Full Idea
The truths of arithmetic are just the true equations involving particular numbers, and universally quantified versions of such equations.
Gist of Idea
The truths of arithmetic are just true equations and their universally quantified versions
Source
Peter Smith (Intro to Gödel's Theorems [2007], 27.7)
Book Reference
Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.258
A Reaction
Must each equation be universally quantified? Why can't we just universally quantify over the whole system?