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    LoyalLoyalJusticeJustice
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    Any such assignment leads to contradiction. — Carmelics
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    Home/Modality & Possibility
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    Challenges→The infinity of the cardinals and of the ordinals cannot be measured by any cardinal or ordinal.

    Any such assignment leads to contradiction.

    Modality & PossibilityTruth & Knowledge
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    If the totality of cardinals were measured by a cardinal, or the totality of ord...The infinity of the cardinals and of the ordinals cannot be measured by any card...There is no set of all cardinal numbers and no set of all ordinal numbers.

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    A Kochen-Specker-type contradiction entails logical inconsistency in t...83%Bacciagaluppi (1995) and Clifton (1996a) showed that such property ass...83%That which involves a contradiction is false80%This yields a contradiction: H+L > H and H > H+L.79%

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    Relatedly, since every set has a cardinality less than that of its power set, there can be no set that contains everything (since such a set would already include all its subsets, and thus be at least as large as its power set). The two results imply that there cannot be a set of all ordinals or a set of all sets. In a similar way one argues that there cannot be a set of all cardinals. As a consequence of the above results we can also answer some of the questions we raised at the beginning: ther

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