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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that The Computational Efficiency Thesis (CET) is supported by a quasi-inductive argument analogous to the quasi-inductive argument for the Church-Turing Thesis (CT).

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.The quasi-inductive argument for CT derives force from convergence across distinct computational models (Turing machines, lambda calculus, recursive functions), whereas CET lacks analogous model-independence.
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    • 2.Polynomial-time tractability is defined relative to a specific machine model; problems tractable on parallel or quantum architectures may remain intractable on Turing machines, undermining the universality CET requires.
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    • 3.Without cross-model convergence, the inductive evidence for CET is merely historical contingency about which algorithms humans have discovered, not a principled basis for a thesis about computational feasibility.
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    Reason for 2 of 2
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    • 1.Cobham and Edmonds' identification of polynomial time with feasibility has been contested by complexity theorists like Parberry and Levin, who note that O(n^100) algorithms are polynomial yet practically infeasible.
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      Think about whether this reason is strong or weak

    • 2.If the extension of 'feasibility' tracked by CET is conceptually unstable or context-dependent, then the inductive evidence for CET fails to converge on a single well-defined thesis in the way CT's evidence converges on computability.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.In cases where we can uniformly compute the values of a function (or decide a problem) for the class of instances we are concerned with in practice, this is typically because a polynomial time algorithm has been discovered that can be implemented on current computing hardware and hence also as a Turing machine.
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    • 2.In cases where we are currently unable to uniformly compute the values of a function (or decide a problem) for all arguments of interest, it is typically the case that no polynomial time algorithm has been discovered.
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    • 3.In many cases where no polynomial time algorithm is known, there is also circumstantial evidence that no such algorithm can exist.
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