The overall frame of the study is determined by applying a not-well-known solution of the problem of logical bridging the notorious gap between statements of being and statements of value to philosophical grounds of thermodynamics. The main hitherto not published significantly new nontrivial result presented in this article is a formal logical inference of a proper physical law of thermodynamics in logically-formalized-theory-Sigma from conjunction of a formal-axiological analog of that physical law in algebra of formal axiology and the assumption of a-priori-ness of knowledge. All the necessary means for constructing the mentioned formal logical inference, namely, a two-valued algebraic system of metaphysics as formal axiology, and a logically formalized axiomatic epistemology system called Sigma are defined precisely.