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snewmark comments on The Proper Use of Doubt - Less Wrong
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I think that unresolved doubt can and does serve a purpose. I think that becoming more comfortable with uncertainty, and refusing to come to a conclusion to avoid the uncomfortable feeling that comes with uncertainty, is valuable. I think that staying in a state of "I don't know" can be psychologically tougher than coming to a conclusion.
Sometimes I see people, or catch myself, jumping to conclusions in order to have a resolution. I've had to train myself to stay in the unresolved state longer, in order to eventually end up having a better answer. That does not necessarily mean seeking that answer right away, and sometimes the path to finding such an answer is not clear.
I don't agree with you that "A doubt that is not investigated might as well not exist. Every doubt exists to destroy itself, one way or the other. An unresolved doubt is a null-op; it does not turn the wheel, neither forward nor back."
I think that a doubt that is not investigated still serves as a placeholder in one's mind, a space carved out for uncertainty, so that if and when new evidence comes in, there is somewhere for a new model that includes it to take shape.
This seems to be popular opinion in the comments, and I'm inclined to agree that doubt can still be useful even if not investigated further. Yudkowsky pointed out above that the word "doubt" seems to have 2 meanings. It can refer either to an emotional state (such as the emotions a child feels when doubting Santa), or to a mathematical uncertainty (when you're not sure your conclusions are statistically significant).
In both cases, I can think of counterexamples where merely doubting without having the opportunity to act on those doubts still proves useful. In the mathematical sense, doubting provides an upper bound for how much you would trust a possibly-erroneous concision without investigating it. The emotional aspect cements this knowledge in your mind, and makes it come to mind much easier if it is needed in the future.
Perhaps doubting can best be thought of as having diminishing returns. The first time you think to doubt a statement, it is tested, and if it has no obvious flaws one can assign it a higher probability than one which hasn't been doubted. Additional thought returns less and less additional certainty, since it is less and less likely to disprove the statement. Eventually, the only value left is as a marker. Even then, the purpose of a red flag is to point out something that is actually uncertain, so the total value of a lingering doubt should go to zero if investigated forever.
Very well written, I just wanted to confirm something, I was under the impression that since nothing has 100% certainty, nothing can have a 0% uncertainty, you could get closer and closer, but you can never actually reach it. If I'm wrong or misunderstanding this I would appreciate it if someone would correct me, thanks.
That's my understanding as well. I was trying to say that, if you were to formalize all this mathematically, and took the limit as number of Bayesian updates n went to infinity, uncertainty would go to zero.
Since we don't have infinite time to do an infinite number of updates, in practice there is always some level of uncertainty > 0%.
There are some forms of doubts that you can easily reduce by simply adding more observations but not all. Seeing an infinitive amount of white swans doen't help you to completely rule out the black one.
MarsColony_in10years: Yeah, thanks. Sorry about the nitpicking.
ChristianKl: I think an infinite number would allow you to rule out the possibility (of a black swan that is). I thought that the problem was simply that we could never get an infinite number of them, but then again: I'm not certain.
To the extend that the word infinitive makes sense, you can see an infinitive number of white swans without seeing a black swan.