Interesting point. Since physics does appear on the surface to be continuous, I can’t rule out continuous propositions. Perhaps the amended saying should read “0 and 1 are not probability masses, and 0 is not a probability density.”
I’ve always been really confused by this but it isn’t clear that an event with P=0 is an impossible event unless we’re talking about the probability of an event in a finite set of possible events. This is how it was explained to me: Think of a dart board with a geometric line across it. That line represents probability space. An event with P=.5 is modeled by marking the middle of the line. If someone throws a dart at the line there is an equal chance that it lands at any point along the line. However, at any given point the probability that the dart lands there is zero.
And, having assigned p(A) = 0 to such an event A I will not be able to rationally update away from zero without completely discarding my former model. There is no evidence that can cause me to rationally update p(A) = 0 to something else ever. Discard it and overwrite with something completely unrelated perhaps, but never update.
Interesting point. Since physics does appear on the surface to be continuous, I can’t rule out continuous propositions. Perhaps the amended saying should read “0 and 1 are not probability masses, and 0 is not a probability density.”
Oh. I was expecting your belief to be as with infinite-set atheism: that we never actually see an infinitely precise measurement.
We don’t, but what if there are infinitely precise truths nonetheless? The math of Bayesianism would require assigning them probabilities.
And, having assigned p(A) = 0 to such an event A I will not be able to rationally update away from zero without completely discarding my former model. There is no evidence that can cause me to rationally update p(A) = 0 to something else ever. Discard it and overwrite with something completely unrelated perhaps, but never update.