Full Idea
Some authors argue that second-order logic (with standard semantics) is not logic at all, but is a rather obscure form of mathematics.
Gist of Idea
Some say that second-order logic is mathematics, not logic
Source
Stewart Shapiro (Higher-Order Logic [2001], 2.4)
Book Reference
'Blackwell Guide to Philosophical Logic', ed/tr. Goble,Lou [Blackwell 2001], p.50