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The paper submits surprising results of systematical investigating a formal-ethical aspect of conjoining Wittgenstein’s, Moore’s, Parmenides’, Gödel’s, and Łukasiewicz’s ideas. A critique of Wittgenstein’s critique of the natural language of ethics and of metaphysics results in submitting and elaborating a new paradigm of metaphysics as formal axiology (in particular, formal ethics). In result, the classical metaphysics and ethics of moral rigor are represented as two-valued algebraic systems of metaphysics and formal ethics respectively. By means of this algebraic model, all the well-known scandal-making metaphysical tenets of Parmenides are produced as translations of corresponding algebraic equations from the symbolic language to the natural one. At the level of submitted discrete mathematical model of formal axiology, Parmenides’ metaphysical (formal-axiological) concepts “consistency” and “inconsistency,” “completeness” and “incompleteness” are compared with Gödel’s logic ones. Formal-axiological meanings of the words “consistency,” “incompleteness,” “being,” “nonbeing,” “movement,” “knowledge,” “belief,” etc., are considered as moral-evaluation-functions determined by one moral-evaluation-variable. Binary moral-evaluation-functions are studied as well. The functions are precisely defined by tables. Precise definitions of “formal-axiological-equivalence,” “formal-axiological-law,” and “formal-axiological contradiction” are submitted. Thus, one can either generate or examine formal-axiological equations of algebra of metaphysics by “computing” relevant compositions of moral-value-functions. Using this “moral-value-table-computation-technique,” one can arrive to a surprising conclusion that both the notorious sentence of Moore (called “epistemic paradox”) and the incompleteness sentence of Gödel are formally-axiologically inconsistent ones: Hence, they are formally-axiologically equivalent. For overcoming the negative psychological effect of such a surprising result, the author has used graphic models explicating the famous Łukasiewicz’s statement “Logic is morality of thought and speech.”

An Equivalence of Moore’s Paradox and Gödel’s Incompleteness Sentence in Two-Valued Algebra of Formal Ethics