Full Idea
Second-order logic is a powerful tool of definition: by means of it alone we can capture mathematical structure up to isomorphism using simple axiom systems.
Gist of Idea
Only second-order logic can capture mathematical structure up to isomorphism
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