12 ideas
11064 | Classes can be reduced to propositional functions [Russell, by Hanna] |
10247 | We have no adequate logic at the moment, so mathematicians must create one [Veblen] |
6407 | The class of classes which lack self-membership leads to a contradiction [Russell, by Grayling] |
6408 | Russell needed three extra axioms to reduce maths to logic: infinity, choice and reducibility [Grayling] |
10418 | Type theory seems an extreme reaction, since self-exemplification is often innocuous [Swoyer on Russell] |
10047 | Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms [Russell, by Musgrave] |
23478 | Type theory means that features shared by different levels cannot be expressed [Morris,M on Russell] |
21718 | Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Russell, by Linsky,B] |
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] |
6414 | Two propositions might seem self-evident, but contradict one another [Grayling] |