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A Computability Argument Against Superintelligence

“It turns out that, yes, there are limits to computations based on the laws of physics. But these still allow for a continuation of exponential growth until non-biological intelligence is trillion of trillions times more powerful than all of human civilization today, contemporary computers included.”

Ray Kurzweil, in “The Singularity is Near: When Humans Transcend Biology”


Using the contemporary view of computing exemplified by recent models and results from non-uniform complexity theory, we investigate the computational power of cognitive systems. We show that in accordance with the so-called extended Turing machine paradigm such systems can be modelled as non-uniform evolving interactive systems whose computational power surpasses that of the classical Turing machines. Our results show that there is an infinite hierarchy of cognitive systems. Within this hierarchy, there are systems achieving and surpassing the human intelligence level. Any intelligence level surpassing the human intelligence is called the superintelligence level. We will argue that, formally, from a computation viewpoint the human-level intelligence is upper-bounded by the \(\Upsigma_2\) class of the Arithmetical Hierarchy. In this class, there are problems whose complexity grows faster than any computable function and, therefore, not even exponential growth of computational power can help in solving such problems, or reach the level of superintelligence.

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    Arithmetical Hierarchy is the hierarchy of unsolvable problems of increasing computational difficulty. The respective problems are defined with the help of certain sets based on the complexity of quantified logic formulas that define them (cf. [6]).


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This research was carried out within the institutional research plan AV0Z10300504 and partially supported by a GA ČR grant No. P202/10/1333

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Correspondence to Jiří Wiedermann.

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A preliminary version of this paper appeared in Proceedings of the AISB’11—Computing and Philosophy, The University of York, York, UK, April 2011, pages 73–79.

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Wiedermann, J. A Computability Argument Against Superintelligence. Cogn Comput 4, 236–245 (2012).

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  • Cognitive systems
  • Intelligence
  • Extended Turing machine thesis
  • Singularity
  • Superintelligence