You don't work around what is impossible. A consistency proof for a theory T is usually a construction of a model of that theory in some context we have confidence in. Godel's theorem shows that that context has to be stronger than T. This isn't some kind of obstruction, it is reality. And there are strong systems we have confidence in.
lmm|1 year ago
What distinction are you drawing? I see no contradiction between something being reality and something being an obstruction to be worked around.