Full Idea
Quine assures us that if the specific mission of second-order logic is quantifying over properties, the task can readily be performed by first-order predicate logic, as in (Ex) x is a property, and (y) y has x.
Gist of Idea
Quine says that if second-order logic is to quantify over properties, that can be done in first-order predicate logic
Source
report of Willard Quine (works [1961]) by José A. Benardete - Metaphysics: the logical approach Ch.10
Book Reference
Benardete,José A.: 'Metaphysics: The Logical Approach' [OUP 1989], p.64