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    The substantivalist can adopt sophisticated versions that... — Carmelics
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    Challenges→Separating space-time structures into manifold and metric opens up problems for determinism beyond the hole argument

    The substantivalist can adopt sophisticated versions that block indeterminism without abandoning the manifold-metric separation, as Hoefer and Maudlin argue.

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    Reasons For

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    Reason for
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    • 1.Separating manifold from metric allows substantivalists to preserve spacetime's causal powers while avoiding privileging particular coordinate systems.
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    • 2.Sophisticated versions can impose symmetry constraints on metric evolution that eliminate indeterministic branching without reducing spacetime to relationalism.
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    • 3.This approach maintains substantivalism's explanatory advantage: spacetime itself grounds facts about spatial-temporal relations and causal structure.
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    Reasons Against

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    Reason against
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    • 1.If the manifold lacks intrinsic structure, imposing deterministic constraints on metrics appears ad hoc—equivalent to positing hidden variables elsewhere.
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    • 2.The manifold-metric separation risks making spacetime metaphysically redundant if metric alone determines all physical facts and causal relations.
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    Free Will & Foreknowledge1 linked

    Related

    If the manifold lacks intrinsic structure, imposing deterministic constraints on...Separating manifold from metric allows substantivalists to preserve spacetime's ...Separating space-time structures into manifold and metric opens up problems for ...Sophisticated versions can impose symmetry constraints on metric evolution that ...
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    The manifold-metric separation risks making spacetime metaphysically redundant i...This approach maintains substantivalism's explanatory advantage: spacetime itsel...

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