Full Idea
Quantifiers are second-order predicates.
Gist of Idea
Quantifiers are second-order predicates
Source
Stephen Read (Thinking About Logic [1995], Ch.5)
Book Reference
Read,Stephen: 'Thinking About Logic' [OUP 1995], p.125
A Reaction
[He calls this 'Frege's insight'] They seem to be second-order in Tarski's sense, that they are part of a metalanguage about the sentence, rather than being a part of the sentence.