Formally Inferring Galileo Galilei Principle of Relativity of Motion in an Axiomatic System “Sigma+V” from a Triple of Nontrivial Assumptions

The present paper submits a result of applying a hitherto unknown logically formalized axiomatic axiology-and-epistemology theory “Sigma+V” to the relativity principle formulated by Galileo Galilei. By this application, the author has continued checking the remarkable (paradigm-breaking) hypothesis that formal-axiological interpreting strictly universal laws of classical theoretical mechanics could have a heuristic value for the theory proper. Along with systematical studying proper algebraic structure of formal axiology of nature, the axiomatic (hypothetic-deductive) method is used in this research as well. The investigation accomplishments are the followings. Galileo Galilei principle of relativity of motion has been represented in a two-valued algebraic system of formal axiology by a wonderful formal-axiological equation which could be called a “formal-axiological analog of Galileo relativity principle”. A precise definition of that algebraic system is given. The remarkable formal-axiological equation has been created (and checked) in that algebraic system by attentive computing relevant compositions of evaluation-functions. Precise definitions of the relevant evaluation-functions are accomplished by tables. The remarkable formula modeling Galileo Galilei principle of relativity of motion (given the appropriate interpretation of the formal theory) has been formally-logically inferred within Sigma+V from a couple of nontrivial assumptions, namely, 1) a precisely defined assumption of a-priori-ness of knowledge, 2) the above-mentioned formal-axiological analog of the relativity principle by Galileo Galilei. A not-manifest but quite exact axiomatic definition of “a-priori-ness of knowledge” is provided. The formal-logical inference is performed in perfect accordance with the mathematical rigor norms formulated within the formalism doctrine by D. Hilbert, therefore, examining the formal deductive inference submitted in the paper can be accomplished easily. Being a nontrivial scientific novelty for proper theoretical physics, hitherto the formal-logical derivation has not been published and discussed elsewhere.

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