A Computability Argument Against Superintelligence

Abstract

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.