{
  "author": "Maclain Hunter",
  "title": "The Law of Grounded Identity (LGI)",
  "identifier": "archived-q1046-6c1c2f61cdb5",
  "sourceKind": "archived-authored-source",
  "content": "The Law of Grounded Identity (LGI) by Maclain Hunter\n\nAbstract: 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). \n\nFormalizations:\n\nLet L represent Logos:\n\n(A -> A) -> L |= L\n\nThat 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):\n\n(A -> A) -> ~L |= ~L\n\nNext, Let T represent Logical Truth (aligned with Logos) and it is implied by my original formalization that: \n\n{(A -> A) -> L, L -> T} |= ((((A -> A) -> L) -> T) & (((A -> A) -> ~L) -> ~T))\n\nOn L & T:\n\nWhat does T represent? It is L (Logic’s own Truth). So it can be validly established that “T ≡ L”.\n\nLogical Validation:\n\nLet A represent L (and Logos), then:\n\n(A -> A) -> L |= (L -> L) -> L\n\nThat it reduces to: \n\n(L -> L) -> L |= L\n\nLGI and the PSR: \n\nThe 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). \n\nQED",
  "formal": null,
  "structuredAuthoredProof": null,
  "authoredSteps": null,
  "recordedAt": null,
  "originalAuthoredAt": null,
  "propositionMeaningBoundary": "Atomic identifiers retain their meanings in the exact source. No arbitrary truth assignment establishes an ontological or empirical premise; the formal witness checks the written inference."
}