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 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 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 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.”. (shrink)

This paper explores the interplay between logic-sensitivity and bitstring semantics in the square of opposition. Bitstring semantics is a combinatorial technique for representing the formulas that appear in a logical diagram, while logic-sensitivity entails that such a diagram may depend, not only on the formulas involved, but also on the logic with respect to which they are interpreted. These two topics have already been studied extensively in logical geometry, and are thus well-understood by themselves. However, the precise details of their (...) interplay turn out to be far more complicated. In particular, the paper describes an elegant and natural interaction between bitstrings and logic-sensitivity, which makes perfect sense when bitstrings are viewed as purely combinatorial entities. However, when we view bitstrings as semantically meaningful entities (which is actually the standard perspective, cf. the term ‘bitstring semantics’!), this interaction does not seem to have a full and equally natural counterpart. The paper describes some attempts to address this situation, but all of them are ultimately found wanting. For now, it thus remains an open problem to capture this interaction between bitstrings and logic-sensitivity from a semantic (rather than merely a combinatorial) perspective. (shrink)