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    Separating space-time structures into manifold and metric... — Carmelics
    Home/Free Will & Foreknowledge
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    Separating space-time structures into manifold and metric opens up problems for determinism beyond the hole argument

    Free Will & Foreknowledge
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.The separation of space-time into manifold and metric facilitates mathematical clarity
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    • 2.The Earman-Norton hole argument shows that this separation introduces indeterminism
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    • 3.Singularities represent additional and more extensive sources of indeterminism arising from the same separation
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.The substantivalist can adopt sophisticated versions that block indeterminism without abandoning the manifold-metric separation, as Hoefer and Maudlin argue.
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    • 2.Leibniz equivalence, which dissolves hole-type indeterminism by identifying diffeomorphic models, is compatible with retaining the manifold-metric distinction.
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    • 3.If indeterminism is eliminated at the level of physical equivalence classes, singularity-based problems require separate and independent justification beyond the hole argument.
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    Reason against 2 of 2
    ?
    • 1.Penrose's cosmic censorship conjecture, if true, would confine singularities behind event horizons, preventing them from generating observationally distinct indeterministic threats.
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    • 2.A problem that is empirically and causally quarantined from the observable universe does not constitute a genuine failure of determinism for the physical world as modeled.
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    Free Will & Foreknowledge

    Related

    A problem that is empirically and causally quarantined from the observable unive...If indeterminism is eliminated at the level of physical equivalence classes, sin...Leibniz equivalence, which dissolves hole-type indeterminism by identifying diff...Penrose's cosmic censorship conjecture, if true, would confine singularities beh...
    +4 moreShow less
    Singularities represent additional and more extensive sources of indeterminism a...The Earman-Norton hole argument shows that this separation introduces indetermin...The separation of space-time into manifold and metric facilitates mathematical c...The substantivalist can adopt sophisticated versions that block indeterminism wi...

    Similar

    Without hole freeness, determinism can fail even in otherwise well-beh...82%Maximality alone does not guarantee hole freeness in the sense require...78%The separation of space-time into manifold and metric facilitates math...76%Causal determinism can fail in relativistic spacetimes for reasons unr...72%

    Source

    AI-extracted1/3 agreementValid
    SEP: determinism-causal
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    The separation of space-time structures into manifold and metric (or connection) facilitates mathematical clarity in many ways, but also opens up Pandora’s box when it comes to determinism. The indeterminism of the Earman and Norton hole argument is only the tip of the iceberg; singularities make up much of the rest of the berg. In general terms, a singularity can be thought of as a “place where things go bad” in one way or another in the space-time model. For example, near the center of a Schwa
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit