Full Idea
Full second-order logic has all the expressive power needed to do mathematics, but has an unworkable model theory.
Gist of Idea
Second-order logic has the expressive power for mathematics, but an unworkable model theory
Source
Stewart Shapiro (Higher-Order Logic [2001], 2.1)
Book Reference
'Blackwell Guide to Philosophical Logic', ed/tr. Goble,Lou [Blackwell 2001], p.34
A Reaction
[he credits Cowles for this remark] Having an unworkable model theory sounds pretty serious to me, as I'm not inclined to be interested in languages which don't produce models of some sort. Surely models are the whole point?