Watercressed comments on Infinite Certainty - Less Wrong

32 Post author: Eliezer_Yudkowsky 09 January 2008 06:49AM

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Comment author: DSherron 28 June 2013 06:48:15PM 0 points [-]

Sure, it sounds pretty reasonable. I mean, it's an elementary facet of logic, and there's no way it's wrong. But, are you really, 100% certain that there is no possible configuration of your brain which would result in you holding that A implies not A, while feeling the exact same subjective feeling of certainty (along with being able to offer logical proofs, such that you feel like it is a trivial truth of logic)? Remember that our brains are not perfect logical computers; they can make mistakes. Trivially, there is some probability of your brain entering into any given state for no good reason at all due to quantum effects. Ridiculously unlikely, but not literally 0. Unless you believe with absolute certainty that it is impossible to have the subjective experience of believing that A implies not A in the same way you currently believe that A implies A, then you can't say that you are literally 100% certain. You will feel 100% certain, but this is a very different thing than actually literally possessing 100% certainty. Are you certain, 100%, that you're not brain damaged and wildly misinterpreting the entire field of logic? When you posit certainty, there can be literally no way that you could ever be wrong. Literally none. That's an insanely hard thing to prove, and subjective experience cannot possibly get you there. You can't be certain about what experiences are possible, and that puts some amount of uncertainty into literally everything else.

Comment author: OccamsTaser 28 June 2013 07:29:39PM 2 points [-]

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?

Comment author: Watercressed 28 June 2013 09:08:03PM 1 point [-]

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.