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    LoyalLoyalJusticeJustice
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    Home/Original/inverse
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    Inverse View

    It is not the case that Kreisel's squeezing argument shows that informal notions of computability resist full capture by any single formal provability criterion.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Church-Turing thesis remains unrefuted: every intuitive notion of computability proposed has reduced to Turing-computable functions.
      ?

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    • 2.Kreisel's squeezing argument conflates 'provability about computability' with 'computability itself'—capturing the former doesn't require capturing the latter.
      ?

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    • 3.Claims about informal notions resisting capture lack empirical support; no concrete counterexample of intuitively computable yet formally uncomputable functions exists.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Church-Turing thesis captures computable functions, yet Kreisel showed informal notions extend to intuitive calculability beyond formal systems.
      ?

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    • 2.Different formal systems (Turing machines, lambda calculus, recursion theory) prove equivalent, yet mathematicians recognize computable tasks outside all.
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    • 3.Gödel's incompleteness implies no single formal criterion can capture all truths about what is computable in our informal mathematical practice.
      ?

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