more from this thinker     |     more from this text

Single Idea 17900

[filed under theme 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility ]

Full Idea

The Axiom of Reducibility ...had the effect of making impredicative definitions possible.

Clarification

Impredicative definitions introduce nothing new

Gist of Idea

The Axiom of Reducibility made impredicative definitions possible

Source

A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)

Book Ref

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.47

The 10 ideas with the same theme [outdated axiom saying functions reduce to basics]:

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]