Summary of the second paragraph here.
Thesis: In any formal system* there exists a proposition that (a) is not provable in a formal system and (b) we can know to be true.
1.) Given any formal system, let proposition (P) be this formula is unprovable in the system
2.) If P is provable, a contradiction occurs.
3.) Therefore, P is known to be unprovable.
4.) If P is known to be unprovable it is known to be true.
5.) Therefore, P is (a) unprovable in a system and (b) known to be true.
*sufficient to give us arithmetic.
Just Thomism 