On rationalization of the foundations of differential calculus

Logical analysis of differential calculus for the purpose of rationalization of the foundations of mathematics is proposed. Methodological basis for analysis is the unity of formal logic and rational dialectics. It is shown that the standard definitions of the concepts “variable quantity”, “infinitesimal (infinitely diminishing) quantity”, and “infinitely large (infinitely increasing) quantity” represent logical errors because these definitions are based on the concept of mathematical process. The correct definition of the concept “variable quantity” and the unified mathematical definition relating to both extreme cases of values of variable quantity (i.e. to the case of arbitrarily small values of the variable quantity and the case of arbitrarily large values of the variable quantity) and the case of arbitrary values of the variable quantity are proposed.