The discussion of problems of contradiction in the development of the socialist economy has not thus far brought scholars to an agreed opinion on this question. The thought has been expressed in this regard that to frame the question as one of defining a basic contradiction of socialism is false and that under socialism only partial and temporary contradictions can occur, which spring up and are resolved in various periods of the development of socialist society.

The author elucidates the ontological basis of elementary mathematical theories and thereby assesses their certainty as a foundation for the more complex theories of modern mathematics, such as mathematical analysis and set theory. He adduces arguments in favor of the position of Frege, who held that geometry can provide a sufficiently broad and certain foundation for mathematics.