Ok, let’s look at a real world example: “drivers in next lane are going faster” suggested by Bostrom. It is true from observer’s point of view but not true from the God’s view.
“The drivers in the next lane are going faster” is true both from a driver’s first-person view and from a god’s eye view. However, none of those two are self-locating probabilities. This is explained by PBA’s position on self-locating probabilities, by the link mentioned above.
The lane assignment can be regarded as an experiment. The lane with more vehicles assigned to it moves slower. Here, from a god’s eye view, if a random car is selected then the probability of it from the slow lane is higher. From a driver’s first-person view, “I” and the other drivers are in symmetrical positions in this lane assigning experiment. So the probability of me being in the slow lane is higher. According to PBA, both probabilities are valid. However, they are not the same concept, though they have the same value. (This point have been illustrated by Question 1 and Question 2 in the link above)
However, neither of them are self-locating probabilities in the anthropic context. Some anthropic reasoning suggests there is an innate reference class for indexicals like “I”. E.g. SSA assumes “I” can be considered a randomly chosen human from all humans. This requires both the first-person to identify “I” and a god’s eye view to do the choosing. It does not depend on any experiment. Compare this with the driver’s first-person view above, the reference class is all drivers on the road. It is defined by the lane assigning experiment. It does not even matter if other drivers are humans or not. They could be all pigs and they would still be in symmetrical positions with me. The PBA argues the self-locating probabilities are invalid. (This point has been demonstrated by Question 3 in the link above.)
Since we are discussing Nick Bostrom’s position, he made the explicit statement in “The Mysteries of Self-Locating Belief and Anthropic Reasoning” that an experiment is unnecessary in defining the reference class. We can always treat “I” as the result of an imaginary sampling process. This is in direct conflict with my PBA. According to PBA, anthropics is not an observation selection effect, just recognizing the perspective of reasoning.
Lastly, you are clearly interested in this topic. I just find the questions you raised have already been covered by the argument presented on my website. I can only recommend you give it a read. Because this question and answer model of communication is disproportionally effort heavy on my part. Cheers.
Ok, let’s look at a real world example: “drivers in next lane are going faster” suggested by Bostrom. It is true from observer’s point of view but not true from the God’s view.
“The drivers in the next lane are going faster” is true both from a driver’s first-person view and from a god’s eye view. However, none of those two are self-locating probabilities. This is explained by PBA’s position on self-locating probabilities, by the link mentioned above.
The lane assignment can be regarded as an experiment. The lane with more vehicles assigned to it moves slower. Here, from a god’s eye view, if a random car is selected then the probability of it from the slow lane is higher. From a driver’s first-person view, “I” and the other drivers are in symmetrical positions in this lane assigning experiment. So the probability of me being in the slow lane is higher. According to PBA, both probabilities are valid. However, they are not the same concept, though they have the same value. (This point have been illustrated by Question 1 and Question 2 in the link above)
However, neither of them are self-locating probabilities in the anthropic context. Some anthropic reasoning suggests there is an innate reference class for indexicals like “I”. E.g. SSA assumes “I” can be considered a randomly chosen human from all humans. This requires both the first-person to identify “I” and a god’s eye view to do the choosing. It does not depend on any experiment. Compare this with the driver’s first-person view above, the reference class is all drivers on the road. It is defined by the lane assigning experiment. It does not even matter if other drivers are humans or not. They could be all pigs and they would still be in symmetrical positions with me. The PBA argues the self-locating probabilities are invalid. (This point has been demonstrated by Question 3 in the link above.)
Since we are discussing Nick Bostrom’s position, he made the explicit statement in “The Mysteries of Self-Locating Belief and Anthropic Reasoning” that an experiment is unnecessary in defining the reference class. We can always treat “I” as the result of an imaginary sampling process. This is in direct conflict with my PBA. According to PBA, anthropics is not an observation selection effect, just recognizing the perspective of reasoning.
Lastly, you are clearly interested in this topic. I just find the questions you raised have already been covered by the argument presented on my website. I can only recommend you give it a read. Because this question and answer model of communication is disproportionally effort heavy on my part. Cheers.