Certainty From Paradoxical Dichotomy by Maclain Hunter

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

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

Certainty From Paradoxical Dichotomy by Maclain Hunter: Premise: P: God is Logic. When God is Logic atheism is illogical, and when God is not Logic atheism is not godly (or necessarily or possibly logical in the sense of being aligned with the Ontological Ground that grounds more contingent aspects of Logic) and still fails to recognize Logic as the Foundational Force or Logos that classical theism posits as God. Let P also represent the Set of logical rules (or “Rule of Logic”) that aligns all valid logical rules and principles with the Law of Identity and Logic’s universal Coherence and immutable self-consistency. The Rule of Logic is the Rule of Logic and this A is A form entails and encompasses all logical rules and/as (or aligned with) First Cause. Logical Proof (Formal Argument): {P <-> P} |= (((P v ~P) & (P <-> ~~P)) & ((P -> P) & (~P -> ~P))) Notes on Formal Structure (Above): I would point out that the FORMAL LOGIC is displaying the traditional rules of Logic (Identity, Non-Contradiction, Excluded Middle) and the PSR (Principle of Sufficient Reason). What we call “double negation elimination” (ie - “P <-> ~~P”) is a way of writing the Law of Non-Contradiction - that P cannot be “not P”. Likewise, “P <-> P” displays the Law of Identity and is appropriately what sits on the left of the entailment sign here, true to the way that Identity (A is A) entails all other logical rules and concepts and is synonymous with the Foundational Coherence of Logic and Reality (Logos a.k.a. God). The argument “P -> P” shows how Reason leads to (causes) Reason (or causality and reasons for things), necessarily. If there were no Rational Ground there would be no need for Reason or reasons, and proof or the PSR (ie - “~P -> ~P”). Conclusion: Ergo: P v ~P: God is Logic or not Logic, but when God is not Logic that is fundamentally because of Logic and the way that God, as a premise or Universal Axiom, and Logic, as the Method of Reasoning and axiomatic Logical Structure, are logically interconnected and coherent (when coherent and valid). Atheism (weak or strong) is illogical as whether God is used (as a term) or not atheism represents a failure to see/affirm Logic properly as the Foundational Force and Ontological Ground (or Universal Source) that it is (tantamount to God in classical theism). At that point the use of the term God becomes a secondary point - as substantively it is also a misunderstanding of Logic itself, and the position/supremacy of Logic (the Supreme Being aka “God”). It is not coherent to have any reasonable doubt of Reason (as God), that’s an unreasonable doubt, so agnosticism and even agnostic theism are not coherent with the Logos and Logic as the rationally coherent Ontological, Logical, Existential, and Epistemological Foundation. This is not my opinion but my unbiased elaboration on what Logic and the Logical Framework show - through consistent reasoning and honest/logical application of logical rules. Truth Table: P↔P╞(((P∨¬P)&(P↔¬¬P))&((P→P)&(¬P→¬P))) TTT TTFT T TTTFT T TTT T FTTFT FTF FTTF T FTFTF T FTF T TFTTF 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.