Home – Home – Jornals – "Philosophy of Education" 2015 number 2

The article is devoted to the analysis of dialectics of the intuitive and formal in the cognition of fundamental disciplines. It discusses the specifics of physics and mathematics as sciences which study a complex of constructive features of human intellect. The article also considers the philosophical importance of formal substantiation of exact sciences, the place and role of intuitive moments in mathematics education, as well as the nature of aesthetics in mathematics as an expression of unity of the formal and intuitive moments in scientific cognition. A considerable attention is paid to the subject of mathematics and scientific study of the dialectics of the formal and intuitive in cognition. The existence of non-material entities, which cannot be observed or captured by conventional means and in the usual state of consciousness, is denied in principle. The feelings associated with these entities will inevitably be attributed to the world of altered states of consciousness and intuition, and, in terms of philosophy, be interpreted as a distortion of reality, appearing somehow in the sensory perception of the objectively existing elements. The concept of intuition in mathematics, considered in a philosophical context, only reaffirms, at best, an important for the theory of knowledge fact that there exist the statements and principles of mathematical knowledge which appear direct for the modern consciousness. In this case, intuitionism refuses to further philosophically investigate the genesis of this directness, so philosophically it is not going forward. Consideration of mathematics as a science, the provisions of which are in need of empirical justification, raises a number of specific issues before the philosophy of mathematics, for example: what is observed in the empirical mathematics, that is, which type of mathematical propositions can be tested in practice? The position and aspirations of mathematical intuitionism have as their premise a negative attitude of the intuitionists to absolutization of logical and formal foundations of mathematics.