more from David Bostock

Single Idea 18127

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

Full Idea

The simple theory of types distinguishes sets into different 'levels', but this is quite different from the distinction into 'orders' which is imposed by the ramified theory.

Gist of Idea

Simple type theory has 'levels', but ramified type theory has 'orders'


David Bostock (Philosophy of Mathematics [2009], 8.1)

Book Reference

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.231

A Reaction

The ramified theory has both levels and orders (p.235). Russell's terminology is, apparently, inconsistent.