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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that Gödel's incompleteness results show that sufficiently expressive formal systems cannot prove all true statements about their own syntactic objects, including complexity class relationships.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Gödel's results apply to undecidable propositions; complexity relationships may be decidable, so incompleteness doesn't necessarily apply.
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    • 2.Complexity classes describe computational resources, not formal syntax, making the application of syntactic incompleteness results unclear.
      ?

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    • 3.Working in stronger formal systems (ZFC, category theory) might suffice to prove complexity relationships, avoiding incompleteness barriers.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Gödel proved formal systems cannot prove all truths about their own syntax, establishing inherent limits on provability.
      ?

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    • 2.Complexity class relationships (like P vs NP) are mathematical truths about formal computational systems, hence subject to Gödelian limits.
      ?

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    • 3.If a system cannot prove all truths about simpler objects (natural numbers), it cannot prove all truths about more complex objects.
      ?

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