On Possibility of Geometrical Approach to the Problem of Substantiation of Mathematics

In the article there are analyzed the preconditions of appearence of geometrical program of substatiation of mathematics. The main obstacles to the development of research in this field are common views about unreliability of geometrical understanding in mathematics. Reabilitation of geometry is possible and the main propositions of its critics in discussions about the basis of mathematics can be disputed. Though, to establish geometrical approach to substantiation of mathematics it is necessary to clarify gnoseological nature of geometrical intuition, its genesis and special role in mathematical thinking. This will mean the return to the number of propositions of the philosophy of mathematics of I. Kant and R. Descartes.

substantiation of mathematics, apriorism, reduction, geometrical intuition, logicism <, http://www.multitran.ru/c/m.exe?t=257176_1_2>,