Philosophy Dictionary of ArgumentsHome
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| Numbers: whether numbers are objects or concepts, has been controversial in the philosophical discussion for millennia. The most widely accepted definition today is given by G. Frege (G. Frege, Grundlagen der Arithmetik 1987, p. 79ff). Frege-inspired notions represent numbers as classes of classes, or as second-level terms, or as that with one measure the size of sets. Up until today, there is an ambiguity between concept and object in the discussion of numbers. See also counting, sets, measurements, mathematics, abstract objects, mathematical entities, theoretical entities, number, platonism._____________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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Kurt Gödel on Numbers - Dictionary of Arguments
Berka I 348 Numbers/Gödel: numbers cannot be braught into a spatial arrangement. Goedel calls numbers classes of classes.(1) >Classes, >Numbers/Frege, >Numbers/Neumann, >Numbers/Zermelo, cf. >Sets, >Set Theory. 1. K. Gödel: Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Mh. Math. Phys. 38 (1931), pp. 175-198._____________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. |
Göd II Kurt Gödel Collected Works: Volume II: Publications 1938-1974 Oxford 1990 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
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Ed. Martin Schulz, access date 2024-04-20