more from John Mayberry

### Single Idea 17792

#### [catalogued under 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic]

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