5 ms·

What's surprising about that belief?

by rictic 4y ago

goatlover 4y ago
It's logically invalid. You can't have an urn filled with only white balls and draw a black ball. That would mean the urn wasn't filled with only white balls. There's zero probability the urn contained only white balls after you draw that black ball. Before you might have given a nonzero probability because you didn't know whether there was a black ball. But once you know there is, you can't have some nonzero belief in there only being white balls.
- rictic 4y ago
  Ah, I thought you you were talking about the urn after the balls had been drawn. Still, I've been to enough magic shows, been fooled by enough subtly-wrong mathematical proofs, been utterly convinced that my program's behavior was impossible, etc that I side with the bayesian perspective here. I don't think there's a single thing that I'm justified in saying is true with 100% probability. Or, in essay form: https://www.lesswrong.com/posts/QGkYCwyC7wTDyt3yT/0-and-1-are-not-probabilities https://www.lesswrong.com/posts/QGkYCwyC7wTDyt3yT/0-and-1-ar...
  - goatlover 4y ago
    > I don't think there's a single thing that I'm justified in saying is true with 100% probability. Not even simple deductive proofs? 2+2=4 by definition. There's no probability for it being wrong. We couldn't do math if that wasn't the case. It's not even correct to assign those kinds of statements a probability. Now there is a possibility for humans to make mistakes with complicated proofs, as you pointed out. But the correct proof doesn't have a probability, only the belief in it being correct. For empirical matters, I'm not sure what sort of probability you could assign to some skeptical scenario like it's all a dream, or nobody exists outside your mind, or we live inside a simulation. We take it that there's a world with other people for granted. Sure, you can be fooled into thinking a black ball was pulled out of an urn of white balls, but whether the urn has all white balls is just a fact, not a probability. And under proper conditions, we should be able to verify that fact. To doubt that is to entertain wild skeptical scenarios where we can't really do science. At any rate, I don't see that sort of reasoning as Bayesian. It's just radical skepticism.
    - rictic 4y ago
      We absolutely can do math in the face of some probability of being wrong about our proofs (and the proofs of our proof systems, and our proofs of the consistency of our logics, and so on). I know this because we do, in fact, do math and some of our proofs are almost certainly wrong. Obviously I couldn't tell you which generally accepted proofs are wrong, only that we've drawn a few black balls from the urn of double-checking-established-proofs already, and so we should not assume that we won't find more. Imre Lakatos' essay Proofs and Refutations is a fun read on the subject. A simple deductive proof of 2+2=4 (say in Peano Arithmetic) is clear enough that I'd give it a very small chance of being wrong, easily less than 10^-9 but certainly not less than 10^-100. To push something below a probability like 10^-100 one would have to be unreasonably confident in things like "I haven't developed a brain injury causing me to be very confident in 2+2=4 and confabulating all other evidence as needed". Such a thing is absurdly unlikely of course, but a 10^-100 occurrence is far, far less likely still. > Sure, you can be fooled into thinking a black ball was pulled out of an urn of white balls, but whether the urn has all white balls is just a fact, not a probability. And under proper conditions, we should be able to verify that fact. To doubt that is to entertain wild skeptical scenarios where we can't really do science. You can verify it enough put the odds of it low enough to arguendo it as true for most purposes, but that's because for most purposes a certain probability of being wrong is acceptable, and once you've pushed something far below that threshold then you can fairly safely ignore it. As an intuition pump, imagine that you have personally drawn the balls from the urn. You drew a black ball and carefully observed it. Then, someone approaches you and offers to make you a bet: if the urn had ever contained a black ball then he would pay you one dollar, otherwise you would owe him a hundred million dollars. He hands you a clear, unambiguous, and legally enforceable contract to that effect. Do you sign? If you believe that there is a 100% chance that you drew a black ball, then there's a zero percent chance that you'll lose this bet. It's a free dollar, why wouldn't you sign it? > To doubt that is to entertain wild skeptical scenarios where we can't really do science. > At any rate, I don't see that sort of reasoning as Bayesian. It's just radical skepticism. We can do science in the face of the probability that we might be wrong about anything and everything, the key thing is to keep in mind the bounds – at least roughly – of the different ways that we can be wrong. It does involve a bit of humility, but not a step change compared to the ordinary scientific humility of "this is the best answer we have so far, but it could be wrong".

What's surprising about that belief?

by rictic 4y ago

What's surprising about that belief?

It's logically invalid. You can't have an urn filled with only white balls and draw a black ball. That would mean the urn wasn't filled with only white balls. There's zero probability the urn contained only white balls after you draw that black ball. Before you might have given a nonzero probability because you didn't know whether there was a black ball. But once you know there is, you can't have some nonzero belief in there only being white balls.

rictic 4y ago
Ah, I thought you you were talking about the urn after the balls had been drawn. Still, I've been to enough magic shows, been fooled by enough subtly-wrong mathematical proofs, been utterly convinced that my program's behavior was impossible, etc that I side with the bayesian perspective here. I don't think there's a single thing that I'm justified in saying is true with 100% probability. Or, in essay form: https://www.lesswrong.com/posts/QGkYCwyC7wTDyt3yT/0-and-1-are-not-probabilities https://www.lesswrong.com/posts/QGkYCwyC7wTDyt3yT/0-and-1-ar...
- goatlover 4y ago
  > I don't think there's a single thing that I'm justified in saying is true with 100% probability. Not even simple deductive proofs? 2+2=4 by definition. There's no probability for it being wrong. We couldn't do math if that wasn't the case. It's not even correct to assign those kinds of statements a probability. Now there is a possibility for humans to make mistakes with complicated proofs, as you pointed out. But the correct proof doesn't have a probability, only the belief in it being correct. For empirical matters, I'm not sure what sort of probability you could assign to some skeptical scenario like it's all a dream, or nobody exists outside your mind, or we live inside a simulation. We take it that there's a world with other people for granted. Sure, you can be fooled into thinking a black ball was pulled out of an urn of white balls, but whether the urn has all white balls is just a fact, not a probability. And under proper conditions, we should be able to verify that fact. To doubt that is to entertain wild skeptical scenarios where we can't really do science. At any rate, I don't see that sort of reasoning as Bayesian. It's just radical skepticism.
  - rictic 4y ago
    We absolutely can do math in the face of some probability of being wrong about our proofs (and the proofs of our proof systems, and our proofs of the consistency of our logics, and so on). I know this because we do, in fact, do math and some of our proofs are almost certainly wrong. Obviously I couldn't tell you which generally accepted proofs are wrong, only that we've drawn a few black balls from the urn of double-checking-established-proofs already, and so we should not assume that we won't find more. Imre Lakatos' essay Proofs and Refutations is a fun read on the subject. A simple deductive proof of 2+2=4 (say in Peano Arithmetic) is clear enough that I'd give it a very small chance of being wrong, easily less than 10^-9 but certainly not less than 10^-100. To push something below a probability like 10^-100 one would have to be unreasonably confident in things like "I haven't developed a brain injury causing me to be very confident in 2+2=4 and confabulating all other evidence as needed". Such a thing is absurdly unlikely of course, but a 10^-100 occurrence is far, far less likely still. > Sure, you can be fooled into thinking a black ball was pulled out of an urn of white balls, but whether the urn has all white balls is just a fact, not a probability. And under proper conditions, we should be able to verify that fact. To doubt that is to entertain wild skeptical scenarios where we can't really do science. You can verify it enough put the odds of it low enough to arguendo it as true for most purposes, but that's because for most purposes a certain probability of being wrong is acceptable, and once you've pushed something far below that threshold then you can fairly safely ignore it. As an intuition pump, imagine that you have personally drawn the balls from the urn. You drew a black ball and carefully observed it. Then, someone approaches you and offers to make you a bet: if the urn had ever contained a black ball then he would pay you one dollar, otherwise you would owe him a hundred million dollars. He hands you a clear, unambiguous, and legally enforceable contract to that effect. Do you sign? If you believe that there is a 100% chance that you drew a black ball, then there's a zero percent chance that you'll lose this bet. It's a free dollar, why wouldn't you sign it? > To doubt that is to entertain wild skeptical scenarios where we can't really do science. > At any rate, I don't see that sort of reasoning as Bayesian. It's just radical skepticism. We can do science in the face of the probability that we might be wrong about anything and everything, the key thing is to keep in mind the bounds – at least roughly – of the different ways that we can be wrong. It does involve a bit of humility, but not a step change compared to the ordinary scientific humility of "this is the best answer we have so far, but it could be wrong".