{
  "author": "Maclain Hunter",
  "title": "Philosophical Algebra by Maclain Hunter",
  "identifier": "hunter-philosophical-algebra",
  "sourceKind": "authored-foundational-record",
  "content": "Philosophical Algebra:\n\nBy Maclain Hunter\n\nSymbols, Terms, and Definitions: note that symbols are intentionally encoded with multiple terms.\n\nP: Premise: The basis of an argument.\n\nQ: Logic: The Method of Reasoning and the process/standard arguments are validated by.\n\nR: God: The Origin and Rule(r) of Existence; The Rational Standard of moral authority. \n\nS: 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. \n\nT: Coherence: The logical alignment of concepts; Unity and integration that amounts to logical equivalence; Validity.\n\nU: Incoherence: The lack of logical alignment; Divergence and/or logical contradiction; invalidity. \n\nP: 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. \n\nQ: Existence: What is; Reality; the Universe; Nature and the Natural Order; Being; That which exists. \n\nR: 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. \n\nS: 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. \n\nT: 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. \n\n~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. \n\nP: 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.\n\nLogical Proof (Formal Reasoning): \n\n{P <-> Q, R <-> Q, S <-> Q, T <-> ~U} |= (((P <-> Q) <-> (R <-> Q) <-> S) <-> T) <-> ~U\n\nConclusion: \n\nValid 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. \n\nSciences 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. \n\nProof, 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. \n\nThere 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”. \n\nTruth Table: \n\nvalid\n\nPQRSTU⎪P↔Q R↔Q S↔Q T↔¬U╞(((P↔Q)↔(R↔Q)↔S)↔T)↔¬U\n\n―――――――――――――――――――――――――――――――――――――――――――――――\n\nTTTTTT⎪TTT TTT TTT TFFT    TTT T TTT TT TT FFT\nTTTTTF⎪TTT TTT TTT TTTF    TTT T TTT TT TT TTF\nTTTTFT⎪TTT TTT TTT FTFT    TTT T TTT TT FF TFT\nTTTTFF⎪TTT TTT TTT FFTF    TTT T TTT TT FF FTF\nTTTFTT⎪TTT TTT FFT TFFT    TTT T TTT FF TT FFT\nTTTFTF⎪TTT TTT FFT TTTF    TTT T TTT FF TT TTF\nTTTFFT⎪TTT TTT FFT FTFT    TTT T TTT FF FF TFT\nTTTFFF⎪TTT TTT FFT FFTF    TTT T TTT FF FF FTF\nTTFTTT⎪TTT FFT TTT TFFT    TTT F FFT FT FT TFT\nTTFTTF⎪TTT FFT TTT TTTF    TTT F FFT FT FT FTF\nTTFTFT⎪TTT FFT TTT FTFT    TTT F FFT FT TF FFT\nTTFTFF⎪TTT FFT TTT FFTF    TTT F FFT FT TF TTF\nTTFFTT⎪TTT FFT FFT TFFT    TTT F FFT TF FT TFT\nTTFFTF⎪TTT FFT FFT TTTF    TTT F FFT TF FT FTF\nTTFFFT⎪TTT FFT FFT FTFT    TTT F FFT TF TF FFT\nTTFFFF⎪TTT FFT FFT FFTF    TTT F FFT TF TF TTF\nTFTTTT⎪TFF TFF TFF TFFT    TFF T TFF FT TT FFT\nTFTTTF⎪TFF TFF TFF TTTF    TFF T TFF FT TT TTF\nTFTTFT⎪TFF TFF TFF FTFT    TFF T TFF FT FF TFT\nTFTTFF⎪TFF TFF TFF FFTF    TFF T TFF FT FF FTF\nTFTFTT⎪TFF TFF FTF TFFT    TFF T TFF TF TT FFT\nTFTFTF⎪TFF TFF FTF TTTF    TFF T TFF TF TT TTF\nTFTFFT⎪TFF TFF FTF FTFT    TFF T TFF TF FF TFT\nTFTFFF⎪TFF TFF FTF FFTF    TFF T TFF TF FF FTF\nTFFTTT⎪TFF FTF TFF TFFT    TFF F FTF TT FT TFT\nTFFTTF⎪TFF FTF TFF TTTF    TFF F FTF TT FT FTF\nTFFTFT⎪TFF FTF TFF FTFT    TFF F FTF TT TF FFT\nTFFTFF⎪TFF FTF TFF FFTF    TFF F FTF TT TF TTF\nTFFFTT⎪TFF FTF FTF TFFT    TFF F FTF FF FT TFT\nTFFFTF⎪TFF FTF FTF TTTF    TFF F FTF FF FT FTF\nTFFFFT⎪TFF FTF FTF FTFT    TFF F FTF FF TF FFT\nTFFFFF⎪TFF FTF FTF FFTF    TFF F FTF FF TF TTF\nFTTTTT⎪FFT TTT TTT TFFT    FFT F TTT TT FT TFT\nFTTTTF⎪FFT TTT TTT TTTF    FFT F TTT TT FT FTF\nFTTTFT⎪FFT TTT TTT FTFT    FFT F TTT TT TF FFT\nFTTTFF⎪FFT TTT TTT FFTF    FFT F TTT TT TF TTF\nFTTFTT⎪FFT TTT FFT TFFT    FFT F TTT FF FT TFT\nFTTFTF⎪FFT TTT FFT TTTF    FFT F TTT FF FT FTF\nFTTFFT⎪FFT TTT FFT FTFT    FFT F TTT FF TF FFT\nFTTFFF⎪FFT TTT FFT FFTF    FFT F TTT FF TF TTF\nFTFTTT⎪FFT FFT TTT TFFT    FFT T FFT FT TT FFT\nFTFTTF⎪FFT FFT TTT TTTF    FFT T FFT FT TT TTF\nFTFTFT⎪FFT FFT TTT FTFT    FFT T FFT FT FF TFT\nFTFTFF⎪FFT FFT TTT FFTF    FFT T FFT FT FF FTF\nFTFFTT⎪FFT FFT FFT TFFT    FFT T FFT TF TT FFT\nFTFFTF⎪FFT FFT FFT TTTF    FFT T FFT TF TT TTF\nFTFFFT⎪FFT FFT FFT FTFT    FFT T FFT TF FF TFT\nFTFFFF⎪FFT FFT FFT FFTF    FFT T FFT TF FF FTF\nFFTTTT⎪FTF TFF TFF TFFT    FTF F TFF FT FT TFT\nFFTTTF⎪FTF TFF TFF TTTF    FTF F TFF FT FT FTF\nFFTTFT⎪FTF TFF TFF FTFT    FTF F TFF FT TF FFT\nFFTTFF⎪FTF TFF TFF FFTF    FTF F TFF FT TF TTF\nFFTFTT⎪FTF TFF FTF TFFT    FTF F TFF TF FT TFT\nFFTFTF⎪FTF TFF FTF TTTF    FTF F TFF TF FT FTF\nFFTFFT⎪FTF TFF FTF FTFT    FTF F TFF TF TF FFT\nFFTFFF⎪FTF TFF FTF FFTF    FTF F TFF TF TF TTF\nFFFTTT⎪FTF FTF TFF TFFT    FTF T FTF TT TT FFT\nFFFTTF⎪FTF FTF TFF TTTF    FTF T FTF TT TT TTF\nFFFTFT⎪FTF FTF TFF FTFT    FTF T FTF TT FF TFT\nFFFTFF⎪FTF FTF TFF FFTF    FTF T FTF TT FF FTF\nFFFFTT⎪FTF FTF FTF TFFT    FTF T FTF FF TT FFT\nFFFFTF⎪FTF FTF FTF TTTF    FTF T FTF FF TT TTF\nFFFFFT⎪FTF FTF FTF FTFT    FTF T FTF FF FF TFT\nFFFFFF⎪FTF FTF FTF FFTF    FTF T FTF FF FF FTF\n\nQ.E.D.",
  "formal": null,
  "structuredAuthoredProof": null,
  "authoredSteps": null,
  "recordedAt": "2026-10-02T17:12:57.950Z",
  "originalAuthoredAt": null,
  "propositionMeaningBoundary": "Atomic identifiers retain their meanings in the exact source. No arbitrary truth assignment establishes an ontological or empirical premise; the formal witness checks the written inference."
}