Identity of indiscernibles
Leibniz's principle that if two things share absolutely every property, they are not two things but one. Max Black's thought experiment of a universe containing nothing but two exactly similar spheres looked like a refutation of it.
Leibniz's principle says that if x and y share every property, then x and y are the same thing. Max Black asked us to imagine a universe containing two exactly similar iron spheres and nothing else. Every property one has, the other has. So either they are one sphere, which the story says they are not, or the principle is false.
The reply that has held up appeals to relations rather than properties: each sphere is two miles from *a sphere*, and neither is two miles from *itself*. The relation is irreflexive, so there must be two. This is why a puzzle in metaphysics turns out to bear on a question in theology — it is the same move, about the same gap.
Where this comes up
Sources
- SEP, “The Identity of Indiscernibles”, on the third grade principle
- Simon Saunders (2006), on Black's spheres