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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that The proof that the principle of Induction can be derived without the axiom of reducibility in a modified theory of types is faulty.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Myhill (1974) and Hazen (1983) independently demonstrated that a repair to Appendix B's proof is achievable within a ramified type theory with substitutional quantification.
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    • 2.If the proof's core strategy is salvageable under modest technical revision, the fault is in the execution rather than the foundational claim that reducibility is dispensable for induction.
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    • 3.A faulty proof of a true theorem does not establish the falsity of the theorem, only the inadequacy of that particular derivation.
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    Reason for 2 of 2
    ?
    • 1.Chwistek and later Feferman showed that significant portions of classical mathematics can be recovered in predicative systems that eschew the axiom of reducibility.
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    • 2.If induction is recoverable predicatively in these alternative frameworks, Russell's Appendix B aim may be directionally correct even if the specific proof is technically flawed.
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    • 3.The historical assessment of Appendix B as simply 'faulty' risks conflating a local inferential error with a wholesale refutation of the predicativist research program it initiated.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The proof proposed in Appendix B purports to derive the principle of Induction without the axiom of reducibility.
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    • 2.The proof contains an error that invalidates the derivation.
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    Strongest counterpoint
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