Modus Ponens, Modus Tollens, and Logos by Maclain Hunter

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.

Modus Ponens, Modus Tollens, and Logos by Maclain Hunter: Premises: P: Logos is the Greek term for Reason and while it can refer to a particular logic, word, or reason, in a limited context, in Greek Philosophy, and by default (unless otherwise specified as a particular form of Logos) refers rationally to Logic in general and the Logical Framework of Reality that is coherent with the First Cause of Logic, the Ground of Reasoning, and the Cause of and Reason for the Universe and Existence (Reality). In Classical Theism and Christianity the Logos is understood as the God of Reason, the One True God, identical to Pure Reason and the YHVH/Elohim of the Torah and Jewish Philosophy and Theology - the True Foundation of Reality synonymous with the Highest Order of Logic and the Absolute Truth. Q: Modus Ponens, as a logical rule that can only exist if the Logos exists, helps to prove the Logos exists, especially when applied to relevant reasoning (such as): A (proof) implies B (the Source of Proof in the Logos). A (proof) exists, therefore B is true and B (the Source of Proof) exists. R: Modus Tollens, as a logical rule that can only exist if the Logos exists, helps to prove the Logos exists, especially when applied to relevant reasoning (such as): C (the nonexistence of the Source of Proof (Logos) and the lack of verifiable proof and Existence) implies D (the nonexistence of the very concept of proof) . A (proof) exists, therefore D is false, ~D is true, and ~C must be true. This means that B (the Source of Proof) is true and the Logos exists as the Source of Proof. S: The characterization or character of Logic (Logos) as metaphysical doesn’t diminish its validity, rationality, or existence. To assume the opposite leads to logical contradiction and a lack of intelligibility in Logic and the most overarching of logical frameworks itself, which is a logical impossibility and an untenable position to hold. T: Counterarguments to logical arguments (including proofs) that fail to respect that Logic is the supreme authority in logical discourse and in Reality, as the entity that grounds all physical and metaphysical (or universal) systems, are inherently incoherent (by being misaligned with and disrespectful towards the Logos which is the very Logic of Reality). This includes but is not limited to atheism and its arguments that fundamentally exist as an attempted counterargument to the Logos (God of Reason) and its existence. U: The attempt of secular philosophies to separate Logic, the First Cause, the Origin of the Universe, and God is inherently incoherent and doesn’t unify these concepts under the framework of Logic as the Logos and rational theistic philosophy does. To deny Logic is God and the Ground of Metaphysics defies Logic. {P, P <-> Q, Q <-> R, R <-> S, S <-> T, T <-> U} |= ((P & Q) & (R & S) & T) & U Conclusion: ((P & Q) & (R & S) & T) & U: P and ~(~P) so Q, R, S, T, and U. Q, R, S, T, U and ~(~P) so P. Also A and B hold true along with ~C and ~D as far as the premises/symbols established in the premises themselves. The rules of Logic including Modus Ponens and Modus Tollens can only exist if the Logos exists as the Ground of Reasoning, and these logical rules, as well as proof and logical reasoning exist, therefore it would be a logical impossibility and contradiction for the Logos to be nonexistent or untrue. The well-established existence of these logical rules provides extremely strong evidence, even irrefutable proof, of the Logos as the Foundation of Existence and the “One True God” (Elohim) of Classical Theism and the Abrahamic Tradition. Calling proofs or assertions of the Logos’s existence (which are inherently rational and supported even if informal, as affirmations of the “Source of Rational Support” itself) “metaphysical claims”, and calling the Logos “metaphysical” doesn’t diminish its rationality and Reality as the very Foundation of Reality all that is physical or metaphysical. In short, no argument against the Logos (the God of Reason) and its existence and superseding rationality and authority cannot logically stand. An argument “against Logos” is the opposite of a valid argument “from Logos” in Logic and philosophical discourse. The assumption of ~T leads to logical contradiction. Any argument that tries to invalidate the Ground of Arguments (Logos - First Cause - God) is inherently self-defeating as it would be unreliable if it were true. The attempt to make Logic “secular” and to detach it from theology and ontology is incoherent. Logic is God (Theos) and the study of Logic encompasses and requires (for completeness and a comprehensive understanding of Reality and its Foundation/Origin) theology - the study of God. It defies Logic to consider Logic secular rather than Divine (of or like God) since Logic is God.

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.