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    Carmelics

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

    It is not the case that Exponentiation is not provably total in IΔ_0

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.IΔ_0 with the axiom Ω_1 (asserting totality of exponentiation) is a consistent extension that many foundationalists accept as the correct base theory.
      ?

      Think about whether this reason is strong or weak

    • 2.The claim conflates provability within a specific weak system with a stronger metaphysical claim about the mathematical nature of exponentiation itself.
      ?

      Think about whether this reason is strong or weak

    • 3.Wilkie and Paris's 1987 result shows unprovability is relative to IΔ_0's restricted induction scheme, not an intrinsic feature of exponentiation's totality.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Edward Nelson's predicativist program in 'Predicative Arithmetic' (1986) disputes that exponential growth is well-defined at all, undermining the comparison premise rather than the conclusion.
      ?

      Think about whether this reason is strong or weak

    • 2.If one adopts Nelson's ultrafinitism, the supporting arguments' P2 begs the question by presupposing a completed infinite domain over which exponentiation's rate of growth is assessed.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.All provably total functions of IΔ_0 are of polynomial rate of growth
      ?

      Think about whether this reason is strong or weak

    • 2.The exponentiation function grows at super-polynomial (exponential) rate
      ?

      Think about whether this reason is strong or weak

    Reason against 2 of 2
    ?
    • 1.All provably total functions of IΔ_0 are of polynomial rate of growth
      ?

      Think about whether this reason is strong or weak

    • 2.Exponentiation grows faster than any polynomial
      ?

      Think about whether this reason is strong or weak

    Next step

    Based on where you are in your exploration

    Strongest counterpoint
    Explore the most compelling reason on the other side.