more from A.C. Grayling

Single Idea 6408

[catalogued under 6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism]

Full Idea

In order to deduce the theorems of mathematics from purely logical axioms, Russell had to add three new axioms to those of standards logic, which were: the axiom of infinity, the axiom of choice, and the axiom of reducibility.

Gist of Idea

Russell needed three extra axioms to reduce maths to logic: infinity, choice and reducibility


A.C. Grayling (Russell [1996], Ch.2)

Book Reference

Grayling,A.C.: 'Russell' [OUP 1996], p.31

A Reaction

The third one was adopted to avoid his 'barber' paradox, but many thinkers do not accept it. The interesting question is why anyone would 'accept' or 'reject' an axiom.