Meta-Mathematics: An exploration of Godels Incompleteness Theorems

The idea that mathematics could contain inherent contradictions acquired much speculation and criticism as it put into question the fundamental system by which we interpret the world. In searching for mathematical proofs that are consistent and hold no contradictions, Hilbert tried different methods one of which involved using models, but this proved logically incomplete, "for even if all the observed facts are in agreement with the axioms, the possibility is open that a hitherto unobserved fact may contradict them and so destroy their title to universality"(20). This gave rise to the clai…