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    Carmelics

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    It is not the case that 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.

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    Reasons For

    1 perspective
    Reason for
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    • 1.Predicative arithmetic severely limits mathematical expressivity; most theorems in analysis become unprovable, not merely reconceptualized.
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    • 2.Exponential growth appears well-defined even within predicative frameworks when formulated via recursion rather than quantification over infinite sets.
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    • 3.Nelson's critique disputes the *justification* of exponential functions but doesn't show they're meaningless—it's a philosophical disagreement, not a mathematical discovery.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Predicativism avoids circular reasoning by rejecting impredicative definitions that presuppose the totality of sets they define.
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    • 2.Exponential functions in standard analysis rely on quantification over infinite sequences, which predicativism legitimately questions as foundationally unclear.
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    • 3.Nelson's approach preserves computational meaningfulness by restricting to finitely constructible numbers, avoiding infinitary assumptions.
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