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Full Idea
Quine charges that the axiom of Reducibility both undoes the effect of the ramification, and commits the theory to a platonist view of propositional functions (which is a theory of sets, once use/mention confusions are cleared up).
Gist of Idea
Reducibility undermines type ramification, and is committed to the existence of functions
Source
report of Willard Quine (Set Theory and its Logic [1963], p.249-58) by Bernard Linsky - Russell's Metaphysical Logic 6.1
Book Ref
Linsky,Bernard: 'Russell's Metaphysical Logic' [CSLI 1999], p.92
| 14459 | Reducibility: a family of functions is equivalent to a single type of function [Russell] |
| 21720 | Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B on Russell/Whitehead] |
| 18130 | Axiom of Reducibility: there is always a function of the lowest possible order in a given level [Russell, by Bostock] |
| 13428 | Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey] |
| 21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
| 18170 | The Axiom of Reducibility is self-effacing: if true, it isn't needed [Quine] |
| 21717 | Reducibility undermines type ramification, and is committed to the existence of functions [Quine, by Linsky,B] |
| 18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
| 21705 | Reducibility says any impredicative function has an appropriate predicative replacement [Linsky,B] |
| 17900 | The Axiom of Reducibility made impredicative definitions possible [George/Velleman] |