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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that NP-complete problems are widely believed to lack polynomial time algorithms

    ?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 polynomial algorithms after finite search constitutes inductive, not deductive, evidence against their existence.
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    • 2.Hume's problem of induction entails that no finite record of failures licenses a nomological conclusion about algorithmic impossibility.
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    • 3.The supporting argument thus conflates pragmatic expectation with ontological fact, a distinction central to Peirce's fallibilism.
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    Reason for 2 of 2
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    • 1.Baker, Gill, and Solovay (1975) demonstrated that P vs NP is independent of relativized models, suggesting proof techniques are currently insufficient to settle the question.
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      Think about whether this reason is strong or weak

    • 2.Epistemic humility requires distinguishing 'we lack proof of X' from 'X is false', a distinction Lakatos emphasized in his methodology of research programmes.
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    • 3.Widespread belief among practitioners, however well-credentialed, constitutes sociological consensus rather than philosophical justification for treating a claim as settled.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Extensive effort has been devoted to finding efficient solutions for NP-complete problems such as INTEGER PROGRAMMING and TSP without success
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    • 2.The existence of a polynomial time algorithm for any NP-complete problem would imply P = NP, which runs strongly counter to expectation
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    Strongest counterpoint
    Explore the most compelling reason on the other side.