Lean verification registry · Authored proofs · The Logos Architecture
Written formal sequents verified
Axiom-free: true · 1 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: 2026-10-02T20:42:32.100Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:38:11.172Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: a9a7aefc5ea45036d8698113400a74cd2413da18f05c51608ce45a69275ec159
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
{P, P -> Q, Q -> R, R <-> 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.
Evidence Requires Logic by Maclain Hunter
Premises:
P: demand for “evidence” (or proof) presupposes the validity of logical reasoning. One must use Logic to demand evidence.
Q: If Logic (Logos) is denied, then no coherent evidence can be demanded.
R: Therefore, demanding evidence already affirms the necessity of Logos.
S: This is a logically sound ontological argument for Logos. Assume otherwise for a moment, and that the premises (P, Q, R, and S) are unsound. Testing that assumption leads to logical contradictions where logically derived concepts like evidence and proof (including this proof) might somehow exist absent all Logic and logics - the Universal Logos and all local “logoi” it contains. That is of course absurd and this absurdity is resolved in a logical fashion easily by simply accepting the premises and proof here.
Logical Proof:
{P, P -> Q, Q -> R, R <-> S} |= (P & Q) -> (R & S)
Conclusion: {P, Q, R, S}:
Logic is plainly evident as the “Root of Proof and Evidence”. If not then the existence of proof and evidence would itself absurdly be “not evident or proven” (or feasible). It is certain that the Logos (or Universal Logic) exists along with proofs like this one which you cannot coherently deny the existence of (if and since you are reading this).
This, and the fact that you can observe this proof, means that this proof is allowing you to empirically observe the same Order that the Cosmos itself relies upon, also understood as the “God of Reason” or “Logos” - the God of the Bible that many atheists and theists alike have asked to be “shown”.
If you have asked then you have now received.
Truth Table Analysis:
PQRS⎪P P→Q Q→R R↔S╞(P&Q)→(R&S)
TTTT⎪T TTT TTT TTT TTT T TTT
TTTF⎪T TTT TTT TFF TTT F TFF
TTFT⎪T TTT TFF FFT TTT F FFT
TTFF⎪T TTT TFF FTF TTT F FFF
TFTT⎪T TFF FTT TTT TFF T TTT
TFTF⎪T TFF FTT TFF TFF T TFF
TFFT⎪T TFF FTF FFT TFF T FFT
TFFF⎪T TFF FTF FTF TFF T FFF
FTTT⎪F FTT TTT TTT FFT T TTT
FTTF⎪F FTT TTT TFF FFT T TFF
FTFT⎪F FTT TFF FFT FFT T FFT
FTFF⎪F FTT TFF FTF FFT T FFF
FFTT⎪F FTF FTT TTT FFF T TTT
FFTF⎪F FTF FTT TFF FFF T TFF
FFFT⎪F FTF FTF FFT FFF T FFT
FFFF⎪F FTF FTF FTF FFF T FFF
Q.E.D.