The theoretical work done by positing non-existent abstract objects in noneism—grounding mathematical truth, enabling reference—is identical to the work abstract objects do in platonism.

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Mathematical truth(as used in philosophy of science): A statement that is logically correct within a mathematical system, regardless of whether it describes anything real.
Platonism(Ontology of mathematics): The position that abstract mathematical entities exist independently, supported here by the claim that our best scientific theories quantify over such entities.
abstract objects(The target of Platonist ontological claims): Objects referred to by singular terms in literally true sentences that cannot be paraphrased away; includes mathematical objects (e.g., numbers), propositions, properties, relations, sentence types, possible worlds, logical objects, and fictional objects.
grounding(Drawn from contemporary metaphysics; proposed as potentially applicable to understanding the foundations of legality.): A metaphysical relation in which some entities or facts are more foundational than others, providing a hierarchical structure of the world.

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