Grounds for renewal and mathematization of logic and their historical characteristics

Abstract

In the context of the genealogy of classical logic, the philosophical foundations of its renewal and mathematization, which took place starting from the middle of the 19th century, are being considered. Attention is paid to the philosophical foundations and grounds for updating logic renewal and applying to it the basic principles of arithmetic. In terms of the genealogy of logic and the process of its reformation, the role of mathematical research relevant at that time, which became an important basis and prerequisite in this process, is analyzed. The role of G. Frege's activities in the direction of the mathematization of logic and the creation of systems for counting statements and predicates is analyzed and determined. Classical key differences between syllogistics and modern types of predicate logics are studied. On the basis of these provisions, conclusions are formed that allow us to understand the main philosophical foundations in the creation of mathematical logic, and a consistent genealogy of these foundations is built.