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    Maximality alone does not guarantee hole freeness in the ... — Carmelics
    Home/Free Will & Foreknowledge
    HistoryEditSee Inverse

    Maximality alone does not guarantee hole freeness in the sense required to prevent causal determinism from failing prior to any consideration of time machines.

    CausationFree Will & Foreknowledge
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
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    • 1.Maximality rules out surgically mutilated spacetimes.
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    • 2.Maximality does not rule out all spacetimes that lack hole freeness in the technically defined sense.
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    • 3.Hole freeness requires that the future domain of dependence of a spacelike hypersurface cannot be isometrically embedded as a proper subset of the future domain of dependence of its image in another spacetime.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Geroch (1977) established that maximal spacetimes can still admit naked singularities that disrupt global hyperbolicity without violating maximality conditions.
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    • 2.If maximality already excludes the most physically relevant pathological spacetimes, the residual cases lacking hole freeness are physically unrealizable edge cases that do not threaten causal determinism in any robust sense.
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    • 3.A condition that fails only in physically degenerate or measure-zero cases cannot be said to genuinely undermine causal determinism as a foundational physical principle.
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    Reason against 2 of 2
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    • 1.Earman and Norton's hole argument demonstrates that diffeomorphic equivalence classes, not individual spacetime models, are the proper locus of physical content in general relativity.
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    • 2.If physically meaningful spacetime structure is invariant under the relevant isometric embeddings, then the technical failure of hole freeness within a maximality framework reflects a representational artifact rather than a genuine breakdown of determinism.
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    Free Will & ForeknowledgeCausation

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    Modality & Possibility3 linked

    Related

    A condition that fails only in physically degenerate or measure-zero cases canno...Earman and Norton's hole argument demonstrates that diffeomorphic equivalence cl...Geroch (1977) established that maximal spacetimes can still admit naked singular...Hole freeness requires that the future domain of dependence of a spacelike hyper...
    +4 moreShow less
    If maximality already excludes the most physically relevant pathological spaceti...If physically meaningful spacetime structure is invariant under the relevant iso...Maximality does not rule out all spacetimes that lack hole freeness in the techn...Maximality rules out surgically mutilated spacetimes.

    Similar

    Without hole freeness, determinism can fail even in otherwise well-beh...88%Hole freeness precludes an important mode of failure of causal determi...86%Maximality does not rule out all spacetimes that lack hole freeness in...84%The gap between maximality and hole freeness gives the would-be time m...82%

    Source

    AI-extracted1/3 agreementValid
    SEP: time-machine
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    The would-be time machine operator need not capitulate in the face of Krasnikov’s theorem. Recall that the main difficulty in specifying the conditions for the successful operation of Thornian time machines traces to the fact that the standard form of causal determinism does not apply to the production of CTCs. But causal determinism can fail for reasons that have nothing to do with CTCs or other acausal features of relativistic spacetimes, and it seems only fair to ensure that these modes of fa
    Extraction notes

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

    Details

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