Aleksander K. Cherkashin

V.B. Sochava Institute of Geography SB RAS

Different methods of Kant's philosophical system are studied from the standpoint of mathematical and geographical sciences. This system is considered as part of the meta-theoretical approach, represented by means of methodological, mathematical and statistical analysis. The procedures of vector stratification (bundle) of the categorical feature space on manifolds developed in differential geometry are used as a model of transcendental analytics. Vector bundle algebra models the procedures of transcendental dialectical logic in the form of triadic systems of knowledge organization. The observed reality is described in terms of coordinate space. A priori knowledge is represented by a manifold, on which the tangent bundle of space into a system of independent layers as opposites is carried out. The bundle layers represent the laws of pure absolute knowledge, excluding the conventions of cognition of reality. The universal equations of these relations are derived, and examples of the application of these equations and their relations for the analysis of statistical data and the creation of system theories are presented. It is assumed that the joint work of philosophers, mathematicians and geographers will make it possible to coordinate transcendental concepts and laws to create a united field of meta-theoretical research.

Transcendental analytics, fibration procedures, spatial manifolds, triadic schemes, dialectical logic, statistical analysis, metatheoretical knowledge, general theory of systems, rules of inference