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    Carmelics

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    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 Predicativism is a compromise between classical and constructive viewpoints in mathematics

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Predicativism rejects impredicative definitions as logically vicious, not merely as a pragmatic concession to constructive sensibilities.
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    • 2.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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    • 3.A view with its own foundational rationale distinct from both poles is not a compromise but a third, autonomous position.
      ?

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    Reason for 2 of 2
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    • 1.Solomon Feferman's work shows predicative mathematics can recover nearly all scientifically applicable analysis, undermining the framing that it sacrifices classical power.
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    • 2.A position that loses almost nothing of practical mathematical significance relative to classical mathematics is not genuinely intermediate but asymptotically classical in reach.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Predicativism accepts the excluded middle on the natural numbers, which is a classical commitment
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    • 2.Predicativism makes the existence of sets depend on definability, which is a constructive constraint
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