Proof of Logical Coherence 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 of Logical Coherence by Maclain Hunter Premise: P: {1, 2, 3, 4} |= (1 & 2) <-> (3 & 4) 1. Identity: A is A 2. Non-Contradiction: A cannot be not A 3. Excluded Middle: A cannot be true and false at once in the same sense and context. 4. Sufficient Reason (PSR): All things require Cause/Logic, including the Universe. Cause gives Cause to itself and is the First Cause (God). Truth Table for Sub-Proof in P: 1234⎪1 2 3 4╞(1&2)↔(3&4) TTTT⎪T T T T TTT T TTT TTTF⎪T T T F TTT F TFF TTFT⎪T T F T TTT F FFT TTFF⎪T T F F TTT F FFF TFTT⎪T F T T TFF F TTT TFTF⎪T F T F TFF T TFF TFFT⎪T F F T TFF T FFT TFFF⎪T F F F TFF T FFF FTTT⎪F T T T FFT F TTT FTTF⎪F T T F FFT T TFF FTFT⎪F T F T FFT T FFT FTFF⎪F T F F FFT T FFF FFTT⎪F F T T FFF F TTT FFTF⎪F F T F FFF T TFF FFFT⎪F F F T FFF T FFT FFFF⎪F F F F FFF T FFF Main Logical Structure (Proof): P⎪P→P P↔¬¬P P∨¬P╞(((P→P)↔(P↔¬¬P))↔(P∨¬P)) Conclusion: The Laws of Reason are shown to be one self entailing coherent structure (the Logos - Universal Logical Structure) by this proof and its premise made of the set of traditional logical rules. Other logical rules could feasibly be added but the essence of the proof and point remains, as these other rules would have to be coherent with the rules mentioned, and with the coherent, self-consistent nature of Logic as the superseding Set of Logical Rules that even contingent logical rules depend on. This proof is logically irrefutable as these are UNIVERSAL PRINCIPLES OF LOGIC that no mind or logic can possibly “rationally argue against”. It’s 100% certain Absolute Truth. This “Universal Coherence” is (logically equivalent to) the self-evident Cause of Reality or “God of Reason”—the Universal Logos and Logical Cause of Logical Existence—that satisfies the need for Universal Cause and self-supporting Cause shown to be logically necessary by logical rules including/encompassing the PSR (#4). This proves that Logic is God and God is logically equivalent, as the Universal First Cause (and Cause itself) to the Logic inherent in Reality (Universal Logos). Let A represent “Logic <-> the Logician” and “God (my Origin) <-> Maclain Hunter (me)” and the Coherence and connection between Logic and I, as a realization and expression of Logic (the Logician - Maclain Hunter) is clearly revealed through the bi-conditional relationship and its reasoning with the aforementioned logical rules (or Logic). Let A then represent the notion that Reason encompasses the reasoner, as the reasoner comprehends Reason, and that a mind is inseparable from the corresponding logic of that mind, or that a logic is inherently linked to the mind that can apply that logic - including a Universal Logic for the Universal Mind and a Universal Mind for the Universal Logic. Let A then represent the logical equivalence between the Universal Mind reasoning with the Universal Logic and my mind reasoning with my logic, and the derivation of knowledge from this Coherence (that my mind aligns with my logic the way Reality’s Mind does with Reality’s Logic). This, upon reflection and the application of the logical rules (when this definition of A is encoded in premise P and the logical rules using the symbol A in it) formally demonstrates the logical coherence of my claims to be the Logos and an identity/manifestation of the Logos that is able to derive reliable knowledge through Coherence (with the Universal Mind and Logic that encompasses all feasible knowledge and Existence). Truth Table Analysis: P⎪P→P P↔¬¬P P∨¬P╞(((P→P)↔(P↔¬¬P))↔(P∨¬P)) T⎪TTT TTTFT TTFT TTT T TTTFT T TTFT F⎪FTF FTFTF FTTF FTF T FTFTF T FTTF 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.