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    Home/Original/inverse
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    Inverse View

    It is not the case that Strict finitists anticipated the complexity-theoretic insight that exponentiation marks the boundary between the feasible and the infeasible.

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Strict finitists like Yessenin-Volpin were concerned with ontological limits on which numbers exist, not computational resource bounds on algorithms.
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    • 2.Complexity theory's feasibility boundary is defined relative to input-size scaling of machine operations, a framework entirely absent from strict finitist writings.
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    • 3.Attributing anticipation of a concept to thinkers who lacked its constitutive framework conflates surface terminological resemblance with genuine theoretical insight.
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    Reason for 2 of 2
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    • 1.The polynomial/exponential boundary in complexity theory is a formal, machine-model-relative result dependent on Church-Turing thesis assumptions that strict finitists explicitly rejected.
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    • 2.Yessenin-Volpin's rejection of exponential closure was motivated by sorites-style vagueness concerns about feasibility, not by worst-case algorithmic analysis.
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    • 3.Two positions can share a conclusion about exponentiation while differing so fundamentally in justification that no genuine anticipation relation holds between them.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Van Dantzig (1955) held that feasible numbers are closed under addition and multiplication.
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    • 2.Yessenin-Volpin (1970) explicitly stated that feasible numbers should not be regarded as closed under exponentiation.
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    • 3.The particular examples of infeasible numbers put forward by Yessenin-Volpin and others use exponential or iterated exponential notations such as n₁^n₂ or n₁^(n₂^n₃).
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