> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/300-logic/logic-principles/id.md).

# 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.