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: 2026-10-02T16:20:06.223Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:42:00.707Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: f73d4a7c5b829d1f96652209359d2510180a141ee2bf52d1889887ce5a65ca3b
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.
The Falseness of Falsifiability by Maclain Hunter:
Premises:
P: Assume Karl Popper’s proposed scientific principle of falsifiability is valid, and universally applicable. This leads to logical contradiction as the (alleged) principle itself is unfalsifiable by its own standard. Ergo it is a self-defeating standard that amounts to a hypocritical principle.
Q: Assume that First Cause could not be falsified and thus couldn’t be scientifically true. Well this wouldn’t make the First Cause of Existence untrue, as the Standard and Origin of the very Reality that defines and decides Objective Truth, it would make human sciences and scientific principles, namely Poppers nonsensical self defeating principle requiring falsifiability, flawed and untrue - objectively.
R: Assume that it is actually rational to say that for something to be true you must be able to prove it false. This leads to logical contradiction and absurdity where the most purely and universally true things, like God (Logos - First Cause - Logic - Universal Truth - Reality) could not be true as a result of always being impossible to objectively prove false in any sort of truly coherent manner. Therefore we know that the concept of falsifiability is invalid, failing to properly acknowledge Universal Truth (First Cause - Logic), to prove itself, to avoid negating itself, and failing to provide non-arbitrary (logical) standards for the derivation and validation of Truth. It (rationally) must be done away with, even in science and realms of empiricism, not only in the rational sciences (ie - Philosophy), to avoid logical incoherence in scientific theory, testing, and understanding.
S: Assume the negation of the premises {P, Q, R, S}. This assumption leads to logical contradiction that violates the logical rules, namely the Law of Non-Contradiction, and leads to paradoxes where Logic itself is undermined by the requirement for true claims to be possible to prove wrong (which defies the universally valid and objectively true nature of tautological and logically consistent Logic, and concepts associated with it like the God of Reason or Origin of Logic in Logic itself - the Order that gave birth to the Cosmos deterministically and beyond all contingency and probability. Therefore we can safely and logically confirm the premises including this one must be logically true.
Logical Argument (Proof):
{P, P <-> Q, Q <-> R, R <-> S} |= (P & Q) & (R & S)
Ergo: The logically incoherent scientific principle of falsifiability, proposed by Popper, is falsified and refuted, like universal skepticism requires us to be skeptical of it too, by itself applied consistently and universally - the hallmark of illogical things and objectively flawed rules, arguments, logics, and concepts.
Logic proves itself to be valid in profound ways no reasoned principle can ever refute or stand rationally against without contradiction and objective invalidity. Logic is logical, while falsifiability fails as falsified, false, and flawed.
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
Implications for Logic and Science:
This proof and the refutation of the principle of falsifiability paves the way for more truly modern sciences through/as “sensed logics” (reasoning and inquiry coherent with and using the Logic of Reality) - applying Logic and engaging in intertwined observation in a rational, not necessarily “empirical” (which can mean “Pure Reason ignoring”) manner.
A major issue in academics today is the false dichotomy presented between Logic and science historically that has led to a pernicious form of logically ignorant science (perhaps more so than scientifically ignorant logicians).
Science itself is a manifestation of Reality’s Logic contingent upon even Classical Logic and Philosophy. Fundamentally observation provides a way for reasoning and Logic to receive input and to align with Reality properly. This ability helps allow the Logos and Logic manifest to prove itself through itself and real-world Coherence, aiding in the logical shaping of the Cosmos.
Logically and naturally, however, observation doesn’t need to or rationally get to ignore Reason, and people cannot reasonably prioritize (fallible and contingent) sensation over Pure Logic (as some or all definitions of empiricism include/demand to their detriment).
There is no conflict in Logic making sense (literally and figuratively), and with sense then sensing Logically (through reasoning and logically grounded sensory observation). That is merely “logical consistency” applied to these (subjectivity transcending) matters.
Fundamentally applying Logic to what we observe is the logical way to navigate Reality and transcend the limitations inherent in limited/finite contexts and perspectives like those human beings consistently find themselves in.
Q.E.D.