  Now, of course, both quantum and classical objects of the same kind – such as electrons, say – are indistinguishable in the sense that they possess all intrinsic properties – charge, spin, rest mass etc. – in common. However, quantum objects are indistinguishable in a much stronger sense in that it is not just that two or more electrons possess the same intrinsic properties but that – on the standard understanding – no measurement whatsoever could in principle determine which one is which. If the non-intrinsic, state-dependent properties are identified with all the monadic or relational properties which can be expressed in terms of physical magnitudes standardly associated with self-adjoint operators that can be defined for the objects, then it can be shown that two bosons or two fermions in a joint symmetric or anti-symmetric state respectively have the same monadic properties and the same relational properties one to another (French and Redhead 1988; see also Butterfield 1993). This has immediate implications for the Principle of the Identity of Indiscernibles which, expressed crudely, insists that two things which are indiscernible, must be, in fact, identical. 