The gist of Goedel's theorem seems to be found in the fact that our language becomes a pitfall when it is used for self-reflection. Any formal system which we could have thought of (till now) has the same flaw.

No human-made formal system appears to be capable of self-reflection; yet any human can do it.

Why are our brains "made" in such peculiar way? As if there is a blind spot which prevents us from seeing the source of light. Will we be able to develop a workaround this spot? If the answer is yes, what sort of "language" will be used for such purpose (i.e. the formal system for which Goedel proof does not hold)? Will it be a "language" at all? What is, after all, the definition of the concept of "language"?