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    Feferman's own analysis of predicativity shows that any o... — Carmelics
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    Challenges→Autonomous progressions of theories properly internalize the general concept of progressions of theories

    Feferman's own analysis of predicativity shows that any ordinal recognition procedure relies on prior comprehension principles not internal to the progression.

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    1 reason for
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    Reasons For

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    • 1.Feferman's autonomous progression of ordinals requires external criteria to validate each step, which cannot be self-justifying within the system.
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    • 2.Predicative definitions must avoid impredicative circularity, necessitating foundational comprehension principles that transcend the ordinal hierarchy itself.
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    • 3.The very notion of 'recognizing' an ordinal as admissible presupposes conceptual resources not generated by prior stages of the progression.
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    Reasons Against

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    • 1.Feferman's own formal work shows ordinal notations can be inductively defined without external appeals; the progression is mathematically self-contained.
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    • 2.Calling comprehension principles 'external' conflates the metatheory with the object theory; internal coherence doesn't require complete self-sufficiency.
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    • 3.Many ordinal recognition procedures in constructive mathematics succeed through recursive verification, not prior abstract comprehension assumptions.
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    Proof of definition segments1 linkedTruth & Knowledge1 linked

    Related

    Autonomous progressions of theories properly internalize the general concept of ...Calling comprehension principles 'external' conflates the metatheory with the ob...Feferman's autonomous progression of ordinals requires external criteria to vali...Feferman's own formal work shows ordinal notations can be inductively defined wi...
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    Many ordinal recognition procedures in constructive mathematics succeed through ...Predicative definitions must avoid impredicative circularity, necessitating foun...The very notion of 'recognizing' an ordinal as admissible presupposes conceptual...

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