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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 Ramsey and Wittgenstein showed that type distinctions, when applied to propositional functions, generate an infinite hierarchy that cannot itself be described within the system without violating its own constraints.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Later type theory (Church, Martin-Löf) successfully formalizes hierarchies within systems without the claimed self-description barrier.
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    • 2.The claim conflates the inability to describe *all* types from within a single level with inability to describe the hierarchy itself formally.
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    • 3.Set-theoretic frameworks manage comparable hierarchies (cumulative hierarchy) without requiring transcendence of their own constraints.
      ?

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    Reasons Against

    1 perspective
    Reason against
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    • 1.Russell's paradox demonstrates that unrestricted comprehension leads to contradiction, necessitating hierarchical type restrictions.
      ?

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    • 2.Any formal system adequate to describe its own type hierarchy must contain resources that exceed the system's expressive power.
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    • 3.Ramsey and Wittgenstein's work shows self-referential description of type systems generates vicious circle violations that theory must prevent.
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