Why would you have problems with Gödel's incompleteness theorems (which are, I assume, the ones you are referring to), and why do you put 'theorem' in quotes as if they aren't actually theorems?
A sort of uneasiness about their symbolic basis to start off with, nothing subsequent - I can follow it. Lack of understanding. That 'it smells' feeling. I'm not suggest they are wrong, just asking. Its okay to ask?
Well perhaps you have the same problem as Whitehead and Russell? In GEB Hofstadter IIRC is quite harsh on them for their intellectual timidity in not being able to face the paradox inherent in Godel's Theorem...Paradoxes can "feel" uncomfortable.
That sufficiently capable logical systems are necessarily incomplete can be uncomfortable, especially if the beauty of completeness has been your lifelong goal.
But on the other hand, it's very cool that this provides an opening for consciousness and free will to arise.
If you want something that will feel more intuitive then quantum computing since democritus has a proof related to Turing machines that always seemed far more intuitive to me. http://www.scottaaronson.com/democritus/lec3.html
