Suppose we grant the possibility of otherwise indiscernible objects that are asymmetrically related. Then we have not just a counterexample to the weak Principle, but an interesting further weakening to the Third Grade Principle, namely that in cases where the Weak Principle fails the otherwise indiscernible objects stand in a symmetric but irreflexive relation — “Third Grade” because based on Quine’s third grade of discrimination (1976). Recently Saunders has investigated this, noting that fermions but not bosons are third grade discriminable (2006).