Identity of Indiscernibles

The identity of indiscernibles is a metaphysical principle holding that there cannot be two distinct objects that share every one of their properties: entities x and y are identical if every predicate true of x is also true of y and vice versa, so that no two distinct things, such as two snowflakes, can be exactly alike in every respect. The principle is attributed to Gottfried Wilhelm Leibniz, though philosophers disagree about whether Leibniz intended only its converse, the indiscernibility of identicals, often called Leibniz's law, or the conjunction of both principles; either way it is counted among his central metaphysical commitments alongside the principle of noncontradiction and the principle of sufficient reason. Because some predicates must be excluded from the principle to avoid triviality or contradiction, the philosophical literature distinguishes stronger and weaker versions of it, and the principle has also been invoked to motivate notions of noncontextuality in quantum mechanics.