Single Idea 14132

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

Full Idea

The properties of number must be capable of proof without appeal to the general properties of progressions, since cardinals can be independently defined, and must be seen in a progression before theories of progression are applied to them.

Gist of Idea

Properties of numbers don't rely on progressions, so cardinals may be more basic

Source

Bertrand Russell (The Principles of Mathematics [1903], §243)

Book Reference

Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.251


A Reaction

Russell says there is no logical priority between ordinals and cardinals, but it is simpler to start an account with cardinals.