The identity of indiscernibles is an ontological principle which states that two or more objects or entities are identical (are one and the same entity), if they have all their properties in common. That is, entities x and y are identical if any predicate possessed by x is also possessed by y and vice versa. A related principle is the indiscernibility of identicals, discussed below.

The principle is also known as Leibniz's law since a form of it is attributed to the German philosopher Gottfried Wilhelm Leibniz. It is one of his two great metaphysical principles, the other being the principle of sufficient reason. Both are famously used in his arguments with Newton and Clarke in the Leibniz-Clarke correspondence.

Some philosophers have decided, however, that it is important to exclude certain predicates - or purported predicates - from this principle. This is necessary to avoid either triviality or contradiction. For example (as detailed below), the predicate which denotes whether an object is equal to x (often considered a valid predicate).

As a consequence, there are a few different versions of the principle in the philosophical literature, of varying logical strength - and some of them are termed "the strong principle" or "the weak principle" by particular authors, in order to distinguish between them. Quine thought that the failure of substitutivity in intensional contexts (e.g., "Sally believes that p," "It is necessarily the case that q") shows that modal logic is an impossible project. Saul Kripke holds that this failure may be the result of the use of the disquotational principle implicit in these proofs, and not a failure of substitutivity as such.

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