French, Redhead and later Butterfield proved results showing that bosons, fermions, parabosons and parafermions -- supposing that they can be considered individuals -- violate the identity of indiscernibles. In this talk I generalize their results still further, (i) to a wider range of properties, and (ii) to every kind of quantum particle in the (p,q) scheme of Hartle, Stolt and Taylor. I will show that a certain kind of maximal violation of the identity of indiscernibles by a pair of particles is equivalent to their being mutually (anti-)symmetrized.