This states that something exists. Without this axiom, “entities” could “possibly”.

Without identity, statements in general would be impossible because they, too, would have no identity no statement exist, but they would have no identity and, for this reason, would likewise possess no properties. In such a reality, it follows that no perception or knowledge would be possible either; particularly, we could not form arguments against the axiom of identity. In Objectivism, this axiom is also designated as “A is A”: every identity has definite properties and no others.

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