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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that It is unlikely that a polynomial time algorithm exists for any NP-complete problem.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Absence of discovered proof is not evidence of absence, as Hume's problem of induction warns against inferring universal laws from finite empirical records.
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      Think about whether this reason is strong or weak

    • 2.The history of mathematics contains numerous problems resistant to solution for centuries before breakthroughs occurred, including Fermat's Last Theorem and the primality testing problem.
      ?

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    • 3.The argument from 'extensive effort' tacitly assumes human mathematical ingenuity has adequately explored the solution space, an epistemically unjustified presumption.
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      Think about whether this reason is strong or weak

    Reason for 2 of 2
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    • 1.The supporting argument conflates pragmatic unlikelihood with logical impossibility, a modal fallacy that Kripke's framework on necessity and possibility explicitly warns against.
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      Think about whether this reason is strong or weak

    • 2.P=NP remaining unproven means current complexity theory cannot rule out the existence of a polynomial algorithm, making 'unlikely' a sociological claim rather than a mathematical one.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Extensive effort has been devoted to finding efficient solutions for particular NP-complete problems such as INTEGER PROGRAMMING and TSP.
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      Think about whether this reason is strong or weak

    • 2.No polynomial time algorithm has been found for any NP-complete problem despite this extensive effort.
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    • 3.The existence of a polynomial time algorithm for any NP-complete problem would imply polynomial time algorithms for all problems in NP, which runs strongly counter to expectation.
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    Strongest counterpoint
    Explore the most compelling reason on the other side.