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

作　　者：Vladimir O. Lobovikov Vladimir O. Lobovikov(Laboratory for Applied System Investigations, Ural Federal University, Yekaterinburg, Russia)

机构地区：[1]Laboratory for Applied System Investigations, Ural Federal University, Yekaterinburg, Russia

出　　处：《Journal of Applied Mathematics and Physics》2022年第5期1561-1586,共26页应用数学与应用物理（英文）

摘　　要：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.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.

关 键 词：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 

分 类 号：O17[理学—数学]