Cool, I think we’ve found our fundamental disagreement. I do not agree that “numerically correct within the context of conventional probability theory” is meaningful. That’s guessing the teacher’s password, rather than understanding how probability theory models reality.
In objective outside truth (if there is such a thing), all probabilities are 1 or 0 - a thing happens or it doesn’t. Individual assessments of probability are subjective, and are about knowledge of the thing, not the thing itself. Probabilities used in this way are predictions of future evidence.
If you don’t specify what evidence you’re predicting, it’s easy to get confused about what calculation you should use to calculate your probability.
Oh that’s an interesting way to approach things! If you were asked : a fair coin is tossed, what is the probability it will land on head—wouldn’t you reply 1⁄2, and wouldn’t you for your reply be relying on such a thing as conventional probability theory?
Yes for the first half, no for the second. I would reply 1⁄2, but not JUST because of conventional probability theory. It’s also because the unstated parts of “what will resolve the prediction”, in my estimation and modeling, match the setup of conventional probability theory. It’s generally assumed there’s no double-counting or other experience-affecting tomfoolery.
All right—but here the evidence predicted would simply be “the coin landed on heads”, no? I don’t really the contradiction between what you’re saying and conventional probability theory (more or less all which was developped with the specific idea of making predictions, winning games etc.) Yes I agree that saying “the coin landed on heads with probability 1/3″ is a somewhat strange way of putting things (the coin either did or did not land on heads) but it’s a shorthand for a conceptual framework that has firmly simple and sound foundations.
Cool, I think we’ve found our fundamental disagreement. I do not agree that “numerically correct within the context of conventional probability theory” is meaningful. That’s guessing the teacher’s password, rather than understanding how probability theory models reality.
In objective outside truth (if there is such a thing), all probabilities are 1 or 0 - a thing happens or it doesn’t. Individual assessments of probability are subjective, and are about knowledge of the thing, not the thing itself. Probabilities used in this way are predictions of future evidence.
If you don’t specify what evidence you’re predicting, it’s easy to get confused about what calculation you should use to calculate your probability.
Oh that’s an interesting way to approach things! If you were asked : a fair coin is tossed, what is the probability it will land on head—wouldn’t you reply 1⁄2, and wouldn’t you for your reply be relying on such a thing as conventional probability theory?
Yes for the first half, no for the second. I would reply 1⁄2, but not JUST because of conventional probability theory. It’s also because the unstated parts of “what will resolve the prediction”, in my estimation and modeling, match the setup of conventional probability theory. It’s generally assumed there’s no double-counting or other experience-affecting tomfoolery.
All right—but here the evidence predicted would simply be “the coin landed on heads”, no? I don’t really the contradiction between what you’re saying and conventional probability theory (more or less all which was developped with the specific idea of making predictions, winning games etc.) Yes I agree that saying “the coin landed on heads with probability 1/3″ is a somewhat strange way of putting things (the coin either did or did not land on heads) but it’s a shorthand for a conceptual framework that has firmly simple and sound foundations.