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    Home/Original/inverse
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    Inverse View

    It is not the case that The polynomial time many-one reducibility relation ≤_P is a preorder (reflexive and transitive).

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Polynomial time computability presupposes a fixed machine model, yet Church-Turing thesis variants leave the notion of 'feasible' computation model-relative.
      ?

      Think about whether this reason is strong or weak

    • 2.If the underlying notion of polynomial time is model-relative, then the transitivity proof inherits that relativity, making ≤_P a preorder only relative to a chosen computational substrate, not absolutely.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.The identity reduction witnessing reflexivity is trivially well-defined only if problems are individuated extensionally as sets of strings, collapsing intensional distinctions philosophers like Carnap and Frege treat as meaningful.
      ?

      Think about whether this reason is strong or weak

    • 2.If problems are individuated intensionally—by their meaning or cognitive content rather than their extension—then two co-extensional but intensionally distinct problems may not be genuinely self-reducible via a single canonical function, undermining the reflexivity premise.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.≤_P is reflexive: every problem is reducible to itself.
      ?

      Think about whether this reason is strong or weak

    • 2.≤_P is transitive: the composition of two polynomial time computable functions is also polynomial time computable, so if X ≤_P Y and Y ≤_P Z then X ≤_P Z.
      ?

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