Study of irrational systems by extending the logical-mathematical apparatus

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, num- bers and graphs are often hard to perceive abstract entities, which are particularly numerous in philosophy. 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 supply 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 ir- rational 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.