Full Idea
The Peano Axioms are logical consequences of a statement constituting the core of an explanation of the notion of cardinal number. The infinity of cardinal numbers emerges as a consequence of the way cardinal number is explained.
Gist of Idea
The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals
Source
Crispin Wright (Frege's Concept of Numbers as Objects [1983], 4.xix)
Book Reference
Wright,Crispin: 'Frege's Conception of Numbers' [Scots Philosophical Monographs 1983], p.168
A Reaction
This, along with Idea 13896, nicely summarises the neo-logicist project. I tend to favour a strategy which starts from ordering, rather than identities (1-1), but an attraction is that this approach is closer to counting objects in its basics.
Related Ideas
Idea 13896 The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes [Wright,C]
Idea 17312 It is more explanatory if you show how a number is constructed from basic entities and relations [Koslicki]