A realist about properties can straightforwardly extend first-order quantification to include predicate positions, as in '∃P P(x)', thereby securing commitment to universals on purely Quinean grounds.
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Realist (about properties)(as used in metaphysics)
Someone who believes that properties—like redness or hardness—actually exist as real things in the world, not just as ideas in our heads.
first-order quantification(Cited as a motivation for using reification operators instead of higher-type Montagovian semantics)
Quantification ranging only over individuals, as opposed to higher-order quantification which ranges over predicates or functions of higher types
properties(Contrasted with substances as ontologically dependent entities.)
Entities that depend for their existence on substances, being properties of individual objects.
universals(Debated in Lefèvre's Disceptatio de universali between two students of Chrysippus's academy)
Either what particular classes of things share, or what those who reason say they share (decided by convention)
∃P P(x)(as used in logic and metaphysics)
A logical formula meaning 'there exists some property P such that x has that property'—the symbol ∃ means 'there exists' and P(x) means 'x has property P'.