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    Inverse View

    It is not the case that If a model of computation does not natively support recursion, then defining a function h(y) by primitive recursion over a base function g(y) computable in that model provides no a priori assurance that h(y) is itself computable in that model.

    ?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.Church's Thesis entails that any function intuitively computable by a finite procedure is computable by a Turing Machine, regardless of definitional form.
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    • 2.Primitive recursion is a paradigm case of finite, effective procedure, so any function defined by it over a computable base is already Turing-computable by Church's Thesis.
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    • 3.Therefore, the claim that primitive recursion over a computable base provides 'no a priori assurance' of computability conflates formal proof within a model with the broader epistemological warrant supplied by Church's Thesis.
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    Reason for 2 of 2
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    • 1.Kleene's Normal Form Theorem shows every partial recursive function is expressible via bounded minimization over a primitive recursive predicate, establishing a structural bridge between recursion-theoretic and machine-based models.
      ?

      Think about whether this reason is strong or weak

    • 2.Because this bridge is proven rather than merely conjectured, a function defined by primitive recursion over a computable base inherits computability in any model proven equivalent to the recursive functions, removing the alleged 'a priori' gap.
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    • 3.The supporting arguments conflate the absence of native recursion syntax in a model with the absence of semantic equivalence, but proven inter-reducibility of models dissolves that gap at the level of extensional computability.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Models of computation such as the Turing Machine and Unlimited Register Machine do not natively support recursion as a mode of computation.
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      Think about whether this reason is strong or weak

    • 2.For models that do support primitive recursion, a unique function h(y) satisfying a primitive recursion equation can be shown to exist via external set-theoretic argument.
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    • 3.Simply setting down a recursive definition does not, by itself, establish computability within a given model.
      ?

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