Full Idea
If the logic of arithmetic doesn't have second-order quantifiers to range over properties of numbers, how can it handle induction?
Gist of Idea
The logic of arithmetic must quantify over properties of numbers to handle induction
Source
Peter Smith (Intro to Gödel's Theorems [2007], 10.1)
Book Reference
Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.71