more from Bertrand Russell

Single Idea 14129

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

Full Idea

Ordinals presuppose serial and one-one relations, whereas cardinals only presuppose one-one relations.

Gist of Idea

Ordinals presuppose two relations, where cardinals only presuppose one

Source

Bertrand Russell (The Principles of Mathematics [1903], §232)

Book Reference

Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.243


A Reaction

This seems to award the palm to the cardinals, for their greater logical simplicity, but I have already given the award to the ordinals in the previous idea, and I am not going back on that.

Related Idea

Idea 14128 Some claim priority for the ordinals over cardinals, but there is no logical priority between them [Russell]