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

    It is not the case that Alternative reconstructions of predicativist analysis, such as those explored by Weyl, yield systems with different proof-theoretic strengths than PA.

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    Reasons For

    1 perspective
    Reason for
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    • 1.Many predicativist alternatives, including Weyl's, have been shown proof-theoretically equivalent to PA or subsystems thereof, not fundamentally different in strength.
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    • 2.The claim conflates philosophical differences in reconstruction methodology with actual proof-theoretic divergence without establishing the empirical equivalences differ.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Weyl's predicativist framework restricts quantification over sets defined impredicatively, reducing proof-theoretic resources below PA's full second-order strength.
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    • 2.Different predicativist reconstructions impose varying constraints on set existence axioms, necessarily yielding systems with distinct proof-theoretic ordinals.
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    • 3.Historical analysis shows Weyl's system formalizes only predicatively definable sets, a philosophically motivated restriction that provably limits provable ordinals.
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