Abstract

The article concerns the problems of philosophy of mathematics. The traditional problem of the existence of mathematical objects and truths is solved through the reconstruction of the ontological concepts of the real and possible. The work deals with the problems and development options of certain trends in the philosophy of mathematics. The article describes the arguments in favour of a realistic interpretation of the foundations of mathematics in the light of the extended interpretation of reality. The work contains also the elements of specified ontological interpretation: allocation of the basic components and a detailed interpretation of the arithmetic component