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    Space must be infinite — Carmelics
    Home/Modality & Possibility
    HistoryEditSee Inverse

    Space must be infinite

    Modality & Possibility
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Any finite limit to space would be arbitrary
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    • 2.Arbitrary limits violate the principle of sufficient reason
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Kant argued in the First Antinomy that 'infinite space' is not a coherent object of cognition but an illegitimate extension of regulative ideas.
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    • 2.The PSR applied to spatial extension presupposes space is a substance with determinate properties, which relationalists like Leibniz deny.
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    • 3.Without substantivalism about space, the demand for a sufficient reason for spatial limits loses its referent entirely.
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    Reason against 2 of 2
    ?
    • 1.A finite space need not have a boundary or edge; it can be unbounded yet finite, as in Riemannian curved geometry.
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    • 2.If finite space is topologically closed (like a 3-sphere), there is no privileged limit requiring a sufficient reason.
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    Topics

    Modality & Possibility

    Connections

    2 linked claims · 3 topics

    Natural Theology2 linkedTruth & Knowledge1 linkedDivine Attributes1 linked
    God is infiniteKnowledge is infinite

    Related

    A finite space need not have a boundary or edge; it can be unbounded yet finite,...Any finite limit to space would be arbitraryArbitrary limits violate the principle of sufficient reasonGod is infinite
    +5 moreShow less
    If finite space is topologically closed (like a 3-sphere), there is no privilege...Kant argued in the First Antinomy that 'infinite space' is not a coherent object...Knowledge is infiniteThe PSR applied to spatial extension presupposes space is a substance with deter...

    Source

    AI-extracted1/3 agreementValid
    SEP: clarke
    View source passageHide passage
    Clarke believed that space is necessarily infinite because “to set bounds to space, is to suppose it bounded by something which itself takes up space” or else that “it is bounded by nothing, and then the idea of that nothing will still be space,” and both suppositions are contradictory (D 115, W 2.753). Clarke apparently thought that what has a boundary must be bounded by something else. If so, the argument was not well taken because a sphere, for example, has a boundary which stems from its own
    Extraction notes

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

    Details

    Without substantivalism about space, the demand for a sufficient reason for spat...
    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit