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    Inverse View

    It is not the case that Predicativist analysis is a conservative extension of Peano Arithmetic

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Feferman's reconstruction encodes specific philosophical commitments about predicativity that are themselves contested, not neutral formal choices.
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    • 2.Alternative reconstructions of predicativist analysis, such as those explored by Weyl, yield systems with different proof-theoretic strengths than PA.
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    • 3.A conservative extension result is only as robust as the reconstruction it presupposes, so disputed reconstructions yield disputed conservation results.
      ?

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    Reason for 2 of 2
    ?
    • 1.Proof-theoretic conservation over PA does not establish that predicativist analysis is semantically or ontologically conservative over arithmetic.
      ?

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    • 2.Predicativist analysis quantifies over real numbers and function spaces whose existence is not warranted by the ontology presupposed in Peano Arithmetic.
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    • 3.A theory can be deductively conservative yet introduce new entities and concepts that represent genuine extensions of the original framework's commitments.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Feferman gave a detailed formal presentation of predicativist analysis
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    • 2.Feferman proved that, on a certain reconstruction, the predicativist theory does not prove any new arithmetical statements beyond those provable in Peano Arithmetic
      ?

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