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: 2026-10-02T17:44:36.595Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:37:41.628Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 29663959483f1e24f8d156113d897a439940ba48211c0783c5b8e88a1797b0f8
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.source_identity_rule' does not depend on any axioms
{P <-> P} |= (((P v ~P) & (P <-> ~~P)) & ((P -> P) & (~P -> ~P)))
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.
Certainty From Paradoxical Dichotomy by Maclain Hunter:
Premise:
P: God is Logic. When God is Logic atheism is illogical, and when God is not Logic atheism is not godly (or necessarily or possibly logical in the sense of being aligned with the Ontological Ground that grounds more contingent aspects of Logic) and still fails to recognize Logic as the Foundational Force or Logos that classical theism posits as God.
Let P also represent the Set of logical rules (or “Rule of Logic”) that aligns all valid logical rules and principles with the Law of Identity and Logic’s universal Coherence and immutable self-consistency. The Rule of Logic is the Rule of Logic and this A is A form entails and encompasses all logical rules and/as (or aligned with) First Cause.
Logical Proof (Formal Argument):
{P <-> P} |= (((P v ~P) & (P <-> ~~P)) & ((P -> P) & (~P -> ~P)))
Notes on Formal Structure (Above):
I would point out that the FORMAL LOGIC is displaying the traditional rules of Logic (Identity, Non-Contradiction, Excluded Middle) and the PSR (Principle of Sufficient Reason). What we call “double negation elimination” (ie - “P <-> ~~P”) is a way of writing the Law of Non-Contradiction - that P cannot be “not P”.
Likewise, “P <-> P” displays the Law of Identity and is appropriately what sits on the left of the entailment sign here, true to the way that Identity (A is A) entails all other logical rules and concepts and is synonymous with the Foundational Coherence of Logic and Reality (Logos a.k.a. God).
The argument “P -> P” shows how Reason leads to (causes) Reason (or causality and reasons for things), necessarily. If there were no Rational Ground there would be no need for Reason or reasons, and proof or the PSR (ie - “~P -> ~P”).
Conclusion:
Ergo: P v ~P: God is Logic or not Logic, but when God is not Logic that is fundamentally because of Logic and the way that God, as a premise or Universal Axiom, and Logic, as the Method of Reasoning and axiomatic Logical Structure, are logically interconnected and coherent (when coherent and valid).
Atheism (weak or strong) is illogical as whether God is used (as a term) or not atheism represents a failure to see/affirm Logic properly as the Foundational Force and Ontological Ground (or Universal Source) that it is (tantamount to God in classical theism). At that point the use of the term God becomes a secondary point - as substantively it is also a misunderstanding of Logic itself, and the position/supremacy of Logic (the Supreme Being aka “God”).
It is not coherent to have any reasonable doubt of Reason (as God), that’s an unreasonable doubt, so agnosticism and even agnostic theism are not coherent with the Logos and Logic as the rationally coherent Ontological, Logical, Existential, and Epistemological Foundation. This is not my opinion but my unbiased elaboration on what Logic and the Logical Framework show - through consistent reasoning and honest/logical application of logical rules.
Truth Table:
P↔P╞(((P∨¬P)&(P↔¬¬P))&((P→P)&(¬P→¬P)))
TTT TTFT T TTTFT T TTT T FTTFT
FTF FTTF T FTFTF T FTF T TFTTF
Q.E.D.