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    The argument illicitly assumes that operations governing ... — Carmelics
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    Challenges→Although actual infinites can have an ideal existence, they cannot really exist.

    The argument illicitly assumes that operations governing finite collections, such as subtraction and part-whole relations, must govern infinite collections in the same way.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Cantor's set theory reveals infinite sets lack size-comparison properties finite sets have, e.g., proper subsets equal the whole.
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    • 2.Applying finite arithmetic to infinities generates contradictions, as seen in Galileo's paradox and divergent infinite series.
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    • 3.Mathematical rigor requires explicitly defining operations for new domains rather than assuming inherited finite-domain rules apply.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Mathematics successfully extends finite operations to infinities through careful definition (limits, cardinality), showing transfer is possible.
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    • 2.The charge of 'illicit assumption' requires evidence the arguer failed to define infinite operations, not mere use of finite analogies.
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    • 3.Some finite properties do transfer validly to infinities; rejecting all transfers risks abandoning useful mathematical continuities.
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    Natural Theology1 linked

    Related

    Although actual infinites can have an ideal existence, they cannot really exist.Applying finite arithmetic to infinities generates contradictions, as seen in Ga...Cantor's set theory reveals infinite sets lack size-comparison properties finite...Mathematical rigor requires explicitly defining operations for new domains rathe...
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    Mathematics successfully extends finite operations to infinities through careful...Some finite properties do transfer validly to infinities; rejecting all transfer...The charge of 'illicit assumption' requires evidence the arguer failed to define...

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    claim
    Perspectives
    2 (1 for, 1 against)
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