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.