To the Origins of Fractal Theory

Abstract

The article attempts to give internal contours of historical genesis of the general theory of fractality. Through the analysis of current scientific positions the neces­sity of theoretical comprehension of fractal as a philosophical category is shown and the absence of its unified theory is stated. The article makes logical and methodological reflection of the present ideas about fractality and methods of its research. The authors reveal general definitions of fractality and, through their prism, search for the logical basis of the subject of research. In retrospective movement the genealogy of the theory of fractal is reconstructed and the roots of fractal problematics, which go back to the Pythagorean doctrine of number, are shown. The conclusion is made about the coincidence of the general theory of fractality (understood as dialectics and theory of cognition of its subject) with theoretical mathematics as applied dialectical logic, which reflects a tense con­nection with social needs.