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Unknowns comments on Self-modification is the correct justification for updateless decision theory - Less Wrong
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Perhaps I wasn't clear. I meant that Omega does not actually tell you what logical proposition it used. The phrase "some logical proposition" is literally what Omega says, it is not a placeholder for something more specific. All you have to go on is that of the things that Omega believes with probability .5, on average half of them are actually true.
No. A properly designed AGI should be able to figure out any logical fact that I know.
My point was that one particular argument you made does not actually support your point.
I've given such a logical fact before.
"After thinking about it for a sufficiently long time, the AI at some time or other will judge this statement to be false."
This might very well be a logical fact because it's truth or falsehood can be determined from the AI's programming, something quite logically determinate. But it is quite difficult for the AI to discover the truth of the matter.