What was being trying drawn was a parallel from “A numerical system can be hard to prove correct, in unexpected ways” to “A human system can be hard to prove co

What was being trying drawn was a parallel from “A numerical system can be hard to prove correct, in unexpected ways” to “A human system can be hard to prove correct, in unexpected ways”. Recognising this is part of accepting ones own limits. Gödel in no way proves this, as you note, and my wording should have made it more clear that I understand that. The essence of his result is easily analogised, though.