Saying that Set Theory “solved the problem” by introducing restricted Comprehension is maybe a stretch.
Restricted Comphrension prevents the question from even being asked. So, it “solves it” by removing the object from the domain of discourse.
The Incompleteness Theorems are Meta-Theorems talking about Proper Theorems.
I’m not sure Set Theory has really solved the self-reference problem in any, real sense besides avoiding it. ( which may be the best solution possible)
The closest might be the Recursion Theorems, which allow functions to “build-themselves” by referencing earlier versions of themself. But, that isn’t proper self-reference.
My issue with the practicality of any kind of real world computation of self reference, is I believe it would require infinite time/energy/space. As each time you “update” your current self, you change, and so would need to update again- etc.. You could approximate a RDT decision tree, but not apply it. The exception being for “fixed-points” Decisions which stay constant when we apply the RDT decision algorithm.
The best advice I ever heard for Imposter Syndrome, was
“It’s okay, by definition nobody is qualified to do something- if it is truly cutting edge”
Thank you for this article.