# The Law of Identity (ID)

Each thing, whether a universal or a particular thing, is composed of its own, unique, set of characteristic qualities/properties, which in ancient Greece was known as its **essence**.

**The law of identity** states that each thing is identical with itself, denoted by $$\forall x\ . x=x$$

> The modern formulation of identity is that of Gottfried Leibniz: $$x$$ is the same as $$y$$ iff every predicate true of $$x$$ is true of $$y$$ as well.
