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Full Idea
Russell's theory of types avoided the paradoxes, but it had the result that features common to different levels of the hierarchy become uncapturable (since any attempt to capture them would involve a predicate which disobeyed the hierarchy restrictions).
Gist of Idea
Type theory means that features shared by different levels cannot be expressed
Source
comment on Bertrand Russell (Mathematical logic and theory of types [1908]) by Michael Morris - Guidebook to Wittgenstein's Tractatus 2H
Book Ref
Morris,Michael: 'Guidebook to Wittgenstein's Tractatus' [Routledge 2008], p.112
| 11064 | Classes can be reduced to propositional functions [Russell, by Hanna] |
| 6407 | The class of classes which lack self-membership leads to a contradiction [Russell, by 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] |