Godel's Incompleteness Theorem

Godel's Incompleteness Theorems Wiki
The first theorem is that No program is capable of proving all the facts about the natural numbers.
The second theorem is that If a program can prove some basic facts about the natural numbers, it can't prove that it is consistent.
So what does this have to do with Epistemology?
It means that you can't develop a system that proves everything.
In essence, we're always stuck with incomplete systems.
All theories are incomplete.