Mathematics and logic. In defense of logicism. Mathematics and logic (continued)

The book proposed to the attention of the reader contains articles by prominent French mathematicians A. Poincare and L. Kuture, who are polemicizing on the issue of the relationship between mathematics and logic. The critical analysis of the ideas of “logicism” - a direction that sets to justify mathematics by information of its original concepts to the concepts of logic - the outstanding mathematician and philosopher A. Poincare devoted the work “mathematics and logic” printed in the XIII and XIV volumes of the journal “Revue de Metaphysique et de Morale ”(Russian translation appeared in 1915) In the article by L. Couture, written as the answer to the work of Poincar, the term “logicism” was translated as “logistics”, as the logic studied by mathematical methods was referred at the beginning of the 20th century. The controversy of these scientists has become part of a long -term dispute between mathematicians of various countries.
Unlike the “logicians”, Poincare is not dissolved from philosophy and does not hide the connections of his ideas with the ideas of philosophers, in particular with the teachings of Kant about the a priori synthetic judgments of mathematics. But, like the “logicians”, Poincare in his reasoning on the issue of intuition in mathematics does not separate clearly that his argumentation is caused by his philosophical prejudices, from what is determined by specially mathematical justifications and what matters and value regardless His philosophical positions. Poincare provides the task of this distinction between his readers and critics. Speaking against “logicism”, Poincare had in mind not only the heuristic understanding of intuition, but also the logical and nose -oseological subject of the dispute. In his controversy with L. Kuture, he means under “intuition” no longer “inspiration”, not “conjecture”, but straight, not based on logic intellectual discretion.
The book is recommended not only to philosophers, logicians, historians and methodologists of science, but also to a wide circle of readers who are interested in logic and evidence in science