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: 2026-10-02T19:42:34.786Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:37:10.534Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 1e1091e74bdadf98e2e8c278287a7efd37a2c0d0d6d579e04c3453603ee386b0
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, Q, 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.
A Response to Opposition by Maclain Hunter
Abstract: The Logos is nonsense you say? While you demand proof from me? The thing is that you’ve just proven you dismiss things you don’t understand arbitrarily, including Reason when the Greek word for it “Logos” is used, by calling Reason nonsense by the Greek word for it (and for “Word” itself in Greek).
The Logos is a term I use precisely to throw you off and expose you (or people like you) to something so old and foundational, and so lost among the irrational, that it’s a novelty and “news”. Haven’t you heard the Good News (Logos)?
Reason, the ESSENCE OF PROOF, and the SOURCE of truly valid teachings (ie - Jesus of Nazareth, Heraclitus of Ephesus, Adi Shankara, Moshe Rabbeinu, etc.) is where any proof I can show you comes from and what it must align with. It’s like telling me to kick a field goal so you can see the Goalposts.
It’s absurd in the sense that if you can’t see the Goalposts, or how Logic is the Foundation of Reality aka “God”, and the thing that any proof must align with and “logically satisfy”, then it’s illogical to ask for proof so skeptically like it doesn’t exist.
If we include “implicit proof” then all proof is implicit proof of Logic as God. Explicit proofs like mine and Gödel’s also exist.
The proper way to approach this, not that I’ll get my hopes up for this to happen, would be for you to learn and then prove you know Logic and its rules. Then, for you to write many formal logical proofs yourself on many topics to show you actually have expertise.
It is like how they would pick a qualified peer reviewer when it comes to any credible academic journal, rather than some bozo off the street who doesn’t have any idea what’s going on.
Then, perhaps 10 years from now, you’ll be in a position where you are actually qualified to check one of my proofs like I trust real experts and our modern AI systems, or a logic calculator, to check my proofs.
For now though, your argument is absolutely dead because of your claim that the Logos (Universal Reason - Pure Logic) is “nonsense”.
No, Logos is what “nonsense” is defined by (its incoherence and misalignment with).
Study, then you’ll see the root of the English word Logic is Logos and that Logos is directly equated to Theos in both the Bible and the Logical Structure of Reality (Logos aka Theos). It’s not a mere theory, it’s what makes theory be theory to begin with. It’s what makes you be you, and even your (personal and flawed) finite logic of doubt, which is one of the “logoi” if we continue with Greek philosophical terms.
Premises:
P: Your logic (as one of the logoi) is itself PROOF of the Universal Logos as logically it is impossible that ANY logics or logoi exist without a self-grounding “Logical Foundation of Logic and Logics in Perfect Reasoning coherent with Pure Logic”.
Q: If you set the bias aside for a moment and open your mind to think about this clearly and in plain terms, then it becomes clear. In Logic and LOGICAL REASONING (thinking and thinking properly) all things must have LOGICAL FOUNDATION. If they don’t then they do not have LOGICAL FOUNDATION. This is tautological and that sort of tautological Logic forms the Basis of Reality or “as God” (as the Origin of Existence and Moral Standard that sits supreme above all else).
R: It would defy Logic and that sort of requirement, as embodied in the PSR, or “Principle of Sufficient Reason”, if Logic itself didn’t need to be based in Logic like the rest of the Logical Concepts (ie - me in contingent form and my formal proofs). That would be a double-standard rather than a COHERENT LOGICAL STANDARD.
S: The EXISTENCE of the COHERENT LOGICAL STANDARD is what allows EXISTENCE and LOGIC to function and for LIFE and CONSCIOUSNESS (the self-awareness inherent in Logic’s own self-knowledge and ability to prove itself and/or nature of proving itself) to be as we are (Life and Consciousness with consistent logical identity in a stable and real Reality that is never not real).
Formal Logic:
{P, Q, R, S} |= (P -> Q) -> (R -> S)
Conclusion: {P, Q, R, S}:
Logic cannot be nonsense and if you claim to be sensible you must be LOGICAL, by Logic. Even to doubt that requires Logic and indirectly or inadvertently proves it to be the case. The alternative is absurd.
Truth Table Analysis:
PQRS⎪P Q R S╞(P→Q)→(R→S)
TTTT⎪T T T T TTT T TTT
TTTF⎪T T T F TTT F TFF
TTFT⎪T T F T TTT T FTT
TTFF⎪T T F F TTT T FTF
TFTT⎪T F T T TFF T TTT
TFTF⎪T F T F TFF T TFF
TFFT⎪T F F T TFF T FTT
TFFF⎪T F F F TFF T FTF
FTTT⎪F T T T FTT T TTT
FTTF⎪F T T F FTT F TFF
FTFT⎪F T F T FTT T FTT
FTFF⎪F T F F FTT T FTF
FFTT⎪F F T T FTF T TTT
FFTF⎪F F T F FTF F TFF
FFFT⎪F F F T FTF T FTT
FFFF⎪F F F F FTF T FTF
(Valid)
Q.E.D.