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    The Axiom of Limitation of Size, as formulated by von Neu... — Carmelics
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    Challenges→The Axiom of Limitation of Size implies the Axiom of Choice

    The Axiom of Limitation of Size, as formulated by von Neumann, is itself equivalent to Replacement plus Choice, making the implication circular.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Von Neumann's Limitation of Size directly entails Replacement: any class mapping to a set must be a set, which is Replacement's core content.
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    • 2.The circularity claim is justified because Replacement and Choice together suffice to derive Limitation of Size without additional axioms.
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    • 3.Historical development shows Limitation of Size was motivated by the same concerns—avoiding impredicativity—that justify Replacement independently.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Limitation of Size is a single, unified principle; Replacement+Choice are distinct axioms with separate justifications and logical independence.
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    • 2.Even if logically equivalent, axioms can be non-circular: one formulation may be conceptually fundamental while another is a derived consequence.
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    • 3.The equivalence doesn't show circularity in justification—von Neumann's principle provides independent motivation for accepting Replacement itself.
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    Related

    Even if logically equivalent, axioms can be non-circular: one formulation may be...Historical development shows Limitation of Size was motivated by the same concer...Limitation of Size is a single, unified principle; Replacement+Choice are distin...The Axiom of Limitation of Size implies the Axiom of Choice
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    The circularity claim is justified because Replacement and Choice together suffi...The equivalence doesn't show circularity in justification—von Neumann's principl...Von Neumann's Limitation of Size directly entails Replacement: any class mapping...

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    claim
    Perspectives
    2 (1 for, 1 against)
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