more from B Russell/AN Whitehead

### Single Idea 8746

#### [catalogued under 6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism]

Full Idea

Russell insisted on the vicious circle principle, and thus rejected impredicative definitions, which resulted in an unwieldy ramified type theory, with the ad hoc axiom of reducibility. Ramsey's simpler theory was impredicative and avoided the axiom.

Clarification

See Idea 8730 for impredicative definitions

Gist of Idea

To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it

Source

report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Thinking About Mathematics 5.2

Book Reference

Shapiro,Stewart: 'Thinking About Mathematics' [OUP 2000], p.127

A Reaction

Nowadays the theory of types seems to have been given up, possibly because it has no real attraction if it lacks the strict character which Russell aspired to.

Related Idea

Idea 8730
'Impredicative' definitions refer to the thing being described **[Shapiro]**