On Possibility of Geometrical Approach to the Problem of Substantiation of Mathematics
In the article there are analyzed the preconditions of appearence of geometrical program of substatiation of mathematics. The main obstacles to the development of research in this field are common views about unreliability of geometrical understanding in mathematics. Reabilitation of geometry is pos...
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| Format: | Article |
| Language: | deu |
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Peoples’ Friendship University of Russia (RUDN University)
2010-06-01
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| Series: | RUDN Journal of Philosophy |
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| Online Access: | http://journals.rudn.ru/philosophy/article/view/11657 |
| _version_ | 1818929715132497920 |
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| author | I G Ivanov |
| author_facet | I G Ivanov |
| author_sort | I G Ivanov |
| collection | DOAJ |
| description | In the article there are analyzed the preconditions of appearence of geometrical program of substatiation of mathematics. The main obstacles to the development of research in this field are common views about unreliability of geometrical understanding in mathematics. Reabilitation of geometry is possible and the main propositions of its critics in discussions about the basis of mathematics can be disputed. Though, to establish geometrical approach to substantiation of mathematics it is necessary to clarify gnoseological nature of geometrical intuition, its genesis and special role in mathematical thinking. This will mean the return to the number of propositions of the philosophy of mathematics of I. Kant and R. Descartes. |
| first_indexed | 2024-12-20T03:49:12Z |
| format | Article |
| id | doaj.art-522ea93a7d144c5d8a11eb5892adefa9 |
| institution | Directory Open Access Journal |
| issn | 2313-2302 2408-8900 |
| language | deu |
| last_indexed | 2024-12-20T03:49:12Z |
| publishDate | 2010-06-01 |
| publisher | Peoples’ Friendship University of Russia (RUDN University) |
| record_format | Article |
| series | RUDN Journal of Philosophy |
| spelling | doaj.art-522ea93a7d144c5d8a11eb5892adefa92022-12-21T19:54:30ZdeuPeoples’ Friendship University of Russia (RUDN University)RUDN Journal of Philosophy2313-23022408-89002010-06-0102486011656On Possibility of Geometrical Approach to the Problem of Substantiation of MathematicsI G Ivanov0Московский государственный университет им. М.В. ЛомоносоваIn the article there are analyzed the preconditions of appearence of geometrical program of substatiation of mathematics. The main obstacles to the development of research in this field are common views about unreliability of geometrical understanding in mathematics. Reabilitation of geometry is possible and the main propositions of its critics in discussions about the basis of mathematics can be disputed. Though, to establish geometrical approach to substantiation of mathematics it is necessary to clarify gnoseological nature of geometrical intuition, its genesis and special role in mathematical thinking. This will mean the return to the number of propositions of the philosophy of mathematics of I. Kant and R. Descartes.http://journals.rudn.ru/philosophy/article/view/11657обоснование математикиаприоризмредукциягеометрическая интуициялогицизм |
| spellingShingle | I G Ivanov On Possibility of Geometrical Approach to the Problem of Substantiation of Mathematics RUDN Journal of Philosophy обоснование математики априоризм редукция геометрическая интуиция логицизм |
| title | On Possibility of Geometrical Approach to the Problem of Substantiation of Mathematics |
| title_full | On Possibility of Geometrical Approach to the Problem of Substantiation of Mathematics |
| title_fullStr | On Possibility of Geometrical Approach to the Problem of Substantiation of Mathematics |
| title_full_unstemmed | On Possibility of Geometrical Approach to the Problem of Substantiation of Mathematics |
| title_short | On Possibility of Geometrical Approach to the Problem of Substantiation of Mathematics |
| title_sort | on possibility of geometrical approach to the problem of substantiation of mathematics |
| topic | обоснование математики априоризм редукция геометрическая интуиция логицизм |
| url | http://journals.rudn.ru/philosophy/article/view/11657 |
| work_keys_str_mv | AT igivanov onpossibilityofgeometricalapproachtotheproblemofsubstantiationofmathematics |