Full Idea
Wright proposed removing Frege's basic law V (which led to paradox), replacing it with Frege's 'number principle' (identity of numbers is one-to-one correspondence). The new system is formally consistent, and the Peano axioms can be derived from it.
Clarification
See Idea 5897 for a simplified summary of Peano
Gist of Idea
Frege has a good system if his 'number principle' replaces his basic law V
Source
report of Crispin Wright (Frege's Concept of Numbers as Objects [1983]) by Michèle Friend - Introducing the Philosophy of Mathematics 3.7
Book Reference
Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.71
A Reaction
The 'number principle' is also called 'Hume's principle'. This idea of Wright's resurrected the project of logicism. The jury is ought again... Frege himself questioned whether the number principle was a part of logic, which would be bad for 'logicism'.
Related Idea
Idea 5897 0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Peano, by Flew]