In his objection to the Austrian embrace of radical uncertainty, which Bob mentioned below, Bryan Caplan writes:
"But if people really assigned p=0 to an event, than the arrival of counter-evidence should make them think that they are delusional, not than a p=0 event has occurred."
What Caplan is relying on here is the theory of "Bayesian updating," which supposedly describes how rational thinkers change the probability they assign to a new theory in the light of new evidence. I don't want to go into the details here -- they are unimportant for my point -- but the basic idea is that you "start out" by assigning some "prior probabilities" to various theories about some phenomenon, or outcomes of some event, and then multiply those "priors" by a factor based on how much more or less likely new evidence makes the prior.
For instance, you are a late 19th century physicist, and you are evaluating how likely it is the Newtonian mechanics is the true description of matter in motion. At that time, there would have been physicists who would assign p=1 to it being true, and p=0 to it being false. At the very least, many physicists would have assigned p=0 to something as weird as quantum mechanics being true!
Now, as the years pass, you are presented with startling new evidence about black body radiation, the photoelectric effect, and so on, and with a startling new theory in addition. According to the theory of Bayesian updating, the "rational" response is just to think you must be delusional in believing you have heard this new data! You had assigned an alternative theory a prior of 0, and now no factor the new evidence recommends multiplying that prior by can ever change that initial assignment of p=0.
Of course, that is not what real scientists did at all. Instead, they assigned whole new "priors" -- they thought, "Mon Dieu, I had never considered the possibility of this theory or this evidence, and therefore I was in a state of 'radical uncertainty,' and ought to re-think everything." But allowing that maneuver thwarts the whole motive for Bayesian updating, which is to turn rational choice between theories into a formal, mechanical procedure.
Thank God scientists are not "rational" Bayesian updaters, and thank Bryan Caplan for providing a good example of why it's good that they are not.