Numbers are not needed for anchoring. We could arrange the probabilities of the truth of statements into partially ordered sets. This po set can even include statements about the probabilistic relation between statements.

Well, we should be careful to avoid the barbers paradox though... things like x = {x is more likely then y} are a bad idea

I think it would be better to avoid just making up numbers until we absolutely have to, we actually find our selves playing a lottery for the continued existence of Earth, or there is some numerical process grounded in statistics that provides the numbers, resting on some assumptions. However, by anchoring probabilities in post sets we might get bounds on things for which we can not compute probabilities.