I did write a short article on Douglas R. Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid. I referred to the Incompleteness Theorem — as best as I could understand it — as maintaining that systems are not entirely self-proving, so if you want to justify using one system, you'll have to consult a different system.

https://medium.com/@tuckerlieberman/transgender-reading-of-godel-escher-bach-d6b4105865c2

Maybe you are saying something different?