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Watercressed comments on Infinite Certainty - Less Wrong
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So by that logic I should assign a nonzero probability to ¬(A→A). And if something has nonzero probability, you should bet on it if the payout is sufficiently high. Would you bet any amount of money or utilons at any odds on this proposition? If not, then I don't believe you truly believe 100% certainty is impossible. Also, 100% certainty can't be impossible, because impossibility implies that it is 0% likely, which would be a self-defeating argument. You may find it highly improbable that I can truly be 100% certain. What probability do you assign to me being able to assign 100% probability?
When I say 100% certainty is impossible, I mean that there are no cases where assigning 100% to something is correct, but I have less than 100% confidence in this claim. It's similar to the claim that it's impossible to travel faster than the speed of light.