Identity (philosophy)

Numerical identity is a term that philosophers use to describe an object being the very same object. It is contrasted with qualitative identity which simply means that an object has all the same properties or qualities. An object is only numerically identical to itself but can be qualitatively identical to other objects.

The converse of Leibniz's Law, the principle of the identity of indiscernibles, that if everything true of x is true of y, x is identical with y, is correspondingly trivial if "what is true of x " is understood to include "being identical with x " (as required if Leibniz's Law is to characterise identity uniquely among equivalence relations).