Full Idea
The sole theoretical interest of first-order Peano arithmetic derives from the fact that it is a first-order reduct of a categorical second-order theory. Its axioms can be proved incomplete only because the second-order theory is categorical.
Gist of Idea
1st-order PA is only interesting because of results which use 2nd-order PA
Source
John Mayberry (What Required for Foundation for Maths? [1994], p.412-1)
Book Reference
'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.412