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    On a relational account, comparative similarity among len... — Carmelics
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    Challenges→Determinate similarity and comparability among lengths is explained by Armstrong's partial identity account.

    On a relational account, comparative similarity among lengths is grounded in the ordered structure of real numbers, not partial identity of universals.

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    Reasons For

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    • 1.Real numbers possess a complete ordering that makes comparative claims determinate; universals lack this formal structure.
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    • 2.Length comparisons require precise ratios (e.g., 2:1), which naturally map to numerical relations, not shared properties.
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    • 3.Partial identity of universals cannot explain why lengths form a transitive, asymmetric ordering relation.
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    Reasons Against

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    • 1.Grounding similarity in real numbers merely relocates the problem: why do lengths *correspond* to these abstract numbers?
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    • 2.Universals can encode ordering relations directly; relational structure doesn't require numerical reduction.
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    • 3.The relational account struggles to explain why only certain orderings (not arbitrary ones) ground physical similarity.
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    Related

    Determinate similarity and comparability among lengths is explained by Armstrong...Grounding similarity in real numbers merely relocates the problem: why do length...Length comparisons require precise ratios (e.g., 2:1), which naturally map to nu...Partial identity of universals cannot explain why lengths form a transitive, asy...
    +3 moreShow less
    Real numbers possess a complete ordering that makes comparative claims determina...The relational account struggles to explain why only certain orderings (not arbi...Universals can encode ordering relations directly; relational structure doesn't ...

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