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    Carmelics

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    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that Potential infinity (as Aristotle distinguished from actual infinity) permits only endless progression, not completed totalities amenable to bijection.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Cantor's transfinite mathematics successfully applies bijection to infinite sets without requiring completion, contradicting the claim's necessity.
      ?

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    • 2.Potential infinity itself presupposes a complete infinite totality—the set of all possible steps—making the distinction less fundamental than claimed.
      ?

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    • 3.Modern analysis treats convergent infinite series as determinate wholes; their amenability to bijection shows completed infinities are coherent mathematically.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Potential infinity describes processes that never terminate, like counting: we can always add one more, but never finish the totality.
      ?

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    • 2.Bijection requires comparing complete sets as finished wholes. Endless progressions lack the closure necessary for such comparison.
      ?

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    • 3.Aristotle's distinction preserves mathematical rigor by avoiding paradoxes arising from treating unfinished processes as completed objects.
      ?

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