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. Thus, the correct opinion, pointed out, remains unsubstantiated, since nowhere is it related to the philosophical categories. Houwever, we shall show here that his reflexive definitions, pointed out, do, indeed, connect the mathematical truth with the real word and serve as a substantiation of an one-way ascendancy of mathematics over ethics and the related humanities. Moreover, we shall use for that purpose the clarity introduced by those definitions of Hegel in the way of activating the numbers into interaction.
Reflexion is an infinite series of consecutive negations starting from the quality studied.
In addition to the above Hegel adduces many other arguments, not quoted here, in order to support and substantiate those ones as well as other significant traits of its characteristics. The quantum corresponds to a concrete number of concrete objects. We go back to Hegel's definition of a number, already treated, as an object of mathematics as well as a means of studying the qualities. Since the number represent an inert precisation, an indifferent one, it should be put in correlation one to the other from the exterior. In other words, the rules of reasoning in mathematics should be reduced to forms of studying the rules of the arithmetical operations with the numbers.