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    An actual infinity of entities, whether spiritual or mate... — Carmelics
    Home/Natural Theology
    HistoryEditSee Inverse

    An actual infinity of entities, whether spiritual or material, is impossible.

    Modality & Possibility
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    1 reason for
    2 reasons against

    Reasons For

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    Reason for
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    • Godfrey is convinced that no actual infinity of any kind of entity can exist.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Cantor's transfinite set theory demonstrates that actual infinities form a coherent, consistent mathematical system without logical contradiction.
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    • 2.If actual infinities are logically coherent and instantiated in abstract mathematical reality, the burden of proof shifts to those claiming their metaphysical impossibility.
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    • 3.Aristotle's distinction between potential and actual infinity, while influential, was rejected by Cantor and subsequent mathematicians as a contingent conceptual limitation, not a necessary truth.
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    Reason against 2 of 2
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    • 1.Spinoza and later absolute idealists argued that God or the Absolute just is an actually infinite substance, making actual infinity not only possible but necessary.
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    • 2.If theism requires a God with infinite attributes or knowledge of infinite propositions, denying actual infinity generates a contradiction within natural theology itself.
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    Topics

    Natural TheologyModality & Possibility

    Related

    Aristotle's distinction between potential and actual infinity, while influential...Cantor's transfinite set theory demonstrates that actual infinities form a coher...Godfrey is convinced that no actual infinity of any kind of entity can exist.If actual infinities are logically coherent and instantiated in abstract mathema...
    +2 moreShow less
    If theism requires a God with infinite attributes or knowledge of infinite propo...Spinoza and later absolute idealists argued that God or the Absolute just is an ...

    Similar

    Godfrey is convinced that no actual infinity of any kind of entity can...86%An ordered, actual infinity is impossible (Aristotelian principle)82%Concrete infinities are metaphysically impossible81%There can be no such thing as an actual infinite.80%

    Source

    AI-extracted1/3 agreementValid
    SEP: godfrey
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    Godfrey comments that this objection can also be formulated more forcefully in terms of human souls, i.e., the actual infinity of human souls that would have resulted from an eternal world eternally populated by human beings with immortal souls. Aquinas had considered this form of the objection in his De aeternitate mundi, and had noted that it has not yet been demonstrated that God could not produce an actual infinity of spiritual beings. Godfrey does not adopt this solution, presumably because
    Extraction notes

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

    Details

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