From your text: “If we think that probabilities are transcendal [sic] the principle of indifference offers us a free lunch. We get knowledge about the real world, merely by being ignorant of it. That is absurd.”
Can you clarify what you mean by this?
I don’t find your words very different from Jaynes’ words. He makes it clear that his standard of “objectivity” is encapsulated in the consistency and completeness desiderata 3b and 3c, which ensure that two people reasoning independently from the same background information come to the same conclusions.
The difference is that you frame people’s differences in background information as “different viewpoints” on the same situation, which I find a little confusing; logically, they’re simply different situations that need to be reasoned out independently. There’s no reason to be surprised when they yield different results.
Jaynes certainly agrees that probability is “situational” in your categorization. It can’t be “individual”, since that violates 3c consistency, unless you’re considering people’s mental states to be part of their background information (in which case it’s just “situational.”) “Transcendental” is just the special case of “situational” where everyone has perfect information.
There is a tradition of seeing probabilities as inherent physical properties of randomisation devices. That is what I was trying to get at with “transcendental”. Probability goes beyond what we know we don’t know to reach what is truly uncertain. In this tradition people say that when we toss a coin the probability of heads is 1⁄2 and this is a property of the coin.
I’ve sneaked a peek at section 10.3 How to cheat at coin and die tossing. I think that the Bayesian analysis is that when we toss a coin we exploit the fact that the coin is small compared to the fumble and tremble of human fingers which creates a situation of incomplete information.
What did I mean about the principle of indifference offering us a free lunch? Imagine that you are helping a friend move and you find an electronic dice at the back of a draw. “Oh, that old thing. There was a fault in the electronics. One number came up twice as often as the others.” Your friend hasn’t said which number; he might even have forgotten. According to the principle of indifference the probabilities are 1⁄6 for the first roll. (The probabilities for the second roll are different because the first roll hints weakly as to the number that comes up more often than the others). If we insist on interpreting probabilities as physical properties of randomisation devices, then the principle of indifference seems to be whipping out a soldering iron and mending the defective circuitry, at least for the first roll.
The difference is that you frame people’s differences in background information as “different viewpoints” on the same situation, which I find a little confusing; logically, they’re simply different situations that need to be reasoned out independently.
I think that there is a valid distinction which your observation ignores. When there is a car crash, the witnesses are in different places, one riding in a vehicle, one walking on the pavement. We want to check dates and times because we want to distinguish between “different viewpoints” on the same car crash and “different viewpoints” of two car crashes (perhaps at the same dangerous junction). If we have different viewpoints on the same situation there are consistancy constraints due to there being only a single underlying situation. These constraints are absent when they are simply different situations.
Going back to my piece, the humour of the playing cards rests on Superstish having a hunch, that the card is more likely to be black than red, about the deck that Prankster fixed. Some people say that Superstish is entitled to his hunch. I’m trying to say that he isn’t and also to explain the Bayesian position, which is that he isn’t entitled to his hunch. It is important to my text that there is a single situation. If as author I were to spread the action over two days, with Prankster fixing the deck on day two and Superstish insisting on his hunch on day one, very few people would feel that Superstish was entitled to his hunch. I would be attacking a straw man.
From your text: “If we think that probabilities are transcendal [sic] the principle of indifference offers us a free lunch. We get knowledge about the real world, merely by being ignorant of it. That is absurd.”
Can you clarify what you mean by this?
I don’t find your words very different from Jaynes’ words. He makes it clear that his standard of “objectivity” is encapsulated in the consistency and completeness desiderata 3b and 3c, which ensure that two people reasoning independently from the same background information come to the same conclusions.
The difference is that you frame people’s differences in background information as “different viewpoints” on the same situation, which I find a little confusing; logically, they’re simply different situations that need to be reasoned out independently. There’s no reason to be surprised when they yield different results.
Jaynes certainly agrees that probability is “situational” in your categorization. It can’t be “individual”, since that violates 3c consistency, unless you’re considering people’s mental states to be part of their background information (in which case it’s just “situational.”) “Transcendental” is just the special case of “situational” where everyone has perfect information.
There is a tradition of seeing probabilities as inherent physical properties of randomisation devices. That is what I was trying to get at with “transcendental”. Probability goes beyond what we know we don’t know to reach what is truly uncertain. In this tradition people say that when we toss a coin the probability of heads is 1⁄2 and this is a property of the coin.
I’ve sneaked a peek at section 10.3 How to cheat at coin and die tossing. I think that the Bayesian analysis is that when we toss a coin we exploit the fact that the coin is small compared to the fumble and tremble of human fingers which creates a situation of incomplete information.
What did I mean about the principle of indifference offering us a free lunch? Imagine that you are helping a friend move and you find an electronic dice at the back of a draw. “Oh, that old thing. There was a fault in the electronics. One number came up twice as often as the others.” Your friend hasn’t said which number; he might even have forgotten. According to the principle of indifference the probabilities are 1⁄6 for the first roll. (The probabilities for the second roll are different because the first roll hints weakly as to the number that comes up more often than the others). If we insist on interpreting probabilities as physical properties of randomisation devices, then the principle of indifference seems to be whipping out a soldering iron and mending the defective circuitry, at least for the first roll.
I think that there is a valid distinction which your observation ignores. When there is a car crash, the witnesses are in different places, one riding in a vehicle, one walking on the pavement. We want to check dates and times because we want to distinguish between “different viewpoints” on the same car crash and “different viewpoints” of two car crashes (perhaps at the same dangerous junction). If we have different viewpoints on the same situation there are consistancy constraints due to there being only a single underlying situation. These constraints are absent when they are simply different situations.
Going back to my piece, the humour of the playing cards rests on Superstish having a hunch, that the card is more likely to be black than red, about the deck that Prankster fixed. Some people say that Superstish is entitled to his hunch. I’m trying to say that he isn’t and also to explain the Bayesian position, which is that he isn’t entitled to his hunch. It is important to my text that there is a single situation. If as author I were to spread the action over two days, with Prankster fixing the deck on day two and Superstish insisting on his hunch on day one, very few people would feel that Superstish was entitled to his hunch. I would be attacking a straw man.