Bernarda Riemanna projekt nowej filozofii

• Autorzy: Wójcik W.

Warianty tytułu

EN

Bernard Riemann's new philosophy project

• Języki publikacji: PL

Abstrakty

EN

The paper makes researches of the turning point that was observed in science in the half of the 19th century and the significance of Riemann's philosophical visions, and his scientific achievements that were so much important for appearing the great change. From the beginning of the contemporary times a number of the problems that were caused by the development of mathematics and natural science was still growing. In the 19th century the development faced critical situation, because a number of notions grew unreasonably, arid understanding them to a high degree was based on intuition. All these facts brought about many paradoxes and misunderstandings. Denotation of number notion enlarged (Slii'ds and compound numbers), though it was difficult to give the definition of the new numbers. Although the notions of continuity, compass, function, infinite sequence, differential coefficient, integral, or variable were widely used, in numerous headings of mathematics and physics were defined imprecisely. An attempt at comprehending the notions brought about the necessity of wrestling with secular problems in the process of defining following notions: value, flexure, plane, continuum, variability, and identity. Specifying mathematics' and natural science's principles seemed to be the only solution, but - as it turned out later - it caused other problems. An attempt at specifying geometry brought about appearing the whole pleiad of non - Euclidian geometry systems. Moreover, improving on the real numbers theory resulted in multiplicity theory, which caused further problems. A development of algebra, on the other hand, showed irremovable limits of mathematical exactness (for instance, inability to announce a general formula for roots of the higher than four degree of equations). On the other hand, there appeared new notions and mathematical structures that turned out to be very helpful in describing and explaining many mathematical issues and physical phenomena. Moreover, they included a wealth of philosophical cogitations. First of all, one can number among them such notions as: class (especially infinite class), group, function and miscellany. All these new mathematical notions could be called 'most favourable' to that effect they reveal the significant elements of the reality, and mathematics' and natural science's attendance at the discussion over philosophical problems. For Riemann, a notion of miscellany was 'most favourable'. Having defined it, he tried to construct a notion of repeatedly extensive quantity with comprehensive quantity notions. It was to become a starting point for understanding relation between geometry and a notion of space. Miscellany also is to become a subject of philosophical studies -- it would be a characteristic 'miscellany metaphysics'. This metaphysics would not be a simple sum of worldly wisdom that is imparted by everyday experience, exact sciences and philosophy, but would be a system letting comprehend notions and structures both of the science and our existence. In 1850 Riemann formulated theory, which became the central idea for his scientific searches. In his opinion, one should create a completely unsubsidized mathematical theory, which, having included fundamental laws, would describe sphere of existence filled with different influences, and would merge gravitational, electromagnetic and thermodynamical phenomena. It was a great plan for unification of physics, which, in fact, was tending to unify the whole approachable worldly wisdom. Many scientists in the second half of the 19th century, and in the 2Oth century tried to accept this challenge (J. Cl. Maxwell, H. Helmholtz, H. Hertz, H. Poincare and A. Einstein). A special role is ascribed to the qualifying for assistant - professorship lecture, which was delivered by Riemann on June 10, 1854 in Getynga. In his speech Riemann lays emphasis on the flimsiness of the principles of geometry, and the need of specifying and consolidating them. In Riemann's view, a notion of space itself used in geometry seems to be unprecise. Also, status of the axioms as the first principles of geometry telling the truth of the reality (as it was widely held), and their interdependence, still remains abstruse. Riemann's task is to reveal all these hidden connexions among the axioms of geometry. In his opinion, all hitherto existing miscarriages were caused by the fact that even a comprehensive notion of repeatedly extensive quantity was not formulated. Thanks to terming such notion one could understand a notion of space (that is experienced by us), which, in fact, is a remarkable instance for thrice extensive quantity. Also, a comprehensive notion of quantity should be subjected to a thorough examination and improved. Philosophical considerations of Riemann are not only a common addition to his scientific work, but also are the significant part of his thought. Riemann is constructing the philosophy of world, which in holistic way would explain physical and spiritual influences, and would reveal their reasons. The main principle of this philosophical system is mathematics, and the keystone, filler and fulfilment - metaphysics. For the structure of theory is circular, mathematics and metaphysics are united peculiarly. Unfortunately, Riemann left his work uncompleted. He believed that its realization is possible, and it would be realized in the future thanks to understanding known laws of nature, and on the strength of laying down a law of interaction of heat, light, magnetism and electricity.

Słowa kluczowe

PL

Riemann, Bernard; filozofia

EN

Riemann Bernard; philosophy

• Wydawca: Instytut Historii Nauki im. L. i A. Birkenmajerów Polskiej Akademii Nauk
• Czasopismo: Kwartalnik Historii Nauki i Techniki
• Rocznik: 2007
• Tom: R. 52, nr 2
• Strony: 51--74

Twórcy

autor

Wójcik W.

• Polska Akademia Nauk. Instytut Historii