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irrational comments on Circular belief updating - LessWrong
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I don't think I completely follow everything you say, but let's take a concrete case. Suppose I believe that Dark is extremely powerful and clever and wishes to convince me he doesn't exist. I think you can conclude from this that if I believe he exists, he can't possibly exist (because he'd find a way to convince me otherwise), so I conclude he can't exist (or at least the probability is very low). Now I've convinced myself he doesn't exist. But maybe that's how he operates! So I have new evidence that he does in fact exist. I think there's some sort of paradox in this situation. You can't say that this evidence is screened off, since I haven't considered the result of my reasoning until I have arrived at it. It seems to me that your belief oscillates between 2 numbers, or else your updates get smaller and you converge to some number in between.
LOL.
The argument goes something like this: "I refuse to prove that I exist,'" says God, "for proof denies faith, and without faith I am nothing."
"But," says Man, "The Babel fish is a dead giveaway, isn't it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don't. QED."
"Oh dear," says God, "I hadn't thought of that," and promptly vanishes in a puff of logic.
"Oh, that was easy," says Man, and for an encore goes on to prove that black is white and gets himself killed on the next zebra crossing.”
The scenario you outlined is exactly the same as Daisy's half of the piece ending in A3. The result of your reasoning isn't further evidence, it's screened off by the fact that it's your reasoning, and not the actions of an outside force.