more from B Russell/AN Whitehead

### Single Idea 8691

#### [catalogued under 6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory]

Full Idea

The Russell/Whitehead type theory reduces mathematics to a consistent founding discipline, but is criticised for not really being logic. They could not prove the existence of infinite sets, and introduced a non-logical 'axiom of reducibility'.

Gist of Idea

The Russell/Whitehead type theory was limited, and was not really logic

Source

comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Michèle Friend - Introducing the Philosophy of Mathematics 3.6

Book Reference

Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.70

A Reaction

To have reduced most of mathematics to a founding discipline sounds like quite an achievement, and its failure to be based in pure logic doesn't sound too bad. However, it seems to reduce some maths to just other maths.