Necessary Correctness and Logical Proof

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.

P: Necessarily I am correct when I state that it would be a contradiction for a “truly coherent (logical) person” to argue against Coherence (Logic) as the Standard of Coherence and the Foundation of Truth and Existence (the True God or Logical Origin). Q: Necessarily we must assume the opposite of P to form the proof for contradiction that explores how ~P would stand against Coherence (Logic), which in this case is clear since P is stating that coherent people need to be coherent with Coherence itself, which is the Foundation of Truth and Standard of what “Coherence” even/actually is. That makes it untenable to assume “not P” (~P) and to hold “not P” as a true premise, thus affirming the Truth in/of P as defined above. R: P is true and aligns with Coherence (Logic) and the set of logical rules that cohere (as Coherence/Logic). This makes the proof itself (and as a whole) true on top of being valid, per the coherent set of logical rules and by the Standard of Logic (Coherence) itself. S: Assume that things (anything) that were coherent with Logic (and Coherence, also understood as the “True God”) were not one/merged with Logic in a coherent (and “flush” or “seamless”) manner identical to and proportional to their coherence. This assumption is internally inconsistent and self-defeating and cannot be true, thus we know the statement that a coherent person is one with God (coherent with Logic) is well supported and even self supporting when God is rightly understood coherently and as Logic/Coherence (the Standard of Truth) itself. T: Assume ~R. This would mean the proof is untrue, which could only happen if the proof and its source are somehow incoherent. R is true, however, so the opposite must be true, that the proof and its source—Logic and the logician (Maclain Hunter)—are coherent. Therefore R being true, in light of T and the broader proof, shows that Logic and the logician (Maclain) are coherent with all coherent things, merged as One (God). The opposite leads to untenable “incoherence between coherent things” - an obvious contradiction. Formal Argument: {P, P <-> Q, P <-> R, Q, Q -> P, P, Q -> R, R, R -> S, T} |= (P & Q) & (R & S) & T Conclusion: {P, Q, R, S, T}: A coherent person dismissing the Coherence of and “that is” the Foundation of Truth (or God) is an untenable and logically contradictory position to hold. The proof is self-evident since its premises prove each other true according to the set of logical rules and by the Standard of Coherence. Likewise, R being true, in light of T and the broader proof, shows that Logic and the logician are coherent with all coherent things, merged as One (God). The opposite leads to untenable “incoherence between coherent things” - an obvious contradiction. It would be a contradiction for me (Maclain Hunter) to write such a valid proof, as R affirms, without being coherent/merged with Logic (the Foundation of Reality also known as God) proportionally to my coherence (which the proof is a display and evidence of). Truth Table Analysis: valid ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ PQRST⎪P P↔Q P↔R Q Q→P P Q→R R R→S T╞(P&Q)&(R&S)&T ―――――――――――――――――――――――――――――――――――――――――――――――――― TTTTT⎪T TTT TTT T TTT T TTT T TTT T TTT T TTT TT TTTTF⎪T TTT TTT T TTT T TTT T TTT F TTT T TTT FF TTTFT⎪T TTT TTT T TTT T TTT T TFF T TTT F TFF FT TTTFF⎪T TTT TTT T TTT T TTT T TFF F TTT F TFF FF TTFTT⎪T TTT TFF T TTT T TFF F FTT T TTT F FFT FT TTFTF⎪T TTT TFF T TTT T TFF F FTT F TTT F FFT FF TTFFT⎪T TTT TFF T TTT T TFF F FTF T TTT F FFF FT TTFFF⎪T TTT TFF T TTT T TFF F FTF F TTT F FFF FF TFTTT⎪T TFF TTT F FTT T FTT T TTT T TFF F TTT TT TFTTF⎪T TFF TTT F FTT T FTT T TTT F TFF F TTT FF TFTFT⎪T TFF TTT F FTT T FTT T TFF T TFF F TFF FT TFTFF⎪T TFF TTT F FTT T FTT T TFF F TFF F TFF FF TFFTT⎪T TFF TFF F FTT T FTF F FTT T TFF F FFT FT TFFTF⎪T TFF TFF F FTT T FTF F FTT F TFF F FFT FF TFFFT⎪T TFF TFF F FTT T FTF F FTF T TFF F FFF FT TFFFF⎪T TFF TFF F FTT T FTF F FTF F TFF F FFF FF FTTTT⎪F FFT FFT T TFF F TTT T TTT T FFT F TTT TT FTTTF⎪F FFT FFT T TFF F TTT T TTT F FFT F TTT FF FTTFT⎪F FFT FFT T TFF F TTT T TFF T FFT F TFF FT FTTFF⎪F FFT FFT T TFF F TTT T TFF F FFT F TFF FF FTFTT⎪F FFT FTF T TFF F TFF F FTT T FFT F FFT FT FTFTF⎪F FFT FTF T TFF F TFF F FTT F FFT F FFT FF FTFFT⎪F FFT FTF T TFF F TFF F FTF T FFT F FFF FT FTFFF⎪F FFT FTF T TFF F TFF F FTF F FFT F FFF FF FFTTT⎪F FTF FFT F FTF F FTT T TTT T FFF F TTT TT FFTTF⎪F FTF FFT F FTF F FTT T TTT F FFF F TTT FF FFTFT⎪F FTF FFT F FTF F FTT T TFF T FFF F TFF FT FFTFF⎪F FTF FFT F FTF F FTT T TFF F FFF F TFF FF FFFTT⎪F FTF FTF F FTF F FTF F FTT T FFF F FFT FT FFFTF⎪F FTF FTF F FTF F FTF F FTT F FFF F FFT FF FFFFT⎪F FTF FTF F FTF F FTF F FTF T FFF F FFF FT FFFFF⎪F FTF FTF F FTF F FTF F FTF F FFF F FFF FF Result: Validated/Confirmed. Q.E.D.

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.