My understanding is that a Bayesian has to be certain of the truth of whatever proposition that she conditions on when updating.
This isn't necessary. In many circumstances, you can approximate the probability of an observation you're updating on to 1, such as an observation that a coin came up heads. An observation never literally has a probability of 1 (you could be hallucinating, or be a brain in a jar, etc.) Sometimes observations are uncertain enough that you can't approximate them to 1, but you can still do the math to update on them ("Did I really see a mouse? I might have imagined it. Update on .7 probability observation of mouse.")
Yeah, but if your observation does not have a probability of 1 then Bayesian conditionalization is the wrong update rule. I take it this was Alex's point. If you updated on a 0.7 probability observation using Bayesian conditionalization, you would be vulnerable to a Dutch book. The correct update rule in this circumstance is Jeffrey conditionalization. If P1 is your distribution prior to the observation and P2 is the distribution after the observation, the update rule for a hypothesis H given evidence E is:
P2(H) = P1(H | E) P2(E) + P1(H | ~E) P2(~E)
If P2(E) is sufficiently close to 1, the contribution of the second term in the sum is negligible and Bayesian conditionalization is a fine approximation.
From the last thread:
Meta: