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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 transfinite cardinal numbers is absolutely infinite in a sui generis non-arithmetical sense, rather than having a cardinal number of its own.

    ?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's own distinction between the 'Absolute Infinite' and transfinite cardinals relies on a theological notion (the Absolute as God's mind) that does not survive secularization.
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      Think about whether this reason is strong or weak

    • 2.Without theological grounding, the claim that the totality is 'sui generis' collapses into either a set-theoretic proper class or an ad hoc stipulation.
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      Think about whether this reason is strong or weak

    • 3.Modern set theories like ZFC and NBG handle the totality of cardinals via the proper class Ord without invoking a non-arithmetical 'absolute infinity' as a distinct metaphysical category.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
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    • 1.If 'absolutely infinite' means having no cardinal number, this is precisely what ZFC already says about proper classes, making the 'sui generis' qualifier redundant rather than explanatory.
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      Think about whether this reason is strong or weak

    • 2.Claiming the totality is non-arithmetical in a unique sense smuggles in an unexplained primitive that violates the principle of ontological parsimony (Ockham's razor) in mathematical ontology.
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      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
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    • 1.There is no largest transfinite cardinal number.
      ?

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    • 2.Although there are infinitely many transfinite cardinal numbers, there is no cardinal number of them.
      ?

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