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    Carmelics

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    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that The totality of all ordinal numbers cannot itself form a set, as shown by the Burali-Forti paradox of 1897.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.The paradox only arises from informal reasoning; formal ZFC proves consistent without assuming all ordinals form a set.
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    • 2.Category theory and other frameworks handle collections of ordinals coherently without requiring the Burali-Forti argument.
      ?

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    • 3.The claim conflates a limitation of set theory axioms with a metaphysical truth about what collections 'can' be.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.If all ordinals formed a set, that set would be an ordinal larger than itself, creating logical contradiction.
      ?

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    • 2.ZFC set theory avoids this paradox by distinguishing sets from proper classes, treating ordinals as the latter.
      ?

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    • 3.Unrestricted comprehension leads to contradiction; some mathematical collections cannot be sets without inconsistency.
      ?

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