Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Skolem's_paradox> ?p ?o. }
Showing items 1 to 40 of
40
with 100 items per page.
- Skolem's_paradox abstract "In mathematical logic and philosophy, Skolem's paradox is a seeming contradiction that arises from the downward Löwenheim–Skolem theorem. Thoralf Skolem (1922) was the first to discuss the seemingly contradictory aspects of the theorem, and to discover the relativity of set-theoretic notions now known as non-absoluteness. Although it is not an actual antinomy like Russell's paradox, the result is typically called a paradox, and was described as a "paradoxical state of affairs" by Skolem (1922: p. 295). Skolem's paradox is that every countable axiomatisation of set theory in first-order logic, if it is consistent, has a model that is countable. This appears contradictory because it is possible to prove, from those same axioms, a sentence that intuitively says (or that precisely says in the standard model of the theory) that there exist sets that are not countable. Thus the seeming contradiction is that a model that is itself countable, and which therefore contains only countable sets, satisfies the first order sentence that intuitively states "there are uncountable sets". A mathematical explanation of the paradox, showing that it is not a contradiction in mathematics, was given by Skolem (1922). Skolem's work was harshly received by Ernst Zermelo, who argued against the limitations of first-order logic, but the result quickly came to be accepted by the mathematical community. The philosophical implications of Skolem's paradox have received much study. One line of inquiry questions whether it is accurate to claim that any first-order sentence actually states "there are uncountable sets". This line of thought can be extended to question whether any set is uncountable in an absolute sense. More recently, the paper "Models and Reality" by Hilary Putnam, and responses to it, led to renewed interest in the philosophical aspects of Skolem's result.".
- Skolem's_paradox wikiPageExternalLink skolem.
- Skolem's_paradox wikiPageExternalLink 1004-toc.htm.
- Skolem's_paradox wikiPageExternalLink pthesis.pdf.
- Skolem's_paradox wikiPageExternalLink skolem_moore.htm&date=2009-10-25+04:16:47.
- Skolem's_paradox wikiPageID "1348798".
- Skolem's_paradox wikiPageRevisionID "570840389".
- Skolem's_paradox first "A.G.".
- Skolem's_paradox hasPhotoCollection Skolem's_paradox.
- Skolem's_paradox id "S/s085750".
- Skolem's_paradox last "Dragalin".
- Skolem's_paradox subject Category:Inner_model_theory.
- Skolem's_paradox subject Category:Mathematics_paradoxes.
- Skolem's_paradox subject Category:Model_theory.
- Skolem's_paradox type Abstraction100002137.
- Skolem's_paradox type Communication100033020.
- Skolem's_paradox type Contradiction107206887.
- Skolem's_paradox type Falsehood106756407.
- Skolem's_paradox type MathematicsParadoxes.
- Skolem's_paradox type Message106598915.
- Skolem's_paradox type Paradox106724559.
- Skolem's_paradox type Statement106722453.
- Skolem's_paradox comment "In mathematical logic and philosophy, Skolem's paradox is a seeming contradiction that arises from the downward Löwenheim–Skolem theorem. Thoralf Skolem (1922) was the first to discuss the seemingly contradictory aspects of the theorem, and to discover the relativity of set-theoretic notions now known as non-absoluteness.".
- Skolem's_paradox label "Paradoks Skolema".
- Skolem's_paradox label "Paradox van Skolem".
- Skolem's_paradox label "Paradoxe de Skolem".
- Skolem's_paradox label "Paradoxo de Skolem".
- Skolem's_paradox label "Skolem's paradox".
- Skolem's_paradox label "Парадокс Скулема".
- Skolem's_paradox label "斯科伦悖论".
- Skolem's_paradox sameAs Paradoxe_de_Skolem.
- Skolem's_paradox sameAs Paradox_van_Skolem.
- Skolem's_paradox sameAs Paradoks_Skolema.
- Skolem's_paradox sameAs Paradoxo_de_Skolem.
- Skolem's_paradox sameAs m.04vr52.
- Skolem's_paradox sameAs Q1096353.
- Skolem's_paradox sameAs Q1096353.
- Skolem's_paradox sameAs Skolem's_paradox.
- Skolem's_paradox wasDerivedFrom Skolem's_paradox?oldid=570840389.
- Skolem's_paradox isPrimaryTopicOf Skolem's_paradox.