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Pythagoreanism and Platonism in mathematics: history and modernity
Abstract.The subject of this research is such philosophical and mathematical disciplines as Pythagoreanism and Platonism, which remain relevant at the present time. The author demonstrate the contribution of Pythagoreans to mathematics, their role in creation of geometric algebra, importance of the discovery of incommensurable segments that propelled the Pythagorean mathematics into crisis. The work examines the essence of the concept of mathematical Platonism, reveals its peculiarities, and demonstrates its dissimilarity from the concept of mathematical Pythagoreanism. The presently existing various forms of mathematical Platonism, as well as their peculiarities are explored. The article provides the main arguments of modern critics of Platonism in mathematics and their weaknesses. The author demonstrates the value of the concept of mathematical Platonism as a model visual thinking, and underlines that a large number of mathematicians remain its adherers. The scientific novelty is defined by the fact that the work actualized the ideas of Pythagoreanism and Platonism, as well as the consequence of a dispute that originated in ancient times and continues today between the supporters of Platonism and their opponents related to the fundamental grounds of mathematics. The author concludes that the results of modern mathematical science give valid arguments that confirm the performance and high efficiency of the concept of Platonism in comparison with other philosophical concepts of mathematics.
Keywords: epistemological Platonism, ontological Platonism, mathematical reality, moderate Platonism, incommensurable segments, abstract mathematical objects, mathematical Platonism, Pythagoreanism, methodological Platonism, full-blooded Platonism
Article was received:09-11-2017
This article written in Russian. You can find full text of article in Russian here .