Mathematical Practice and Mathematical Logic: To the History of Relationship

Abstract

The article annuls the role of practice in the development of mathematics in the 19th century in the formation of mathematical logic. It is shown that the revolutionary transformations of mathematics of the 19th century, which led to an increase in the abstractness of mathematical theories and concepts, was accompanied by an increase in uncertainty regarding the standards of proof, which led to the universal spread of anxiety (J. Gray) as an element of mathematical practice. It is argued that this element of practice was one of the sources of the emergence of mathematical logic, which claims to give rigor and accuracy to mathematics. The article argues that the socio-epistemological analysis of the practice of mathematics and the formation of mathematical logic will clarify the specifics of the development of relations between mathematics and mathematical logic.