Axioms and Illative Reasoning

oscillon writes in and comments: 

"It makes us uncomfortable to need axioms at the bottom of the pile. They are different than everything that lies above them and they look suspiciously like a cheat. We naturally want to break them down and figure out what they're made of, to reason beyond them. Your solution (and Lewis's) is to posit God. Ok, I can't say you're wrong. But that solution is just as far outside the system of logic above it than directly accepting them on faith."
 
Ah, friend, this is