What kind of misrepresentation you are talking about? You have literally just claimed that there is no way to know whether a particular probabilistic model correctly represents the system.
Since what I said was that probability theory makes no restrictions on how to assign values, but that you have to make assignments that are reasonable based on things like the Principle of Indifference, this would be an example of misrepresentation.
If what you are suggesting were true, then the correct answer to “What is a probability of a fair coin toss, about which you know nothing else, to come Heads?”, would be: “It is either 0 or 1, but we can’t tell.
What? No, absolutely not! It would be: we lack any reason to expect any outcome more than another, so we are indifferent between both outcomes so 1⁄2 for both of them. The exact same kind of reasoning for both logical and empirical uncertainty.
You claim that “the probability that the nth digit of pi, in base 10, is 1⁄10 for each possible digit,” is assigning a non-zero probability to nine false statements, and probability that is less than 1 to one true statement. I am saying that it such probabilities apply only if we do not apply the formula that will determine that digit.
I claim that the equivalent statement, when I flip a coin but place my hand over it before you see the result, is “the probability that the coin landed Heads is 1⁄2, as is the probability that it landed Tails.” And that the truth of these two statements is just as deterministic, if I lift my hand. Or if I looked before I hid the coin. Or if someone has a x-ray that can see it. That the probability in question is about the uncertainty when no method is applied that determine the truth of the statements, even when we know such methods exist.
I’m saying that this is not a question in epistemology, not that epistemology is invalid.
And the reason the SB problem is pertinent, is because it does not matter if H+Tue can be observed. It is one of the outcomes that is possible.
Since what I said was that probability theory makes no restrictions on how to assign values, but that you have to make assignments that are reasonable based on things like the Principle of Indifference
That’s not what you’ve said at all. Re-read our comment chain. There is not a single mention of principle of indifference by you there. I’ve specifically brought up an example of a fair coin about which we know nothing else and yet you agreed that any number from 0 to 1 is the right answer to this problem. The first time you’ve mentioned principle of indifference under this post is in an answer to another person, which happened after my alleged misrepresentation of yours.
Now, I’m happy to assume that you’ve meant this all the time and just was unable to communicate your views properly. Please do better next time. But for now let me try to outline your views as far as I understand them, which do appear less ridiculous now:
You believe that probability theory only deals with whether something is a probability space at all—does it fit the axioms or not. And the question which valid probability space is applicable to a given problem based on some knowledge level, doesn’t have a “true” answer. Instead there is a completely separate category of “reasonableness” and some probability spaces are reasonable to a given problem based on the principle of uncertainty, but this is a completely separate domain from probability theory.
Please correct me, what I got wrong and then I hope we will be able to move forward.
You claim that “the probability that the nth digit of pi, in base 10, is 1⁄10 for each possible digit,” is assigning a non-zero probability to nine false statements, and probability that is less than 1 to one true statement.
No, I don’t. I’m ready to entertain this framework, but then I don’t see any difference compared to an example with empirical uncertainty. Do you see this difference? Do you think there is some fundamental reason why we can say that probability of a coin to be Heads is 1⁄2 and yet we can’t say the same about the probability of a particular unknown to us digit of pi to be even?
I am saying that it such probabilities apply only if we do not apply the formula that will determine that digit.
You mean, before we apply the formula, right? Suppose we are going to apply the formula in a moment, we can still say that before we applied it the probability for any digit is 1⁄10, can we? And after we applied the formula we know which digit it is so it’s 1 for this particular digit and 0 for all the rest.
I claim that the equivalent statement, when I flip a coin but place my hand over it before you see the result, is “the probability that the coin landed Heads is 1⁄2, as is the probability that it landed Tails.” And that the truth of these two statements is just as deterministic, if I lift my hand. Or if I looked before I hid the coin. Or if someone has a x-ray that can see it. That the probability in question is about the uncertainty when no method is applied that determine the truth of the statements, even when we know such methods exist.
No disagreement here. Do you agree that the scenarios with logical and empirical uncertainty work exactly the same way?
I’m saying that this is not a question in epistemology
If it’s neither the question of probability theory nor epistemology, what is it a question of? How long are you going to pass the buck of it before engaging with this question? And what is the answer?
Since what I said was that probability theory makes no restrictions on how to assign values, but that you have to make assignments that are reasonable based on things like the Principle of Indifference, this would be an example of misrepresentation.
You claim that “the probability that the nth digit of pi, in base 10, is 1⁄10 for each possible digit,” is assigning a non-zero probability to nine false statements, and probability that is less than 1 to one true statement. I am saying that it such probabilities apply only if we do not apply the formula that will determine that digit.
I claim that the equivalent statement, when I flip a coin but place my hand over it before you see the result, is “the probability that the coin landed Heads is 1⁄2, as is the probability that it landed Tails.” And that the truth of these two statements is just as deterministic, if I lift my hand. Or if I looked before I hid the coin. Or if someone has a x-ray that can see it. That the probability in question is about the uncertainty when no method is applied that determine the truth of the statements, even when we know such methods exist.
I’m saying that this is not a question in epistemology, not that epistemology is invalid.
And the reason the SB problem is pertinent, is because it does not matter if H+Tue can be observed. It is one of the outcomes that is possible.
That’s not what you’ve said at all. Re-read our comment chain. There is not a single mention of principle of indifference by you there. I’ve specifically brought up an example of a fair coin about which we know nothing else and yet you agreed that any number from 0 to 1 is the right answer to this problem. The first time you’ve mentioned principle of indifference under this post is in an answer to another person, which happened after my alleged misrepresentation of yours.
Now, I’m happy to assume that you’ve meant this all the time and just was unable to communicate your views properly. Please do better next time. But for now let me try to outline your views as far as I understand them, which do appear less ridiculous now:
You believe that probability theory only deals with whether something is a probability space at all—does it fit the axioms or not. And the question which valid probability space is applicable to a given problem based on some knowledge level, doesn’t have a “true” answer. Instead there is a completely separate category of “reasonableness” and some probability spaces are reasonable to a given problem based on the principle of uncertainty, but this is a completely separate domain from probability theory.
Please correct me, what I got wrong and then I hope we will be able to move forward.
No, I don’t. I’m ready to entertain this framework, but then I don’t see any difference compared to an example with empirical uncertainty. Do you see this difference? Do you think there is some fundamental reason why we can say that probability of a coin to be Heads is 1⁄2 and yet we can’t say the same about the probability of a particular unknown to us digit of pi to be even?
You mean, before we apply the formula, right? Suppose we are going to apply the formula in a moment, we can still say that before we applied it the probability for any digit is 1⁄10, can we? And after we applied the formula we know which digit it is so it’s 1 for this particular digit and 0 for all the rest.
No disagreement here. Do you agree that the scenarios with logical and empirical uncertainty work exactly the same way?
If it’s neither the question of probability theory nor epistemology, what is it a question of? How long are you going to pass the buck of it before engaging with this question? And what is the answer?