Should one require ‘extraordinary evidence for extraordinary claims’? I somehow feel that this notion is misguided
Extraordinary just means low probability. So if some claim is extraordinary (in this case, aliens) then it has a low probability. Similarly, you would need extraordinary evidence to update the prior to the “ordinary” range. If you look at the simple version of Bayes Theorem, it is P(H | E) = P(E | H)P(H) / P(E). If both P(E) and P(H) are low (i.e. extraordinary) then they will sort of cancel each other out and P(H | E) will be close to P(E | H). So the missing part of that phrase is the probability of the evidence given that the hypothesis (aliens) is true. This has to be a high probability.
Let’s say that I missed work yesterday. I tell my boss that the reason I missed work was because I was abducted by aliens. Sure, the probability of missing work given that I was abducted by aliens is pretty high, I would say 100%. But missing work in and of itself isn’t extraordinary so it isn’t enough to claim that aliens exist, and there are other more mundane explanations for why I would miss work. Maybe they aren’t 100%, but using BT in its entirety would still favor the more mundane explanations over the extraordinary one. On the other hand, if I walked into work with some sort of alien technology, this might be considered extraordinary evidence.
Personally, TV documentaries and eyewitness testimony aren’t extraordinary enough to move my prior about alien visitations in any really significant manner. There are other more mundane explanations for their existence that don’t have anything to do with aliens. Given that aliens don’t exist, I would still expect to see such evidences since humans aren’t perfect; people (and technology) will make all sorts of errors. Errors at a much higher rate than my prior for the existence of aliens.
Extraordinary just means low probability. So if some claim is extraordinary (in this case, aliens) then it has a low probability. Similarly, you would need extraordinary evidence to update the prior to the “ordinary” range. If you look at the simple version of Bayes Theorem, it is P(H | E) = P(E | H)P(H) / P(E). If both P(E) and P(H) are low (i.e. extraordinary) then they will sort of cancel each other out and P(H | E) will be close to P(E | H). So the missing part of that phrase is the probability of the evidence given that the hypothesis (aliens) is true. This has to be a high probability.
Let’s say that I missed work yesterday. I tell my boss that the reason I missed work was because I was abducted by aliens. Sure, the probability of missing work given that I was abducted by aliens is pretty high, I would say 100%. But missing work in and of itself isn’t extraordinary so it isn’t enough to claim that aliens exist, and there are other more mundane explanations for why I would miss work. Maybe they aren’t 100%, but using BT in its entirety would still favor the more mundane explanations over the extraordinary one. On the other hand, if I walked into work with some sort of alien technology, this might be considered extraordinary evidence.
Personally, TV documentaries and eyewitness testimony aren’t extraordinary enough to move my prior about alien visitations in any really significant manner. There are other more mundane explanations for their existence that don’t have anything to do with aliens. Given that aliens don’t exist, I would still expect to see such evidences since humans aren’t perfect; people (and technology) will make all sorts of errors. Errors at a much higher rate than my prior for the existence of aliens.