Hellman's modal structuralism provides face-value readings of mathematical claims as truths about possible structures rather than abstract objects, satisfying the same data about speaker intentions.

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Face-value reading(in describing how we should interpret mathematical claims): Taking a statement at face value means understanding it in its most straightforward, literal sense without looking for hidden meanings.
Hellman(as the philosopher whose theory is being discussed): Geoffrey Hellman is a contemporary philosopher who developed a theory about how we should understand mathematics—specifically, he argues that mathematical statements are really claims about possible structures rather than claims about abstract objects that exist independently.
Modal structuralism(as used in metaphysics): A philosophical approach that explains what things are by describing their possible relationships and structures rather than their hidden essences.
Structuralism (in philosophy of mathematics)(in describing what mathematicians are really talking about): The view that mathematics is fundamentally about patterns and relationships between elements in systems, rather than about special abstract objects called numbers.

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