Full Idea
Dedekind's demonstrations nowhere - not even where he comes to cardinals - involve any property distinguishing numbers from other progressions.
Gist of Idea
Dedekind failed to distinguish the numbers from other progressions
Source
comment on Bertrand Russell (The Principles of Mathematics [1903], p.249) by Stewart Shapiro - Philosophy of Mathematics 5.4
Book Reference
Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.175
A Reaction
Shapiro notes that his sounds like Frege's Julius Caesar problem, of ensuring that your definition really does capture a number. Russell is objecting to mathematical structuralism.