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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that 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.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Church-Turing equivalence proofs themselves rely on informal intuitions about 'computation,' making them meta-theoretically circular rather than foundationally transparent.
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    • 2.Transferring computability via model equivalence assumes the property is *structural* and *model-invariant*; this itself requires justification independent of the equivalence proof.
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    • 3.An 'a priori gap' may persist epistemically: even if formally proven equivalent, why believe the models capture *all* computability? Proof doesn't address scope questions.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Model equivalence proofs (Church-Turing thesis) establish formal isomorphisms, not mere conjecture, between recursive functions and other computational frameworks.
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    • 2.Primitive recursion's computability is intrinsic to its definition; model equivalence transfers this property deductively, not inductively or by assumption.
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    • 3.The 'a priori gap' assumes computability requires external validation; proven equivalence dissolves this by showing the property holds across all equivalent formalisms.
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