Historical, Philosophical, Political and Law Sciences, Culturology and Study of Art. Issues of Theory and Practice. Tambov: Gramota, 2011. № 1. P. 112-117.
THE PROBLEM OF THE PRIORITY OF CLASSIC AND NON-CLASSIC GEOMETRIES WHEN APPLYING THEM TO THE WORLD STUDY AS A MODERN PROBLEM OF PHILOSOPHY
Koveshnikov Evgeniy Valerievich, Kadeeva Oksana Evgenyevna
Ussuriysk State Pedagogical Institute
Abstract. The article reveals the historical and philosophical side of the problem of incompleteness and uncertainty of Euclid's geometry axiomatics and its paradoxes, the formation of alternative geometries by Lobachevsky, Riemann and Mandelbrot. The authors discuss the following question: which geometry is preferable for the mathematical description of World and Nature. The positions of maths, physics, psychology and philosophy concerning the above mentioned problems are shown.
Key words and phrases: геометрия Евклида, геометрия Евклида-Гильберта, геометрия Лобачевского, геометрия Римана, геометрия Мандельброта, неопределённость, неполнота, аксиоматика, фракталы, пространство, концептуальные и перцептуальные пространства, Euclid's geometry, Euclid and Hilbert's geometry, Lobachevsky's geometry, Riemann's geometry, Mandelbrot's geometry, uncertainty, incompleteness, axiomatics, fractals, space, conceptual and perceptual spaces
Open the whole article in PDF format. Free PDF-files viewer can be downloaded .
References:
Veil' G. O filosofii matematiki / per. s nem.; predisl. S. A. Yanovskoi; vstup. st. A. P. Yushkevicha. Izd. 2-e, stereotipnoe. M.: KomKniga, 2005. 128 s.
Gil'bert D. Osnovaniya geometrii. Petrograd: Seyatel', 1923.
Gott V. S. Filosofskie voprosy sovremennoi fiziki. M.: Vysshaya shkola, 1972. 416 s.
Efimov N. V. Vysshaya geometriya. 7-e izd. M.: FIZMATLIT, 2003. 584 s.
Iovlev N. N. Vvedenie v elementarnuyu geometriyu i trigonometriyu Lobachevskogo. M.-L.: Gosudarstvennoe izdatel'stvo, 1930.
Lantsosh K. Al'bert Einshtein i stroenie kosmosa. M.: Nauka, 1967. 160 s.
Mandel'brot B. Fraktal'naya geometriya prirody. M.: Institut komp'yuternykh issledovanii, 2002. 656 s.
Mostepanenko A. M. Prostranstvo-vremya i fizicheskoe poznanie. M.: Atomizdat, 1975. 216 s.
Petrov Yu. P. Istoriya i filosofiya nauki: matematika, vychislitel'naya tekhnika, informatika. SPb.: BKhV-Peterburg, 2005. 448 s.
Reikhenbakh G. Filosofiya prostranstva i vremeni. Izd. 2-e, stereotipnoe. M.: Editorial URSS, 2003. 320 s.
Rid K. Gil'bert. M.: Nauka, 1977.
Riman B. Sochineniya / per. s nem.; pod red. V. L. Goncharova. M.-L.: Gos. izd. tekhniko-teoretich. lit., 1948.
Smogorzhevskii A. S. O geometrii Lobachevskogo. M.: Gos. izd. tekhniko-teoretich. lit., 1957.
Fridman A. A. Mir kak prostranstvo i vremya. 2-oe izd. M.: Nauka, 1965. 112 s.
Evklidovykh" nachal" vosem' knig" / per. s grech. T. Petrushevskogo. Sankt-Peterburg, 1819.
Einshtein i razvitie fiziko-matematicheskoi mysli: sbornik statei / otv. redaktor A. T. Grigor'yan. M.: Akademiya nauk SSSR, 1962. 210 s.
Русский
