The Solo Numero Paradox

by István Aranyosi


Leibniz notoriously insisted that no two individuals differ solo numero, that is, by being primitively distinct, without differing in some property. The details of Leibniz's own way of understanding and defending the principle— known as the principle of identity of indiscernibles (henceforth "the Principle")—is a matter of much debate. However, in contemporary metaphysics an equally notorious and discussed issue relates to a case put forward by Black (1952) as a counterexample to any necessary and nontrivial version of the principle. Black asks us to imagine, via one of the fictional characters of his dialogue, a world consisting solely of two completely resembling spheres, in a relational space. The supporter of the principle is then forced to admit that although there are ex hypothesi two objects in that universe, there is no property (except trivial ones), not even relational ones, to distinguish them, and hence the necessary version of the principle is falsified.