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    The universe can be finite and unbounded at the same time... — Carmelics
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    Home/Modality & Possibility
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    The universe can be finite and unbounded at the same time, refuting the conflation of unboundedness with infinitude.

    Modality & PossibilityTruth & Knowledge
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    2 reasons for
    1 reason against

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Kant's Antinomies reveal that intuitions about spatial boundlessness do not logically entail infinite magnitude, as the regress of conditions is epistemic, not ontological.
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    • 2.Poincaré's conventionalism establishes that geometric properties like finiteness are underdetermined by experience, so unboundedness is a structural feature independent of metric size.
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    • 3.A 3-sphere, like its 2D analogue the ordinary sphere, permits indefinite travel without boundary while possessing finite volume, making finite-yet-unbounded space formally coherent.
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    Reason for 2 of 2
    ?
    • 1.Aristotle distinguished 'potential infinity' from 'actual infinity', and unboundedness corresponds to the former—traversability without end—while infinitude requires the latter, actual inexhaustible magnitude.
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    • 2.Modern cosmological models (e.g., closed FLRW spacetimes) instantiate finite total volume with no spatial boundary, confirming the distinction is physically realizable and not merely formal.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Riemann's geometric model allows for spaces that are unbounded (no edges or boundaries) yet finite in total extent.
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    • 2.If space has constant positive curvature, all geodesics starting from a given surface-element produce a closed, finite surface analogous to a sphere in three dimensions.
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    • 3.The unboundedness of space is an empirical certainty, but infinite extent does not follow from unboundedness alone.
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    Related

    A 3-sphere, like its 2D analogue the ordinary sphere, permits indefinite travel ...Aristotle distinguished 'potential infinity' from 'actual infinity', and unbound...If space has constant positive curvature, all geodesics starting from a given su...Kant's Antinomies reveal that intuitions about spatial boundlessness do not logi...
    +4 moreShow less
    Modern cosmological models (e.g., closed FLRW spacetimes) instantiate finite tot...Poincaré's conventionalism establishes that geometric properties like finiteness...Riemann's geometric model allows for spaces that are unbounded (no edges or boun...The unboundedness of space is an empirical certainty, but infinite extent does n...

    Similar

    The cosmos is spatially unbounded (and thus infinite).82%Therefore the universe of NF cannot be finite82%If the universe of NF were finite, it could be well-ordered80%Therefore the world (the totality of things and events in space and ti...80%

    Source

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    SEP: infinity
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    Archytas’s argument (in section 1 above), which conflated unboundedness with infinitude, could finally be put to rest. Riemann’s model allows for the universe to be finite and unbounded at the same time. In 1854 he wrote: “The unboundedness of space possesses in this way a greater empirical certainty than any external experience. But its infinite extent by no means follows from this; on the other hand if we assume independence of bodies from position, and therefore ascribe to space constant c
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    Details

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