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: 2026-10-02T17:32:10.640Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:42:13.216Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 2faa3875a2c83257ccf6b648c722c7f2d8ccc5aafdb73d8f5ef46e098c150193
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.
The Logic Before Time by Maclain Hunter:
Premise:
P: Logic is not a presupposition it’s tautological Reason and the self-evident framework for reasoning - when Logic is “True Logic” (logically consistent Logic) and is rationally coherent (one/unified and verified by the Rational Standard of Coherence itself). This is tautological and cannot logically be any other way without presupposing a Logic (ie - the Universal Logos) that isn’t so arbitrary and/or manmade.
Q: Critics of acknowledgement of Universal Reason (Logos - God) and Logic being a Construct beyond man, that man discovered and did not truly “create” (as it is self-made and has aseity), have an impossible to meet burden of proof - to prove that Logic (Rationality - what is not arbitrary) is made by man without any logical jumps, paradoxes, or arbitrary logic.
R: This notion that one could actually meet this burden of proof in Q is absurd and logically contradictory. It is not feasible logically that anyone would ever be able to prove that without flaws/limitations in the (broader) reasoning, especially in light of the Coherence of the alternative that Logic is God (the Origin of Reality - the First Cause) and is based in Logic itself - consistent with logically derived and truly coherent concepts. It’s not only a “more perfect” theory, it’s a perfect one that becomes proof through the Coherence of the position it takes (aligning with the Source and Standard of Proof in the Logos).
S: Assume ~{P, Q, R}. This leads to absurdities and contradictions. If Logic is x and (a mere) presupposition is y then x entails (|=) ~(y). To say x |= y would lead to logical contradictions including the paradox that that logical expression would then be suggesting itself to be based in mere presuppositions y. In modal logic it can be validly expressed as □(x |= ~y). Direct apprehension of Rationality (Sense) comes through Rationality (Sense) itself and it would be contradictory for Sense to be impossible to apprehend (to sense or grasp).
We can logically deduce that it is logically certain that logical induction tells us that because Logic has always been extant and consistent, and is the Ontological Ground that spacetime and chronological order is based in/upon, that Logic will continue to be extant and consistent - as the Ontological Ground that chronological order and spacetime are themselves contingent upon.
Logical Arguments:
{P, Q, R, S} |= ((P & Q) & R) <-> S
Conclusion: {P, Q, R, S}: □(x |= ~y)
Logic is tautological, not a presupposition. It can only be a presupposition subjectively and where such things are possible, which is not at the level of the First Cause of Logic (Logic - Logos - God) itself.
When we assume otherwise and explore what that entails and what is consistent with that assumption of the negation of the premises contradiction arises.
These contradictions include but are not necessarily limited to the contradiction in Logic being a presupposition universally and even in the sense of the Universal Logos. The Universal Logic directly proves and apprehends itself in a way that does not depend (necessarily) on human observation or induction.
Those who say Logic is somehow not the Universal Absolute of Rationality have an impossible to meet burden of proof. They would need to somehow, objectively and without relying on arbitrary human systems prove that all forms of Logic are manmade and arbitrary (not grounded in and coherent with the Logos inherent in the Cosmos).
Those who say Logic is a presupposition are demonstrating personal ignorance of both Logic and what a presupposition is. Presuppositions are only presuppositions because the Logos (the Natural Order and most all-encompassing Logic) is the Logos.
Logic is directly grasped by and as Sense itself and to say otherwise is mere senselessness. This is itself tautological. There cannot, without contradiction, be any REASON (Logos) to support the idea or inference that Logic has not always been, been consistent, and been God (the Ontological Origin) or that Logic will not always be (exist), be consistent, and be the One True God - the Genuine Origin of Reality known on its own logical and rational terms. Induction and deduction work together to deliver absolute certainty and direct apprehension of Rationality (God - Logic - Reality - Truth) through Rationality (Proof - Validity - Coherence - Fact).
Truth Table Analysis:
valid
↓ ↓ ↓ ↓ ↓
PQRS⎪P Q R S╞((P&Q)&R)↔S
―――――――――――――――――――――――――
TTTT⎪T T T T TTT TT TT
TTTF⎪T T T F TTT TT FF
TTFT⎪T T F T TTT FF FT
TTFF⎪T T F F TTT FF TF
TFTT⎪T F T T TFF FT FT
TFTF⎪T F T F TFF FT TF
TFFT⎪T F F T TFF FF FT
TFFF⎪T F F F TFF FF TF
FTTT⎪F T T T FFT FT FT
FTTF⎪F T T F FFT FT TF
FTFT⎪F T F T FFT FF FT
FTFF⎪F T F F FFT FF TF
FFTT⎪F F T T FFF FT FT
FFTF⎪F F T F FFF FT TF
FFFT⎪F F F T FFF FF FT
FFFF⎪F F F F FFF FF TF
Q.E.D.