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    Hellman's modal structuralism shows set-theoretic truths ... — Carmelics
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    Challenges→Claims about sets are claims about objects of a different kind from ordinary physical objects

    Hellman's modal structuralism shows set-theoretic truths express possibilities about structural relations, not truths about independently existing abstract objects.

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    Reasons For

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    Reason for
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    • 1.Modal structuralism avoids the epistemological problem of how we access causally inert abstract objects.
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    • 2.Set theory's applicability to physical structures suggests it describes possibilities, not independent entities.
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    • 3.Modal language ('could be', 'necessarily') better captures what mathematicians actually express than realism.
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    Reasons Against

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    Reason against
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    • 1.Modal structuralism must explain what grounds possibility claims if not actual abstract structures themselves.
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    • 2.Set-theoretic theorems prove specific facts (e.g., Cantor's diagonal argument), not merely structural possibilities.
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    • 3.Rejecting abstract objects leaves unclear how modal claims escape being arbitrary stipulations about 'possibilities'.
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    Connections

    2 topics

    Modality & Possibility1 linkedPhilosophy of Language1 linked

    Related

    Claims about sets are claims about objects of a different kind from ordinary phy...Modal language ('could be', 'necessarily') better captures what mathematicians a...Modal structuralism avoids the epistemological problem of how we access causally...Modal structuralism must explain what grounds possibility claims if not actual a...
    +3 moreShow less
    Rejecting abstract objects leaves unclear how modal claims escape being arbitrar...Set theory's applicability to physical structures suggests it describes possibil...Set-theoretic theorems prove specific facts (e.g., Cantor's diagonal argument), ...

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    2 (1 for, 1 against)
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