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    Carmelics

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    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that Autonomous progressions of theories can characterize finitism and predicativism in a mathematically precise way

    ?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.Weyl's predicativism was grounded in an informal conceptual commitment to definability from natural numbers, not in a formal ordinal-indexed hierarchy of systems.
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      Think about whether this reason is strong or weak

    • 2.Translating predicativism into autonomous progressions up to Γ₀ imposes a set-theoretic framework that Weyl would have rejected as itself impredicative in spirit.
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    • 3.A mathematically precise characterization that distorts the foundational motivation it purports to capture fails as a faithful account of the philosophical position.
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    Reason for 2 of 2
    ?
    • 1.The notion of 'correctness' in the boot-strapping procedure presupposes an antecedent grasp of the very ordinal notions the progression is meant to characterize.
      ?

      Think about whether this reason is strong or weak

    • 2.Feferman himself acknowledged that the autonomous condition requires recognizing which ordinal notations are 'legitimate,' a judgment that cannot be formalized without circularity.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The boot-strapping process generates a hierarchy of theories starting from an accepted base theory T_0 via an extension procedure T -> T' that leads from a correct theory to a more encompassing correct theory
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      Think about whether this reason is strong or weak

    • 2.The language of the theories contains a formula Acc(x) such that provability of Acc(a-bar) in a correct theory entails that a belongs to the constructive ordinals O
      ?

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