more from Peter Smith

### Single Idea 10619

#### [catalogued under 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic]

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?