Belief inertia and awareness-evidence commutativity

It is alleged that imprecise probabilism can render one unable to update one’s credence in light of new evidence. While such belief inertia by itself is already quite worrying, I argue that it has other worrying epistemic implications that were previously unnoticed. It opens the possibility that one’s doxastic state depends not only on the evidence one has but also on the temporal order between awareness growth and evidence acquisition. I find this implication difficult to accept.