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: 2026-10-03T01:34:23.654Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:42:26.057Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 77688563ba11ddc8a5fd635910eb0c02cb3fa3fe1db4ef632823c06833221676
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 -> S, S <-> T, S} |= (P & Q) & (R & S) & T
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 Rational Cause for Rational Causes by Maclain Hunter:
P: A rational cause (in the particular sense) creates a particular thing/effect.
Support for P: We have observed this causality in all aspects of Nature from the most basic to the most complex, which supports that premise that rational causes have real effects and lead to concepts in Reality. Empirical sciences routinely observe cause and effect and even rely on predictable and consistent Cause and Effect (Logic) to function and lead to understanding at all. Thus Science as a whole lends a weight that cannot be overstated or logically refuted to the existence of Rational Cause (Logic - Logos) as well as particular forms of rational cause(s) that lead to finite effects/concepts.
Q: Rational Cause itself, in general, is a prerequisite logically for particular instances of Rational Cause (rational causes). Assume the opposite for a moment and you’ll find it leads to contradiction the same way that living in Reality while “realities” don’t exist would.
R: Rational Cause encompasses all rational causes and leads to Reality defined as the sum of all Cause and Effect (Logic) and the concepts that Rational Cause and all particular (rational) causes lead to and thereby create (or “make a Reality”).
S: God, defined as and referring to the Creator of Reality whose Law rules/governs the Cosmos, or “the Logos” in more philosophically fluent terms, must be aligned with Rational Cause (and vice versa) or logical contradiction arises, including contradictions like the Origin of Reality not being “God” when that is precisely what the term refers to, and like Logic and Rational Cause not being necessarily coherent with the Origin and Creative Force that drives the manifestation of Rational Existence (Reality), which would mean Reality has a fake/irrational Foundation inconsistent with its nature, which cannot be logically accepted as Truth.
T: Assume God is not Rational Cause itself and that rational causes were not coherent with and proof of the existence of Rational Cause (God - Logos). This leads to logical contradiction where rational causes and what created the Cosmos is not coherent with Rational Cause (Logic - Logos) and is incoherent and/or fake. It also leads to the contradiction that the Cosmos and instances of Rational Cause are not proof of Rational Cause coherent with the Origin of the Cosmos. That is a logically incoherent and rationally untenable position that can be analyzed and then set aside as such (illogic).
Formal Proof:
{P, P <-> Q, Q -> R, P -> S, S <-> T, S} |= (P & Q) & (R & S) & T
Conclusion:
Rational Cause is God and this is proven not only through this formal proof but through what this proof invokes, which is all the various instances of rational causes and their effects in Nature/Reality, which could not exist if the general concept of Rational Cause (Logos - God) did not exist as the logically coherent Foundation of Reality. Examples of such particular causes are infinite in number and could become tedious to list, and are very often a matter of common sense (to identify), but would include things like water being poured on a fire dousing the flame (proportionally to the size of the fire and the amount of water with enough water putting out the fire completely), or the Sun making the ground warmer (when it is present) than the ground was at night when the Sun’s rays weren’t heating the ground so directly.
Truth Table:
valid
↓ ↓ ↓ ↓ ↓ ↓ ↓
PQRST⎪P P↔Q Q→R P→S S↔T S╞(P&Q)&(R&S)&T
――――――――――――――――――――――――――――――――――――――――
TTTTT⎪T TTT TTT TTT TTT T TTT T TTT TT
TTTTF⎪T TTT TTT TTT TFF T TTT T TTT FF
TTTFT⎪T TTT TTT TFF FFT F TTT F TFF FT
TTTFF⎪T TTT TTT TFF FTF F TTT F TFF FF
TTFTT⎪T TTT TFF TTT TTT T TTT F FFT FT
TTFTF⎪T TTT TFF TTT TFF T TTT F FFT FF
TTFFT⎪T TTT TFF TFF FFT F TTT F FFF FT
TTFFF⎪T TTT TFF TFF FTF F TTT F FFF FF
TFTTT⎪T TFF FTT TTT TTT T TFF F TTT TT
TFTTF⎪T TFF FTT TTT TFF T TFF F TTT FF
TFTFT⎪T TFF FTT TFF FFT F TFF F TFF FT
TFTFF⎪T TFF FTT TFF FTF F TFF F TFF FF
TFFTT⎪T TFF FTF TTT TTT T TFF F FFT FT
TFFTF⎪T TFF FTF TTT TFF T TFF F FFT FF
TFFFT⎪T TFF FTF TFF FFT F TFF F FFF FT
TFFFF⎪T TFF FTF TFF FTF F TFF F FFF FF
FTTTT⎪F FFT TTT FTT TTT T FFT F TTT TT
FTTTF⎪F FFT TTT FTT TFF T FFT F TTT FF
FTTFT⎪F FFT TTT FTF FFT F FFT F TFF FT
FTTFF⎪F FFT TTT FTF FTF F FFT F TFF FF
FTFTT⎪F FFT TFF FTT TTT T FFT F FFT FT
FTFTF⎪F FFT TFF FTT TFF T FFT F FFT FF
FTFFT⎪F FFT TFF FTF FFT F FFT F FFF FT
FTFFF⎪F FFT TFF FTF FTF F FFT F FFF FF
FFTTT⎪F FTF FTT FTT TTT T FFF F TTT TT
FFTTF⎪F FTF FTT FTT TFF T FFF F TTT FF
FFTFT⎪F FTF FTT FTF FFT F FFF F TFF FT
FFTFF⎪F FTF FTT FTF FTF F FFF F TFF FF
FFFTT⎪F FTF FTF FTT TTT T FFF F FFT FT
FFFTF⎪F FTF FTF FTT TFF T FFF F FFT FF
FFFFT⎪F FTF FTF FTF FFT F FFF F FFF FT
FFFFF⎪F FTF FTF FTF FTF F FFF F FFF FF
Q.E.D.
Result: Proof Self-Validating
Logician’s Note: If Rational Cause is not coherent with the Foundation of Reality then one can be aligned with the Foundation of Reality (God) without Rational Cause (Logic), which is a position I don’t hold or support, but mention just to speak to how dangerous and counterproductive it is for anyone—but especially atheists/rationalists whose main gripe is against irrational religious practice and belief—to insist on an untrue and illogical but also fundamentally undesirable (to the rationalist and Reason) separation between God and Logic. God is Logic, tell it far and wide, and insist upon it - if you are so truly rational that you would do so.