  The main question that arises in light of the independence results is whether one can justify new axioms that settle the statements left undecided by the standard axioms.  There are two views.  On the first view, the answer is taken to be negative and one embraces a radical form of pluralism in which one has a plethora of equally legitimate extensions of the standard axioms.  On the second view, the answer is taken (at least in part) to be affirmative, and the results simply indicate that ZFC is too weak to capture the mathematical truths. This topic is quite involved and lies outside the scope of the present article.    