The article is a reflection on the Pythagorean thesis “Everything is a number”, which metaphorically expresses the all-pervading role of mathematics in science and culture in general. It is fixed that all the fundamental concepts of mathematics that form its supporting frame are transcendental. The specifics of the system approach is revealed in comparison with the Cartesian one through the prism of mathematics. It is shown that the Cartesian approach dominates in research activities within the framework of the emerging mathematical theory, while the systematic approach dominates in research activities related to a more or less formed theory. The features of the relationship between the reasonable thinking and rational thinking in mathematical activity are analyzed. It has been established that the movement of mathematical thought is accompanied by reciprocal transitions of reasonable thinking into rational thinking, and rational thinking into reasonable thinking. The relationship between classical formal logic and dialectical logic in mathematical activity is considered. The conclusion is made about the heuristic nature of modern logic associated with the potential of logical semantics.
For citation:
Kogalovsky S.R. “Everything is a number”: (Faces of mathematics), Ivanovo State University Bulletin, Series: Humanities, 2022, iss. 4, pp. 168—178.