic quantum statistics, but why do there appear to be only bosons and fermions in the world when the permutation symmetry group allows the possibility of many more types? French and Rickles (2003) offer an overview of the above and related issues, and a new twist in the tale can be found in Saunders (2006). Saunders discusses permutation symmetry in classical physics, and argues for indistinguishable classical particles obeying classical statistics. He argues that the differences between quantum and classical statistics, for certain classes of particles, therefore cannot be accounted for solely in terms of indistinguishability. For further discussion and references see French and Krause (2006), Ladyman and Bigaj (2010), Caulton and Butterfield (2012), and the related SEP entry  identity and individuality in quantum theory.