On the history of analysis. The formation of definitions

Abstract: The mathematical analysis was conceived in XVII century in Newton and Leibniz works. The problem of logical rigor in definitions was considered by Arnauld and Nicole in "Logique ou l'art de penser". They were the first, who distinguished between the volume of the concept and its structure. They created a tradition which was strong in math till XIX century, especially in France. The definitions were in binomial nomenclature mostly, but another type of definition appears in Cantor theory - it was the descriptive definition. As it used to be in human sciences, first the object had only one characteristic, then as the research continued it enriched with new characteristics so we have full-fledged conception. In this way the mathematics acquired its own creativity. In 1915 Lusin laid down a new principle of the descriptive theory: a structural characteristic is done, the analytical form had to be found. New schools of descriptive set theory appeared in Moscow in the first half of the 20th century.