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Full Idea
Permitting quantification into predicate position and adding second-order variables leads to second-order logic.
Gist of Idea
Second-order logic needs second-order variables and quantification into predicate position
Source
Joseph Melia (Modality [2003], Ch.2)
Book Ref
Melia,Joseph: 'Modality' [Acumen 2003], p.40
A Reaction
Often expressed by saying that we now quantify over predicates and relations, rather than just objects. Depends on your metaphysical commitments.