Formal Inferring the Law of Conservation of Energy from Assuming A-Priori-ness of Knowledge in a Formal Axiomatic Epistemology System Sigma

Abstract

The research purpose is invention (construction) of a formal logical inference of the Law of Conservation of Energy within a logically formalized axiomatic epistemology-and-axiology theory Sigma from a precisely defined assumption of a-priori-ness of knowledge. For realizing this aim, the following work has been done: 1) a two-valued algebraic system of formal axiology has been defined precisely and applied to proper-philosophy of physics, namely, to an almost unknown (not-recognized) formal-axiological aspect of the physical law of conservation of energy; 2) the formal axiomatic epistemology-andaxiology theory Sigma has been defined precisely and applied to properphysics for realizing the above-indicated purpose. Thus, a discrete mathematical model of relationship between philosophy of physics and universal epistemology united with formal axiology has been constructed. Results: 1) By accurate computing relevant compositions of evaluation-functions within the discrete mathematical model, it is demonstrated that a formal-axiological analog of the great conservation law of proper physics is a formal-axiological law of two-valued algebra of metaphysics. (A precise algorithmic definition of the unhabitual (not-well-known) notion "formal-axiological law of algebra of metaphysics" is given.) 2) The hitherto never published significantly new nontrivial scientific result of investigation presented in this article is a formal logical inference of the law of conservation of energy within the formal axiomatic theory Sigma from conjunction of the formal-axiological analog of the law of conservation of energy and the assumption of a-priori-ness of knowledge.

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

“…The formal axiomatic theory Σ+V is an outcome of significant mutations in (and additions to) the logically formalized axiomatic epistemology-and-axiology systems Σ [38] [40] [41], Σ+C [39], and [42]. For constructing a sufficiently precise definition of the formal axiomatic system Σ+V, it is indispensable to provide exact definitions of its basic concepts, namely, the concept "alphabet of object-language of Σ+V", the abstract syntactic notion "term of Σ+V", the abstract syntactic concept "formula of Σ+V", and, finally, the fundamental notion "axiom of Σ+V".…”

“…For constructing a sufficiently precise definition of the formal axiomatic system Σ+V, it is indispensable to provide exact definitions of its basic concepts, namely, the concept "alphabet of object-language of Σ+V", the abstract syntactic notion "term of Σ+V", the abstract syntactic concept "formula of Σ+V", and, finally, the fundamental notion "axiom of Σ+V". Exact definitions of the mentioned basic concepts of Σ+V are analogous to the definitions of corresponding concepts of Σ [38] [40] [41] and Σ+C [39].…”

“…One of successful attempts of such using the "mole-hole" in Σ is presented in the article "Formal Inferring the Law of Conservation of Energy from Assuming A-Priori-ness of Knowledge" [41]. Then, being inspired by feeling that the result is positive, I had decided to continue exploiting the "mole-hole" in Σ with respect to some other necessarily universal laws of theoretical physics, for example, in relation to the third Newton's law of mechanics, but in this concrete relation results were negative.…”

“…))) a formal-logical proof of which in the formal theory Σ (having nothing to do with vectors) has been published originally in [38] [40] [41]. In the above-defined formal axiomatic theory Σ+V, the wonderful theorem-scheme (Aα ⊃ ((…”