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