criterion of identity

In philosophy, the "criterion of identity" refers to the conditions under which two things are considered the same. This concept is primarily concerned with numerical identity, meaning there is only one entity that is both things. This is distinct from descriptive identity, where two things are merely duplicates of each other.1

Logicians express numerical identity with the symbol "=", adhering to two axioms: everything is identical to itself (x = x), and if two things are identical, they share all the same properties (Leibniz's law). This means if x is identical to y, then whatever is true of x is also true of y. Philosophical debates often explore apparent exceptions to this law, particularly concerning identity over time, such as the famous Ship of Theseus paradox.1