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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Paul Lorenzen on Infinity - Dictionary of Arguments
Berka I 266 "Over-countable"/infinite/LorenzenVsSet theory: fable realm of the "Over-Countable". ((s) is not constructible). >constructivism, >Set theory. Berka I 272 Infinite/premisses/dialogical logic/Lorenzen: one can state a step number l e0 = ω exp ω exp ω exp... P can thus first calculate an ordinal number I The calculation process is recursive, so even in the narrowest sense constructive. >Constructivism, >Recursion, >Recursivity, >Calculability. The statement forms that are used in the consistency proof are generally not recursive.(1) >Consistency, >Proofs, >Provability. 1. P. Lorenzen, Ein dialogisches Konstruktivitätskriterium, in: Infinitistic Methods, (1961), 193-200_____________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. |
Lorn I P. Lorenzen Constructive Philosophy Cambridge 1987 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
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Ed. Martin Schulz, access date 2024-04-19