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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that The theory of Turing machines is the most general theory of computation possible.

    ?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.Hypercomputation models (e.g., Accelerating Turing Machines, oracle machines) can compute functions that classical Turing machines provably cannot.
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    • 2.Turing's own formalization in 1936 was grounded in human cognitive limitations, not in the intrinsic limits of physical or abstract computation.
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    • 3.A theory bounded by human cognitive assumptions cannot claim maximal generality without begging the question against physically realizable super-Turing processes.
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    Reason for 2 of 2
    ?
    • 1.Analog computation models, as defended by Pour-El and Richards, can compute real-valued functions over continuous domains that are Turing-uncomputable.
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    • 2.If physically instantiated analog processes exceed Turing-machine expressibility, then 'most general' must be relativized to discrete symbol manipulation, not computation as such.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The theory of Turing machines is based on a very limited set of assumptions about what computing is.
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    • 2.Turing machines are universal, which points to their generality.
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    • 3.It is difficult to conceive in what sense a more powerful system could be 'more' universal than a universal system.
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