This is not a statement among many. It is the precondition for any statement. To deny the Law of Identity (A = A) to say “a thing is not itself” – requires that the denial mean what it says and not its opposite. The act of denial assumes the identity of the words used. The attempt to reject identity performs identity. The axiom is inescapable.
Identity is the singular, mandatory requirement for existence. To exist is not a property added to a substance, it is the physical manifestation of a fully resolved identity A = A. If a physical configuration is perfectly self-identical, it possesses an absolute truth value and manifest as a coordinate within physical reality. A thing cannot be real without being itself, and it cannot be itself without being real. In the reality we exist, logical consistency is strictly identical to physical existence: the self-identical is mandatory, and the paradoxical is physically impossible.
If A = A is rejected, the rejection is incoherent. No symbol can refer stably to anything, including itself. The processor crashes.