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: 2026-10-02T16:20:01.587Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:41:22.928Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 8bd8c1e324dbdd45f5e088ce01c766e470019695a267ea1e64b15598d156d26b
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.
Law of Identity
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
Reason as the Ship of Theseus by Maclain Hunter:
The Paradox of the Ship of Theseus Restated:
Imagine a ship, the Ship of Theseus, sailing across the seas. Over time, each of its parts—its boards, its sails, its rudder—begin to wear out and are replaced with new ones. Eventually, every single piece of the ship has been replaced. Is this still the same ship, or is it a completely new one? Suppose all the old parts that were replaced were collected and reassembled into a ship. Which one is the true Ship of Theseus—the one made of entirely new parts or the one made of the original parts?
The Solution to the Paradox:
Premises:
P: □: The Highest Order of Logic (L) is the most all-encompassing form of Logic, and is the Logic that is Logic according to Logic. Limited scopes and forms of Logic (ie - finite logics) are what they are because of Logic (L) and must have Coherence (c) with self-consistent (L-coherent) Logic (c, L). □: This Logos (L) gives rise to all logoi (finite logics), these logoi represented as s here, following and contingent upon Logical Order (L) and makes all an interconnected whole (all), coherent as one (c, L).
Q: Assume we accept the premise that the Ship of Theseus paradox rests on, that a contingent concept (s) can feasibly find its true identity in contingency (s) and changing integrals (s), rather than Logic (L) as the Logical Ground and Absolute (L), and as the truest and most universal/foundational (least contingent or, “~(s < L)”) aspect of all concepts. □: This cannot be so, and we cannot accept that premise because it defies Logic (L) as established in the Cosmos and in premise P, through Coherence (c). When the choice is between Coherence (c) and paradox the choice has been made clear by Logic (L) itself, and the coherent and logical, paradox collapsing path forward is the Logical Way (□ (L)).
R: The question of whether the new ship or the old ship is the True Ship (the Universal Identity or “L” of the ship or s) ignores that Logic (L) is by definition and through Coherence (c) that Universal Identity and metaphorical “True Ship” (L, c,). Also, the question leads to paradox by presenting a classic example of a false dilemma. There’s no coherent reason in involved there in saying why they can’t all be the ship ((□(L) & ∀(s)).
S: Assume the negation of the premises {P, Q, R, S}. This leads to logical contradiction, famously in the form of the Ship of Theseus paradox itself, thus the premises must be true. If we assume the negation of the premises {P, Q, R, S}, this also then leads to the invalidity in the proof that could otherwise resolve the Ship of Theseus paradox by pointing out that the purported paradox is a mere false dichotomy that ignores the universal nature of Coherence (c) and Logic/Identity (L). All is and equals all the Law of Identity and Logic (L) tell us, and to contradict that with notions that things are not one is a violation of the Law of Non-Contradiction that is mutually exclusive with Universal Logic and Truth (c, L), which means that per the Law of the Excluded middle the proposal that the ship’s “True Identity” is not Reason (L) and all (L, s, c) can be deduced with certainty to be false (while L as Universal Logic and Identity is Absolute Truth).
Logical Argument (Proof):
{P, P <-> Q, Q <-> R, R <-> S} |= (P & Q) & (R & S)
Ergo: {P, Q, R, S}, ((□(L) & ∀(s)):
The paradox has been resolved through Universal Logic (L) and Integrated Identity (L, c, s). The paradox always presented a false dilemma that could have justified moving past it rationally, but once we understand that even a metaphorical ship is a contingent concept (s) that Logic (L) undergirds, the abase becomes even more definitive. The ship is Logic, while Logic (L), the First Cause of Logic (L) and contingent Existence (s), makes ships and logoi (s) be ships and logoi (s) in an (Law of) Identity and L (Logos) consistent manner. ALL is and equals ALL as A is A and A cannot be “not A”.
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 F TTT
TFTF⎪T TFF FFT TFF TFF F TFF
TFFT⎪T TFF FTF FFT TFF F FFT
TFFF⎪T TFF FTF FTF TFF F FFF
FTTT⎪F FFT TTT TTT FFT F TTT
FTTF⎪F FFT TTT TFF FFT F TFF
FTFT⎪F FFT TFF FFT FFT F FFT
FTFF⎪F FFT TFF FTF FFT F FFF
FFTT⎪F FTF FFT TTT FFF F TTT
FFTF⎪F FTF FFT TFF FFF F TFF
FFFT⎪F FTF FTF FFT FFF F FFT
FFFF⎪F FTF FTF FTF FFF F FFF
Q.E.D.