Any sense in which Godel's incompleteness theorem implied that Artificial General Intelligence was impossible would also imply that General Intelligence is impossible; the human brain isn't immune to the laws of logic. The human brain is just a very complex, possibly quantum, computer. Short of believing in some kind of supernatural human soul, there's no reason to expect a sufficiently complex computer couldn't match the human brain (although it's an open question whether we could build a sufficiently complex computer).
I think that there are other mechanisms apart from computation; the question is - are they operant in our universe? The implication of the answer being "no" is that we are automaton, free will does not exist (it isn't even an illusion, you are as much a puppet thinking about it as you are trying to change your fate. Well, moving on from there we can dismantle all of the morality and humanity of our lives and not change one jot becuase we have no choice. I don't believe that any one has observered anything that isn't reducable to computation, but then again, perhaps our cognitive capabilities simply can't do that.
>The implication of the answer being "no" is that we are automaton, free will does not exist (it isn't even an illusion, you are as much a puppet thinking about it as you are trying to change your fate.
This is implied by logic anyway. Why do we make decision X at time T? Because of who we are at time T. Why are we that person at time T? Because of decisions made at time T-1. Why did we make those decision at T-1? Because of who we were then, which was the restult of decisions made at T-2. If we continue this process, we reach T-only-a-baby, when we were incapable of conscious decision making. So causally all our actions can be traced back to something we can't control. Unless, some of our decisions were entirely the result of chance, but in this case we still don't have free will, we just have actions that are random instead of predetermined.
I think that there are a lot of assumptions in that chain. When you or I ask why did we make a decision X we can formulate answers but, for my account, I don't have access to all of the components of my thinking - I cannot articulate what I feel is really going on. I think that randomness in the universe is very hard to account for too - I was impressed by an essay that Scott Aaronson wrote about this : https://www.scottaaronson.com/papers/giqtm3.pdf but I have read it several times and I am afraid I don't really understand it.
We have yet to duplicate anything even near human intelligence or introspective abilities with computation. We therefore have no existence proof that human mind is purely computational in nature. I think we can safely say that computation is necessary to produce a mind, but we cannot yet say for certain that it is sufficient.
Mind may require something else that we don't yet understand. (Not necessarily claiming it would have to be supernatural, just not yet understood. Perhaps quantum computation or some other kind of quantum effect?)
