idea
A system that knows it is incomplete
A strong enough system can prove “if I’m consistent, there is a true statement I can’t prove”. So it can know it has a blind spot, but it can never point to what is in it, and it cannot be sure it is consistent either. That is Socrates in formal dress: it knows that it doesn’t know, but not what it doesn’t know.
The idea that such a system may be another level of consciousness has exactly this shape.