Lobovikov, V.O. (2016) A Structural-Functional Analogy between Logic and Pure A-Priori Knowledge of Nature, Exemplified by the Third Newton’s Law of Mechanics (Implication and Correction in Logic as Vector Operations, and the Third Newton’s Law as the Law of Contraposition) [Strukturno-funkcional’naya analogiya mezhdu logikoj i chistym estestvoznaniem a priori na primere tret’ego zakona N’yutona (Implikaciya i korrekciya v logike kak vektornye operacii, i tretij zakon N’yutona kak zakon kontrapozicii)]. Proceedings of Ural Federal University. Series 3: Social Sciences, 11, 31-44. (in Russian)

has been cited by the following article:

• TITLE: Formally Deriving the Third Newton’s Law from a Pair of Nontrivial Assumptions in a Formal Axiomatic Theory “Sigma-V”

  AUTHORS: Vladimir O. Lobovikov

  KEYWORDS: Third Law of Newton’s Mechanics, Logically Formalized Axiomatic Theory Σ-V, Two Valued Algebraic System of Metaphysics as Formal Axiology, A-Priori Knowledge, Formal Derivation from Assumption

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.5, May 18, 2022

  ABSTRACT: The article is devoted to hitherto never undertaken applying an almost unknown logically formalized axiomatic epistemology-and-axiology system called “Sigma-V” to the Third Newton’s Law of mechanics. The author has continued investigating the extraordinary (paradigm-breaking) hypothesis of formal-axiological interpreting Newton’s mathematical principles of natural philosophy and, thus, has arrived to discrete mathematical modeling a system of formal axiology of nature by extracting and systematical studying its proper algebraic aspect. Along with the proper algebraic machinery, the axiomatic (hypothetic-deductive) method is exploited in this investigation systematically. The research results are the followings. 1) The Third Newton’s Law of mechanics has been modeled by a formal-axiological equation of two-valued algebraic system of metaphysics as formal axiology. (Precise defining the algebraic system is provided.) The formal-axiological equation has been established (and examined) in this algebraic system by accurate computing compositions of relevant evaluation-functions. Precise tabular definitions of the evaluation-functions are given. 2) The wonderful formula representing the Third Newton’s Law (in the relevant physical interpretation of the formal theory Sigma-V) has been derived logically in Sigma-V from the presumption of a-priori-ness of knowledge. A precise axiomatic definition of the nontrivial notion “a-priori-ness of knowledge” is given. The formal derivation is implemented in strict accordance with the rigor standard of D. Hilbert’s formalism; hence, checking the formal derivation submitted in this article is not a difficult task. With respect to proper theoretical physics, the formal inference is a nontrivial scientific novelty which has not been discussed and published elsewhere yet.