Український математичний конгрес - 2009

Петро Трохимчук (Волинський національний університет ім. Лесі Українки, Луцьк, Україна)

Natural approach of foundation of mathematics

The basis of natural approach of the foundation of mathematics is represented. This method (polymetric doctrine [1]) is based on the nature of mathematics (formalization, analyses and synthesis of all possible knowledge and scince [2]). The basic elements of this doctrine are: functional theory of numbers, generalized mathematical transformations (15 minimal types) and hybrid theory of systems (10 minimal types). Polymetric method is the theory of variable hierachy and open system. Therefore this method is more full as other methods in foundations of mathematics. It may be represented as realization of A.N.Whitehead idea of creation of "organismic" mthematics [3].The basic applications of this approach are discussed too.

[1] Trokhimchuck P.P. Mathematical foundation of knowledge. Polymetrical doctrine. - Lutsk: Vezha, 2009. - 520 p. (In Ukrainian)
[2] Ruzha I. Foundation of mathematics. - Kiev: Vushcha Shkola, 1981. - 352 p. (In Russian)
[3] Whitwhead A.N. Science and the modern world. - New York: Pelican Mentor Books, 1948. - 224 p.