Gödelian arguments don't affect open proof systems
Gödel's theorem distinguishes between open and closed proof systems. The former interact with the environment via a stream of inputs, are potentially noncomputable, immune to Gödelian arguments, and may yet be as creative and insightful as humans.
Gödel's theorem implies a sharp distinction between open and closed proof systems.
Open proof systems continuously interact with the environment through a steady stream of inputs.
An open proof systerm is, in fact, a potentially infinite set of systems, and at the limit thus has the potential to be incomplete.
Because they are potentially incompete, open systems are immune to Gödelian arguments, and may turn out to be as creative and insightful as humans are.
Albert E Lyngzeidetson and Martin K. Solomon (1994).
Closed proof system: a proof system that has no interaction with the external world and so does not involve any rules of inference other than those that it started with.
Open proof system: a proof system that continually interacts with its environment through sensors in such a way that it evolves and incorporates stronger and stronger rules of inference in its system.