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Full Idea
Russell held that classes can be reduced to propositional functions.
Gist of Idea
Classes can be reduced to propositional functions
Source
report of Bertrand Russell (Mathematical logic and theory of types [1908]) by Robert Hanna - Rationality and Logic 2.4
Book Ref
Hanna,Robert: 'Rationality and Logic' [MIT 2006], p.38
A Reaction
The exact nature of a propositional function is disputed amongst Russell scholars (though it is roughly an open sentence of the form 'x is red').
| 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] |