IMO, arbitrariness cascades down levels of concreteness.
That doesn’t mean the answer can be arbitrarily picked. If I arbitrarily decide on a statement being a theorem in a set theory, I might still be wrong even if its axioms are in some sense arbitrary.
That doesn’t mean the answer can be arbitrarily picked. If I arbitrarily decide on a statement being a theorem in a set theory, I might still be wrong even if its axioms are in some sense arbitrary.