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    Poincaré and Weyl grounded predicativism in a principled ... — Carmelics
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    Challenges→Predicativism is a compromise between classical and constructive viewpoints in mathematics

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

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    • 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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    Reasons Against

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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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    Related

    Claiming independence from classical/constructive logic is misleading—predicativ...Classical mathematics relies on impredicative definitions (e.g., least upper bou...Poincaré and Weyl's approach succeeds because it identifies a genuine logical pr...Predicativism is a compromise between classical and constructive viewpoints in m...
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    Predicativism's neutrality between classical and constructive systems shows it a...The vicious-circle principle itself lacks principled justification—it reflects i...Vicious-circle prohibition avoids self-referential definitions that undermine ma...

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