The measure problem If mathematicians were like philosophers, trying to fully resolve an issue before advancing, then there would be no progress in mathematics. So, wherever there is doubt, they create an axiom and tell their colleagues to invoke it in their work, if and when they like. In this way, they avoid the search for truth, so that to focus solely on mathematical work, numbers and proof: they just need to say which axioms were used, and leave the 'what really is the case' to philosophers. Mathematical axioms, in the way they are used by mathematicians, do not have anything to do with 'truth' in the real sense, they are just there to help them in their games. After all, if something was obviously true and accepted by everyone, we wouldn't have an axiom for it, would we? :)