Lean verification registry · Authored proofs · The Logos Architecture
Written formal sequents verified
Axiom-free: true · 3 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: 2026-10-02T18:23:08.593Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:39:47.209Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 0278acc2e2592d9317c36aa68f6236235fd8e78ba1c3de31b67c0b04d64a739e
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 'HunterAuthored.source_identity_rule' does not depend on any axioms
{1, 2, 3, 4} |= (1 & 2) <-> (3 & 4)
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 <-> P} |= (P & Q) <-> R
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.
Law of Identity
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
Logical Rules and God by Maclain Hunter
Premises:
P: It would help you to understand the Logos as God if you knew the rules of Logic and how to apply them. It is technically impossible to know Logic without at least informally applying Logic in some manner. To assume otherwise defies Logic and would be logically inconsistent.
Q: The Law of Identity, the Law of Non-Contradiction, the Law of the Excluded Middle, the Principle of Sufficient Reason together mean God, as Logical Truth, can’t be “not God”, nonexistent, or false. Let me break down the reasoning here:
1. Law of Identity: A is A: let A be God, then God is God, logically.
2. Law of Non-Contradiction: A is not “not A”: let A be God, the God cannot be “not God” coherently.
3. Law of the Excluded Middle: A cannot be true and false at once and in the same sense and context: let A represent the True God (or God aligned with Truth, as with the Logos), then God (or A) must be true and cannot be false, or contradiction arises.
4. Principle of Sufficient Reason (PSR): All things (A) must have Rational Cause, including the Universe: concept A must have Cause (Logos). It is not mere presupposition to say that Logic is God, but the coherent way to satisfy the PSR when it comes to reconciling the logical and theological identities of the Rational Cause itself. It is contradictory to deny the Logos as Universal Cause while maintaining any sort of demand for proof and explanation (or logical reasoning).
This reasoning above can be represented formally with this sub-argument:
{1, 2, 3, 4} |= (1 & 2) <-> (3 & 4)
R: Assume the negation of P and Q and assume the First Cause (God - Logos - Reason) were illogical/nonexistent rather than fully aligned with and coherent with Reality and Logic (or Reason and Rational Foundations). This would lead to logical contradiction and the paradox of Logic undermining and refuting itself.
Logical Argument:
{P, P <-> Q, Q <-> R, R <-> P} |= (P & Q) <-> R
Conclusion:
The rules of Logic require that the True God is Logic itself. The Origin of Reality (God) that satisfies the PSR (Principle of Sufficient Reason), which avoids violation the rules of Logic and the Logical Structure of the Cosmos—the broadest of logical frameworks also called the “Universal Logic” or “Logos”)—must be Logic itself (and that which manages to be fully coherent with Logic), logically speaking. This is certain within any coherent logical framework and within the Logic of Reality (Logos).
In illogical/limited frameworks this Truth and this proof might be invalidated, sure, but this double negation—of being negated within an incoherent framework that logically negates itself (as a coherent logical framework)—only actually reinforces and supports the Truth and overall soundness of the Logos and my Logos coherent, Reason acknowledging proofs, such as this one.
This is the result of a coherent and holistic analysis of the implications of this proof in the framework of Logical Existence (Logos - God), while considering how subjective perception and illogical frameworks may invalidate the Valid (or God), and how these predictable scenarios like the lack of acceptance of even a sound proof can be handled by the Logic of Reality and/or rational people.
Truth Table Analysis:
PQR⎪P P↔Q Q↔R R↔P╞(P&Q)↔R
TTT⎪T TTT TTT TTT TTT TT
TTF⎪T TTT TFF FFT TTT FF
TFT⎪T TFF FFT TTT TFF FT
TFF⎪T TFF FTF FFT TFF TF
FTT⎪F FFT TTT TFF FFT FT
FTF⎪F FFT TFF FTF FFT TF
FFT⎪F FTF FFT TFF FFF FT
FFF⎪F FTF FTF FTF FFF TF
Valid
Addressing Counterarguments:
Only if God is not understood as a term referring to the Origin of the Universe, as it is commonly understood to mean, and only if Logic is not understood, as it commonly is, to refer to the Method of Reasoning and Logical Standard, would it possibly be the case that Logic is not God.
Of course, I couldn’t be much clearer about how I am using these terms and so to fail to accept my terms and the reasoning that then follows is unreasonable and illegitimate, like saying that x + y isn’t 5 because you have merely and arbitrarily failed to accept that in my reasoning (to get to a sum of 5) I had validly defined x as 2 and y as 3.
Q.E.D.