more from David Bostock

Single Idea 18102

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers]

Full Idea

It is the usual procedure these days to identify a cardinal number with the earliest ordinal number that has that number of predecessors.

Gist of Idea

A cardinal is the earliest ordinal that has that number of predecessors


David Bostock (Philosophy of Mathematics [2009], 4.5)

Book Reference

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.111

A Reaction

This sounds circular, since you need to know the cardinal in order to decide which ordinal is the one you want, but, hey, what do I know?