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    Basic Law V requires that the domain of extensions be as ... — Carmelics
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    Challenges→The addition of Basic Law V to second-order logic implies a contradiction.

    Basic Law V requires that the domain of extensions be as large as the domain of concepts, since every concept maps to an extension.

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    A domain cannot be simultaneously strictly larger than another domain and equal ...Second-order logic requires that the domain of concepts be strictly larger than ...The addition of Basic Law V to second-order logic implies a contradiction.

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    In a total one-to-one mapping from concepts to extensions, the cardina...87%Second-order logic requires that the domain of concepts be strictly la...87%Hume's Principle does not require that the domain of numbers be as lar...84%Basic Law V (Vb) implies that if concepts F and G differ, then the ext...83%

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    Thus, the addition of Basic Law V to second-order logic implies an impossible situation in which the domain of concepts has to be strictly larger than the domain of extensions while at the same time the domain of extensions has to be as large as the domain of concepts.

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