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: 2026-10-02T20:57:52.298Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:42:09.739Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: e90490726127e3c6a1bac523aa85ebbb09829f06da7ea2064e3af39d0b8b882b
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
{A -> B, A -> C} |= A -> (B & C)
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} |= (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.
Logic is Logic
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
The Grounding of Logic by Maclain Hunter
Key Definitions:
God: the Ontological Ground; the Ruler and Maker of the Cosmos; the Moral Standard and Authority; the First Cause of Logic; Universal Reason; the Supreme Entity; the Logos (the God of Pure Reason and Coherent Logic); Truth; Coherence (ie - God is God; Ehye Asher Ehye; I Am What I am)
Logic: the Epistemological Ground and Process that aligns itself dynamically with Reality and the First Cause (Logos); the Method of Reasoning; the Way of Knowing Reality; the Formal Structure that allows for Existence and reasoning (ie - deduction, induction, and inference); Truth; Coherence (ie - Logic is Logic; A is A; x == x)
Reality: the State of Existence; the Way of Things; the Logic of the Universe; the Rational Structure and Truth of Existence; the State or Quality of having Existence or Substance; Truth; Coherence (ie - Reality is Reality; Reality’s ultimate Oneness)
Premises:
P: Logic is, logically speaking, the Standard and Process by which Truth and what is correct/valid is determined. Even valid interpretations and states of Reality (including physical laws) must not break logical rules or there is logical contradiction.
Q: God, defined as the Origin of Reality and the First Cause of Reality/Logic sets the tone for what human logics and logical reasoning must align with. If logics don’t align with First Cause then they are (tautologically) misaligned with First Cause (Logic’s Ground - God) - thus logically incoherent in the framework of that Highest Order of Logic determined by Reality’s Identity and identity consistent First Cause. Logic must be aligned with Reality’s First Cause. If you have Logic (A) then you have Reality (B), and Reality’s Origin also called God (C), and this proof proves there is Logic (A), thus this proof existing (even if logically invalid - which also requires the existence of Logic to determine) proves that B and C or Reality and Reality’s Origin (God) exist. This can be formalized as:
{A -> B, A -> C} |= A -> (B & C)
R: God, in our subjective conception of God, must be logically coherent with logics that are logically coherent with the First Cause and the Highest Order of Logic, or contradiction arises.
S: Assume the negation of the premises. This leads to logical contradiction where either/both the Foundation of Reality (or God) and the “Way We Know Reality” (Logic) are misaligned and and logically incoherent - which cannot be, logically speaking, and for a stable and intelligible Reality to exist where we can even ponder these things and write a proof like this that refers to itself (in this way). Note also that the acceptance or denial of the premises is not to be both rational and arbitrary at once. It is not that I accept the premises because I merely want to, but because accepting them satisfies Logic and allows the proof to satisfy Logic while the assumption of the negation and the denial of the premises or any single premises does not.
Formal Reasoning:
{P, P & Q, Q & R, R & S} |= (P <-> Q) <-> (R <-> S)
Conclusion: {P, Q, R, S, A, B, C}:
Logic is determined by God (the logically consistent First Cause of Logic) in a self-referential way, like this proof is coherent through self-referencing logical alignment, and this is the only way Reality can exist in such a way that I can write (and you can read) this. This is what we can know when we listen to what Logic has to say about itself.
Logic being proof of Reality & God entails “A -> (B & C)” and vice versa.
This is not a dual grounding of Unified Reason (God - Logic) but dual purposes and aspects of the unified answer singular Logic of Reality (Source of Existence - God - Logos) that allows for both Existence and the logical reasoning (and minds) that process information within Reality.
Flaw would have to be found in the premises but to find a flaw in these premises would mean finding a flaw in Logic and the “Reality-Coherence” (the alignment with Existence) of Logic itself - destroying what premises formal logics in general are built upon. This is not the path forward, accepting what can and does satisfy Logic is the path forward (to Wisdom and valid understanding of the Logos).
Schools of thought like atheism and naturalism can’t avoid the Foundation of Self-Existent Logic. Even if we say Reality came to be in a “Natural Way” (by a “Universal Logic”) that’s no different than the Logos (Universal Logic) and would wrongly be dividing what is logical from what is natural (creating a false dilemma).
Even if we say that Logic has no Origin (God - Logos), ignoring the PSR and the need for all things including Logic and Reality to have Logical Cause (in Logic or logically derived concepts), then Logic is self-existent as the Logical Ground of Logic, reasoning, and systems STILL. Atheism and naturalism are cheap excuses for a (logically impossible) “valid way around Logic” - which fundamentally, when “logics” are seen as “ways” and/or “rational ways” is tantamount or saying we might find a “way around ways” - which is completely absurd and a violation of the Law of Non-Contradiction.
Denying the PSR to deny that a God is necessary for the Universe and logics, and a God (Universal Cause) consistent with Logic (per the PSR) is absurd, but it makes it inconsistent to require reasoning from people for anything then, including their belief in a God (ie - theism). Atheists often like to have it both ways where the implication of the PSR is ignored when it comes to God and the need for God’s existence as Logic that the PSR implies, while maintaining a similar or identical principle when it comes to theists needing to prove God exists to justify theism (ie - produce rational cause for belief). Be consistent and respect the PSR. Again, it’s not optional, it’s a well reasoned logical rule. To fail to respect it is incoherent and can be known as such when measured properly against the logical ruleset.
To deny that Logic is God just to avoid admitting there is a God is also invalid as God is an English word with a specific meaning, referring to that which rules and underpins Truth and Reality, and it is illogical to deny that Logic holds this position and plays this role - especially if the complaint against some notions or statements about God is that they are unreasonable and unscientific. If you respect Reason then respect that Reason is Number One in the Logical Order - the Supreme Being.
Logic understood holistically is both descriptive and prescriptive, and must be for our reasoning and the Structure of Reality (Universal Logic) to cohere and exist as a unified structure of Existence and understanding. Alternatives lead to contradictions where Logic and/or Reality could somehow be illogically sourced from something outside of and distinct from Logic - which contradicts the very identity of a “Logical Origin”.
Having delusional notions where Logic and Reality might be logically grounded outside of Logic is logically incoherent - even if someone “may” posit that.
Note also that while the terms as defined may be considered “rational extensions” of the Oxford English Dictionary definitions of the terms they are exactly that, definitions aligned with and extending rationally off of them.
Logic is the Logical, Ontological, and Epistemological Ground, in Logic, it doesn’t matter what naturalists or any other -ist or -ism has to say about it, as they are not Logic (and playing the role of Logic within the framework of Logic).
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 FFF TTT T FTF
TFTT⎪T TFF FFT TTT TFF F TTT
TFTF⎪T TFF FFT TFF TFF T TFF
TFFT⎪T TFF FFF FFT TFF T FFT
TFFF⎪T TFF FFF FFF TFF F FTF
FTTT⎪F FFT TTT TTT FFT F TTT
FTTF⎪F FFT TTT TFF FFT T TFF
FTFT⎪F FFT TFF FFT FFT T FFT
FTFF⎪F FFT TFF FFF FFT F FTF
FFTT⎪F FFF FFT TTT FTF T TTT
FFTF⎪F FFF FFT TFF FTF F TFF
FFFT⎪F FFF FFF FFT FTF F FFT
FFFF⎪F FFF FFF FFF FTF T FTF
(Valid)
Q.E.D.