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    Carmelics

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    It is not the case that 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.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Church's Thesis is an unprovable philosophical claim about intuitive computability, not a theorem that validates the argument's conclusion.
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    • 2.The claim conflates 'paradigm case of finite procedure' with 'provably equivalent to Turing computability'—distinct logical steps.
      ?

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    • 3.Some primitive recursive functions are not efficiently Turing-computable in practice, challenging the functional equivalence claim.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Primitive recursion uses only bounded loops and composition, operations executable by any Turing machine without modification.
      ?

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    • 2.Church's Thesis claims all intuitively computable functions are Turing-computable; primitive recursion exemplifies intuitive computability.
      ?

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    • 3.No primitive recursive function requires oracles, infinite lookahead, or non-mechanical steps—all mechanically simulable.
      ?

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