This is not.. really the right takeaway from his work. That not every true statement within a system is provable from its axioms, or that the consistency of a s

This is not.. really the right takeaway from his work. That not every true statement within a system is provable from its axioms, or that the consistency of a system is not provable within that system, does not mean that axioms are not useful. Indeed, what math is not grounded in the end by axioms?