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    Predicativism is a compromise between classical and const... — Carmelics
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    Predicativism is a compromise between classical and constructive viewpoints in mathematics

    Truth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 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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    Reasons Against

    2 perspectives
    Reason against 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 against 2 of 2
    ?
    • 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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    Related

    A position that loses almost nothing of practical mathematical significance rela...A view with its own foundational rationale distinct from both poles is not a com...Poincaré and Weyl grounded predicativism in a principled vicious-circle prohibit...Predicativism accepts the excluded middle on the natural numbers, which is a cla...
    +3 moreShow less
    Predicativism makes the existence of sets depend on definability, which is a con...Predicativism rejects impredicative definitions as logically vicious, not merely...Solomon Feferman's work shows predicative mathematics can recover nearly all sci...

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    An intermediate position is that defended by classical “predicativists” such as Poincaré and Weyl. The theory, presented in a satisfactory logical way by Feferman and others, accepts the excluded middle on the natural numbers (and as such it is arguably committed to the existence of the set of natural numbers and in any case to accepting bivalence on the natural numbers) but does not accept the existence of the power set of the natural numbers. According to predicativism (see Feferman 2005), set
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    Details

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    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit