Imagine we supposedly had two different objects, and that they shared all of the same characteristics; suppose that nothing we could say to describe one of these objects couldn’t equally be said of the other. The two would then be indiscernible; that is, would be such that we would not possibly be able to tell them apart.
German philosopher Gottfried Wilhelm Leibniz (1646–1716) would say that such a case is impossible. In his view, we could never have two things that are exactly alike in every single respect: they must differ in at least some small way, or else we’d really just have one object here, not two. This principle is called the ‘identity of indiscernibles’ or ‘Leibniz’s law’. It says that if two things are genuinely indiscernible, they must really be identical in the sense of being one and the same thing. A later philosopher, Max Black (1909–1988), conceived of a hypothetical scenario that appears to prove Leibniz’s law wrong. The scenario involves an exactly symmetrical universe containing nothing but two perfectly round, pure and solid equally-sized iron spheres. Because of the emptiness and symmetry of the universe, we would not even be able to distinguish the two spheres in terms of their location. We would have no other object to distinguish them even by relational characteristics. | |||