Full Idea
The natural-number structure is a pattern common to any system of objects that has a distinguished initial object and a successor relation that satisfies the induction principle
Gist of Idea
Natural numbers just need an initial object, successors, and an induction principle
Source
Stewart Shapiro (Philosophy of Mathematics [1997], Intro)
Book Reference
Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.5
A Reaction
If you started your number system with 5, and successors were only odd numbers, something would have gone wrong, so a bit more seems to be needed. How do we decided whether the initial object is 0, 1 or 2?