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- Impredicativity abstract "In mathematics and logic, a self-referencing definition is called impredicative. More precisely, a definition is said to be impredicative if it invokes (mentions or quantifies over) the set being defined, or (more commonly) another set which contains the thing being defined.The opposite of impredicativity is predicativity, which essentially entails building stratified (or ramified) theories where quantification over lower levels results in variables of some new type, distinguished from the lower types that the variable ranges over. A prototypical example is intuitionistic type theory, which retains ramification but discards impredicativity.Russell's paradox is a famous example of an impredicative construction, namely the set of all sets which do not contain themselves. The paradox is whether such a set contains itself or not — if it does then by definition it should not, and if it does not then by definition it should.The greatest lower bound of a set X, glb(X), also has an impredicative definition; y = glb(X) if and only if for all elements x of X, y is less than or equal to x, and any z less than or equal to all elements of X is less than or equal to y. But this definition also quantifies over the set (potentially infinite, depending on the order in question) whose members are the lower bounds of X, one of which being the glb itself. Hence predicativism would reject this definition.".
- Impredicativity wikiPageExternalLink predicativity.pdf.
- Impredicativity wikiPageExternalLink Predicativism.html.
- Impredicativity wikiPageID "1930406".
- Impredicativity wikiPageLength "10994".
- Impredicativity wikiPageOutDegree "45".
- Impredicativity wikiPageRevisionID "686011741".
- Impredicativity wikiPageWikiLink Axiom_of_reducibility.
- Impredicativity wikiPageWikiLink Begriffsschrift.
- Impredicativity wikiPageWikiLink Bertrand_Russell.
- Impredicativity wikiPageWikiLink Burali-Forti_paradox.
- Impredicativity wikiPageWikiLink Cantors_paradox.
- Impredicativity wikiPageWikiLink Category:Concepts_in_logic.
- Impredicativity wikiPageWikiLink Category:Mathematical_logic.
- Impredicativity wikiPageWikiLink Category:Philosophy_of_mathematics.
- Impredicativity wikiPageWikiLink Category:Recursion.
- Impredicativity wikiPageWikiLink Category:Self-reference.
- Impredicativity wikiPageWikiLink Cesare_Burali-Forti.
- Impredicativity wikiPageWikiLink Dedekind_chain.
- Impredicativity wikiPageWikiLink Definition.
- Impredicativity wikiPageWikiLink Ernst_Zermelo.
- Impredicativity wikiPageWikiLink Frank_P._Ramsey.
- Impredicativity wikiPageWikiLink Gottlob_Frege.
- Impredicativity wikiPageWikiLink Gödel,_Escher,_Bach.
- Impredicativity wikiPageWikiLink Hans_Reichenbach.
- Impredicativity wikiPageWikiLink Henri_Poincaré.
- Impredicativity wikiPageWikiLink Hermann_Weyl.
- Impredicativity wikiPageWikiLink Infimum_and_supremum.
- Impredicativity wikiPageWikiLink Infinite_set.
- Impredicativity wikiPageWikiLink Intuitionistic_type_theory.
- Impredicativity wikiPageWikiLink Jean_van_Heijenoort.
- Impredicativity wikiPageWikiLink John_P._Burgess.
- Impredicativity wikiPageWikiLink Logic.
- Impredicativity wikiPageWikiLink Mathematics.
- Impredicativity wikiPageWikiLink Natural_number.
- Impredicativity wikiPageWikiLink Paradox.
- Impredicativity wikiPageWikiLink Parametric_polymorphism.
- Impredicativity wikiPageWikiLink Peano_axioms.
- Impredicativity wikiPageWikiLink Philosophy_of_mathematics.
- Impredicativity wikiPageWikiLink Richards_paradox.
- Impredicativity wikiPageWikiLink Russells_paradox.
- Impredicativity wikiPageWikiLink Second-order_arithmetic.
- Impredicativity wikiPageWikiLink Self-reference.
- Impredicativity wikiPageWikiLink Set_theory.
- Impredicativity wikiPageWikiLink Solomon_Feferman.
- Impredicativity wikiPageWikiLink Stephen_Cole_Kleene.
- Impredicativity wikiPageWikiLink Stratification_(mathematics).
- Impredicativity wikiPageWikiLink Vicious_circle_principle.
- Impredicativity wikiPageWikiLinkText "Impredicativity".
- Impredicativity wikiPageWikiLinkText "Predicativity".
- Impredicativity wikiPageWikiLinkText "impredicative definitions".
- Impredicativity wikiPageWikiLinkText "impredicative".
- Impredicativity wikiPageWikiLinkText "impredicativity".
- Impredicativity wikiPageWikiLinkText "predicative analysis".
- Impredicativity wikiPageWikiLinkText "predicative".
- Impredicativity wikiPageWikiLinkText "predicativism".
- Impredicativity wikiPageWikiLinkText "predicativist".
- Impredicativity wikiPageWikiLinkText "predicativity".
- Impredicativity wikiPageUsesTemplate Template:IEP.
- Impredicativity wikiPageUsesTemplate Template:Reflist.
- Impredicativity subject Category:Concepts_in_logic.
- Impredicativity subject Category:Mathematical_logic.
- Impredicativity subject Category:Philosophy_of_mathematics.
- Impredicativity subject Category:Recursion.
- Impredicativity subject Category:Self-reference.
- Impredicativity type Concept.
- Impredicativity type Field.
- Impredicativity comment "In mathematics and logic, a self-referencing definition is called impredicative.".
- Impredicativity label "Impredicativity".
- Impredicativity sameAs Q3149511.
- Impredicativity sameAs Imprédicativité.
- Impredicativity sameAs Impredicativo.
- Impredicativity sameAs m.066zg4.
- Impredicativity sameAs Q3149511.
- Impredicativity sameAs 非直谓性.
- Impredicativity wasDerivedFrom Impredicativity?oldid=686011741.
- Impredicativity isPrimaryTopicOf Impredicativity.