### Single Idea 13428

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

Full Idea

The Axiom of Reducibility asserted that to every non-elementary function there is an equivalent elementary function [note: two functions are equivalent when the same arguments render them both true or both false].

Gist of Idea

Reducibility: to every non-elementary function there is an equivalent elementary function

Source

Frank P. Ramsey (The Foundations of Mathematics [1925], §2)

Book Reference

Ramsey,Frank: 'Philosophical Papers', ed/tr. Mellor,D.H. [CUP 1990], p.191

A Reaction

Ramsey in the business of showing that this axiom from Russell and Whitehead is not needed. He says that the axiom seems to be needed for induction and for Dedekind cuts. Since the cuts rest on it, and it is weak, Ramsey says it must go.