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Full Idea
A defence of the ramified theory of types comes in seeing it as a system of intensional logic which includes the 'no class' account of sets, and indeed the whole development of mathematics, as just a part.
Gist of Idea
Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets
Source
report of Bertrand Russell (Mathematical logic and theory of types [1908]) by Bernard Linsky - Russell's Metaphysical Logic 6.1
Book Ref
Linsky,Bernard: 'Russell's Metaphysical Logic' [CSLI 1999], p.93
A Reaction
So Linsky's basic project is to save logicism, by resting on intensional logic (rather than extensional logic and set theory). I'm not aware that Linsky has acquired followers for this. Maybe Crispin Wright has commented?
Related Idea
Idea 15376 Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting]
| 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] |