Definitions, Etymology, and Elaborations 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.

Definitions, Etymology, and Elaborations by Maclain Hunter: Premises: {P, Q, R, S, T, U}: P: Logic: The Logical Standard and means of reasoning the facts of Reality. Etymology and Elaboration: The word Logic is derived from the Greek word for Reason, which is “Logos”, solidifying the case that a proper understanding of Logic is the one most fully coherent with Pure Reason (Logos) and that these two English terms, Reason and Logic, are logically equivalent (when we are talking about coherent Logic and/or coherent Reason). Q: God: The Origin of Existence; the Moral Standard; the Supreme Being; the Logos, or “Universal Logic”, in rational/orthodox traditions coherent with Logic. Etymology and Elaboration: The word God links back to gothic translation of the Bible and the New Testament’s (Greek) term “Theos” (Ruler, Observer, Overseer) which in that same set of texts is linked directly to “Logos” (Divine Reason; Universal Order, Natural Cause; Proper Order), notably in the Gospel of John chapter 1 verse 1, reinforcing the logical philosophy that understands Logic and Logos (Reason as a universal) as the “Rational Basis” — the God/Origin that actually makes sense, to put it simply. R: Irrefutable: impossible to reasonably deny or logically disprove; that which aligns with the Logical Standard (Logic) to well to be shown rationally to be misaligned with the Logical Standard of Logic. Etymology and Elaboration: From Latin “irrefutabilis” which like the English derivative means that something is not possible to rebut. Logically speaking, Logic is irrefutable and so is anything truly and demonstrably (provably) coherent with Logic, like the Foundation of Reality as it actually is (in its real form, sense, and coherent state). S: Science: The process of gaining knowledge through empirical inquiry using the/a logically valid scientific method; empirical observation; the use of rational experimentation to understand the nature of the real world. Etymology and Elaboration: The word science comes from the Latin word for knowledge/knowing “scire”, which again shows how we are putting a different name on the same substantive concept or closely related aspects of it (that we can refer to as Logic, Reason, or Rationality among other terms like Truth or Reality), and that on a logical, scientific, realistic, linguistic, mathematical, and philosophical level we have support for seeing these concepts and fields coherently and as mutually supporting, not incoherent and as fields or concepts working against each other (which some might for instance assume or think of God and the sciences). T: Mathematics: Definition: The aspect of reasoning and academics that deals with numbers, arithmetic, algebra, calculus, and calculation (or statistics and probabilities); the abstract science dealing with numbers, quantities, and spaces (which includes geometry). Etymology and Elaboration: The word “mathematics” comes from the Greek “manthanein” which refers to learning and the method of learning (systematically), which is coherent with Logic and touches on why Math and Logic are substantively identical in certain contexts, though math has a stricter focus that Logic in the broadest sense of the Universal Order. Even still, we could talk about the “Mathematics of the Universe” and would be talking about a more similar concept to what I am speaking about when I speak of Logic (the Highest Order of Logic or “Logos”) being equivalent to God. The etymology and definition of “mathematics” and the success of math in helping us understand the Universe supports rational (mono)theistic notions of the Logos (the God of Reason - the True Origin) being the Ultimate Source of Knowledge and “omniscient” - holding all feasible knowledge while being the method of knowing (that knowledge) in a coherent/unified fashion. U: Proof: Evidence or argument establishing or helping to establish a fact or the truth of a statement; Law the spoken or written evidence in a trial; the action or process of establishing the truth of a statement; a series of stages in the resolution of a mathematical or philosophical problem. Etymology and Elaboration: The word “proof” shares the same Latin root “probare” as the word probe, supporting the linguistic and logical connection, and a longstanding/foundational one, between testing/probing, evidence, argument (to include logical proofs), mathematical and philosophical inquiry, and the concept of proof. Logical Proof (Formal Structure): {P, P <-> Q, Q <-> R, R <-> S, S <-> T, T <-> U, U -> P} |= ((P & Q) & (R & S) & T) & U Conclusion: ((P & Q) & (R & S) & T) & U: Logic is inextricably and irrefutably linked to science and math, as well as the True God (Logos - Theos) and the concept of proof. This coherence of Logic and the Foundation of Existence (God) is what allows for coherent sciences and mathematics, and is what allows us to prove anything at all (including logically, theologically, scientifically—including “physically” in physical sciences—and/or mathematically). This also means that Logic and logical coherence is essential to any of these fields of study and cannot be rationally ignored. Truth Table Analysis: valid ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ PQRSTU⎪P P↔Q Q↔R R↔S S↔T T↔U U→P╞((P&Q)&(R&S)&T)&U ――――――――――――――――――――――――――――――――――――――――――――――――――― TTTTTT⎪T TTT TTT TTT TTT TTT TTT TTT T TTT TT TT TTTTTF⎪T TTT TTT TTT TTT TFF FTT TTT T TTT TT FF TTTTFT⎪T TTT TTT TTT TFF FFT TTT TTT T TTT FF TT TTTTFF⎪T TTT TTT TTT TFF FTF FTT TTT T TTT FF FF TTTFTT⎪T TTT TTT TFF FFT TTT TTT TTT F TFF FT FT TTTFTF⎪T TTT TTT TFF FFT TFF FTT TTT F TFF FT FF TTTFFT⎪T TTT TTT TFF FTF FFT TTT TTT F TFF FF FT TTTFFF⎪T TTT TTT TFF FTF FTF FTT TTT F TFF FF FF TTFTTT⎪T TTT TFF FFT TTT TTT TTT TTT F FFT FT FT TTFTTF⎪T TTT TFF FFT TTT TFF FTT TTT F FFT FT FF TTFTFT⎪T TTT TFF FFT TFF FFT TTT TTT F FFT FF FT TTFTFF⎪T TTT TFF FFT TFF FTF FTT TTT F FFT FF FF TTFFTT⎪T TTT TFF FTF FFT TTT TTT TTT F FFF FT FT TTFFTF⎪T TTT TFF FTF FFT TFF FTT TTT F FFF FT FF TTFFFT⎪T TTT TFF FTF FTF FFT TTT TTT F FFF FF FT TTFFFF⎪T TTT TFF FTF FTF FTF FTT TTT F FFF FF FF TFTTTT⎪T TFF FFT TTT TTT TTT TTT TFF F TTT TT FT TFTTTF⎪T TFF FFT TTT TTT TFF FTT TFF F TTT TT FF TFTTFT⎪T TFF FFT TTT TFF FFT TTT TFF F TTT FF FT TFTTFF⎪T TFF FFT TTT TFF FTF FTT TFF F TTT FF FF TFTFTT⎪T TFF FFT TFF FFT TTT TTT TFF F TFF FT FT TFTFTF⎪T TFF FFT TFF FFT TFF FTT TFF F TFF FT FF TFTFFT⎪T TFF FFT TFF FTF FFT TTT TFF F TFF FF FT TFTFFF⎪T TFF FFT TFF FTF FTF FTT TFF F TFF FF FF TFFTTT⎪T TFF FTF FFT TTT TTT TTT TFF F FFT FT FT TFFTTF⎪T TFF FTF FFT TTT TFF FTT TFF F FFT FT FF TFFTFT⎪T TFF FTF FFT TFF FFT TTT TFF F FFT FF FT TFFTFF⎪T TFF FTF FFT TFF FTF FTT TFF F FFT FF FF TFFFTT⎪T TFF FTF FTF FFT TTT TTT TFF F FFF FT FT TFFFTF⎪T TFF FTF FTF FFT TFF FTT TFF F FFF FT FF TFFFFT⎪T TFF FTF FTF FTF FFT TTT TFF F FFF FF FT TFFFFF⎪T TFF FTF FTF FTF FTF FTT TFF F FFF FF FF FTTTTT⎪F FFT TTT TTT TTT TTT TFF FFT F TTT TT FT FTTTTF⎪F FFT TTT TTT TTT TFF FTF FFT F TTT TT FF FTTTFT⎪F FFT TTT TTT TFF FFT TFF FFT F TTT FF FT FTTTFF⎪F FFT TTT TTT TFF FTF FTF FFT F TTT FF FF FTTFTT⎪F FFT TTT TFF FFT TTT TFF FFT F TFF FT FT FTTFTF⎪F FFT TTT TFF FFT TFF FTF FFT F TFF FT FF FTTFFT⎪F FFT TTT TFF FTF FFT TFF FFT F TFF FF FT FTTFFF⎪F FFT TTT TFF FTF FTF FTF FFT F TFF FF FF FTFTTT⎪F FFT TFF FFT TTT TTT TFF FFT F FFT FT FT FTFTTF⎪F FFT TFF FFT TTT TFF FTF FFT F FFT FT FF FTFTFT⎪F FFT TFF FFT TFF FFT TFF FFT F FFT FF FT FTFTFF⎪F FFT TFF FFT TFF FTF FTF FFT F FFT FF FF FTFFTT⎪F FFT TFF FTF FFT TTT TFF FFT F FFF FT FT FTFFTF⎪F FFT TFF FTF FFT TFF FTF FFT F FFF FT FF FTFFFT⎪F FFT TFF FTF FTF FFT TFF FFT F FFF FF FT FTFFFF⎪F FFT TFF FTF FTF FTF FTF FFT F FFF FF FF FFTTTT⎪F FTF FFT TTT TTT TTT TFF FFF F TTT TT FT FFTTTF⎪F FTF FFT TTT TTT TFF FTF FFF F TTT TT FF FFTTFT⎪F FTF FFT TTT TFF FFT TFF FFF F TTT FF FT FFTTFF⎪F FTF FFT TTT TFF FTF FTF FFF F TTT FF FF FFTFTT⎪F FTF FFT TFF FFT TTT TFF FFF F TFF FT FT FFTFTF⎪F FTF FFT TFF FFT TFF FTF FFF F TFF FT FF FFTFFT⎪F FTF FFT TFF FTF FFT TFF FFF F TFF FF FT FFTFFF⎪F FTF FFT TFF FTF FTF FTF FFF F TFF FF FF FFFTTT⎪F FTF FTF FFT TTT TTT TFF FFF F FFT FT FT FFFTTF⎪F FTF FTF FFT TTT TFF FTF FFF F FFT FT FF FFFTFT⎪F FTF FTF FFT TFF FFT TFF FFF F FFT FF FT FFFTFF⎪F FTF FTF FFT TFF FTF FTF FFF F FFT FF FF FFFFTT⎪F FTF FTF FTF FFT TTT TFF FFF F FFF FT FT FFFFTF⎪F FTF FTF FTF FFT TFF FTF FFF F FFF FT FF FFFFFT⎪F FTF FTF FTF FTF FFT TFF FFF F FFF FF FT FFFFFF⎪F FTF FTF FTF FTF FTF FTF FFF F FFF FF FF 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.