Russian Federation
This paper examines the question of how we should evaluate Bernhard Riemann's innovations in the field of geometry from the point of view of the original Leibnizianism, that is, as formulated in the presentation of Leibniz himself. Here we will also consider the question of whether the Leibnizian paradigm is a special kind of phenomenon. As we know, Leibniz himself rejected the idea of the possibility of multidimensional spaces. This can be seen, for example, in paragraph 351 of his Theodicy. However, the Leibnizian paradigm contains principles that could later contribute to the discovery of non-Euclidean geometries and the development of such a field of knowledge as the geometry of multidimensional spaces. A special place here is occupied by the principle of sufficient reason, which could play a role in finding sufficient grounds for each position of geometry, including for axioms. As is known, it was the search for the foundations for the fifth postulate of Euclid’s geometry that led Lobachevsky to the idea of non-Euclidean geometry.
Riemann, Leibniz, non-Euclidean geometry, curvature of space, multidimensional space, Leibnizianism, Leibnizian paradigm
1. Kant I. Sochineniya. V 8-mi t. - T.1. - M.: ChORO, 1994 - 544 s.
2. Kozlov A.A. Sochineniya v chetyreh tomah. T.1. Svoe slovo. Melitopol': FLP Odnorog T.V., NPU, 2017. - 606 s.
3. Leybnic G.V. Sochineniya v chetyreh tomah, tom 1. - M.: Mysl', 1982. - 636 s.
4. Leybnic G.V. Sochineniya v chetyreh tomah, tom 3. - M.: Mysl', 1984. - 734 s.
5. Leybnic G.V. Sochineniya v chetyreh tomah, tom 4. - M.: Mysl', 1989. - 554 s.
6. Monstyrskiy M.I. Bernhard Riman. Topologiya. Fizika. - M., 1999. - 188 s.
7. Fisher K. Istoriya novoy filosofii. Tom 4. Immanuil Kant i ego uchenie. Chast' pervaya. - Spb.: Izdanie t-va «Znanie», 1906 - 635 s.
8. Fisher K. Istoriya novoy filosofii. Tom 4. Immanuil Kant i ego uchenie. Chast' vtoraya. - Spb.: Izdanie t-va "Znanie", 1906 - 657 s.
