You can attack the idea more directly as well. Whilst we don't have machines running computable functions that exhibit general intelligence, we unequivocally ha

You can attack the idea more directly as well. Whilst we don't have machines running computable functions that exhibit general intelligence, we unequivocally have ones that exhibit narrow intelligence. Things like telling the difference between cats and dogs by looking at photos, playing superhuman go, learning to play Mario, etc. This gives us an indication that computable functions are capable of a very broad range of interesting behaviours. So then, the question becomes, what is the fundamental, lawful difference between narrow and general intelligence, that would cause effectively computable functions to be able to perform behaviours that we classify as narrow, but not broad ones? This would also seem surprising and arbitrary a priori.