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: 2026-10-02T20:57:51.702Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:40:03.590Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 3207637d827abc163cd406c4a45ef729e468a484d4b696971aeefcf942ffbff9
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} |= (S -> R) -> (Q -> P)
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.
Maclain Hunter on Monads
Premises:
P: Leibniz’s Monadology posits that monads are the simple substances (plural) that underlie individual identity. He arrives here following the PSR and an axiom of simplicity.
Q: I say, however, in regard to P, that it doesn’t make sense why there would then be monads or “simples” plural as the Ultimate Cause (Logos) or Fundamental Reality (Theos - Arche) instead of the Logos as “the Foundational Universal Principle”.
R: I don’t agree with Leibniz that there must ultimately be disconnected and independent “monads” (plural), but rather insist that Reality is better explained logically as the infinite manifestation of the Logos.
S: This Root of Existence (God - Logos) is “Self-Sufficient Reason” itself. This therefore better aligns, and more necessarily aligns with the Principle of Sufficient Reason than mere monads and Monadology.
Formal Reasoning:
{P, P -> Q, Q -> R, R -> S} |= (S -> R) -> (Q -> P)
Conclusion: {P, Q, R, S}:
Reality as the (infinite/complete) manifestation of the Logos—the Logic of Reality (also called God in theological terms)—better satisfies Logic and the PSR than theories that independent monads are fundamental.
Logical singularity is ultimately more coherent and necessary/fundamental than monadic pluralism.
Leibniz talked about God harmonizing the monads but this contradicts any claim to monads being fundamental (non-contingent) or independent (and not extant within a unified logical framework matching the Logos).
Even if/while we accept monads as a valid philosophical concept, the plural and finite forms of the universal concept of the Monad (singular and beyond a single finite instantiation of the Monad) would be contingent STILL upon that broader and more fundamental concept of the Monad.
The Monad itself could then and STILL only be considered God and the Foundation of the Cosmos by aligning with the Logos—being fully coherent—as the Universal Order and Logical Foundation of Existence (God).
This is akin to the way that the concept of “the Home” logically transcends and supersedes, and gives Coherence/Identity to, any/every finite and specific instance or example of a house/home (ie - my home).
Truly, if the Monad is so fully coherent with the Logos that the Monad is God and fundamental then it can still be argued that the important part logically remains that God is fully coherent with Logic (and “Theos = Logos”) rather than it mattering so much that a proprietary term like “Monad” can be applied to the Origin and God (or what is fundamental to the Universe).
Multiplicity is always derivative in Logic, as the logical concept is derived from logically complete Logic (even and especially when the “logical concept” in question is “logically complete Logic” itself).
Monads, plural and in a finite context, must logically equate to the Logos (or the Infinite Monad) in the universal and singular sense, in that same context and with the same limitations imposed by that finite context, with its terms and conditions.
This requires that monads (plural) be contingent and in flux according to changes in context and the interactions of the full range of contexts with each other and with the Logical Ground (Logos - Logic - the Essence of the Monad).
Truth Table Analysis:
PQRS⎪P P→Q Q→R R→S╞(S→R)→(Q→P)
TTTT⎪T TTT TTT TTT TTT T TTT
TTTF⎪T TTT TTT TFF FTT T TTT
TTFT⎪T TTT TFF FTT TFF T TTT
TTFF⎪T TTT TFF FTF FTF T TTT
TFTT⎪T TFF FTT TTT TTT T FTT
TFTF⎪T TFF FTT TFF FTT T FTT
TFFT⎪T TFF FTF FTT TFF T FTT
TFFF⎪T TFF FTF FTF FTF T FTT
FTTT⎪F FTT TTT TTT TTT F TFF
FTTF⎪F FTT TTT TFF FTT F TFF
FTFT⎪F FTT TFF FTT TFF T TFF
FTFF⎪F FTT TFF FTF FTF F TFF
FFTT⎪F FTF FTT TTT TTT T FTF
FFTF⎪F FTF FTT TFF FTT T FTF
FFFT⎪F FTF FTF FTT TFF T FTF
FFFF⎪F FTF FTF FTF FTF T FTF
(Valid)
Q.E.D.