The Unreasonable Effectiveness of Mathematics in the Natural Sciencesin the Сontext of the Ideas of Platonism
The emergence of intuitionism in the philosophy of mathematics at the beginning of XX century was the first alarming signal that mathematics had lost its empirical base. This caused a lot of discussions in the formation of science itself, and as a result should lead to the problem of substantiating the interaction of mathematics and natural sciences. The question posed by Nobel Prize winner E. Wigner about the "unreasonable effectiveness of mathematics in the natural sciences" gets a new significance, since the interaction with the science that has lost its empirical base can lead to development anomalies. The author looks for the roots of the answer to the question of "unreasonable effectiveness" in the factors that played a role in the formation of mathematization of the natural sciences, and further assesses the significance of each one at the current stage. It was defined that the essential role had been played by the following factors: - creation of the alphabetic symbolics by F. Viète in algebra as the operational system without which it would hardly have been possible to implement Galileo Galilei's purpose; - the accuracy of the language of mathematics - a characteristic that was a priority in comparison with other languages; - in peculiarities of the hermeneutical tradition originating in the Middle Ages when «the thing was speaking» and it was possible to decipher the world through the symbols; - in the release of the reprinting of Proclus «A commentary on the first book of Euclid’s elements» (1533) - promotion of the idea of mathesis universalis. Considering the significance of factors at the present stage, the author concludes that the mathesis universalis project has retained its potential in Platonic views on the nature of mathematics. Given the obvious fact that mathematics is a product of culture, at present the ideas of Platonism (of Realismin mathematics)are rapidly losing their popularity [1], therefore, at this stage they cannot substantiate the effectiveness of mathematics in natural science. The identified factors of accuracy of the language of mathematics and the presence of developed mathematical models (as an operating apparatus) continue to be significant for the union of mathematics and natural science, but insufficient to justify "unreasonable effectiveness in the natural sciences". Summing up, one can conclude that the ideas of Platonism continue to play a much larger role in mathematics than it may seem at first glance.