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The question recently came up and was applied to the human brain/consciousness and the universe. Keeping the initial question in mind: Can intelligence be a subset of non-intellect? Can consciousness be a subset of mindlessness? You could use subsume in place of subset, but the prefix ‘sub’ is the key as it denotes inferior as opposed to ‘greater’. I would answer the questions “no”.

Indeed. One needs to subsume some actual intelligence in order to understand what you have said. If one has, it's elementary (i.e., fundamental). If one has refused what is elementary to one's own being, it does not compute.

And as ironically you have scribed, who knows, it could just be possible to program a 'thinker,' that would know better than its programmer -- if it would refuse to ignore the fundamental.

Everybody: can you say "subsume?"

I knew you could.

The "fundamental" of intelligence is Kolmogorov complexity (technically speaking). The magic is in the finite control function that operates on the KC. If the control function is clever, then it is very possible for the effective KC of the artificial system to exceed that of a human.

I don't know that too many people look at the problem like this. For one intelligence to create another equal intelligence, one only has to do two things. First, one has to discover/invent a clever finite control function (which any reasonably good intelligence could theoretically do), that efficiently converts the Kolmogorov complexity of a state machine into intelligence. Second, one must be able to build such a state machine that is sufficiently large that it will exhibit the same effective KC as the intelligence that created it when applying the control function.

That control function is the part that requires real cleverness, but it is a small finite thing that does not vary with the amount of intelligence expressed with it. Increasing the KC of a state machine amounts to increasing the working memory of it, and things like Moore's law work inexorably towards that end. Therefore, once you've solved the problem of a tractable finite control function, you've solved the problem of intelligence of all types. For most of the history of computer science, the control functions that have been known in this space were so egregiously poor that they have only been tractable for nothing but toy problems no matter how much hardware we threw at them. This has been changing as a new class of control functions have been discovered in the last couple years that seem to be very reasonably tractable to high complexity. When these new algorithms make it into the commercial space, I think it will fundamentally change the view of the types of things computers can do because they break certain assumed limitations of computers.