Philosophy Dictionary of ArgumentsHome
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| Infinity, infinite, philosophy: the result of a procedure that never ends, e.g. counting or dividing, or e.g. the continued description of a circular motion. In lifeworld contexts, infinitely continued processes such as infinite repetition or never-ending waiting are at least not logically contradictory. A formation rule does not have to exist for an infinite continuation to occur, as is the case, for example, with the development of the decimal places of real numbers. See also limits, infinity axiom, repetition, finitism, numbers, complex/complexity._____________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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Zeno on Infinity - Dictionary of Arguments
Thiel I 169 Infinity/Zeno/Thiel: Problem of infinitely small quantities. Could a series of infinitely many points linked to each other be produced? Zeno of Elea (5th century BC). It is precisely because of the possibility of an infinite number of divisions that we cannot build the entire route "from the bottom". There are no first building blocks. Zeno's paradox: the arrow never arrives, it appears to never be able to leave the bow. Thiel I 170 In today's usual computational "resolution" it is preceeded as following: Achilles 5m/s, turtle 5cm/s. Lead over 15 m. The lead of the turtle is increased by 5 cm per sec but simultaneously reduced by 20 m. From 1500 + 5t 500t = 0 is obtained as the time t of the overtaking: t = 1500/495 s, slightly more than 3 seconds. Modern representations use decimal fraction notation: 3.030303 .... Vs: the essential is hidden, namely The sequence 3 + (3 divided by 102, 104, 106, etc.). This sequence can only represent a finite value. But the riddle is only repeated once again for the layman by the decimal fraction. >Paradoxes._____________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. |
Zeno T I Chr. Thiel Philosophie und Mathematik Darmstadt 1995 |
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Ed. Martin Schulz, access date 2024-04-19