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    A domain cannot be simultaneously strictly larger than an... — Carmelics
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    Home/Modality & Possibility
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    Challenges→The addition of Basic Law V to second-order logic implies a contradiction.

    A domain cannot be simultaneously strictly larger than another domain and equal in size to that same domain.

    Modality & PossibilityTruth & Knowledge
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    Basic Law V requires that the domain of extensions be as large as the domain of ...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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    SEP: frege-theorem
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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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