Full Idea
The metatheory of second-order logic is hopelessly set-theoretic, and the notion of second-order validity possesses many if not all of the epistemic debilities of the notion of set-theoretic truth.
Gist of Idea
Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems
Source
George Boolos (On Second-Order Logic [1975], p.45)
Book Reference
Boolos,George: 'Logic, Logic and Logic' [Harvard 1999], p.518
A Reaction
Epistemic problems arise when a logic is incomplete, because some of the so-called truths cannot be proved, and hence may be unreachable. This idea indicates Boolos's motivation for developing a theory of plural quantification.