Can anyone please explain to me, in down-to-earth terms, why the axioms of ZF(C) make sense and should be accepted as "true".
If that's too much to ask, at least give a justification for why we should expect the axioms to be consistent (or if they're not, why that doesn't matter).
>inb4 someone invokes Godel
I'm not asking for a rigorous elementary proof of consistency, but rather any kind of philosophical justification, which is much more general than what Godel's results apply to.