Knowing Logic and Proof — Full Supplied Copy

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

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

Knowing Logic and Proof by Maclain Hunter Premises: P: Logic is lawfully defined by non-contradiction of Logic (universally), and all logical “rules” plural are forms and subsets of non-contradiction of the Logos (of Universal Logic), like the LEM is logical non-contradiction applied to binary Truth values. Q: The semantics of P elaborate on logical rules and how they actually cohere under Logos as the Singular/Ultimate Law. This is a demonstration of knowledge of Logic that can be validly referred to (here in Q). R: It is absurd that I would explain Logic (as in P) and to explicitly point of that I had (as in Q) while I don’t know Logic. This valid explanation and argument that I am giving this explanation is by definition “proof” or an argument pointing with Reason and reasoning to the Truth and Reality (see OED definition of proof, it is similar). S: R suggests I know what proof is and how it is defined by the dictionary (in English) and Logic (logically). Logical proof fully coherent with Logic is logically equivalent to Logic and Coherence and cannot be “not Logic” or “not coherent” without contradiction. This proof stands as Logic sans demonstrated incoherence. Formal Argument: {P, P -> Q, Q -> R, R -> S} |= (P & Q) -> (R & S) Ergo: The proof above uses valid structure and self-referential semantics to show I know validly what proof and Logic (as defined by Coherence and Lawful Order as the Rule of Logic and the Rule logical rules must themselves align with) are. To refute me you would have to find contradiction and apply the Lawful Order of Logical Non-Contradiction (or Logos) I am describing which would be mere elenctic support for my position that Logic is about non-contradiction of Lawful Order. The formal entailment is truth-functionally valid; the semantic premises identify the performed reasoning as an instance of knowledge of Logic and proof. Thus the formal validity and the reflexive semantic content jointly constitute the claimed demonstration. Truth Table Analysis: 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 T TTT TFTF⎪T TFF FTT TFF TFF T TFF TFFT⎪T TFF FTF FTT TFF T FFT TFFF⎪T TFF FTF FTF TFF T FFF FTTT⎪F FTT TTT TTT FFT T TTT FTTF⎪F FTT TTT TFF FFT T TFF FTFT⎪F FTT TFF FTT FFT T FFT FTFF⎪F FTT TFF FTF FFT T FFF FFTT⎪F FTF FTT TTT FFF T TTT FFTF⎪F FTF FTT TFF FFF T TFF FFFT⎪F FTF FTF FTT FFF T FFT FFFF⎪F FTF FTF FTF FFF T FFF (Valid) QED

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.