Single Idea 14131

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers]

Full Idea

Dedekind's ordinals are not essentially either ordinals or cardinals, but the members of any progression whatever.

Gist of Idea

Dedekind's ordinals are just members of any progression whatever

Source

report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - The Principles of Mathematics §243

Book Reference

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


A Reaction

This is part of Russell's objection to Dedekind's structuralism. The question is always why these beautiful structures should actually be considered as numbers. I say, unlike Russell, that the connection to counting is crucial.