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> His problem seems to be the extension of it to epistemology Isn't that a bit of a strawman? Bayesian epistemology as stated would require someone to believe

by qsort 5y ago

> His problem seems to be the extension of it to epistemology Isn't that a bit of a strawman? Bayesian epistemology as stated would require someone to believe something like "drawing without replacement from this urn, I got 100 white balls and 1 black ball, therefore there is a nonzero probability that this urn contains only white balls", which is not a belief I can imagine anybody to seriously hold.

pmoriarty 5y ago
See "The gambler's fallacy is not a fallacy"[1] (which was recently discussed[2] on HN). [1] - https://www.kevindorst.com/stranger_apologies/the-gamblers-fallacy-is-not-a-fallacy https://www.kevindorst.com/stranger_apologies/the-gamblers-f... [2] - https://news.ycombinator.com/item?id=30973324 https://news.ycombinator.com/item?id=30973324
rictic 5y ago
What's surprising about that belief?
- goatlover 5y 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 5y 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 5y 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 5y 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".
MatteoFrigo 5y ago
Here is my understanding of what Deutsch and the paper by Popper/Miller are trying to say. There are three concepts involved: an evidence "e", for example "I extracted 1 black ball"; a hypothesis "h", for example "the urn does not contain only white balls"; a theory "h <- e" that, by means of logic or otherwise, deduces the hypothesis from the evidence. Your (qsort) theory is that if you see a black ball then the hypothesis is correct. Everybody, including you, me, and Deutsch, agree that if the probability of the evidence goes up, then the probability of the hypothesis goes up as well. What Deutsch and Popper/Miller are also saying, however, is that if the probability of the evidence goes up then the probability of the theory goes down (proof in the paper). I need to study the paper more carefully, because I am not 100% sure that it is strictly correct (there are many factors that would transform a < into <= if they were 1, and I suspect that some are), but I believe the weaker statement that if the evidence goes up the probability of the theory does not go up at all. In any case, this conclusion is consistent with what all scientists have believed forever: the only way to increase confidence in a theory is to try to break it. Or at least they believed this until fact checkers and censorship came along and threw the baby away with the bathwater.
- o_nate 5y ago
  This is the best explanation I’ve seen yet of what Deutsch was getting at. I think he actually has a good point. The problem with misapplications of Bayesian probability is that they tend to produce a bogus sense of progress while eliding the interesting questions. For example take the hypothetical statement: “The news that a supercomputer has defeated the reigning Go champion has increased the probability that machines are capable of consciousness.” The form of this statement completely obscures the interesting question, which is: What is the causal connection between being good at Go and consciousness. There is an unspoken theory that the two are connected, but the statement offers no evidence for it, and hence is meaningless.
  - goatlover 5y ago
    For some reason, the Go example reminds me of the monolith in Clarke's 3001 and the protomolecule in The Expanse. The book authors describe both as very advanced technology that lack consciousness. They do what they're designed to do, but they do not experience doing it, and thus lack the advantage of a certain kind of relfective awareness the conscious constructs they create, such as Dave or Miller, do possess. The Star Trek holodeck also sometimes accomplishes this. I have no idea whether it's possible to create a machine that can generate conscious simulations without itself being conscious. But there's no Bayesian reasoning to apply to such scenarios, since we have no idea as of yet. They're philosophical arguments. And applying to that to current technology is misplaced.
chrisdirkis 5y ago
I could believe it, in this[1] sense. "It is possible to draw a black ball from an urn full of white balls, without any tricks" would pretty much upset my entire epistemic grounding, but with sufficient evidence, I don't see why I would refuse to believe it. Thus, I have no problem assigning it a non-zero (but insanely low) probability. [1] https://www.lesswrong.com/posts/6FmqiAgS8h4EJm86s/how-to-convince-me-that-2-2-3 https://www.lesswrong.com/posts/6FmqiAgS8h4EJm86s/how-to-con...
- emmelaich 5y ago
  Likewise the odds of drawing the ace of spades from a deck of cards is not 1/52. It is extremely close though.
dragonwriter 5y ago
Unless you replace the balls after drawing, there is a nonzero probability that the urn contains only white balls after the draw, though the probability is zero (under the assumption of stable ball colors) that it contained all white balls before the draw.
keithnz 5y ago
I think it's more like the black swan problem, you only see white swans such that you believe there is only white swans ( such that historically people made reference to a black swan to imply something that clearly didn't exist ). Which is the problem of induction. Eventually new knowledge was introduced and the knowledge situation completely changed.

by qsort 5y ago

pmoriarty 5y ago

See "The gambler's fallacy is not a fallacy"[1] (which was recently discussed[2] on HN). [1] - https://www.kevindorst.com/stranger_apologies/the-gamblers-fallacy-is-not-a-fallacy https://www.kevindorst.com/stranger_apologies/the-gamblers-f... [2] - https://news.ycombinator.com/item?id=30973324 https://news.ycombinator.com/item?id=30973324

rictic 5y ago

What's surprising about that belief?

goatlover 5y 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 5y 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 5y 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 5y 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".

MatteoFrigo 5y ago

Here is my understanding of what Deutsch and the paper by Popper/Miller are trying to say. There are three concepts involved: an evidence "e", for example "I extracted 1 black ball"; a hypothesis "h", for example "the urn does not contain only white balls"; a theory "h <- e" that, by means of logic or otherwise, deduces the hypothesis from the evidence. Your (qsort) theory is that if you see a black ball then the hypothesis is correct. Everybody, including you, me, and Deutsch, agree that if the probability of the evidence goes up, then the probability of the hypothesis goes up as well. What Deutsch and Popper/Miller are also saying, however, is that if the probability of the evidence goes up then the probability of the theory goes down (proof in the paper). I need to study the paper more carefully, because I am not 100% sure that it is strictly correct (there are many factors that would transform a < into <= if they were 1, and I suspect that some are), but I believe the weaker statement that if the evidence goes up the probability of the theory does not go up at all. In any case, this conclusion is consistent with what all scientists have believed forever: the only way to increase confidence in a theory is to try to break it. Or at least they believed this until fact checkers and censorship came along and threw the baby away with the bathwater.

o_nate 5y ago
This is the best explanation I’ve seen yet of what Deutsch was getting at. I think he actually has a good point. The problem with misapplications of Bayesian probability is that they tend to produce a bogus sense of progress while eliding the interesting questions. For example take the hypothetical statement: “The news that a supercomputer has defeated the reigning Go champion has increased the probability that machines are capable of consciousness.” The form of this statement completely obscures the interesting question, which is: What is the causal connection between being good at Go and consciousness. There is an unspoken theory that the two are connected, but the statement offers no evidence for it, and hence is meaningless.
- goatlover 5y ago
  For some reason, the Go example reminds me of the monolith in Clarke's 3001 and the protomolecule in The Expanse. The book authors describe both as very advanced technology that lack consciousness. They do what they're designed to do, but they do not experience doing it, and thus lack the advantage of a certain kind of relfective awareness the conscious constructs they create, such as Dave or Miller, do possess. The Star Trek holodeck also sometimes accomplishes this. I have no idea whether it's possible to create a machine that can generate conscious simulations without itself being conscious. But there's no Bayesian reasoning to apply to such scenarios, since we have no idea as of yet. They're philosophical arguments. And applying to that to current technology is misplaced.

chrisdirkis 5y ago

I could believe it, in this[1] sense. "It is possible to draw a black ball from an urn full of white balls, without any tricks" would pretty much upset my entire epistemic grounding, but with sufficient evidence, I don't see why I would refuse to believe it. Thus, I have no problem assigning it a non-zero (but insanely low) probability. [1] https://www.lesswrong.com/posts/6FmqiAgS8h4EJm86s/how-to-convince-me-that-2-2-3 https://www.lesswrong.com/posts/6FmqiAgS8h4EJm86s/how-to-con...

emmelaich 5y ago
Likewise the odds of drawing the ace of spades from a deck of cards is not 1/52. It is extremely close though.

dragonwriter 5y ago

Unless you replace the balls after drawing, there is a nonzero probability that the urn contains only white balls after the draw, though the probability is zero (under the assumption of stable ball colors) that it contained all white balls before the draw.

keithnz 5y ago

I think it's more like the black swan problem, you only see white swans such that you believe there is only white swans ( such that historically people made reference to a black swan to imply something that clearly didn't exist ). Which is the problem of induction. Eventually new knowledge was introduced and the knowledge situation completely changed.