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    LoyalLoyalJusticeJustice
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    Home/Original/inverse
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    Inverse View

    It is not the case that The polynomial-time functions being 'total' in M means only that M satisfies their defining axioms, not that they are total over the genuine natural numbers, making the claim modal-epistemically ambiguous.

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    Reasons For

    1 perspective
    Reason for
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    • 1.If totality-in-M has no truth conditions independent of what M satisfies, the distinction between 'in M' and 'genuine' becomes meaningless.
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    • 2.Polynomial-time function definitions are recursively constructive and model-independent; their totality doesn't depend on which axioms we posit.
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    • 3.Calling this 'modal-epistemically ambiguous' conflates semantic indeterminacy with our ignorance—the functions are either total or not.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Model M's axioms may be consistent yet incomplete regarding standard arithmetic, so 'totality in M' underdetermines reality.
      ?

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    • 2.Distinguishing formal provability from metaphysical truth requires acknowledging that satisfying axioms doesn't entail genuine totality.
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    • 3.Polynomial-time functions' behavior depends on which model interprets them, creating irreducible epistemic ambiguity about their actual scope.
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