Impredicativity is the property you may want to dig into for formal proofs on why self references can be problematic. There is an important difference between

Impredicativity is the property you may want to dig into for formal proofs on why self references can be problematic. There is an important difference between semantically complete and syntactically complete that may cause some barriers. Gödels completeness theorem is about semantic completeness while his incompleteness theorems are about syntactic completeness. From Wikipedia: > A formal system is syntactically complete if and only if no unprovable sentence can be added to it without introducing an inconsistency. 'This statement is false', which Gödel mapped to natural numbers is an example of that inconsistency. If KC was computable, there would be an infinity of paradoxes like the interesting number paradox. The Berry paradox that is linked to in the INP link in the page has a subheading that relates it to KC computability. https://en.m.wikipedia.org/wiki/Berry_paradox https://en.m.wikipedia.org/wiki/Berry_paradox