Related: http://en.wikipedia.org/wiki/Gentzen%27s_consistency_proof http://en.wikipedia.org/wiki/Gentzen%27s_consistency_proof basically a proof of sorts that

Related: http://en.wikipedia.org/wiki/Gentzen%27s_consistency_proof http://en.wikipedia.org/wiki/Gentzen%27s_consistency_proof basically a proof of sorts that Peano arithmetic is consistent based on primitive recursive arithmetic and the "intuitively obvious" idea that there should exist no infinite decreasing sequence of numbers in any set with a minimum element. Also, the consistency of ZFC can be "proven" by proving the existence of a weakly inaccessible cardinal, which is a sort of thing whose existence obviously cannot be proven from within ZFC...