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    If sets exist only where physical objects are located, th... — Carmelics
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    Challenges→Maddy's early immanent realism can account for the massive infinities in mathematics.

    If sets exist only where physical objects are located, the transfinite hierarchy beyond beth-omega lacks any spatiotemporal grounding, undermining the account.

    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
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    Reasons For

    1 perspective
    Reason for
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    • 1.Physical objects instantiate only finite collections; transfinite sets require grounding beyond matter.
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    • 2.Sets lacking spatiotemporal location cannot causally influence physical reality or justify their necessity.
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    • 3.Mathematical ontology should satisfy parsimony; abstract entities without physical correlates multiply entities unnecessarily.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Abstract objects need not be spatiotemporally located; numbers exist independently of physical instantiation.
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    • 2.Beth-omega's existence follows from set-theoretic axioms; grounding requires only logical consistency, not physical location.
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    • 3.Denying transfinite sets undermines mathematics itself; physics relies on real analysis presupposing uncountable infinities.
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    Related

    Abstract objects need not be spatiotemporally located; numbers exist independent...Beth-omega's existence follows from set-theoretic axioms; grounding requires onl...Denying transfinite sets undermines mathematics itself; physics relies on real a...Maddy's early immanent realism can account for the massive infinities in mathema...
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    Mathematical ontology should satisfy parsimony; abstract entities without physic...Physical objects instantiate only finite collections; transfinite sets require g...Sets lacking spatiotemporal location cannot causally influence physical reality ...

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    Perspectives
    2 (1 for, 1 against)
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