I'm unconvinced that GAI is possible in practice, and only marginally more convinced it's possible in theory.
Consider how buggy most software is. Consider that we have nothing approaching a general theory of computation. Consider that we cannot measure the quality of any given non-trivial piece of software. Consider that we don't even know what "quality" means in this context.
Consider there are minor mathematical issues - the halting problem, P != NP, the Incompleteness Theorems - which strongly suggest that all possible symbolic systems must be either incomplete or lacking rigour.
Consider that the thinking around AI is an unholy mess of millenarianism, techno-evangelism, philosophical confusion between unrelated concepts (learning, personality, emotional drives, sentience, self-improvement, general intelligence, "magical" post-human physics...) and wishful thinking.
I'm completely happy that we can build AIs for specific domains that perform better in those domains than humans do - because we already have.
I'm fairly sure we can build learning machines that can analyse a domain and provide a practically useful overview of it to a much deeper and broader extent than we do already.
I'm also fairly sure that process has practical and mathematical limits which are analogous to the transistor size limit for Moore's Law, and that the nature of symbolic computation itself makes it the most difficult of all domains to master.
My guess is there won't ever be a post-singularity god-AI. But there will be AIs that appear smarter than all humans in specific areas. And that these AIs will continue to be dumb slave machines which do what we tell them to, because domain mastery is completely orthogonal to any requirement for sentience, personality, or motivation.