Based on what we know of how algorithms work, it can be demonstrated mathematically that algorithms cannot deal with non-computable concepts:
There is another way to prove a negative besides exhaustively enumerating the possibilities
With artificial general intelligence (AGI), if we can identify something algorithms cannot
do, and show that humans can do it then we’ve falsified the AGI position without running an infinite number of experiments across all possible algorithms. Eric Holloway, “The Flawed Logic behind “Thinking” Computers, Part II” at Mind Matters
If Eric is correct, a great deal of the hype we hear in media is based not only on improbable concepts (the usual stuff) but impossible ones. See, for example, Top Ten AI hypes of 2018
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See also: “Thinking” computers? Some logical problems with the idea
Computer Engineer Eric Holloway: Artificial Intelligence Is Impossible
and
Eric Holloway: ID As A Bridge Between Francis Bacon And Thomas Aquinas