Full Idea
It might be argued that any proof by induction is revealing the explanation of the theorem, namely, that it holds by virtue of the structure of the natural numbers.
Gist of Idea
If inductive proofs hold because of the structure of natural numbers, they may explain theorems
Source
Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.1)
Book Reference
Colyvan,Mark: 'An Introduction to the Philosophy of Mathematics' [CUP 2012], p.82
A Reaction
This is because induction characterises the natural numbers, in the Peano Axioms.