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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that Mathematical analysis would collapse if the axiom of reducibility is abandoned.

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Ramsey showed that the axiom of reducibility could be replaced by treating propositional functions extensionally, collapsing the ramified hierarchy without sacrificing analytic results.
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    • 2.If an alternative logical foundation preserves the definition of real numbers without reducibility, then analysis does not depend on that axiom essentially.
      ?

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    • 3.Ramsey's revision, accepted by later logicists including Carnap, constitutes a historically grounded existence proof that analysis survives reducibility's abandonment.
      ?

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    Reason for 2 of 2
    ?
    • 1.Weyl and Brouwer demonstrated that a substantial portion of classical analysis can be reconstructed using predicativist or intuitionistic methods without impredicative axioms.
      ?

      Think about whether this reason is strong or weak

    • 2.If core results of analysis survive without reducibility, the claim of total collapse is demonstrably overstated.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Real numbers cannot be defined using Dedekindian classes without the axiom of reducibility.
      ?

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    • 2.Mathematical analysis depends on the definition of real numbers via such classes.
      ?

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