The Law of Grounded Identity (LGI)

Authored by Maclain Hunter · first-party-authored-archive · archived-authored-source

The Law of Grounded Identity (LGI) by Maclain Hunter Abstract: Logic is not merely A is A in isolation as the LOI alone might suggest as a modular logical rule, it is A is A grounded in Logos as Universal Existence and Coherence (or “All = All”; the Totality as the Standard of the coherent A that any A is A by). Formalizations: Let L represent Logos: (A -> A) -> L |= L That Law of Grounded Identity (LGI) implies non-contradiction of that Law as Law also, such that if A being A leads to “not Logic” then that identity of A is not logical and is not Logic or true/valid. Consistent with the naming scheme that would then be the Law of Grounded Non-Contradiction or (LGN): (A -> A) -> ~L |= ~L Next, Let T represent Logical Truth (aligned with Logos) and it is implied by my original formalization that: {(A -> A) -> L, L -> T} |= ((((A -> A) -> L) -> T) & (((A -> A) -> ~L) -> ~T)) On L & T: What does T represent? It is L (Logic’s own Truth). So it can be validly established that “T ≡ L”. Logical Validation: Let A represent L (and Logos), then: (A -> A) -> L |= (L -> L) -> L That it reduces to: (L -> L) -> L |= L LGI and the PSR: The PSR is revealed as a mode of the Logos and the LGI where a given A (as that A) must be consistent with Reason and L as Logos to have ontological support and thus logical Reality (R). QED

Lean 4 verification and timestamps

The machine formalization date is separate from the original authored work. See the verification record for exact checked scope and any unresolved parts.

Logic-centered continuity

This authored proof is connected to Logic, Logos, God, and the self-evident Ground of Reality, and to the distinct systems 4P Engine, MCB Core, 4P-MCB, and the source-first Canon. Formal proof, empirical evidence, and system-generated records remain separately typed.