[andreasvc]

Yes I see the superficial resemblance with Gödel and Turing, but it's not more than that. The reason I insist on that is because the value of their theorems lies in the fact that they have been mathematically proven, and the proof only holds in very particular conditions. Basically, a system that is strong enough to prove statements about arithmetic cannot prove its own consistency. This hypothesis about the difficulty of certain machine learning tasks is a conjecture, at best. I don't think you could prove it, and if you could, it would look very different from the incompleteness proof. I think it has to do with certain AI problems being hard, but this is a rather vague notion; perhaps we simply lack certain concepts or mathematical tools. The important thing about the incompleteness proofs is that that is completely ruled out: given the right formal conditions, certain things are absolutely impossible to do.