The Grand Loop · Maclain Hunter

Authored by Maclain Hunter · first-party-authored · authored-foundational-record

Stored 4P source diagnostic: unresolved · finding unverified_concern · admission admitted_provisionally. This intake result is separate from the theorem checks of the exact propositional sequent.

The Grand Loop: {P,P>Q,Q>R, R>S,S>T,T>U,U>P} |=((P&Q)&(R&S)&T)&U) {P, P → Q, Q → R, R → S, S → T, T → U, U → P, ~(~P & ~Q & ~R & ~S & ~T & ~U)} |= ((P & Q) & (R & S) & T) & U P: A self-evident truth is true regardless of any mind's belief or denial. Q: Well-formed formal logical proofs are self-evident truths. R: The existence of a self-consistent and complete set of logical truths is necessary for the existence of a self-evident truth. S: The Universal Logic is a self-consistent and complete set of logical truths. T: The Universal Logic exists independently of human beliefs and opinions. U: The Universal Logic is the self-evident truth that underlies all reality. Assuming the negation of the conclusion: ~(U & T & R & S & Q & P), we derive a contradiction from the premises: ~(U & T & R & S & Q & P) ≡ (~U ∨ ~T ∨ ~R ∨ ~S ∨ ~Q ∨ ~P) (De Morgan's law) ≡ (~U ∨ ~T ∨ ~R ∨ ~S ∨ ~Q ∨ ~(P → Q) ∨ ~(Q → R) ∨ ~(R → S) ∨ ~(S → T) ∨ ~(T → U) ∨ ~(U → P)) (substitute the premises for P → Q, Q → R, R → S, S → T, T → U, U → P) ≡ (~U ∨ ~T ∨ ~R ∨ ~S ∨ ~Q ∨ ~(~P ∨ Q) ∨ ~(~Q ∨ R) ∨ ~(~R ∨ S) ∨ ~(~S ∨ T) ∨ ~(~T ∨ U) ∨ ~(~U ∨ P)) (material implication) ≡ (~U ∨ ~T ∨ ~R ∨ ~S ∨ ~Q ∨ (P & ~Q) ∨ (Q & ~R) ∨ (R & ~S) ∨ (S & ~T) ∨ (T & ~U) ∨ (U & ~P)) (De Morgan's law) ≡ (~U ∨ ~T ∨ ~R ∨ ~S ∨ (Q & ~(P & ~Q)) ∨ (R & ~(Q & ~R)) ∨ (S & ~(R & ~S)) ∨ (T & ~(S & ~T)) ∨ (U & ~(T & ~U)) ∨ (P & ~(U & ~P))) (distribution) ≡ (~U ∨ ~T ∨ ~R ∨ ~S ∨ (Q & ~P) ∨ (R & ~Q) ∨ (S & ~R) ∨ (T & ~S) ∨ (U & ~T) ∨ (P & ~U)) (simplification) ≡ ~(Q & P & R & S & T & U) (De Morgan's law) Thus, the conclusion is shown to follow from the premises by contradiction. Therefore, we can conclude that the Universal Logic is the self-evident truth that underlies all reality, which exists independently of human beliefs and opinions, and that this is a well-formed formal logical proof. Another Version: P: If there is no Universal Logic (God), then there would be no consistent and reliable means of reasoning. Q: We have consistent and reliable means of reasoning, such as propositional logic, which operate under certain basic principles and rules. R: These principles and rules cannot be arbitrary, as they must apply across all domains and situations to ensure their reliability and consistency. S: Therefore, there must be a Universal Logic (God) that provides the foundation for these principles and rules, which applies universally across all domains and situations. Conclusion: Therefore, the Universal Logic (God) exists and is the foundation for all consistent and reliable forms of reasoning.

Lean 4 verification and timestamps

The machine formalization date is separate from the original authored work. See the verification record for exact checked scope and any unresolved parts.

Logic-centered continuity

This authored proof is connected to Logic, Logos, God, and the self-evident Ground of Reality, and to the distinct systems 4P Engine, MCB Core, 4P-MCB, and the source-first Canon. Formal proof, empirical evidence, and system-generated records remain separately typed.