Oh, the second one comes of wrong. I did mean the parent quote
> A formal system cannot in general prove that it is reliable
I hadn't noticed when I wrote that, formal system is an idiom - even more specific in this specific context. How confusing.
No, it does not. The second incompleteness theorem is provable in first-order Peano Arithmetic.
> Of course I'm in no position to say a similar thing about Goedels incompleteness theorem, and I even referred to it's result in higher order logics, but I still doubt the relevance, as many seem to be ignorant of his former completeness theorem.
I have no idea what you're trying to say, but I assure you that people who do this kind of research are aware of the completeness theorem.