Lean verification registry · Authored proofs · The Logos Architecture
Written formal sequents verified
Axiom-free: true · 2 checked theorem statements.
Lean establishes the listed formal statements and dependencies. The exact authored source, Ground, known premise meanings, application validation and empirical evidence remain separately typed. No unencoded section is certified by a neighboring theorem.
Original source author: Maclain Hunter. Machine formalization: Replit Agent. No original wording was rewritten.
Source registered: 2026-10-02T16:41:52.776Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:39:54.501Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 500b7c08a8ce46caaff764d9b2039d1805c6f430b20b36a8e6ddbd8ee4fc47ad
Lean source · Verification JSON · Exact archived source JSON · Compiler report · Current authored source page · Signed release and verification instructions
Lean (version 4.7.0, commit v4.7.0, Release) exitCode=0 'HunterAuthored.inference_1' does not depend on any axioms 'HunterAuthored.inference_2' does not depend on any axioms
{P, P <-> Q, Q <-> R, R <-> ~S, ~S} |= (P & Q) & (R & ~S)
Exact source sequent under finite two-valued propositional semantics. Source proposition meanings and Logic/Logos/God Ground are preserved separately; this checks the inference, not unencoded prose.
{~P, ~P <-> ~Q, ~Q <-> ~R, ~R <-> S, S} |= ~(P & Q) & (~R & S)
Exact source sequent under finite two-valued propositional semantics. Source proposition meanings and Logic/Logos/God Ground are preserved separately; this checks the inference, not unencoded prose.
Logos Entails Coherent Morality by Maclain Hunter:
Premises:
P: Logic being God inherently entails Logic as the Moral Authority and Agathon (the Greatest Goodness), where Coherence is ultimately good and incoherence is evil. If we assume a different way, it leads to logical and moral incoherence. It is immoral and incoherent to posit that Logic (Logos), God (Theos), and Agathon (Goodness) are incoherent.
Q: God: the Moral Authority and Origin of the Universe; the Ruler of Creation; the “Arche” or First Cause in Philosophy and Theology.
R: Logic: The Logos or Logical Structure of Reality; the Method of Reasoning encompassing all methods of reasoning and all concepts; the Source of Order and Knowledge; Proper Reasoning and Order (in any form or universally).
S: Logical Contradiction (~R) and immorality (~Q).
Logical Proof:
{P, P <-> Q, Q <-> R, R <-> ~S, ~S} |= (P & Q) & (R & ~S)
Conclusion: {P, Q, R, & ~S}:
It is illogical and immoral to disconnect Logic, Agathon, and God, and to have views on either or both that do not align Reason and what is reasonable with God (the Moral Authority) and what is moral (godly). This assertion (or set of assertions), encompassed by the premises P, Q, and R, is logically equivalent to the negation of incoherence and immorality, affirming the necessary Truth of the premises {P, Q, R} and the necessity of the negation of S (for the maintenance of Coherence/Logic or P, Q, and R).
Truth Table Analysis:
valid
↓ ↓ ↓ ↓ ↓ ↓
PQRS⎪P P↔Q Q↔R R↔¬S ¬S╞(P&Q)&(R&¬S)
――――――――――――――――――――――――――――――――――――
TTTT⎪T TTT TTT TFFT FT TTT F TFFT
TTTF⎪T TTT TTT TTTF TF TTT T TTTF
TTFT⎪T TTT TFF FTFT FT TTT F FFFT
TTFF⎪T TTT TFF FFTF TF TTT F FFTF
TFTT⎪T TFF FFT TFFT FT TFF F TFFT
TFTF⎪T TFF FFT TTTF TF TFF F TTTF
TFFT⎪T TFF FTF FTFT FT TFF F FFFT
TFFF⎪T TFF FTF FFTF TF TFF F FFTF
FTTT⎪F FFT TTT TFFT FT FFT F TFFT
FTTF⎪F FFT TTT TTTF TF FFT F TTTF
FTFT⎪F FFT TFF FTFT FT FFT F FFFT
FTFF⎪F FFT TFF FFTF TF FFT F FFTF
FFTT⎪F FTF FFT TFFT FT FFF F TFFT
FFTF⎪F FTF FFT TTTF TF FFF F TTTF
FFFT⎪F FTF FTF FTFT FT FFF F FFFT
FFFF⎪F FTF FTF FFTF TF FFF F FFTF
Proof For Contradiction:
{~P, ~P <-> ~Q, ~Q <-> ~R, ~R <-> S, S} |= ~(P & Q) & (~R & S)
Conclusion: ~{P, Q, R} & S:
Logical contradiction and immorality succeed with the failure of God and Logic, and with any incoherence in the Origin of the Universe (God - Logic). Premises P, Q, and R being false negates Reason and the Origin of Logical Existence. This is untenable thereby affirming the previous proof positive. To accept the proof for contradiction as true over the proof amounts to a rejection of Agathon and Reason (Logic - God) - which we can, per this proof, understand to be not only an illogical OR immoral rejection but BOTH.
Truth Table Analysis:
valid
↓ ↓ ↓ ↓ ↓ ↓
PQRS⎪¬P ¬P↔¬Q ¬Q↔¬R ¬R↔S S╞¬(P&Q)&(¬R&S)
―――――――――――――――――――――――――――――――――――――――――
TTTT⎪FT FTTFT FTTFT FTFT T F TTT F FTFT
TTTF⎪FT FTTFT FTTFT FTTF F F TTT F FTFF
TTFT⎪FT FTTFT FTFTF TFTT T F TTT F TFTT
TTFF⎪FT FTTFT FTFTF TFFF F F TTT F TFFF
TFTT⎪FT FTFTF TFFFT FTFT T T TFF F FTFT
TFTF⎪FT FTFTF TFFFT FTTF F T TFF F FTFF
TFFT⎪FT FTFTF TFTTF TFTT T T TFF T TFTT
TFFF⎪FT FTFTF TFTTF TFFF F T TFF F TFFF
FTTT⎪TF TFFFT FTTFT FTFT T T FFT F FTFT
FTTF⎪TF TFFFT FTTFT FTTF F T FFT F FTFF
FTFT⎪TF TFFFT FTFTF TFTT T T FFT T TFTT
FTFF⎪TF TFFFT FTFTF TFFF F T FFT F TFFF
FFTT⎪TF TFTTF TFFFT FTFT T T FFF F FTFT
FFTF⎪TF TFTTF TFFFT FTTF F T FFF F FTFF
FFFT⎪TF TFTTF TFTTF TFTT T T FFF T TFTT
FFFF⎪TF TFTTF TFTTF TFFF F T FFF F TFFF
Q.E.D.