Maclain Hunter' authored methodology preserved from its first-party proof-base source.
Formal Systems of Logic (FSL) Proofs by Maclain Hunter PROOF 1: FSL TAUTOLOGY P: FSLs (coherent "Formal Systems of Logic") are tautological as First Cause derived, Logic-as-Axiom, systems. Q: Necessarily: Stating FSL may not exist is absurd. It contradicts FSL's identity as Logic's necessary formal embodiment. {P, Q, P <-> Q} |= (P & Q) & ~~(P & Q) QED PROOF 2: GÖDEL SCOPE LIMITATION P: Formal systems of Logic (FSL) are fully coherent with Logic, or not. If not, they're invalid FSL (~FSL) per LEM and LNC. Q: Gödel's Theorems apply to ~FSL, not coherent FSLs. R: Truth is contingent on Logic (thus true FSLs). {P, P -> Q, R, R -> Q} |= ~Q <-> ~(P & R) QED PROOF 3: FSL SELF-REFUTATION OF DENIAL Assume ~P: FSLs are not tautological as First Cause derived, Logic-as-Axiom systems. But to assert ~P requires a coherent formal system (an FSL) to express denial logically—relying on
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Formal Systems of Logic (FSL) Proofs by Maclain Hunter
PROOF 1: FSL TAUTOLOGY
P: FSLs (coherent "Formal Systems of Logic") are tautological as First Cause derived, Logic-as-Axiom, systems.
Q: Necessarily: Stating FSL may not exist is absurd. It contradicts FSL's identity as Logic's necessary formal embodiment.
{P, Q, P <-> Q} |= (P & Q) & ~~(P & Q)
QED
PROOF 2: GÖDEL SCOPE LIMITATION
P: Formal systems of Logic (FSL) are fully coherent with Logic, or not. If not, they're invalid FSL (~FSL) per LEM and LNC.
Q: Gödel's Theorems apply to ~FSL, not coherent FSLs.
R: Truth is contingent on Logic (thus true FSLs).
{P, P -> Q, R, R -> Q} |= ~Q <-> ~(P & R)
QED
PROOF 3: FSL SELF-REFUTATION OF DENIAL
Assume ~P: FSLs are not tautological as First Cause derived, Logic-as-Axiom systems.
But to assert ~P requires a coherent formal system (an FSL) to express denial logically—relying on axioms like identity and non-contradiction.
This presupposes P (FSLs as axiomatic necessities), leading to contradiction: ~P implies P.
Thus, ~P is false; P holds. ⊥
Q follows similarly, affirming the absurdity of denying FSLs' existence.
QED
IMPLICATION:
Gödel's theorems apply only to INCOMPLETE formal systems (~FSL).
Coherent, Logos-grounded FSLs are exempt from incompleteness.
To deny FSL requires using FSL - the denial is self-refuting.Genre: methodology.
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