Proof I Know Proof by 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.

Proof I Know Proof by Maclain Hunter: Premises: P: If you truly know proof you should be able to prove that with proof, otherwise a paradox and contradiction arises. Why can’t you (if not) - we would be reasonable to ask. Q: Proof encompasses evidence and arguments (ie - logical proofs) that demonstrate Truth or facts within Reality. My ability to coherently explain what proof is, with a rational definition aligned with the Oxford English Dictionary (OED) definition of “proof” and the classical (philosophical) understanding of what “proof” is, within a formal argument and valid logical proof, demonstrates that I have a perfect understanding of what proof is and/or can be. R: This proof and the coherent explanation given in premise Q satisfy the expectation of P that a logician like me should be able to prove we know what proof is with a formal argument and rigorous explanation, avoiding the paradox that could be seen as arising if I could not prove that I know what proof is - while being a purported expert on proof and a master of Logic whose forte is supposed to be proof writing and proof theory. S: Assume ~(P, Q, R). This leads to logical contradiction as it would mean that experts on proof aren’t expected to prove that consistent with their field of expertise - which is logically inconsistent. It would also be inconsistent with my demonstration, which validly used dictionary definitions of proof and reductio ad absurdum to derive the proof. Accepting the premises is consistent with Logic, the nature of proof, and the dictionary (OED) definition of proof, and my ability to write a valid argument semantically within a syntactically sound structure. The structural validity can be and has been confirmed with a Logic calculator. Logical Argument (Formal Proof): {P, P <-> Q, Q <-> R, R <-> S} |= (P & Q) & (R & S) Conclusion: {P, Q, R, S}: It is evident in this proof that I (Maclain Hunter - the logician) know what proof is. The hallmarks of proof including internal, logical, and universal consistency are satisfied. It’s not fallaciously circular, it’s tautological, and/as premises are true and valid. Air’s not saying I know proof because I can prove I know proof but am not doing it. It is saying I know proof because I am writing this proof and proving it as I speak to you (here). It’s different from a statement that begs the question by starting and concluding with a premise that lacks rational support. Here rational support is not external to Logic (but it need not logically be), it is derived from the Logos and Logical Structure. This is not a lack of rational support, and because the demonstration is formal and visible, possible to observe in physical Reality, it is empirically valid also. It would be a contradiction if this were not the case, as it would mean we cannot sense Logic (and Rational Sense) itself - which would be a senseless and untenable position. 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 Q.E.D.

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.