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    Concrete infinities are metaphysically impossible — Carmelics
    Home/Natural Theology
    HistoryEditSee Inverse

    Concrete infinities are metaphysically impossible

    Natural Theology
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
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    • 1.Mathematical possibility does not entail metaphysical possibility
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    • 2.Concrete infinities violate metaphysically necessary truths concerning causal powers
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Cantorian set theory demonstrates that actually infinite collections are logically and mathematically coherent without internal contradiction.
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    • 2.The burden of proof falls on those claiming metaphysical impossibility to identify which specific metaphysical necessity concrete infinities violate.
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    • 3.Hilbert's Hotel paradoxes show only that infinite collections behave counter-intuitively, not that they are metaphysically impossible.
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    Reason against 2 of 2
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    • 1.Aristotle's distinction between potential and actual infinity, rehabilitated by Graham Oppy, allows that denying actual infinities requires independent metaphysical argument beyond mathematical intuition.
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    • 2.Craig's inference from 'abstractly impossible to visualize' to 'metaphysically impossible' conflates epistemic limitations with ontological constraints on reality.
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    Natural Theology

    Related

    Aristotle's distinction between potential and actual infinity, rehabilitated by ...Cantorian set theory demonstrates that actually infinite collections are logical...Concrete infinities violate metaphysically necessary truths concerning causal po...Craig's inference from 'abstractly impossible to visualize' to 'metaphysically i...
    +3 moreShow less
    Hilbert's Hotel paradoxes show only that infinite collections behave counter-int...Mathematical possibility does not entail metaphysical possibilityThe burden of proof falls on those claiming metaphysical impossibility to identi...

    Similar

    Concrete infinities violate metaphysically necessary truths concerning...86%The absurdities resulting from attempting to apply basic arithmetical ...84%An actual infinity of entities, whether spiritual or material, is impo...81%An ordered, actual infinity is impossible (Aristotelian principle)78%

    Source

    AI-extracted1/3 agreementValid
    SEP: cosmological-argument
    View source passageHide passage
    Loke (2017: 55–61; see Craig and Sinclair, 2009: 105–6) replies to the above objections by arguing that what is mathematically possible is not always metaphysically possible. For example, the quadratic equation \(x^2=4\) can have two mathematically consistent results for \(x\): 2 or −2, but if the question is “how many people carried the box home”, the answer cannot be −2, for in the concrete world it is metaphysically impossible that −2 people carry a box home. Thus, the conclusion of 2 people
    Extraction notes

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

    Details

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