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    Carmelics

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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 Poincaré and Weyl grounded predicativism in a principled vicious-circle prohibition, making it a foundational stance independent of classical or constructive commitments.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.The vicious-circle principle itself lacks principled justification—it reflects intuition rather than foundational necessity or logical derivation.
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    • 2.Classical mathematics relies on impredicative definitions (e.g., least upper bounds) that are mathematically indispensable, not optional commitments.
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    • 3.Claiming independence from classical/constructive logic is misleading—predicativism presupposes specific proof-theoretic constraints that embed foundational choices.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Vicious-circle prohibition avoids self-referential definitions that undermine mathematical rigor regardless of constructive or classical logic.
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    • 2.Poincaré and Weyl's approach succeeds because it identifies a genuine logical problem (impredicativity) independent of broader foundational commitments.
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    • 3.Predicativism's neutrality between classical and constructive systems shows it addresses fundamental principles deeper than either framework.
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