(These are excerpts from my book "Intelligence is not Artificial")
The Frame Problem
A stumbling block towards the creation of truly intelligent machines is still the frame problem, formulated by John McCarthy in "Some Philosophical Problems from the Standpoint of Artificial Intelligence" (1969): he asked whether it is possible, in principle, to calculate all the effects on the world of an action.
For example, one day a friend left his expensive phone in the car and simply covered it with his very inexpensive jacket. Minutes later his wife ran back to the car because she was feeling cold and picked up his jacket. When they got back to the car, someone had broken the window and stolen the phone. The act of picking up the jacket (for an absolutely legitimate reason) had changed the state of the world in many obvious ways (now the jacket was no longer in the car, she was no longer cold, etc) but also in other subtler ways, including the fact that now the phone was visible to thieves.
David Chapman perhaps proved mathematically the impossibility of artificial general intelligence when he proved that the frame problem is NP-complete (it belongs to the class of "nondeterministic polynomial" problems) and hence probably inherently unsolvable ("Planning for Conjunctive Goals", 1987).
To be fair, mathematicians still haven't proven whether it is, in principle, possible to construct an efficient algorithm that can solve NP-complete problems: the majority consensus is that it is not possible, but the jury is still out.
Of course, it all depends on what we mean by "solving a problem", as Wim Hordijk has discussed in "The Algorithmic Mind and what it Means to Solve a Problem" (2014) in response to Stuart Kauffman's claim that that the mind is not algorithmic ("Minds And Machines", 2011).
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