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Lumifer comments on Rationality Quotes August 2013 - Less Wrong
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Nope. "I'm certain that X is true now" is different from "I am certain that X is true and will be true forever and ever".
I am absolutely certain today is Friday. Ask me tomorrow whether my belief has changed.
In fact, unless you're insane, you probably already believe that tomorrow will not be Friday!
(That belief is underspecified- "today" is a notion that varies independently, it doesn't point to a specific date. Today you believe that August 16th, 2013 is a Friday; tomorrow, you will presumably continue to believe that August 16th, 2013 was a Friday.)
Not exactly that but yes, there is the reference issue which makes this example less than totally convincing.
The main point still stands, though -- certainty of a belief and its time-invariance are different things.
I very much doubt that you are absolutely certain. There are a number of outlandish but not impossible worlds in which you could believe that it is Friday, yet it might not be Friday; something akin to the world of The Truman Show comes to mind.
Unless you believe that all such alternatives are impossible, in which case you may be absolutely certain, but incorrectly so.
Define "absolute certainty".
In the brain-in-the-vat scenario which is not impossible I cannot be certain of anything at all. So what?
So you're not absolutely certain. The probability you assign to "Today is Friday" is, oh, nine nines, not 1.
Nope. I assign it the probability of 1.
On the other hand, you think I'm mistaken about that.
On the third tentacle I think you are mistaken because, among other things, my mind does not assign probabilities like 0.999999999 -- it's not capable of such granularity. My wetware rounds such numbers and so assigns the probability of 1 to the statement that today is Friday.
So if you went in to work and nobody was there, and your computer says it's Saturday, and your watch says Saturday, and the next thirty people you ask say it's Saturday... you would still believe it's Friday?
If you think it's Saturday after any amount of evidence, after assigning probability 1 to the statement "Today is Friday," then you can't be doing anything vaguely rational - no amount of Bayesian updating will allow you to update away from probability 1.
If you ever assign something probability 1, you can never be rationally convinced of its falsehood.
That's not true. There are ways to change your mind other than through Bayesian updating.
Sure. But by definition they are irrational kludges made by human brains.
Bayesian updating is a theorem of probability: it is literally the formal definition of "rationally changing your mind." If you're changing your mind through something that isn't Bayesian, you will get the right answer iff your method gives the same result as the Bayesian one; otherwise you're just wrong.
The original point was that human brains are not all Bayesian agents. (Specifically, that they could be completely certain of something)
... Okay?
Okay, so, this looks like a case of arguing over semantics.
What I am saying is: "You can never correctly give probability 1 to something, and changing your mind in a non-Bayesian manner is simply incorrect. Assuming you endeavor to be /cough/ Less Wrong, you should force your System 2 to abide by these rules."
What I think Lumifer is saying is, "Yes, but you're never going to succeed because human brains are crazy kludges in the first place."
In which case we have no disagreement, though I would note that I intend to do as well as I can.
Yes.
No, unless you define "rationally changing your mind" this way in which case it's just a circle.
Nope.
The ultimate criterion of whether the answer is the right one is real life.
While I'm not certain, I'm fairly confident that most people's minds don't assign probabilities at all. At least when this thread began, it was about trying to infer implicit probabilities based on how people update their beliefs; if there is any situation that would lead you to conclude that it's not Friday, then that would suffice to prove that your mind's internal probability is not Friday.
Most of the time, when people talk about probabilities or state the probabilities they assign to something, they're talking about loose, verbal estimates, which are created by their conscious minds. There are various techniques for trying to make these match up to the evidence the person has, but in the end they're still just basically guesses at what's going on in your subconscious. Your conscious mind is capable of assigning probabilities like 0.999999999.
Taking a (modified) page from Randaly's book, I would define absolute certainty as "so certain that one cannot conceive of any possible evidence which might convince one that the belief in question is false". Since you can conceive of the brain-in-the-vat scenario and believe that it is not impossible, I would say that you cannot be absolutely certain of anything, including the axioms and logic of the world you know (even the rejection of absolute certainty).
I don't have to believe that the alternatives are impossible; I just have to be certain that the alternatives are not exemplified.