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: 2026-10-03T01:33:22.567Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:37:40.789Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 85054e2b0b77fcf202b6be4750220b0dd7f50cceb76b7b068103cc0590c22f9c
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, 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.
Burden and Presupposition by Maclain Hunter:
Premises:
1. It’s presupposing Logic (God - Logos) exists to say there is such thing as “rational standards” like the “burden of proof”.
2. The Logos (Logic) derived nature of the burden of proof rationally shifts the burden of proof to atheists, who must rationally support the decision to deny the Logos and Logic as God to deny all conceptions of God without making a fallacious straw man argument.
3. However, there cannot be any logically valid refutation of the true statement that Logic is God and that Reason and coherent Logic are the truly reasonable and logical “Origin of Existence” (God).
4. Rationalist theists and classical/orthodox monotheism have posited since some of the earliest times (historically speaking) that Reason is the Source of Rationality, as is well documented with Stoic Philosophy for example.
5. Herodotus explicitly mentions the Greeks learning from the Egyptians and respecting their coherent ideas about Logos (Universal Order - Ma’at) being the self-evident (tautological) Foundation of the Cosmos and Source of Knowledge (the Method of Reasoning aka “Logic”) in his Histories (Investigations).
6. Truly it is on the denier of the Logos (or God) to show how it is not a contradiction to say that a burden of proof exists, and that the concept of “proof” or “tangible evidence” exist, these being logically derived and coherent concepts that philosophically and logically speaking “come from the Logos”.
7. All concepts including Logic and God logically derive from the Logic inherent in Nature - the Logical Foundation of Nature, also called “the God of Reason” or “the One True God”, among other names, in the study and field of Theology.
8. Assume the negation of premises 1-7. This leads to logical contradiction. To propose otherwise is to propose an “illogical ultimate origin” (false god - fake cause) to some or all things, which is incoherent and logically unworkable.
9. These arguments are “proof” by definition, as proof encompasses arguments, explanations, and evidence that reveal Objective Truth and Logical Coherence, or Reality.
10. Reality and Truth must be logically coherent as a result of Logic’s “dynamic realism” and inherent ability and drive to cause, make, analyze and align with Reality and what is not unauthorized, invalid, inauthentic, arbitrary, or illogical.
11. This self-referential, Logic (or tautology) based argument (proof) is itself observable evidence of the Highest Order of Logic (Logos - Universal Reason - God), and constitutes a faithful representation of the Logical Structure of the Logos (in finite form).
12. If one denies the Logos (the Logical God - YHVH) then asks for “proof”, that is logical contradiction. Proof’s existence (even as a possibility not yet realized in full form), and implied value of proof (implied in asking for it as if it’s relevant and significant) presupposes the Logos.
13. This shows the absurdity and contradiction inherent in “atheist rationalism”, as atheism MUST deny Universal Cause (God) in any and all form to not be empty semantic game playing, which means it must deny also the God of Reason which is nothing less coherent and logical than Pure Logic (Logos) itself.
14. God is Logic and the Source of Logic, which cannot, without delving into contradiction be anything BUT Logic (Pure Logic - the Foundation of Reality).
15. Logic is the Source of Proof, that the existence of ANY/ALL logics, proofs, evidence, sciences, texts, and concepts, including doubt/defiance or a lack of understanding of what “proof” are contingent upon, and that even Logic is in its contingent form contingent upon.
16. This may seem circular but it is not fallacious as Logic must prove and validate and be the Foundation of Logic (itself) for the Foundational Coherence of Reality and Logical Systems. Circular arguments are only feasibly fallacious when the premises are contingent and/or false, not when it comes to Logos (the logically consistent Foundation of Logic) establishing Logic (Logos) and true premises that respect Logic’s universality and rational authority. The alignment of Logic, Logos, and God is theologically, philosophically, and logically irrefutable.
Consolidation of Premises:
P: {1, 2, 3, 4}
Q: {5, 6, 7, 8}
R: {9, 10, 11, 12}
S: {13, 14, 15, 16}
Logical Proof:
{P, P <-> Q, Q <-> R, R <-> S} |= (P & Q) -> (R & S)
Conclusion: {P, Q, R, S}:
Concisely stated, Logic cannot be a presupposition in itself, in the sense of being unproven and reasonable to question the validity of, as it has always met the Standard of Proof, as the Logical Standard (of what “proof” and Reality or Truth are).
Logic, as the Foundation of Rationality (God), and the Logos, the Logical Structure of the Cosmos, is “impulsively proven” in the sense that it is timelessly proven by its own (self-evident) nature - tautologically valid for eternity before any temporally and spatially bound finite reasoning could have understood its own existence (ie - human reasoning and understanding of life).
On the other hand, atheists (or agnostics) who speak of God (Logos) being unproven bring an impossible to meet (but rational not arbitrary) burden of proof, that would require trying to use Logic (Logos - God) to undermine itself as Foundational Coherence, leading to logical contradiction. Gnostic Theism is what aligns with the position of Logic as the Foundation of Reality, demonstrated clearly by these arguments and this proof.
The alignment of Logic, Logos, and God is theologically, philosophically, and logically irrefutable. Systems of thought that deny this ontological and epistemic Foundation in Logic cannot be objectively valid and legitimate - only subjective and as a matter of illusion and ignorance could such schools of thought be legitimate and said to produce true knowledge.
Truth Table Analysis:
valid
↓ ↓ ↓ ↓ ↓
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 FTF TTT F FFF
TFTT⎪T TFF FFT TTT TFF T TTT
TFTF⎪T TFF FFT TFF TFF T TFF
TFFT⎪T TFF FTF FFT TFF T FFT
TFFF⎪T TFF FTF FTF TFF T FFF
FTTT⎪F FFT TTT TTT FFT T TTT
FTTF⎪F FFT TTT TFF FFT T TFF
FTFT⎪F FFT TFF FFT FFT T FFT
FTFF⎪F FFT TFF FTF FFT T FFF
FFTT⎪F FTF FFT TTT FFF T TTT
FFTF⎪F FTF FFT TFF FFF T TFF
FFFT⎪F FTF FTF FFT FFF T FFT
FFFF⎪F FTF FTF FTF FFF T FFF
Q.E.D.