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Full Idea
The types is 'ramified' because there are further differences between the type of a function defined in terms of a quantifier ranging over other functions and the type of those other functions, despite the functions applying to the same simple type.
Gist of Idea
Types are 'ramified' when there are further differences between the type of quantifier and its range
Source
Bernard Linsky (Russell's Metaphysical Logic [1999], 1)
Book Ref
Linsky,Bernard: 'Russell's Metaphysical Logic' [CSLI 1999], p.4
A Reaction
Not sure I understand this, but it evidently created difficulties for dealing with actual mathematics, and Ramsey showed how you could manage without the ramifications.
| 18774 | Definite descriptions, unlike proper names, have a logical structure [Linsky,B] |
| 18776 | Contextual definitions eliminate descriptions from contexts [Linsky,B] |
| 21704 | 'Impredictative' definitions fix a class in terms of the greater class to which it belongs [Linsky,B] |
| 21705 | Reducibility says any impredicative function has an appropriate predicative replacement [Linsky,B] |
| 21703 | Types are 'ramified' when there are further differences between the type of quantifier and its range [Linsky,B] |
| 21714 | The ramified theory subdivides each type, according to the range of the variables [Linsky,B] |
| 21713 | Did logicism fail, when Russell added three nonlogical axioms, to save mathematics? [Linsky,B] |
| 21715 | For those who abandon logicism, standard set theory is a rival option [Linsky,B] |
| 21719 | Extensionalism means what is true of a function is true of coextensive functions [Linsky,B] |
| 21721 | Higher types are needed to distinguished intensional phenomena which are coextensive [Linsky,B] |
| 21723 | The task of logicism was to define by logic the concepts 'number', 'successor' and '0' [Linsky,B] |
| 21727 | Definite descriptions theory eliminates the King of France, but not the Queen of England [Linsky,B] |
| 21729 | Construct properties as sets of objects, or say an object must be in the set to have the property [Linsky,B] |