Full Idea
Brand higher-order logic as unintelligible if you will, but don't conflate it with set theory.
Gist of Idea
Higher-order logic may be unintelligible, but it isn't set theory
Source
Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131)
Book Reference
-: 'Journal of Philosophy' [-], p.131
A Reaction
[he gives Boolos 1975 as a further reference] This is simply a corrective, because the conflation of second-order logic with set theory is an idea floating around in the literature.