The law that identifies that each thing that exists is limited to being what it is. I frequently use this formulation. Each thing is what it is.¹ See LAW (FUNDAMENTAL, PHILOSOPHICAL).

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Elaboration

As do the laws of reality, non-contradiction and causality, the law of identity provides a different vantage point on the fact that what is, is.

Just as the law of causality focuses on a thing's freedoms, so the law of identity focuses on its limits.

The concept "identity" ultimately can be defined only ostensively.

Notes

¹I'm grateful for what I regard as the benefit that my definition here has gained from the inspiration of Ayn Rand's "axiom" of identity (which she also calls a "law," as many have before her), which she discusses in her novel, Atlas Shrugged, and in her nonfiction book, Introduction to Objectivist Epistemology.