more from this thinker | more from this text
Full Idea
Poincaré suggested that what is wrong with an impredicative definition is that it allows the set defined to alter its composition as more sets are added to the theory.
Gist of Idea
Impredicative definitions are wrong, because they change the set that is being defined?
Source
David Bostock (Philosophy of Mathematics [2009], 8.3)
Book Ref
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.252
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] |