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Full Idea
An 'impredicative' definition is one that uses the terms being defined in order to give the definition; in some way the definition is then circular.
Gist of Idea
An 'impredicative' definition seems circular, because it uses the term being defined
Source
Michèle Friend (Introducing the Philosophy of Mathematics [2007], Glossary)
Book Ref
Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.172
A Reaction
There has been a big controversy in the philosophy of mathematics over these. Shapiro gives the definition of 'village idiot' (which probably mentions 'village') as an example.
| 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] |