Philosophy Dictionary of ArgumentsHome
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| Finitism: Finitism in mathematics is a philosophical school of thought that holds that only finite mathematical objects exist. Finitists believe that mathematics should be based on concrete objects and operations that can be physically carried out. See also Intuitionism. _____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. | |||
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Bernulf Kanitscheider on Finitism - Dictionary of Arguments
I 154ff Einstein universe/Kanitscheider: The Einstein universe is static, cylindrical, all clocks can be synchronized. Worldwide simultaneity can be defined here. First relativistic model, but could not do justice to the red shift discovered a short time later! The Einstein universe led to a revival of finitism. Here the Riemannian idea of the compatibility of finiteness and unboundedness is realized. Finite space content, but no outer limits, medieval idea. Every point can be regarded as a center. ((s) Three-dimensional space is curved like the two-dimensional surface of a cylinder). Gravitation: conceived as a metric field, is determined by its properties in the infinitely small. However, the Riemannian idea of infinitesimal geometry, largely realized in RT, entails the uncertainty according to which guiding principles the extension to a universal metric and topology should proceed. The Minkowski space (Minkowski world) is pseudo-Euclidean in the small and medium size range. >Minkowski space. I 157 It is the consequence of the geometrization of the dynamics, the absorption of all inertial forces into the metric guiding field, that the physical geometry gets purely local character. Proximity character of geometry: Consequence: multiplicity of the topological coherence forms with which the local metric is compatible! If one identifies every point of the spherical space with the diametral point, one arrives at the elliptic space. (In three-dimensional space even infinitely many closed and finite elliptic space forms). Two-dimensionally, the spherical can be thought of as a one-sided surface on which a cog maintains its sense of rotation. On the elliptic surface it has the sense of rotation reversed! From this follows that the center of the wheel has already covered a closed path after passing through a semicircle._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
Kanitsch I B. Kanitscheider Kosmologie Stuttgart 1991 Kanitsch II B. Kanitscheider Im Innern der Natur Darmstadt 1996 |
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> Counter arguments against Kanitscheider
> Counter arguments in relation to Finitism
Ed. Martin Schulz, access date 2024-04-19