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Artificial general intelligence is the intelligence of a machine that could successfully perform any intellectual task that a human being can.

Would an artificial general intelligence have to be Turing complete?

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    $\begingroup$ That is not a normal definition of a General AI. Arguably a modern PC meets the criteria - there is a large degree of interpretation possible in your use of "capable" and "computational" which you may want to fix (be careful, lest you exclude human intelligences!) Hence AGI is often defined around imagined behaviour of the system, or refers to traits of human cognition such as types of memory, perception and reasoning. $\endgroup$ – Neil Slater Jun 16 at 7:58
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My answer is yes, but in a trivial way. The least you would expect from an intelligent agent is that it is able to execute a given Turing machine on a given input. This requires actually no intelligence, just following rules. If however, you are referring to the capability of predicting if the Turing machine will terminate on the given input, that is another matter. I don't think it is reasonable to expect such "undecidable" computational power for an agent to be generally intelligent.

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A system is Turing complete if it can be used to simulate any Turing machine.

Given the Church-Turing thesis (which has not yet been proven), a human brain can compute any function that a Turing machine can (given enough time and space), but the reverse is not necessarily true, given that the human brain might be able to compute more functions than a Turing machine. Intuively, humans are thus Turing complete (even though, to prove this, you need a formal model of the human), that is, given enough time and space, a human can compute anything that a Turing machine can.

Hence, an AGI, defined as an AI with human-level intelligence, needs to be Turing complete, otherwise there would be at least one function that a human can calculate but the AGI cannot, which would not make it as general as a human.

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