Eliezer_Yudkowsky comments on Parapsychology: the control group for science - Less Wrong
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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. (Edit again: You can skip the rest of this paragraph and the next if you are smarter than me and already get continuous probability distributions. I'm obviously behind today.)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.
I think the probability of any particular complex entity, event or law existing can be said to have a probability of zero absent a creator or natural selection or some other mechanism for enabling complexity. Of course this is really counterintuitive since our evolved understanding of probability deals with finite sets of possibilities. Also it means that 'impossible' can't be assigned a probability. (Edit: Also, the converse is true. The probability that the dart lands anywhere other than the spot you pick is 1 so certainty can't be mapped as 1 either.)
Also, imperfect Bayesians will sometimes assign less than ideal probabilities to things. A perfect Bayesian would presumably never wrongly declare something impossible because it could envision possible future evidence that would render the thing possible. But regular people are going to misinterpret evidence and fail to generate hypotheses so they might sometimes think something is impossible only to later have it's possibility thrown in their faces.
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.