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: 2026-10-03T01:35:12.341Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:38:35.104Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: acecf78f3efffb81bd0c1a213cd730ee4b74b7bede74ca1bc2d7aa20191e9e71
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} |= (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.
God as the Origin of Logic and Reality by Maclain Hunter:
Definitions of Key Terms:
God: The Origin (or Creator/Maker) and Ruler of Logical Existence, associated with the Logos in Christianity and Classical Theism - referring to the Logical Framework underlying all Reality and the Divine Reason that stood as Universal Cause to found the Cosmos in an orderly and lawful (real and rational) fashion; the One True God (the God that is God according to Logic and beyond the subjective beliefs of mankind).
Logic: The Method of Reasoning; the Framework that allows for the rational exploration of Reality and the logically coherent Structure of Reality (Logos) and to know Objective Truth; the Process of Realization that Reality itself depends on the processing and rationalization of; Proper Order; the Proper Way to Think, Act, and Be (Reason - the Way).
Logos: The Logical Structure of Reality that is logically consistent and which serves as the logically necessary First Cause and “Foundation of the Universe” (God).
Premises:
P: The “Ultimate Logical Origin” and the “Origin of Logic” (the “God of Reason”) is and MUST, for the sake of logical consistency, coherence, rationality, and REALITY, be LOGIC (Reason - Logos) itself.
Q: To have an illogical/unreasonable Origin of Logic and Reason would be as untenable as having a Foundation of Reality (God) that wasn’t/isn’t real (a Reality).
R: Assume “not P” and/or “not Q”. This is logically untenable and leads to logical contradictions - namely the incoherence of the Origin of Logic and Logic and between the Origin of Reality and Logic (the real and logical Origin of Existence also known as “God” and that qualifies as “God” by definition as the Principle, as well as the entity and “Process of Realization” (the “Method of Reasoning” a.k.a. “Logic”), that made/created all that was/is made/created by the First Cause of Logic (Logos). There is no potential counterargument to Logic coherent with the Foundation of Reality (or the Foundation of Reality aka God that is coherent with Logic). That is a logical and real/performative contradiction that is not feasible.
Formal Argument (Logical Proof):
{P, P <-> Q, Q <-> R} |= (P & Q) <-> R
Conclusion: {P, Q, R}:
The Origin of Logic and Reality must be Logic - namely “Real Logic” of the sort that is “Logic according to Logic”. This is the logically consistent “One True God” who is the Method of Reasoning (and “realization”) that makes the Cosmos be the Cosmos and that makes that which is made/created be that which is made/created (as a matter of logical identity and rational processing). We know the proof holds because of premise R which explores the contradiction and proves that this negation of the premises P and Q leads to a specific logical contradiction - namely the untenable incoherence between Logic and the “Origin of Logic and Reality” (Logos - God - Logic).
Any alleged “counterargument to Logos (or God, or Logic) that denies the validity of Logic (or Logos, or God) must also contend with the fact that all reasoning, including the counterargument itself, is predicated on logical principles and the Logical Foundation of Reality (Logic - Logos - God - Origin). Any assertion that works to undermine Logic must ultimately rely on it at the same time, rendering it incoherent and self-defeating (not feasible and totally futile).
That helps us to understand why Logic and this argument are indeed irrefutable, as coherent concepts without that sort of self-undermining incoherence (invalidity - illogic). It would defy Logic if Logic were not Logic as it would defy the True God (Logic) if the True God were not the True God (Logic) - this is tautological and logically certain even if the conclusion and premises are seen as controversial or “religious” in nature by some people subjectively (a logically irrelevant factor).
Truth Table:
P | Q | R
T | T | T
T | T | F
T | F | F
T | F | T
F | T | F
F | T | T
F | F | T
F | F | F
Validity of Premises:
Premise P: P is valid/true, as it follows from the principles of sufficient reason and identity.
Premise Q: Q is also valid/true. If logic were not logical, it would be a contradiction in terms, and if reality were not real, it would be a contradiction.
Premise R: R is valid/true, as it follows from the principles of non-contradiction and the self-reference of logic.
Result: The proof stands validated and as a truthful formal argument, as the premises P, Q, and R are necessarily true so the conclusion flow/follows from them and remains true/valid (logical).
Q.E.D.