18203 | Avoid non-predicative classifications and definitions [Poincaré] |
8746 | To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro] |
18126 | A set does not exist unless at least one of its specifications is predicative [Russell, by Bostock] |
18128 | Russell is a conceptualist here, saying some abstracta only exist because definitions create them [Russell, by Bostock] |
18124 | Vicious Circle says if it is expressed using the whole collection, it can't be in the collection [Russell, by Bostock] |
8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro] |
10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
18131 | If abstracta only exist if they are expressible, there can only be denumerably many of them [Bostock] |
18134 | Predicativism makes theories of huge cardinals impossible [Bostock] |
18136 | If we can only think of what we can describe, predicativism may be implied [Bostock] |
18135 | If mathematics rests on science, predicativism may be the best approach [Bostock] |
18132 | The predicativity restriction makes a difference with the real numbers [Bostock] |
18133 | The usual definitions of identity and of natural numbers are impredicative [Bostock] |
13663 | Some reject formal properties if they are not defined, or defined impredicatively [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
15370 | Predicativism says mathematical definitions must not include the thing being defined [Horsten] |