Godel's Proof

by Ernest Nagel

The proof attempts to settle the consistency of elliptic geometry by appealing to the consistency of Euclidean geometry. What emerges, then, is only this: elliptic geometry is consistent if Euclidean geometry is consistent. The authority of Euclid is thus invoked to demonstrate the consistency of a system which challenges the exclusive validity of Euclid. The inescapable question is: Are the axioms of the Euclidean system itself consistent?

Lol so true. Consistency of elliptic geometry is proved by taking help of Euclid geometry. But then we had rejected the idea that Euclidian axioms are true hence consistent. We are back to square one.