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    Potential infinity (as Aristotle distinguished from actua... — Carmelics
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    Challenges→The integers can be placed in a one-to-one correspondence with the natural numbers.

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

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    1 reason for
    1 reason against

    Reasons For

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    Reason for
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    • 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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    Reasons Against

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    Reason against
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    • 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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    Related

    Aristotle's distinction preserves mathematical rigor by avoiding paradoxes arisi...Bijection requires comparing complete sets as finished wholes. Endless progressi...Cantor's transfinite mathematics successfully applies bijection to infinite sets...Modern analysis treats convergent infinite series as determinate wholes; their a...
    +3 moreShow less
    Potential infinity describes processes that never terminate, like counting: we c...Potential infinity itself presupposes a complete infinite totality—the set of al...The integers can be placed in a one-to-one correspondence with the natural numbe...

    Details

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