Philosophy Dictionary of ArgumentsHome
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| Infinity Axiom: The infinity axiom is an axiom of set theory, which ensures that there are infinite sets. It is formulated in e.g. such a way that a construction rule is specified for the occurrence of elements of a described set. If {x} is the successor of x, the continuation is formed by the union x U {x}. See also set theory, successor, unification, axioms._____________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 Infinity Axiom - Dictionary of Arguments
Berka I 367 Axiom of infinity/Gödel: the axiom of infinity can be formulated as follows: "There is exactly a countable number of individuals".(1) >Infinity, >Individuals, >Countability, >Quantification, >Validity/Gödel. 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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> Counter arguments against Gödel
> Counter arguments in relation to Infinity Axiom
Ed. Martin Schulz, access date 2024-04-28