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    Weyl's predicativism was grounded in an informal conceptu... — Carmelics
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    Challenges→Autonomous progressions of theories can characterize finitism and predicativism in a mathematically precise way

    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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    Reasons For

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    • 1.Weyl's writings emphasize intuitive constructibility from natural numbers rather than formal proof-theoretic hierarchies as his foundational constraint.
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    • 2.Predicativism fundamentally concerns conceptual intelligibility, not formal systematics—definability captures this better than ordinal indexing.
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    • 3.Weyl rejected impredicative set theory on conceptual grounds before formal ordinal hierarchies were developed to formalize predicative strength.
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    Reasons Against

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    • 1.Informal conceptual commitments require formal explication to avoid vagueness; ordinal hierarchies provide the necessary precision Weyl's framework lacks.
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    • 2.Modern predicativism (Feferman, others) uses ordinal-indexed systems precisely because definability-from-naturals alone cannot determine proof-theoretic boundaries.
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    • 3.Without formal ordinal structure, Weyl's notion of 'definability' remains ambiguous and cannot rigorously distinguish predicative from impredicative reasoning.
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    Proof of definition segments1 linkedModality & Possibility1 linked

    Related

    Autonomous progressions of theories can characterize finitism and predicativism ...Informal conceptual commitments require formal explication to avoid vagueness; o...Modern predicativism (Feferman, others) uses ordinal-indexed systems precisely b...Predicativism fundamentally concerns conceptual intelligibility, not formal syst...
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    Weyl rejected impredicative set theory on conceptual grounds before formal ordin...Weyl's writings emphasize intuitive constructibility from natural numbers rather...Without formal ordinal structure, Weyl's notion of 'definability' remains ambigu...

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