What exactly do you mean by "empiricism does not hold"? Do you mean that there are no laws governing reality? Is that even a thinkable notion? I'm not sure. Or perhaps you mean that everything is probabilistically independent from everything else. Then no update would ever change the probability distribution of any variable except the one on whose value we update, but that is something we could notice. We just couldn't make any effective predictions on that basis - and we would know that.