Generally if you approach probability as an extension of logic, probability is always relative to some evidence. Hardcore frequency dogmatists like John Venn for example thought that this is completely wrong: “the probability of an event is no more relative to something else than the area of a field is relative to something else.”
So thinking probabilities existing as “things itself” taken to the extreme could lead one to the conclusion that one cant say much for example about single-case probabilities. Lets say I take HIV-test and it comes back positive. You dont find it weird to say that it is not OK to judge probabilities of me having the HIV based on that evidence?
So thinking probabilities existing as “things itself” taken to the extreme could lead one to the conclusion that one cant say much for example about single-case probabilities.
Thinking probabilities can exists in the territory leads to no such conclusion. Thinking probabilities exist only in the territory may lead to such a conclusion, but that is a strawman of the points that are being made.
It would be insane to deny that frequencies exist, or that they can be represented by a formal system derived from the Kolmogorov (or Cox) axioms.
It would also be insane to deny that beliefs exist, or that they can be represented by a formal system derived from the Kolmogorov (or Cox) axioms.
I think this confusion would all go away if people stopped worrying about the semantic meaning of the word “probability” and just specified whether they are talking about frequency or belief. It puzzles me when people insist that the formal system can only be isomorphic to one thing, and it is truly bizarre when they take sides in a holy war over which of those things it “really” represents. A rational decision maker genuinely needs both the concept of frequency and the concept of belief.
For instance, an agent may need to reason about the proportion (frequency) P of Everett branches in which he survives if he makes a decision, and also about how certain he is about his estimate of that probability. Let’s say his beliefs about the probability P follow a beta distribution, or any other distribution bounded by 0 and 1. In order to make a decision, he may do something like calculate a new probability Q, which is the expected value of P under his prior. You can interpret Q as the agent’s beliefs about the probability of dying, but it also has elements of frequency.
You can make the untestable claim that all Everett branches have the same outcome, and therefore that Q is determined exclusively by your uncertainty about whether you will live or die in all Everett branches. This would be Bayesian fundamentalism. You can also go to the other extreme and argue that Q is determined exclusively by P, and that there is no reason to consider uncertainty. That would be Frequentist fundamentalism. However, there is a spectrum between the two and there is no reason we should only allow the two edge cases to be possible positions. The truth is almost certainly somewhere in between.
Thinking “probability exists only in the territory” is exactly taking the idea that probabilities exists as “things itself” to the extreme as i wrote. This view is not a strawman of dogmatic frequentists position, as you can see from the John Venn quote.
I feel the need to point that i have tried to describe the context of the debate where the heuristic: “uncertainty exists in the map, not in the territory” was given in the first place. This whole historical debate started from the idea that probability as a degree of belief does not mean anything. This was the start. “Fallacious rubbish”, as Fisher puts it.
I have tried to show that one can have this very extreme position even if there exists only epistemic uncertainty. One can answer to this position by describing how in some situations the uncertainty exists in the map, not in the territory. This is the context where that general heuristic is used and the background that it should be judged against.
“A rational decision maker genuinely needs both the concept of frequency and the concept of belief.” Amen!
Generally if you approach probability as an extension of logic, probability is always relative to some evidence/
Maybe, but so what? That doesn’t establish any point of interest. It doesn’t establish Bayes over Frequentisim, since frequentists still need evidence. And it doesn’t establish subectivity over objectivty, because if there are objective probabilities, you still need evidence to know what they are.
The invalid argument I alluded to elsewhere in this thread is the argument that if there is subjective probability, based on limited information, then there is no objective probability.
So thinking probabilities existing as “things itself” taken to the extreme could lead one to the conclusion that one cant say much for example about single-case probabilities.
“Don’t take objective probability to an extreme” is very different to “reject objective probability”.
Such as?
Generally if you approach probability as an extension of logic, probability is always relative to some evidence. Hardcore frequency dogmatists like John Venn for example thought that this is completely wrong: “the probability of an event is no more relative to something else than the area of a field is relative to something else.”
So thinking probabilities existing as “things itself” taken to the extreme could lead one to the conclusion that one cant say much for example about single-case probabilities. Lets say I take HIV-test and it comes back positive. You dont find it weird to say that it is not OK to judge probabilities of me having the HIV based on that evidence?
Thinking probabilities can exists in the territory leads to no such conclusion. Thinking probabilities exist only in the territory may lead to such a conclusion, but that is a strawman of the points that are being made.
It would be insane to deny that frequencies exist, or that they can be represented by a formal system derived from the Kolmogorov (or Cox) axioms.
It would also be insane to deny that beliefs exist, or that they can be represented by a formal system derived from the Kolmogorov (or Cox) axioms.
I think this confusion would all go away if people stopped worrying about the semantic meaning of the word “probability” and just specified whether they are talking about frequency or belief. It puzzles me when people insist that the formal system can only be isomorphic to one thing, and it is truly bizarre when they take sides in a holy war over which of those things it “really” represents. A rational decision maker genuinely needs both the concept of frequency and the concept of belief.
For instance, an agent may need to reason about the proportion (frequency) P of Everett branches in which he survives if he makes a decision, and also about how certain he is about his estimate of that probability. Let’s say his beliefs about the probability P follow a beta distribution, or any other distribution bounded by 0 and 1. In order to make a decision, he may do something like calculate a new probability Q, which is the expected value of P under his prior. You can interpret Q as the agent’s beliefs about the probability of dying, but it also has elements of frequency.
You can make the untestable claim that all Everett branches have the same outcome, and therefore that Q is determined exclusively by your uncertainty about whether you will live or die in all Everett branches. This would be Bayesian fundamentalism. You can also go to the other extreme and argue that Q is determined exclusively by P, and that there is no reason to consider uncertainty. That would be Frequentist fundamentalism. However, there is a spectrum between the two and there is no reason we should only allow the two edge cases to be possible positions. The truth is almost certainly somewhere in between.
Thinking “probability exists only in the territory” is exactly taking the idea that probabilities exists as “things itself” to the extreme as i wrote. This view is not a strawman of dogmatic frequentists position, as you can see from the John Venn quote.
I feel the need to point that i have tried to describe the context of the debate where the heuristic: “uncertainty exists in the map, not in the territory” was given in the first place. This whole historical debate started from the idea that probability as a degree of belief does not mean anything. This was the start. “Fallacious rubbish”, as Fisher puts it.
I have tried to show that one can have this very extreme position even if there exists only epistemic uncertainty. One can answer to this position by describing how in some situations the uncertainty exists in the map, not in the territory. This is the context where that general heuristic is used and the background that it should be judged against.
“A rational decision maker genuinely needs both the concept of frequency and the concept of belief.” Amen!
Maybe, but so what? That doesn’t establish any point of interest. It doesn’t establish Bayes over Frequentisim, since frequentists still need evidence. And it doesn’t establish subectivity over objectivty, because if there are objective probabilities, you still need evidence to know what they are.
The invalid argument I alluded to elsewhere in this thread is the argument that if there is subjective probability, based on limited information, then there is no objective probability.
“Don’t take objective probability to an extreme” is very different to “reject objective probability”.