Which Questions Are Anthropic Questions?
I will try to keep this shot, just want to use some simple problems to point out what I think is a commonly overlooked point in anthropic discussions.
1. The Room Assignment Problem
You are among 100 people waiting in a hallway. The hallway leads to a hundred rooms numbered from 1 to 100. All of you are knocked out by a sleeping gas and each put into a random/unknown room. After waking up, what is the probability that you are in room No. 1?
This is just an ordinary probability question. All room numbers are symmetrical, the answer is simply 1%. It is also easy to imagine taking part in similar room-assigning experiments a great number of times, the relative fraction of you waking up in room No.1, or any other number, would approach 1%.
It is safe to say this is not an anthropic question. Even for people with the metaphysical stance that all probabilities are anthropic, it is undeniable that we have been solving such questions successfully without any anthropic considerations.
2. The Incubator
An incubator enters the hallway. It will enter room No.1 and creat a person in it then does the same for the other 99 rooms. It turns out you are one of the people the incubator has just created. You wake up in a room and is made aware of the experiment setup. What is the probability that you are in room No.1?
While this question may seem trivial, it is an anthropic question. In ordinary problems like Question 1, an event refers to a unique experiment outcome, a distinct possible world. But this incubator problem, objectively speaking, is deterministic. Knowing the exact process from a god’s eye view still leaves uncertainty because the uncertainty comes from the fact that you are unsure of your own location in this only world, e.g. which physical person is the subjective self. This kind of same-world event is the crux of anthropic paradoxes. E.g. the sleeping beauty problem is special because of the two awakenings both in the Tails world.
Also worth noting the frequentist model is much trickier to imagine. While the incubator has no problem performing this job ten thousand times, and creating a million people in the process, it seems absurd to say you are one of the people created in each experiment, that you are ten thousand people. Obviously, this is not a run-of-the-mill question.
3. Incubator + Room Assignment
This time the incubator creats 100 people in the hall way, you are among the 100 people created. Each person is then assigned to a random room. What is the probability that you are in Room 1?
This is just an ordinary probability question. In fact, it is Question 1 with some background story of how you got in the hallway before the experiment began. Whether you were there because of the incubator or some other process does not affect the room-assigning process. Different room numbers still reflect unique assignments and different possible worlds.
Instead of taking which physical person is the self as a given fact, some might want to treat it the same way as in Question 2, implying besides the room assignment process, the uncertainty also comes from which physical person the self is. This would lead to undesirable consequences. However, that is not the focus of this post. Even if one endorses this approach it is undeniable that Questions 2 and 3 are different in nature. The former’s uncertainty entirely depends on the single-world self-location while the latter doesn’t.
Almost all anthropic discussions implicitly treat Questions 2 and 3 as the same problem not worth differentiating. Some, e.g. Nick Bostrom IMSMR, explicitly stated that they ought to be regarded as equivalent. But this position is not accompanied by any explanation. It is treated as an intuitive thing to simply accept.
But such equivalency links anthropic problems with ordinary ones. It requires justification. One possible justification, which I think is also one major reason why the equivalency seems so intuitive, is that all popular anthropic theories, including both SSA and SIA, as long as they consider the self as a random sample, would treat Question 2 the same way as Question 1. From this, it follows Question 2 and 3 are equivalent as well.
In reality, however, the arguments sometimes take the opposite direction. People take the equivalency as an indisputable fact and from there argue for the credibility of common anthropic assumptions. Without an independent justification for the purposed equivalency, this logic is circular.