### Single Idea 21705

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

Full Idea

The Axiom of Reducibility avoids impredicativity, by asserting that for any predicate of given arguments defined by quantifying over higher-order functions or classes, there is another co-extensive but predicative function of the same type of arguments.

Gist of Idea

Reducibility says any impredicative function has an appropriate predicative replacement

Source

Bernard Linsky (Russell's Metaphysical Logic [1999], 1)

Book Reference

Linsky,Bernard: 'Russell's Metaphysical Logic' [CSLI 1999], p.4

A Reaction

Eventually the axiom seemed too arbitrary, and was dropped. Linsky's book explores it.

Related Idea

Idea 21704
'Impredictative' definitions fix a class in terms of the greater class to which it belongs **[Linsky,B]**