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    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that CET's extension of 'feasible' to all polynomial time functions can diverge from practical feasibility.

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    Reasons For

    1 perspective
    Reason for
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    • 1.CET classifies functions as feasible whenever their best algorithm runs in O(n^k) time, regardless of how large the constant factor or exponent is.
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    • 2.Functions requiring algorithms with time complexity such as 2^1000·n or n^1000 cannot in practice be computed for most or all inputs of interest.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Cobham's thesis, while theoretically elegant, was formulated as a mathematical convenience, not an empirical claim about human computational practice.
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    • 2.Hartmanis and Stearns's foundational complexity work explicitly acknowledges that polynomial time is a proxy for tractability, not a precise boundary of feasibility.
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    • 3.A classification scheme that systematically mislabels n^1000 computations as 'feasible' fails the philosophical criterion of extensional adequacy for any concept claiming empirical grounding.
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    Reason against 2 of 2
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    • 1.Wittgenstein's rule-following considerations imply that the normative application of 'feasible' is anchored in forms of life, not abstract mathematical definitions divorced from actual computational practice.
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    • 2.The divergence between CET's polynomial boundary and practical feasibility constitutes a counterexample in the tradition of reflective equilibrium, where theoretical principles must cohere with considered judgments about specific cases.
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