DOI:   10.22412/1993-7768-11-1-9


Vadim V. Kortunov, PhD (Dr. Sc.) in Philosophy, Professor Russian State University of Tourism and Service, Moscow, Russian Federation. E-mail:

Every lecturer who had a chance to teach Humanities to students of non-humanitarian directions of training, probably had difficulties with understanding and learning the material. Students oriented towards formulas, numbers and graphs are often hard to perceive abstract entities, which are particularly numerous in phi- losophy. We offer to use widely logical-mathematical language in learning to describe metaphysical systems, categories, and reasoning. As an example of such use of the logical-mathematical language in the article, we will focus on several philosophical ideas which are not quite rational in modern science and which, we believe, are particularly difficult for a student to understand. Irrational systems are understood as systems in which there are essential elements that are fundamentally not amenable to a strictly rational understanding or even description. These include most of the known systems, for example, religion, art, man and universe. Classical formal logic was fulfilled long ago and has been taking the position of a finished science for many centuries. In parallel with it there is a development of various systems of non-classical logic which attempt either to sup- ply it, or to describe the unknown shape of our thinking. It seems to us that it is possible to use the combined logical-mathematical language, which could, at least, describe the so-called “unscientific”, the irrational system of reality, because irrational systems just count 95% of experience. Systems such as man, the universe, the soul, consciousness, art, religion, image, infinity are totally or partially irrational and not amenable to scientific description. Art, religion and philosophy try to describe these systems, but the method they describe is also irrational. We tend to assume that it is possible to use a rational language, which would take the liberty of adequately describing these systems, at least, if not studying them.

Keywords: logic, irrationality

I would like to уxpress special thanks to Sergei Lavrenchenko, PhD (Cand.Sc.) in physical and mathematical Sciences of Department of mathematical and natural Sciences of the Russian state University of tourism and service», without him this work would not have happenedat all. As a result of extensive correspondence work has been rethought and most of the recommendations of Sergei Lavrenchenko were implemented in this work. Also thank Elena Bryzgalina, the head of the Department of philosophy of education in Philosophical faculty of Moscow state University, who had acquainted me with many experts in the field of logic and mathematics, who helped to develop and present the article.
I had an interesting debate with Professor Alex Broom (Humboldt-Universität zu Berlin) and Professor Henry Stamberger (University of Alabama). Many of the ideas expressed by them, I hope I will be able to implement in my further scientific work.
I want to express my gratitude to the editor of the journal of Symbolic Logic, Mr. Alessandro Berarducci, who proposed to translate and publish an article in his magazine.
The paper is the first attempt to give a formal logical-mathematical description of irrational theses, extended logical-mathematical apparatus produced by the subsequent synthesis of logical and mathematical languages to describe a non-obvious philosophical statements. For the first time logical-mathematical language is in- cluded the author’s interpretation of Euler diagram and the theory of limits.