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    Basic Law V's presupposed one-to-one correlation thus vio... — Carmelics
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    Challenges→The correlation that Basic Law V sets up between concepts and extensions must be one-to-one.

    Basic Law V's presupposed one-to-one correlation thus violates a provable cardinality constraint, independently of Russell's Paradox.

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    1 reason for
    1 reason against

    Reasons For

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    Reason for
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    • 1.Basic Law V maps each concept to a unique extension, creating a bijection that presumes cardinality parity between concepts and their extensions.
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    • 2.By Cantor's theorem, the power set of any set exceeds the set's cardinality, so no bijection can exist between all concepts and all their extensions.
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    • 3.This cardinality mismatch is a structural flaw independent of whether paradoxical concepts like the Russell set actually exist.
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    Reasons Against

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    Reason against
    ?
    • 1.Basic Law V need not assume bijection between all concepts and extensions—only that coextensive concepts map to identical extensions, a weaker claim.
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    • 2.Cantor's theorem applies to completed infinite sets, but conceptual domains may not form the kind of completed totality required for the theorem's proof.
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    • 3.The cardinality objection conflates metaphysical extension-formation with set-theoretic cardinality constraints that may not apply to Frege's logical universe.
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    Truth & Knowledge1 linkedPhilosophy of Language1 linked

    Related

    Basic Law V maps each concept to a unique extension, creating a bijection that p...Basic Law V need not assume bijection between all concepts and extensions—only t...By Cantor's theorem, the power set of any set exceeds the set's cardinality, so ...Cantor's theorem applies to completed infinite sets, but conceptual domains may ...
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    The cardinality objection conflates metaphysical extension-formation with set-th...The correlation that Basic Law V sets up between concepts and extensions must be...This cardinality mismatch is a structural flaw independent of whether paradoxica...

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