Weak discernibility
Quine's idea that two things can be told apart not by any property either has on its own, but by a relation neither can have to itself. Black's two spheres are two because each is two miles from another sphere and no sphere is two miles from itself.
Quine distinguished grades of telling things apart. The strongest names each thing individually. The weakest — his third grade — does not name or describe either thing, and works only by a relation neither can have to itself.
It is the weakest way of being two, and it is enough. If a stands in R to b, and nothing stands in R to itself, then a and b are not the same thing, even if nothing else in the world distinguishes them. Simon Saunders used this to rescue Leibniz's principle from Black's spheres and to discern electrons in states where nothing else could.
There is a published objection worth knowing, because it is the same objection this material keeps producing: whether a relation really is irreflexive can look like something you can only settle once you already know the relata are two.
Where this comes up
Sources
- W. V. O. Quine, “Grades of Discriminability” (1976)
- Simon Saunders (2006); Muller & Saunders, “Discerning Fermions”