Reflexive Substantion of an One-Way Ascendancy of Mathematics over Ethics ABSTRACT: Russell and Popper are concordant with Plato with respect to the independence of mathematics upon the sensations. Beth shares the opinion of the complete independence between the world of science and mathematics and that of psychology. Essenin-Vol’pin’s opinion is of an ascendance of ethics and jurisprudence over mathematics. For the first time, the position of Plato, Russell, and Popper are substantiated in this paper through Hegel’s reflexive natural scientific method. The external activation of numbers into interaction through arithmetical operations, adopted by him, has been taken as a basis of this substantion. This is the reason why mathematical rules of reasoning are exact-they represent a pure product of the ‘third world.’ The rules of ethics and the related humanities are their reflective approximate reverberations. Ascendancy of the rules of such types of science over mathematics is impossible due to the irreversibility of the reflexion. The problem of the interaction between the psychical and the thinking worlds as reverberations of the material one has been treated much earlier by ancient philosophy. Plato excludes any dependence of mathematics, it being the most brilliant representative of the mental world, of the sensations. Russell [1] (I. pp. 237-238) is concordant with the above. He considers that the mathematical truth is “applicable solely to the symbols,” the symbols being “words,” that “do not signify anything in the real world.” Thus, the correct opinion, pointed out, remains unsubstantiated, since nowhere is it related to the philosophical categories. In the substantion, offered by this paper, we proceed from the assumption that the variety of the mathematical symbols, at any rate, is reduced to and ensues from the aim: namely-to study the quantitative characteristics of “the qualities” from “the being.” That connects the mathematical symbols with “the real world,” i.e.-it reveals the possibility of a substantiating, since those characteristics interact. Following the construction of the foundations of mathematics, we should agree that the interaction among its concepts (i.e. the rules of the mathematical reasoning) is reduced to the interaction among the natural numbers. Hegel defines them reflexively [2], [3] ensuing from “the qualities” of “the beig” which (conversely) indicates that the mathematical truth denotes something “in the real world.” Russell has pointed out that “Hegel’s philosophy is very difficult-he is …the most difficult to grasp of all great philosophers” [1] (III., p. 337), thus associating him with the philosophers “willing to spread confusion in mathematics” [1] (III.