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Full Idea
When a definition contains a quantifier whose range includes the very entity being defined, the definition is said to be 'impredicative'.
Gist of Idea
Impredicative definitions quantify over the thing being defined
Source
A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2)
Book Ref
George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.35
A Reaction
Presumably they are 'impredicative' because they do not predicate a new quality in the definiens, but make use of the qualities already known.
| 17241 | A defined name should not appear in the definition [Hobbes] |
| 15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
| 10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
| 18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
| 21704 | 'Impredictative' definitions fix a class in terms of the greater class to which it belongs [Linsky,B] |
| 10031 | Impredicative definitions quantify over the thing being defined [George/Velleman] |
| 22285 | Impredicative definitions are circular, but fine for picking out, rather than creating something [Potter] |
| 8721 | An 'impredicative' definition seems circular, because it uses the term being defined [Friend] |
| 10882 | Predicative definitions only refer to entities outside the defined collection [Horsten] |