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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that ZFC cannot refute the Continuum Hypothesis (CH)

    ?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.Gödel's constructible universe L is a highly restrictive model that excludes many sets mathematicians independently accept as real.
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    • 2.The consistency of CH with ZFC in an artificially constrained model does not establish that ZFC lacks the resources to refute CH in all intended models.
      ?

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    • 3.Large cardinal axioms, which extend ZFC, generate inner models where CH fails, suggesting ZFC's silence on CH reflects incompleteness, not neutrality.
      ?

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    Reason for 2 of 2
    ?
    • 1.Forcing extensions, developed by Cohen, demonstrate that ¬CH is also consistent with ZFC, meaning ZFC is equally powerless to prove CH.
      ?

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    • 2.A claim that ZFC 'cannot refute' CH is misleading if ZFC also cannot prove CH, since both results together establish ZFC's fundamental inadequacy on this question.
      ?

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    • 3.Penelope Maddy and others argue that set-theoretic practice supplies quasi-empirical evidence favoring ¬CH, implying the formal claim obscures a substantive mathematical dispute.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Gödel showed that the inner model L satisfies ZFC together with CH
      ?

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    • 2.If a statement holds in a model of ZFC, then ZFC cannot refute that statement
      ?

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    Strongest counterpoint
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