  This raises a challenge for the two aforementioned optimistic views concerning the nature of mathematical truth.  To begin with it shows that we cannot work with a fixed axiom system T.  We will always need to introduce new axioms.  More importantly, it raises the question of how one is to justify these new axioms, for as one continues to add stronger and stronger axioms the claim that they are either self-evident or definitive of the subject matter will grow increasingly more difficult to defend.