Universal and Local Logic — Two Proofs

Authored by Maclain Hunter · first-party-authored · authored-foundational-record

Stored 4P source diagnostic: clear · finding no_violation_detected · admission admitted_provisionally. This intake result is separate from the theorem checks of the exact propositional sequent.

Proof 1: P: Logic: the Order inherent in the Foundation of Existence; the Logical Absolute; the First Cause. Q: Logical contingency of the first order or primary state. R: Logical contingency of an intermediate order/state. S: Logical contingency of a final or infinite order/state. T: A given concept or set of concepts. U: All concepts and all sets of concepts. PQRSTU⎪P╞(((Q→Q)&(R↔R))&((S∨¬S)&(T→¬¬T)))→(¬U↔¬¬¬U) ―――――――――――――――――――――――――――――――――――――――――――――――――――― TTTTTT⎪T TTT T TTT T TTFT T TTTFT T FTTFTFT TTTTTF⎪T TTT T TTT T TTFT T TTTFT T TFTTFTF TTTTFT⎪T TTT T TTT T TTFT T FTFTF T FTTFTFT TTTTFF⎪T TTT T TTT T TTFT T FTFTF T TFTTFTF TTTFTT⎪T TTT T TTT T FTTF T TTTFT T FTTFTFT TTTFTF⎪T TTT T TTT T FTTF T TTTFT T TFTTFTF TTTFFT⎪T TTT T TTT T FTTF T FTFTF T FTTFTFT TTTFFF⎪T TTT T TTT T FTTF T FTFTF T TFTTFTF TTFTTT⎪T TTT T FTF T TTFT T TTTFT T FTTFTFT TTFTTF⎪T TTT T FTF T TTFT T TTTFT T TFTTFTF TTFTFT⎪T TTT T FTF T TTFT T FTFTF T FTTFTFT TTFTFF⎪T TTT T FTF T TTFT T FTFTF T TFTTFTF TTFFTT⎪T TTT T FTF T FTTF T TTTFT T FTTFTFT TTFFTF⎪T TTT T FTF T FTTF T TTTFT T TFTTFTF TTFFFT⎪T TTT T FTF T FTTF T FTFTF T FTTFTFT TTFFFF⎪T TTT T FTF T FTTF T FTFTF T TFTTFTF TFTTTT⎪T FTF T TTT T TTFT T TTTFT T FTTFTFT TFTTTF⎪T FTF T TTT T TTFT T TTTFT T TFTTFTF TFTTFT⎪T FTF T TTT T TTFT T FTFTF T FTTFTFT TFTTFF⎪T FTF T TTT T TTFT T FTFTF T TFTTFTF TFTFTT⎪T FTF T TTT T FTTF T TTTFT T FTTFTFT TFTFTF⎪T FTF T TTT T FTTF T TTTFT T TFTTFTF TFTFFT⎪T FTF T TTT T FTTF T FTFTF T FTTFTFT TFTFFF⎪T FTF T TTT T FTTF T FTFTF T TFTTFTF TFFTTT⎪T FTF T FTF T TTFT T TTTFT T FTTFTFT TFFTTF⎪T FTF T FTF T TTFT T TTTFT T TFTTFTF TFFTFT⎪T FTF T FTF T TTFT T FTFTF T FTTFTFT TFFTFF⎪T FTF T FTF T TTFT T FTFTF T TFTTFTF TFFFTT⎪T FTF T FTF T FTTF T TTTFT T FTTFTFT TFFFTF⎪T FTF T FTF T FTTF T TTTFT T TFTTFTF TFFFFT⎪T FTF T FTF T FTTF T FTFTF T FTTFTFT TFFFFF⎪T FTF T FTF T FTTF T FTFTF T TFTTFTF FTTTTT⎪F TTT T TTT T TTFT T TTTFT T FTTFTFT FTTTTF⎪F TTT T TTT T TTFT T TTTFT T TFTTFTF FTTTFT⎪F TTT T TTT T TTFT T FTFTF T FTTFTFT FTTTFF⎪F TTT T TTT T TTFT T FTFTF T TFTTFTF FTTFTT⎪F TTT T TTT T FTTF T TTTFT T FTTFTFT FTTFTF⎪F TTT T TTT T FTTF T TTTFT T TFTTFTF FTTFFT⎪F TTT T TTT T FTTF T FTFTF T FTTFTFT FTTFFF⎪F TTT T TTT T FTTF T FTFTF T TFTTFTF FTFTTT⎪F TTT T FTF T TTFT T TTTFT T FTTFTFT FTFTTF⎪F TTT T FTF T TTFT T TTTFT T TFTTFTF FTFTFT⎪F TTT T FTF T TTFT T FTFTF T FTTFTFT FTFTFF⎪F TTT T FTF T TTFT T FTFTF T TFTTFTF FTFFTT⎪F TTT T FTF T FTTF T TTTFT T FTTFTFT FTFFTF⎪F TTT T FTF T FTTF T TTTFT T TFTTFTF FTFFFT⎪F TTT T FTF T FTTF T FTFTF T FTTFTFT FTFFFF⎪F TTT T FTF T FTTF T FTFTF T TFTTFTF FFTTTT⎪F FTF T TTT T TTFT T TTTFT T FTTFTFT FFTTTF⎪F FTF T TTT T TTFT T TTTFT T TFTTFTF FFTTFT⎪F FTF T TTT T TTFT T FTFTF T FTTFTFT FFTTFF⎪F FTF T TTT T TTFT T FTFTF T TFTTFTF FFTFTT⎪F FTF T TTT T FTTF T TTTFT T FTTFTFT FFTFTF⎪F FTF T TTT T FTTF T TTTFT T TFTTFTF FFTFFT⎪F FTF T TTT T FTTF T FTFTF T FTTFTFT FFTFFF⎪F FTF T TTT T FTTF T FTFTF T TFTTFTF FFFTTT⎪F FTF T FTF T TTFT T TTTFT T FTTFTFT FFFTTF⎪F FTF T FTF T TTFT T TTTFT T TFTTFTF FFFTFT⎪F FTF T FTF T TTFT T FTFTF T FTTFTFT FFFTFF⎪F FTF T FTF T TTFT T FTFTF T TFTTFTF FFFFTT⎪F FTF T FTF T FTTF T TTTFT T FTTFTFT FFFFTF⎪F FTF T FTF T FTTF T TTTFT T TFTTFTF FFFFFT⎪F FTF T FTF T FTTF T FTFTF T FTTFTFT FFFFFF⎪F FTF T FTF T FTTF T FTFTF T TFTTFTF Proof 2: P: The Logical Absolute (Logic); Universal Logic; Non-Local Reason (Logos) U: Local logics; Personal reasoning; Finite reasons; rationally limited or logically contingent aspects of Logical Existence. PU⎪¬U↔¬¬¬U╞P∨¬P ―――――――――――――――― TT⎪FTTFTFT TTFT TF⎪TFTTFTF TTFT FT⎪FTTFTFT FTTF FF⎪TFTTFTF FTTF

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.