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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that Feasibility is preserved under limited recursion on notation

    ?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.The polynomial bound on auxiliary functions presupposes a fixed machine model, but feasibility judgments are model-relative in ways that undermine universal closure claims.
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    • 2.Cobham's original characterization of feasibility via limited recursion on notation tacitly assumes sequential computation, excluding parallel models where the bound fails to generalize.
      ?

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    Reason for 2 of 2
    ?
    • 1.Intensional properties of functions—such as how a computation proceeds, not just its input-output behavior—are not preserved under compositional closure, as Kreisel's squeezing arguments reveal.
      ?

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    • 2.If feasibility is an epistemic or pragmatic notion tracking humanly tractable computation, then formal closure under recursion on notation conflates mathematical tractability with physical realizability.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The basis functions F_0 are feasibly computable
      ?

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    • 2.Feasibility is preserved under composition
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    • 3.When f(x,y) is defined by limited recursion on notation, the number of recursive steps is proportional to the length of y's binary representation rather than to the value of y itself
      ?

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