The Identity Constraint (A = A) requires that “the whole” – the totality of all that exists – be a single, determinate object with a fixed identity. The phrase “the whole” must refer to the same thing at all times, otherwise it fails to pick out a unique referent and the statement “the whole exists” has no stable truth value.
Now consider a dynamic model of time: the past is gone, the future does not yet exist, and only the present is real. In such a model, the whole at t₁ is W₁ (the set of all existents at t₁), and the whole at t₂ is W₂ (a different set). Since W₁ ≠ W₂, “the whole” does not name a single object; it names a succession of distinct entities. The maximal referent shifts, and the Identity Constraint is violated globally.
Local change within a static block – a leaf being green at one coordinate and red at another – does not violate A = A, because both coordinates are equally real and permanently fixed within the unchanging 4‑dimensional solid. The leaf’s states are different parts of the same whole, not a change in the whole’s own composition.
To preserve a fixed identity for the whole, every coordinate that is real must be permanently real. No coordinate can be added (there is no external source) and none can be removed (deletion would alter the whole’s identity). Therefore, the whole is a completed, unchanging 4‑dimensional solid containing all spatial and temporal locations simultaneously.
To reject Theorem 3 is to assert that the whole can gain or lose parts while remaining the same whole – a violation of identity. The processor crashes.