If nominalists can give a complete account of predicate-sharing through physical or linguistic structure alone, the Platonist explanatory appeal to universals becomes redundant rather than informative.

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Platonist(describing a philosophy of mathematics): A philosopher who believes that abstract things like numbers and mathematical truths exist in a real, independent way—not just as ideas in people's heads, but as actual things in a special realm of their own.
explanatory appeal(as describing how Platonists explain predicate-sharing): When someone uses a concept or idea to explain why something is true or how something works.
nominalists(as the subject of the statement): Philosophers who believe that only concrete, individual things exist (like this specific red apple), and that abstract concepts like 'redness' or 'justice' aren't real things—they're just words we use to group similar objects together.
predicate-sharing(as the phenomenon being explained): The fact that many different things can have the same quality or description—like how multiple objects can all be 'red' or how multiple animals can all be 'dogs.'

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