Full Idea
We shall endeavour to see whether it is possible to follow through the strategy adumbrated in 'Grundlagen' for establishing the Peano Axioms without at any stage invoking classes.
Gist of Idea
The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes
Source
Crispin Wright (Frege's Concept of Numbers as Objects [1983], 4.xvi)
Book Reference
Wright,Crispin: 'Frege's Conception of Numbers' [Scots Philosophical Monographs 1983], p.131
A Reaction
The key idea of neo-logicism. If you can avoid classes entirely, then set theory paradoxes become irrelevant, and classes aren't logic. Philosophers now try to derive the Peano Axioms from all sorts of things. Wright admits infinity is a problem.
Related Idea
Idea 13899 The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals [Wright,C]