Lean verification registry · Authored proofs · The Logos Architecture
Written formal sequents verified
Axiom-free: true · 2 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: 2026-10-02T16:57:27.325Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:39:45.320Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 5fa03c3b38b505522b3c08e029f8d05a875de67b2f534689ec6f46a1864f1bb0
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.source_identity_rule' 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.
Logic is LOGIC
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
Logical Ontology by Maclain Hunter:
Premises:
P: Logic is the Ontological Ground, logically. I’m explicitly stating that it is objective, self-evident, & proven through an infinite # of logics/proofs: Logic is LOGIC’S OWN Ontological Ground (God). By framing it subjectively, insisting my statement should be “Logic is MY Ontological Ground” you’re creating an invalid straw man (if you dare).
Q: Assume then “~P”. This leads to logical contradiction, thus proving P through the contradiction, because Logic has to be grounded in Logic for logical consistency and to avoid the paradox and illogic of Logic having an illogical/non-logical origin.
R: You can’t have coherent empirical science (real science) that ignores or defies and does not inherently, through acknowledging Logic’s (the Logos’s - the Universal Order’s - God’s) rational rule, verify the Logos (the One True God of Pure Reason known to Hebrew teachers as YHVH). Science remains bound to Logic logically, to maintain validity.
Science remains bound to all coherent metaphysics and metaphysical or ontological/epistemological requirements (from Logic or the Logos itself). Assuming otherwise leads to an incoherent “Philosophy of Science” and “Logic of Science” that becomes both scientifically unfounded and logically untenable. Science cannot be coherently seen as a way “around” Logic and Coherence.
Science is fundamentally a ways of exploring Reality logically and methodically, and of bridging experimental/experiential knowledge with Pure Logic, to both validate the observations and sensory information AND confirm the “Real Coherence” of our logics, meaning that it is a way and opportunity for us to make sure that Pure Reason and our notion of it are actually matching Reality (which Pure Reason always has and does, when not misunderstood).
This is consistent with Logic but also with much of the biblical corpus including the Gospel of John and Moshe’s Torah where Reason or the Ultimate Source of Knowledge (the Highest Order of Logic) is the Supreme Creator and God (Theos - Elohim).
The God of the Bible is clearly stated in these texts and the classical theology to be the Logos, Reason or the self-consistent Source of Reason (still Reason). The Bible uses similar arguments and process of elimination to that which I used in premise P and Q to prove (in one of the ways the Bible proves God exists as Reason) that God must be Reason and the God of Truth (Objective Validity itself or a directly equivalent and objectively coherent concept) instead of nothing (ie - what is competently illogical and incoherent or not one) or any false/mythological god - like those we can (and it does) acknowledge humans have considered God in the past (to their detriment and as a result of their rational misalignment aka “incoherence”).
This does not change the Coherent True Origin (the One True God) or that an honest and charitable (or even just not “completely ignorant”) logical interpretation of the text reveals this, as I have here demonstrated through sound reasoning that indeed represents the Bible fairly without assuming anything about it, while explaining (one way of) how it actually does accurately target and even logically prove the True Origin (Logos).
S: For a denier of the Logos (ie - atheists, agnostics, and irrational theists) no FEASIBLE “valid point” (logical argument - proof) can be made that does not end up a contradiction/paradox within that position. That is especially so for atheism or a belief system (or position) that denies all gods including the Logos (Logic) as the God of Reason (the Logical Origin of Logical Existence).
Even logical positions and points, that are so objectively and logically, become contradictions within the context of the atheist position. It’s part of why atheism is philosophical and intellectual poison, even more so than irrational theism and poorly reasoned blind faith in God (which can then at least be consistently supported by logical proof later or eventually, or that others have provided to help support those believers beliefs, as I have and do). Those who adopt such a position rob themselves of the ability to have a coherent and consistent philosophy or worldview.
Logical Argument:
{P, P -> Q, Q -> R, R -> S} |= (P & Q) -> (R & S)
Conclusion: {P, Q, R, S}:
Logic is God (the Ontological Ground) to Logic and by Logic’s own Standard (of Logic). No other could fill that role without descending into instability and absurdity, and the whole Universe doing so also (ultimately being destroyed as a result, along with observed fine tuning and the ability to coherently engage in scientific inquiry and empirical observation). It cannot be so, I have proven here, through a form of reduction ad absurdum or proof for the contradiction.
While one remains an atheist even LOGICAL ARGUMENTS, that would for a theist or non-denier/non-doubter be perfectly valid, become an internal inconsistency and instance of incoherence because of the elected framework and (illogical) “philosophy” the atheist has chosen and refuses to repent for and reject (or move away from).
Only by acknowledging the Logos and the validity and acceptance of the theist position can an atheist (like my former self) remediate this issue and start having logical arguments work for them and not against them again.
This is not inconsistency and a double standard but consistency and what happens when you deny the First Cause (of God) is the Logical Standard (of Logic).
The Bible is not the basis of my arguments but I believe in good faith exploration of concepts and schools of thought, meaning an intellectually honest approach.
I would be lying if I said that I don’t think the Abrahamic theology, as an example, holds Reason to be God. Many don’t know this but it’s not to say the most elevated and advanced level of the theology isn’t exactly as I’m saying it is, where Reason is God and Pure Logic makes and rules the Cosmos through Coherence (God’s Oneness) itself.
I would also be lying if I said I don’t see any evidence of God in or when analyzing the existence of the Bible, or that I don’t see any logical arguments and proofs (even if I could cherry pick or find illogical interpretations of many passages that aren’t prime examples of logical arguments and perhaps are not meant to be, like many of the songs in Psalms for example, or the fiat laws for ancient Israel in Leviticus that are meant only for Israel in its ancient form).
These insights and biblical commentary are consistent with Logic and my premises, and are critical to understanding the intersection of Reason and faith, God and science, and the Bible’s proof of and evidence presented for the existence of a God coherent with Order and Coherence itself - the rational basis for a coherent “monotheism”.
Some atheists (or the like) may argue that they believe in or acknowledge Logic but just “not as God or a deity”, but this would be to ignore the meanings of terms and the logical relationships demonstrated. It is denying Logic (as Logic is by its own Law), and twists well defined language/concepts, to say that Logic is “not the Ontological Ground” logically and that Logic is something less than (rationally) supreme.
Likewise it is illogical to posit that God is nothing, or nonsense, or to in any way and from either side (logically or theologically) separate God and Logic or the Method of Reasoning and the Ontological Ground, though an atheist trying to avoid the collapse of their position at all costs has an obvious incentive to TRY - as acknowledging the unity of God and Logic is absolutely devastating to their position, a true “death knell”, as it was to my own (former) atheism.
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 FTT TTT F FFT
TTFF⎪T TTT TFF FTF TTT F FFF
TFTT⎪T TFF FTT TTT TFF T TTT
TFTF⎪T TFF FTT TFF TFF T TFF
TFFT⎪T TFF FTF FTT TFF T FFT
TFFF⎪T TFF FTF FTF TFF T FFF
FTTT⎪F FTT TTT TTT FFT T TTT
FTTF⎪F FTT TTT TFF FFT T TFF
FTFT⎪F FTT TFF FTT FFT T FFT
FTFF⎪F FTT TFF FTF FFT T FFF
FFTT⎪F FTF FTT TTT FFF T TTT
FFTF⎪F FTF FTT TFF FFF T TFF
FFFT⎪F FTF FTF FTT FFF T FFT
FFFF⎪F FTF FTF FTF FFF T FFF
Q.E.D.