Full Idea
The mathematically significant properties and relations of natural numbers arise from the successor function that orders them; the natural numbers are identified simply as the objects that answer to this basic function.
Gist of Idea
Numbers are identified by their main properties and relations, involving the successor function
Source
Fraser MacBride (Structuralism Reconsidered [2007], §1)
Book Reference
'Oxf Handbk of Philosophy of Maths and Logic', ed/tr. Shapiro,Stewart [OUP 2007], p.563
A Reaction
So Julius Caesar would be a number if he was the successor of Pompey the Great? I would have thought that counting should be mentioned - cardinality as well as ordinality. Presumably Peano's Axioms are being referred to.