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Jiro comments on Absolute Authority - Less Wrong
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This is supposed to be an argument against giving anything an 100% probability. I do agree with the concept, but this particular argument seems wrong. It's based on Conservation of Expected Evidence (if the "technical reasons of probability theory" refer to something else, let me know). However, the Bayes rule doesn't just imply that "having a chance of changing your mind" -> "you are not 100% certain", it also gives us bounds on what posteriors we can have. If we evaluate a 5% chance to changing our minds on something, that would seem to imply that we cannot put a >95% in our original claim.
So, the reason I reject this is as follows:
EY lays out possible evidence for 2+2=3 here. Imagine you believe at 50% level that someone will cause you to view that evidence tomorrow. Hypnosis, or some other method. Applying Bayes rule like EY seems to be applying it here, you should evaluate right now at most a 50% chance that 2+2=4. I think the rational thing to do in that situation (where putting the earplugs together does in fact show 2+2 equaling 4), is to believe that 2+2=4, with around the same much confidence as you do now. Therefore, there is something wrong with this line of reasoning.
If anyone can point to what I'm doing wrong, or thinks that in the situation I outlined, the rational thing to do is to evaluate a 50% or lower chance of 2+2=4, I'd like to hear about it.
Not everything that changes your mind is evidence within the meaning of Conservation of Expected Evidence. If there's a 50% chance you will believe X tomorrow, but that situation involves believing X because you're hypnotized, that's not evidence at all and you should not change your current beliefs based on that.
So then, moving on to the argument that "because I might believe 2+2=3 tomorrow (albeit very unlikely), I can't believe 2+2=4 100% today".
If Omega tells you that tomorrow you will believe that 2+2=3, most of your probability mass is concentrated in the possibility that 2+2=4, but you'll be somehow fooled, perhaps by hypnosis or nano-editing of your brain. Very little if any probability mass is for the theory that 2+2 really equals 3, and you'll have the major revelation tomorrow. In order to use this thought experiment to show that I don't have 100% confidence in 2+2=4, you need to assert that the second probability exists, however the thought experiment is also consistent with the first probability being high or one and the second being zero (you can't assume I agree that zero is not a probability, or you're begging the question).