more from A.George / D.J.Velleman

### Single Idea 17899

#### [catalogued under 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order]

Full Idea

The first-order version of the induction axiom is weaker than the second-order, because the latter applies to all concepts, but the first-order applies only to concepts definable by a formula in the first-order language of number theory.

Gist of Idea

Second-order induction is stronger as it covers all concepts, not just first-order definable ones

Source

A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7 n7)

Book Reference

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.195