Mathematicians consider them to be true because they are provably true, i.e., they hold in the unique up to isomorphism model of the theory Ordinals, which subsumes ZFC.
Ok, so Ordinals is the new foundation of mathematics so to speak? Doesn’t that mean that all of mathematics can be formalized within this Ordinals theory?
All of classical mathematics before 1930 can be formalized in the the theory Ordinals. However, formalizing digital computation requires the theory Actors, which is axiomatized here:
(Nope.)