The nominalist is unable to account for the common featur... — Carmelics

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The nominalist is unable to account for the common features of certain rearrangements that can only be explained by reference to a common mathematical structure.

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1.Hilary Putnam's indispensability argument shows mathematical structures appear in the best explanations of physical phenomena across multiple domains.
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2.Nominalist paraphrase strategies (Field 1980) cannot preserve the explanatory unity that identical mathematical structures provide across structurally isomorphic physical systems.
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3.When two distinct physical arrangements share identical symmetry properties, only appeal to a common abstract structure explains why the same invariants appear in both.
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