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    Frege's Basic Law V, which grounds the one-to-one correla... — Carmelics
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    Challenges→There must be at least as many extensions as there are concepts.

    Frege's Basic Law V, which grounds the one-to-one correlation in P2, was proven inconsistent by Russell and abandoned even by Frege himself in 1902.

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    Reasons For

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    • 1.Russell's paradox (1901) definitively showed Basic Law V permits set formation from any property, leading to contradiction.
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    • 2.Frege's own response to Russell acknowledged the law's failure and he abandoned his logicist project without proposing a viable fix.
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    • 3.The inconsistency is mathematically proven and uncontroversial among logicians, making the law's rejection historically inevitable.
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    Reasons Against

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    • 1.Basic Law V's inconsistency doesn't prove Frege abandoned it reluctantly; he may have refined rather than rejected foundational concepts.
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    • 2.Later developments (type theory, set theory axioms) solved the paradox without demonstrating Basic Law V itself was fundamentally flawed in intent.
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    • 3.The claim conflates Russell's proof of inconsistency with Frege's intellectual acceptance; historical evidence of his precise reasoning is limited.
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    Truth & Knowledge1 linkedPhilosophy of Language1 linked

    Related

    Basic Law V's inconsistency doesn't prove Frege abandoned it reluctantly; he may...Frege's own response to Russell acknowledged the law's failure and he abandoned ...Later developments (type theory, set theory axioms) solved the paradox without d...Russell's paradox (1901) definitively showed Basic Law V permits set formation f...
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    The claim conflates Russell's proof of inconsistency with Frege's intellectual a...The inconsistency is mathematically proven and uncontroversial among logicians, ...There must be at least as many extensions as there are concepts.

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