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    Therefore, the claim that primitive recursion over a comp... — Carmelics
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    Challenges→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.

    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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    Key Terms

    Assurance(Contrasted with evidence, which counts in favor of a proposition regardless of intention.)
    A speech act that counts in favor of a proposition only because the speaker intended it to; it cannot be given unintentionally.
    Church's Thesis(Also called the Church-Turing Thesis; surveyed in Section 1.6 of the source text.)
    The claim that the class REC coincides with the class of effectively computable functions.
    Computable base(in computability theory)
    A starting set of mathematical operations or values that a computer or algorithm can actually process and work with.
    Epistemological warrant(in epistemology (the study of knowledge))
    A good, justified reason to believe something is true based on how knowledge works.
    Formal proof

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    (in mathematics and logic)
    A logical argument written in strict, symbolic form that follows explicit rules, showing that something must be true.
    a priori(Frege treats 'analytic' as entailing 'a priori' for arithmetic.)
    Knowable independently of empirical experience; here treated as a consequence of analyticity.
    computability(computer science and philosophy of mathematics)
    The study of what problems can or cannot be solved by following a step-by-step procedure (algorithm) on a computer.
    model(Possible worlds interpretation of S5 adapted for modal nonmonotonic logic)
    A pair <I, S> where I is a set of literals (a state description / possible world) and S is a set of complete, consistent sets of literals (interpretations) with I ∈ S
    primitive recursion(computability theory / recursive function theory)
    A restricted kind of recursion in which a function h with first argument n+1 is defined in terms of h with first argument n, with all other arguments unchanged.

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    Truth & Knowledge1 linkedCausation1 linked

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    If a model of computation does not natively support recursion, then defining a f...

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