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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
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    Inverse View

    It is not the case that In ZF and ZFC, the totality of transfinite cardinal numbers does not qualify as a set having a definite cardinal number of members.

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Cantor himself distinguished between 'consistent multiplicities' (sets) and 'inconsistent multiplicities' (absolute infinities), treating the latter as mathematically real but beyond formal set membership.
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      Think about whether this reason is strong or weak

    • 2.The claim conflates a formal ZF/ZFC limitation with a metaphysical impossibility, when Cantor's absolute infinite (Ω) was intended as a positive theological-mathematical concept, not merely a prohibited construction.
      ?

      Think about whether this reason is strong or weak

    • 3.A system's inability to assign a cardinal to a totality within its own axioms does not entail that the totality lacks a determinate size in any stronger ontological sense.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Alternative foundational systems such as von Neumann–Bernays–Gödel (NBG) set theory formally accommodate proper classes, including the class of all cardinals, as legitimate mathematical objects with determinate extensions.
      ?

      Think about whether this reason is strong or weak

    • 2.If the claim's force depends specifically on ZF/ZFC axiomatics, it is a contingent artifact of one foundational choice rather than a necessary truth about cardinality itself, undermining its use in broader theological arguments about divine power.
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      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Such a set would be too large.
      ?

      Think about whether this reason is strong or weak

    • 2.Were such a set to exist, paradoxical consequences would ensue akin to Russell's paradox.
      ?

      Think about whether this reason is strong or weak

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