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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
Source
A.C. Grayling (Russell [1996], Ch.2)
Book Ref
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.
| 6408 | Russell needed three extra axioms to reduce maths to logic: infinity, choice and reducibility [Grayling] |
| 6414 | Two propositions might seem self-evident, but contradict one another [Grayling] |