I don't understand how Gödel showed limits of AI, or even addressed AI in its modern incarnation, which has little to do with logic. Perhaps some more knowledgeable reader can elucidate?
All of the training you've done on the GPU; all of the coordination done by the CPU; everything… it's all one (absurdly long) boolean expression.
Like all algebraic structures, Boolean algebra is built from an initial set of axioms. Under Gödel's incompleteness theorem, it is therefore true that if Boolean algebra isn't inherently broken (inconsistent), then we can craft questions that cannot be answered using Boolean algebra alone, but this is all your classical computer is capable of doing!
Now, if you're training AI using an analog system or a non-classical computer such as a quantum computer, then this opens up a totally different discussion.
Sure, that's trivial, the travelling salesman problem for example can't be solved exactly, but approximative methods come very close. Given that brains are pattern recognition machines generating probabilities we're already in the approximative regime. Nothing is certain, even science has its revisions.
So does it matter if we can only approximate? For living things the main thing that matters is life, self reproduction, not exactness. As long as they reproduce they are still valid, with all imperfections and approximations. I think the only questions that matter are those related to life, there are plenty of uncomputable things outside self reproduction. This is for biological agents, an AI would be using evolutionary methods to reproduce their digital genes instead.
Computability doesn't take into account how fast you can solve a problem: only if it is possible to solve it at all.
Something like the perfect security of either hiding or binding in a commitment protocol can never be broken given computers of infinite capacity and speed because it's mathematically impossible. That is opposed to computational security, which only states that the property can't be broken within any usable time frame. This is often in the order of hundreds of millions of years in practical cryptographic systems. The point is, it can be technically be done.
Breaking RSA can factored just by brute forcing. It might take a lot of time, but actually doing it is not hard for sufficiently small keys. We just increase the key size until it takes a long time.
Also, the equivalence between the different models of computation for Turing completeness (turing machine, lambda calculus, ...) isn't about complexity classes of the problems, only wether or not the model allow to solve the same set of problems. For example searching in a sorted array is O(log n) on a Von Neumann machine but O(n) on a Turing machine.
1. The difference matters a WHOLE LOT when you're studying computability. If the question you're trying to answer is "Can this be computed exactly?", then the distinction is paramount.
2. Your argument here is functionally equivalent to stating that there exists a largest number since it's trivial to construct a number which would require more digits (in any base you'd like) than subatomic particles in the entire universe to represent in its fully-expanded form… so let's pick this one as the largest and stop worrying about all of that infinity hub-bub!
See the following:
As a very crude example of this kind of limitation, I'm sure I've read a hundred Sci-Fi stories where the humans defeat the AI by posing to it an unsolvable problem, usually a variation of the "liar's paradox", e.g. "this statement is false" (which btw is used by Gödel in his proof). So a human traipses over to the superintelligent AI and blurts "I always lie". Then the AI spends an aeon processing the sentence and then blows up.
Even worse, intelligence itself may turn out to be an uncomputable program that cannot be executed on a computer. In that case- no AI.
In general when the problem is so hard evolutionary methods are suitable. They naturally blend the notion of cost with that of search and cope better with deceptive objectives.
This suffices to explain why there is, indeed "no AI getting stuck inot a loop by a tricky question". Because there is "no AI" at all, certainly not of the kind that can understand a "tricky question" sufficiently well to stumble on the paradox inside it.
For example, GPT-3 has no ability to process "this sentence is false" in such a way as to decide its truth. AlphaGo is not capable of processing language at all, it is only capable of playing board games and it isn't even capable of playing board games by reasoning, only by search. AlphaGo searches a game tree structured as a directed graph, without loops so it's hard to see how it could get stuck on recursive paradoxes anyway.
In general, such systems as exist today do not have the mathematical properties of the formal systems described by Gödel, Church and Turing. They don't even have memories. So they are, let's say immune to incompleteness, because they're not even incomplete.