Philosophical Algebra 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.

Philosophical Algebra: By Maclain Hunter Symbols, Terms, and Definitions: note that symbols are intentionally encoded with multiple terms. P: Premise: The basis of an argument. Q: Logic: The Method of Reasoning and the process/standard arguments are validated by. R: God: The Origin and Rule(r) of Existence; The Rational Standard of moral authority. S: Structure: A construct or arrangement. That which is constructed according to a plan; That which gives a pattern or organization to a thing or things. T: Coherence: The logical alignment of concepts; Unity and integration that amounts to logical equivalence; Validity. U: Incoherence: The lack of logical alignment; Divergence and/or logical contradiction; invalidity. P: Logician: An expert in the study (and use) of Logic. A reasoner who reasons with formal logics or in some rigorous and consistent manner grounded in Logic. Q: Existence: What is; Reality; the Universe; Nature and the Natural Order; Being; That which exists. R: Evidence: Pieces of data or information that support a certain theory or conclusion in a logically valid manner; The basis of a well supported case. S: Proof: A formal argument and/or synthesis of evidence into a formal logical argument which proves the conclusions drawn with logical certainty through use of truthful premises and valid logical structure. T: Law: A rule or set of rules, typically rules that are communal or universal (rather than merely personal) and which have costs or consequences associated with their violation. ~U: Science: A method of drawing inferences from empirical observation; A field of study in which experimentation and testing are used to arrive at reliable understanding. P: Objective Truth: That which accords with Reality and its Order and which enjoys validity as a result of that coherent alignment with Truth’s own standards in Logic. Logical Proof (Formal Reasoning): {P <-> Q, R <-> Q, S <-> Q, T <-> ~U} |= (((P <-> Q) <-> (R <-> Q) <-> S) <-> T) <-> ~U Conclusion: Valid premises used to build argument must cohere with and must be logically equivalent to Logic, which in turn must be coherent and unified with the Origin of Existence (God), in order to be truly grounded. In turn these things are logically equivalent to logical structure (structure) and coherence, which is not incoherence and which is the opposite of incoherence, by definition. It is necessary based on the definitions of terms and the logical structure of the argument that this conclusion is true. Sciences and logicians must be coherent with Logic to be understood as genuine sciences and logicians without contradiction or inauthenticity. Reality (Existence) is coherent with Logic and God, as the coherent and self-consistent Source of Reality. This renders {P, Q, R, S, T, U} coherent along with all those symbols represent in this reasoning. Proof, evidence, and law are coherent with Logic in the universal sense (or they wouldn’t be proof, evidence, and “Universal Law” also understood as Reason or Logic). Proof and evidence, when objectively coherent, satisfy and cohere with Rational Law (Logic). We have proof if and only if the is Existence, and we have proof so there is Existence. There is Existence so there is the Origin of Existence (God) and this God is logically equivalent to any “real proof”, “true logician” (or scientist), any “ethical and coherent lawyer/law”, all “genuine evidence”, any “instance of (or the whole of) Existence”, to “coherently structured premises” (or “coherence, structure, and valid premises”) and “the negation of incoherence”. Truth Table: valid PQRSTU⎪P↔Q R↔Q S↔Q T↔¬U╞(((P↔Q)↔(R↔Q)↔S)↔T)↔¬U ――――――――――――――――――――――――――――――――――――――――――――――― TTTTTT⎪TTT TTT TTT TFFT TTT T TTT TT TT FFT TTTTTF⎪TTT TTT TTT TTTF TTT T TTT TT TT TTF TTTTFT⎪TTT TTT TTT FTFT TTT T TTT TT FF TFT TTTTFF⎪TTT TTT TTT FFTF TTT T TTT TT FF FTF TTTFTT⎪TTT TTT FFT TFFT TTT T TTT FF TT FFT TTTFTF⎪TTT TTT FFT TTTF TTT T TTT FF TT TTF TTTFFT⎪TTT TTT FFT FTFT TTT T TTT FF FF TFT TTTFFF⎪TTT TTT FFT FFTF TTT T TTT FF FF FTF TTFTTT⎪TTT FFT TTT TFFT TTT F FFT FT FT TFT TTFTTF⎪TTT FFT TTT TTTF TTT F FFT FT FT FTF TTFTFT⎪TTT FFT TTT FTFT TTT F FFT FT TF FFT TTFTFF⎪TTT FFT TTT FFTF TTT F FFT FT TF TTF TTFFTT⎪TTT FFT FFT TFFT TTT F FFT TF FT TFT TTFFTF⎪TTT FFT FFT TTTF TTT F FFT TF FT FTF TTFFFT⎪TTT FFT FFT FTFT TTT F FFT TF TF FFT TTFFFF⎪TTT FFT FFT FFTF TTT F FFT TF TF TTF TFTTTT⎪TFF TFF TFF TFFT TFF T TFF FT TT FFT TFTTTF⎪TFF TFF TFF TTTF TFF T TFF FT TT TTF TFTTFT⎪TFF TFF TFF FTFT TFF T TFF FT FF TFT TFTTFF⎪TFF TFF TFF FFTF TFF T TFF FT FF FTF TFTFTT⎪TFF TFF FTF TFFT TFF T TFF TF TT FFT TFTFTF⎪TFF TFF FTF TTTF TFF T TFF TF TT TTF TFTFFT⎪TFF TFF FTF FTFT TFF T TFF TF FF TFT TFTFFF⎪TFF TFF FTF FFTF TFF T TFF TF FF FTF TFFTTT⎪TFF FTF TFF TFFT TFF F FTF TT FT TFT TFFTTF⎪TFF FTF TFF TTTF TFF F FTF TT FT FTF TFFTFT⎪TFF FTF TFF FTFT TFF F FTF TT TF FFT TFFTFF⎪TFF FTF TFF FFTF TFF F FTF TT TF TTF TFFFTT⎪TFF FTF FTF TFFT TFF F FTF FF FT TFT TFFFTF⎪TFF FTF FTF TTTF TFF F FTF FF FT FTF TFFFFT⎪TFF FTF FTF FTFT TFF F FTF FF TF FFT TFFFFF⎪TFF FTF FTF FFTF TFF F FTF FF TF TTF FTTTTT⎪FFT TTT TTT TFFT FFT F TTT TT FT TFT FTTTTF⎪FFT TTT TTT TTTF FFT F TTT TT FT FTF FTTTFT⎪FFT TTT TTT FTFT FFT F TTT TT TF FFT FTTTFF⎪FFT TTT TTT FFTF FFT F TTT TT TF TTF FTTFTT⎪FFT TTT FFT TFFT FFT F TTT FF FT TFT FTTFTF⎪FFT TTT FFT TTTF FFT F TTT FF FT FTF FTTFFT⎪FFT TTT FFT FTFT FFT F TTT FF TF FFT FTTFFF⎪FFT TTT FFT FFTF FFT F TTT FF TF TTF FTFTTT⎪FFT FFT TTT TFFT FFT T FFT FT TT FFT FTFTTF⎪FFT FFT TTT TTTF FFT T FFT FT TT TTF FTFTFT⎪FFT FFT TTT FTFT FFT T FFT FT FF TFT FTFTFF⎪FFT FFT TTT FFTF FFT T FFT FT FF FTF FTFFTT⎪FFT FFT FFT TFFT FFT T FFT TF TT FFT FTFFTF⎪FFT FFT FFT TTTF FFT T FFT TF TT TTF FTFFFT⎪FFT FFT FFT FTFT FFT T FFT TF FF TFT FTFFFF⎪FFT FFT FFT FFTF FFT T FFT TF FF FTF FFTTTT⎪FTF TFF TFF TFFT FTF F TFF FT FT TFT FFTTTF⎪FTF TFF TFF TTTF FTF F TFF FT FT FTF FFTTFT⎪FTF TFF TFF FTFT FTF F TFF FT TF FFT FFTTFF⎪FTF TFF TFF FFTF FTF F TFF FT TF TTF FFTFTT⎪FTF TFF FTF TFFT FTF F TFF TF FT TFT FFTFTF⎪FTF TFF FTF TTTF FTF F TFF TF FT FTF FFTFFT⎪FTF TFF FTF FTFT FTF F TFF TF TF FFT FFTFFF⎪FTF TFF FTF FFTF FTF F TFF TF TF TTF FFFTTT⎪FTF FTF TFF TFFT FTF T FTF TT TT FFT FFFTTF⎪FTF FTF TFF TTTF FTF T FTF TT TT TTF FFFTFT⎪FTF FTF TFF FTFT FTF T FTF TT FF TFT FFFTFF⎪FTF FTF TFF FFTF FTF T FTF TT FF FTF FFFFTT⎪FTF FTF FTF TFFT FTF T FTF FF TT FFT FFFFTF⎪FTF FTF FTF TTTF FTF T FTF FF TT TTF FFFFFT⎪FTF FTF FTF FTFT FTF T FTF FF FF TFT FFFFFF⎪FTF FTF FTF FFTF FTF T FTF FF FF FTF 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.