# Philosophy and Mathematics in the Teaching of Plato: the Development of Idea and Modernity

Liberal Arts in Russia. 2014. Vol. 3. No. 6. Pp. 468-479.

Get the full text (Russian) Email: michailova_mshrc@mail.ru#### Abstract

It is well known that the largest philosophers differently explain the origin of mathematics. This question was investigated in antiquity, a substantial and decisive role in this respect was played by the Platonic doctrine. Therefore, discussing this issue the problem of interaction of philosophy and mathematics in the teachings of Plato should be taken into consideration. Many mathematicians believe that abstract mathematical objects belong in a certain sense to the world of ideas and that consistency of objects and theories really describes mathematical reality, as Plato quite clearly expressed his views on math, according to which mathematical concepts objectively exist as distinct entities between the world of ideas and the world of material things. In the context of foundations of mathematics, so called “Gödel’s Platonism” is of particular interest. It is shown in the article how Platonic objectification of mathematical concepts contributes to the development of modern mathematics by revealing philosophical understanding of the nature of abstraction. To substantiate his point of view, the author draws the works of contemporary experts in the field of philosophy of mathematics.

#### Keywords

- • philosophy of mathematics
- • teaching of Plato
- • Platonism

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