more from John Mayberry

### Single Idea 17793

#### [catalogued under 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic]

Full Idea

If we did not know that the second-order axioms characterise the natural numbers up to isomorphism, we should have no reason to suppose, a priori, that first-order Peano Arithmetic should be complete.

Gist of Idea

It is only 2nd-order isomorphism which suggested first-order PA completeness

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