If non-existent objects genuinely exemplify properties, they must be quantified over, making them exist in any robust ontological sense, thereby undermining the actualist/possibilist distinction the claim relies on.

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Actualist/possibilist distinction(as used in metaphysics): The disagreement between philosophers about whether only real things matter in philosophy, or whether possible-but-not-real things also count.
Exemplify properties(as used in metaphysics): To have or display certain characteristics or qualities—for example, a unicorn exemplifies the property of 'having a horn.'
Ontological: "Ontological" refers to questions about what actually exists or is real. It's concerned with the fundamental nature of being—asking "What kinds of things are there?" rather than "How do we know about them?" For example, an ontological question might be whether numbers, ideas, or God actually exist as real things, or if they're just human inventions.
Quantified over(as used in logic and philosophy of language): When logicians count something as part of what exists or matters when making logical statements (like saying 'there are X things').

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