Necessary Entailment by Maclain Hunter

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

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

Necessary Entailment by Maclain Hunter: Premise: P: Logical Necessity (the One True God - Pure Logic), which is tautological and self entailing, not contingent and possibly a fallacious circular argument like that same “P |= P” structure if P were a contingent (and possibly false rather than absolute and foundational concept). Certainly and necessarily there cannot be fallacious circularity in cohering things (including God) with Logic, otherwise Logic could be undermined and logically prevented from demonstrating the coherence of Logic (itself). Proof: P |= P Conclusion: P: What is logically necessary like the Logos—synonymous with and coherent with Logic, Logical Necessity, Universal Cause (God), Universal Reason (Universal Logic), Universal Order, Coherence, Absolute Truth, etc.—which is not contingent, is logically self-entailing as, through, and coherent with the Logic of Reality (Logos). Reality and the Origin of Reality (God) have a tautological Logic (Logos) and proof (in the sense of an irrefutable and self-evident validity) of this very sort/form undergirding it, as to assume the opposite leads to logical contradiction and P and not P cannot be both true or both false at once. Therefore P is true and not P is not true, as Reality is true and Logic (the True Origin) is true and the negation of these logically necessary and logically irrefutable concepts is necessarily false. Let MP represent my proof of Reality’s Logic (God - Logos) and Reality being tautological, and let RP represent Reality’s, and by proxy God’s (G), proof of itself through itself (and/as G), displayed in the A is A form of Reality being Reality. Also, let G represents God or the Origin of Existence. Then it holds that: {MP, MP <-> RP, RP <-> G, G <-> G, G} |= ((MP <-> RP) & (MP & RP)) & G Now, let MB represent my being, let RB represent Reality’s being, and let C represent the Coherence of concepts (to include MP, MB, RP, and RB). Then it holds that: {MP, MP <-> RP, MP <-> MB, RP <-> RB, MB <-> RB, MB <-> RP, MP <-> RB, MP <-> RP, RP <-> C, MP <-> C, C <-> G, G <-> G, MP, MB, RP, RB, C, G} |= (((MP & RP) & (MB & RB)) & C) & G Ergo, God (G)—the Origin of Logic and the Cosmos)—exists as the Logic of Reality and Full Coherence (C), linked logically to my own proof and being (MP, MB), but also RP and RB. This proof irrefutably proves G (God - Origin). It isomorphically aligns (in finite form) with and is logically equivalent to the (infinite and form transcending or “essential”) proof (RP) that G has for G (ie - G |= G). Again, there cannot be fallacious circularity in cohering things (including God) with Logic - even if structurally or apparently circular (or tautological). Logic must (and does) prove itself. Truth Table Analysis: valid ↓ ↓ P⎪P╞P ―――――― T⎪T T Result: Tautological and necessarily true. 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.