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    CET's extension of 'feasible' to all polynomial time func... — Carmelics
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    Home/Skepticism
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    CET's extension of 'feasible' to all polynomial time functions can diverge from practical feasibility.

    Skepticism
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    2 reasons for
    1 reason against

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 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 for 2 of 2
    ?
    • 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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    Reasons Against

    1 perspective
    Reason against
    ?
    • 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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    SkepticismTruth & Knowledge

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    Proof of definition segments1 linkedModality & Possibility1 linked

    Related

    A classification scheme that systematically mislabels n^1000 computations as 'fe...CET classifies functions as feasible whenever their best algorithm runs in O(n^k...Cobham's thesis, while theoretically elegant, was formulated as a mathematical c...Functions requiring algorithms with time complexity such as 2^1000·n or n^1000 c...
    +3 moreShow less
    Hartmanis and Stearns's foundational complexity work explicitly acknowledges tha...The divergence between CET's polynomial boundary and practical feasibility const...Wittgenstein's rule-following considerations imply that the normative applicatio...

    Similar

    CET's polynomial time criterion can misclassify practically infeasible...84%CET classifies as feasible any function computable in polynomial time,...84%Cobham proposed that the model-independence of polynomial time (suppor...83%The Cobham-Edmonds Thesis identifies feasible computation with polynom...82%

    Source

    AI-extracted1/3 agreementValid
    SEP: computational-complexity
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    Edmonds (1965a) first proposed that polynomial time complexity could be used as a positive criterion of feasibility – or, as he put it, possessing a “good algorithm” – in a paper in which he showed that a problem which might a priori be thought to be solvable only by brute force search (a generalization of \(\sc{PERFECT}\ \sc{MATCHING}\) from above) was decidable by a polynomial time algorithm. Paralleling a similar study of brute force search in the Soviet Union, in a subsequent paper Edmonds
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (2 for, 1 against)
    Edits
    1 edit