5 ms·

This is still a partial knowledge situation - you have the information that there are a certain proportion of colored balls in the chamber, but not the informat

This is still a partial knowledge situation - you have the information that there are a certain proportion of colored balls in the chamber, but not the information about their order. The probability includes the information we do know and allows inferences about information we don’t know.

st1x7 6y ago
Sure, I just can't agree with the parent statement that probability has nothing to do with the object it describes, which is demonstrably false.
- StavrosK 6y ago
  I don't think it's demonstrably false: If you don't know that the coin is weighted, the probability is 50%. Probabilities are predictions and estimates, not fundamentally about the thing itself, but about what we know about the thing.
  - deleted 6y ago
    [deleted]
  - mannykannot 6y ago
    The principle of indifference? I know that it is a commonplace assumption, but feels to me as though one is assuming one has more information than is justified. Coming back to the article's "economist's wager", is it rational to bet with even odds on something you know nothing about? If the assumption is interpreted as a testable hypothesis about outcomes, why would complete ignorance imply any particular result? On the other hand, if it is interpreted strictly as a statement about one's knowledge, why present it exactly as if one had sufficient knowledge of the situation to know that the probability is 0.5? Maybe the author will have an answer in part 2.
  - SAI_Peregrinus 6y ago
    > If you don't know that the coin is weighted, the probability is 50%. No, if it's weighted it's not 50%. Your prior probability is 50%, but neither a Bayesian nor a frequentist would claim the true probability is known before testing.
    - prmph 6y ago
      But that’s the thing: the “true“ probability is unknowable, and may even be an ill-defined concept. It is a deterministic process, so “probability“ is just a simplifying concept to describe our best guess belief about how the coin behaves in the aggregate.
      - SAI_Peregrinus 6y ago
        The true probability requires an infinite sequence of tests, so it's by definition unknowable. But it's what any sort of statistics attempts to approximate.
        myrryr 6y ago
        But, once the approximates are within undetectable differences from the "true probability" then you are done. Because not only is the true probability unknownable, it is also unencodeable, but, if we are to accept a limitation on encoding, then we CAN give a true probability subject to that. Like.... if we are to determine a coins probability to 1 decimal place, then we can do that.
    - jbay808 6y ago
      > the true probability Interesting expression. After testing, it turned out that you flipped it and it landed on heads. Does that mean that you've discovered that the "true probability" for that flip should have been 100% heads?
      - SAI_Peregrinus 6y ago
        IMO (I should have defined this) the true probability would require an infinite sequence of tests to determine.
- shawnz 6y ago
  They didn't say that it has "nothing to do with the object it describes" though. It has to do with your knowledge, which itself has to do with the object your knowledge describes
  - mannykannot 6y ago
    "The probability of that coin toss being 50% does not talk about the coin." I think there is a subtle equivocation going on here.
    - deleted 6y ago
      [deleted]
    - imtringued 6y ago
      Well, it's getting philosophical now. We do not have a way to experience the true nature of the coin. We can only experience an "image" [0] of the coin and we summarize all "images" of that object into knowledge. [0] by image I do include your vision, but also hearing, feeling and other methods of perception.
      - mannykannot 6y ago
        I do not think there is anything very philosophical here, just the point that the claim in the post I was replying to was demonstrably false. I am intrigued by the idea of the coin having a "true nature" that we have no way to experience; I would like to know what this elusive "true nature" is, but if we cannot experience it, I don't suppose you can tell me. Instead, I will settle for an explanation of how you know it has such a true nature.
- jbay808 6y ago
  It has to do with your knowledge of the object. To that extent, it has something to do with the object it describes.

st1x7 6y ago

Sure, I just can't agree with the parent statement that probability has nothing to do with the object it describes, which is demonstrably false.

StavrosK 6y ago
I don't think it's demonstrably false: If you don't know that the coin is weighted, the probability is 50%. Probabilities are predictions and estimates, not fundamentally about the thing itself, but about what we know about the thing.
- deleted 6y ago
  [deleted]
- mannykannot 6y ago
  The principle of indifference? I know that it is a commonplace assumption, but feels to me as though one is assuming one has more information than is justified. Coming back to the article's "economist's wager", is it rational to bet with even odds on something you know nothing about? If the assumption is interpreted as a testable hypothesis about outcomes, why would complete ignorance imply any particular result? On the other hand, if it is interpreted strictly as a statement about one's knowledge, why present it exactly as if one had sufficient knowledge of the situation to know that the probability is 0.5? Maybe the author will have an answer in part 2.
- SAI_Peregrinus 6y ago
  > If you don't know that the coin is weighted, the probability is 50%. No, if it's weighted it's not 50%. Your prior probability is 50%, but neither a Bayesian nor a frequentist would claim the true probability is known before testing.
  - prmph 6y ago
    But that’s the thing: the “true“ probability is unknowable, and may even be an ill-defined concept. It is a deterministic process, so “probability“ is just a simplifying concept to describe our best guess belief about how the coin behaves in the aggregate.
    - SAI_Peregrinus 6y ago
      The true probability requires an infinite sequence of tests, so it's by definition unknowable. But it's what any sort of statistics attempts to approximate.
      - myrryr 6y ago
        But, once the approximates are within undetectable differences from the "true probability" then you are done. Because not only is the true probability unknownable, it is also unencodeable, but, if we are to accept a limitation on encoding, then we CAN give a true probability subject to that. Like.... if we are to determine a coins probability to 1 decimal place, then we can do that.
  - jbay808 6y ago
    > the true probability Interesting expression. After testing, it turned out that you flipped it and it landed on heads. Does that mean that you've discovered that the "true probability" for that flip should have been 100% heads?
    - SAI_Peregrinus 6y ago
      IMO (I should have defined this) the true probability would require an infinite sequence of tests to determine.
shawnz 6y ago
They didn't say that it has "nothing to do with the object it describes" though. It has to do with your knowledge, which itself has to do with the object your knowledge describes
- mannykannot 6y ago
  "The probability of that coin toss being 50% does not talk about the coin." I think there is a subtle equivocation going on here.
  - deleted 6y ago
    [deleted]
  - imtringued 6y ago
    Well, it's getting philosophical now. We do not have a way to experience the true nature of the coin. We can only experience an "image" [0] of the coin and we summarize all "images" of that object into knowledge. [0] by image I do include your vision, but also hearing, feeling and other methods of perception.
    - mannykannot 6y ago
      I do not think there is anything very philosophical here, just the point that the claim in the post I was replying to was demonstrably false. I am intrigued by the idea of the coin having a "true nature" that we have no way to experience; I would like to know what this elusive "true nature" is, but if we cannot experience it, I don't suppose you can tell me. Instead, I will settle for an explanation of how you know it has such a true nature.
jbay808 6y ago
It has to do with your knowledge of the object. To that extent, it has something to do with the object it describes.