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: 2026-10-02T16:41:39.658Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:38:46.663Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 9950aaebefe3419b08b0a7dff00badecb9ac26a58654dfba612c02c54c4322b1
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.
How Motion Works by Maclain Hunter:
Zeno’s Arrow Paradox Restated:
Zeno argues that for an arrow to be in motion, it must be in a specific position at every moment in time. However, at any given instant, the arrow is not moving—it is at rest in a particular place. Since time is made up of an infinite series of instants, at each instant, the arrow is not moving. Therefore, Zeno concludes that the arrow never actually moves because, at each moment, it is stationary.
Premises:
P: The Arrow Paradox is not a true paradox as it is easily understood through proper logical reasoning and a thorough understanding of Geometry, specifically the space-less and timeless nature of points compared to the continuity and time inherent in lines (and line based shapes). In the alleged paradox the conclusion is a non-sequitur, negating sequence (motion) universally, based on an invalid inference from a hypothetical scenario where motion (sequence) was explicitly removed (which only negates it from the hypothetical not universally) - which is arbitrary. Indeed the (infinite) nature of Universal Logic and the point entail motion, time, lines, timelines, spaces, spacetime, and spacetime geometries without logical contradiction.
Q: It would contradict Logic if there were motion in a point, as points are fundamentally coherent, transcending and underlying spaces and timelines. It is akin to how it would be contradictory for there to be a fixed definition for a concept explicitly defined as having no fixed definition. Linear time and motion emerge from point based structures and the sort of “instants” being discussed in the paradox, through the continuous application of Logic to these coherent logical and geometric structures/concepts.
R: Assume the negation of P and Q. This leads to logical contradiction where shapes and time (or spacetime) don’t emerge from fundamental logical and geometric principles and concepts, many that are themselves logically necessary (like Coherence and Logic or the Geometric and Logical Structure of the Cosmos itself), like the point. This also leads to the Arrow Paradox itself, while the rationality and rational acceptance of the premises truth provides a path to the resolution of the paradox, and a clearer understanding of how the Logic of the Cosmos is an unwavering (ubiquitous and infinite) Source of motion (local existence, continuity, and finite concepts including locations and finite causes).
S: This proof offers a/the solution to the Arrow Paradox in Universal Logos and the logoi it encompasses, or the answer to all questions (or paradoxes) found in Reason and all reasons in other words - to include the discrete reasoning here in this proof and its premises. Logic, coherent with the First Cause (also called God or the Logos), entails motion in its (Logic’s) universal, absolute, and motionless form, as the Universal Logos, and demands, in each instant where there is coherent interaction, that motion is recursively entailed.
Logical Proof:
{P, P -> Q, Q -> R, R -> S} |= (P & Q) & (R & S)
Conclusion: {P, Q, R, S}:
Logic and points, like the most fundamental and undefined or spaceless of concepts must have no motion as the Ground of Contingency and Motion - while contingent beings like humans experience time and motion, which does objectively emerge from the Motionless Ground (Logos - the Origin - the Prime Mover), precisely because it is the contingent manifestation of the Absolute (Logic).
The contingent manifestation experiences the contingent (and Absolute) with the same sort of continuity/consistency that is inherent in the very geometric and logical construction of the Cosmos, namely shapes and geometric concepts other than the point (from which all construction emerges).
It is not a contradiction for fundamental aspects of systems that include motion are not themselves in motion, like points/instants in a timeline, and like Reason (should not move, as a Logical Standard) while continuous reasoning (or endless thinking) occurs.
Logical Consistency (Coherence - Logos) encompasses BOTH (not either/or) “unwavering lack of change” (in Logic/Reality) and “an eternal state of change” (in reasoning/realities) unified into one coherent and complete Existence that has both aspects of motion (including mortality) and aspects of motionlessness (Eternity).
Truly the paradox would arise if Reality were not fundamentally the process of Logic applying Logic to itself with perfect consistency as Logic demands we (Logos/logoi) do to be coherent and self-sustaining (feasible and not illogical or “not ourself”). It is only consistent that Logic would apply Logic to know Logic as a logician would and must (to be a genuine logician). This explains why the Absolute (or Logic) leads logically to continuous spacetime (or endless reasoning).
Reality itself arises from the logical and geometric structure of the Logos, existing as a (undefined/infinite) point, the “First Point” (or State, or Cause) of Existence, from which all else emerges as a result of the finite and continuous relationships intrinsic to the point’s relationship to itself - which amounts to an undefined relationship with the underlying point, or, in other words “Infinite Motion and Reasoning”.
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 F TTT
TFTF⎪T TFF FTT TFF TFF F TFF
TFFT⎪T TFF FTF FTT TFF F FFT
TFFF⎪T TFF FTF FTF TFF F FFF
FTTT⎪F FTT TTT TTT FFT F TTT
FTTF⎪F FTT TTT TFF FFT F TFF
FTFT⎪F FTT TFF FTT FFT F FFT
FTFF⎪F FTT TFF FTF FFT F FFF
FFTT⎪F FTF FTT TTT FFF F TTT
FFTF⎪F FTF FTT TFF FFF F TFF
FFFT⎪F FTF FTF FTT FFF F FFT
FFFF⎪F FTF FTF FTF FFF F FFF
Q.E.D.