If you repeat the experiment, does who you call I stay the same (e.g., they might not get selected at all)? If so, then that person was labeled as special a priori, and if they find themself in a room, then the probability of blue is 0.99.
But.. I’m arguing that anyone who is selected, whether it is one person or 99 people, will all think of themselves as I. When you think of frequentist properties then, you have to think about the label switching each time. That changes everything. The fact that you were selected just means that someone was selected, and that was a probability 1 event. Thus, probability of blue door is .5.
The frequentist perspective requires no special labeling. It’s an outside observation that requires no concept of I. Keeping tabs on all the results we would simply see that 99% of people would have been correct to guess they were in a blue room.
The frequentist perspective requires no special labeling. It’s an outside observation that requires no concept of I. Keeping tabs on all the results we would simply see that 99% of people would have been correct to guess they were in a blue room.
It’s hard to keep the indexicals out. You used one yourself when you wrote “99% of people would have been correct to guess they were in a blue room.” (Emphasis added.) Granted: this particular use of an indexical can be avoided by writing “99% of people put into rooms would have been correct to guess that everyone who is in a room was in a blue room.” Then there are no indexicals in the conclusions that the people reach.
However, there is still an indexical implicit in each person’s reasoning procedure. Each person reasons according to the following rule: “If I am put into a room, guess that everyone who is in a room is in a blue room.”
That, as I understand it, is neq1′s point. If indexicals are ruled out of the reasoning process, then the people in your scenario can get no further than “If someone is put into a room, then guess that everyone who is in a room is in a blue room.” With this reasoning procedure, only half the people will guess right.
If you rule out indexicals completely how can you even begin to reason about the probability of a statement (“I am in a blue room”) that uses an indexical?
If you rule out indexicals completely how can you even begin to reason about the probability of a statement (“I am in a blue room”) that uses an indexical?
We shouldn’t rule out indexicals in your scenario, but we should understand their meaning in a non-indexical way.
In your scenario, where everyone in the pool of people exists, we can just suppose that each person has a unique identifier, such as a unique proper name. Then, for each proper name N, the person named “N” can reason according to the rule “Upon learning that N is in a room, guess that N is in a blue room.” This allows them to achieve the 0.99 success rate that indexical reasoning allows.
[ETA: Note that this means that each person N is employing a different rule. This is reasonable because N will have learned that information regarding N is especially reliable. We can imagine minds that could go through this reasoning process without ever thinking to themselves “Hey, wait a minute — I myself am N.”]
In real life, people share proper names. But we can still suppose that each person can be picked out uniquely with some set of non-indexical properties.
For example, there might be more than one person who is named “Bob”. There might be more than one person who is named “Bob” and was born on January 8th, 1982. There might even be more than one person who is named “Bob”, was born on January 8th, 1982, and has red hair. But, if we keep adding predicates, we can eventually produce a proper definite description that is satisfied by exactly one person in the pool.
This is what justifies the kind of indexical reasoning that works so well in your scenario.
What makes the scenario in the OP different is this: Some of the possible people in the “pool” are distinguished from the others only by whether they exist. The problem here is that existence is not a predicate (according to most analytic philosophers). Thus, “exists” is not among the properties that we can use to pick out a unique individual with a proper definite description. That’s what makes it problematic to carry over indexical reasoning to the scenario in the OP.
Regardless of if “I” is a valid index in this case though, certainly “person P used the word ‘I’ and concluded ‘I am in a blue room’ ” is a valid predicate, even if person P’s use of “I” was gibberish.
We can then say that 99% of people, if they concluded that gibberish, would have gone on to conclude the gibberish, “I was, in fact, right to conclude that I was in a blue room.”
Um, no. It’s not even controversial that you’re wrong in this case.
(For purposes of intuition, let’s say there are just 100 people in the world. Do you really think that finding yourself selected is no evidence of blue?)
Um, no. It’s not even controversial that you’re wrong in this case.
About what, precisely, is neq1 wrong? neq1 agreed with Jordan that the probability of blue in Jordan’s scenario was 0.99. However, as neq1 rightly points out, in Jordan’s scenario a specific individual is distinguished prior to the experiment. This doesn’t happen in neq1′s scenario.
If neq1 was saying that any person who finds themselves selected in that scenario should conclude “blue” with probability 0.99, then I’ve misunderstood his/her last sentence.
If Laura exists, she’ll ask P(blue door | laura exists). Laura=I
If Tom exists, he’ll ask P(blue door | Tom exists). Tom=I
If orthonormal exists, s/he will ask P(blue door | orthonormal exists). orthonormal=I
and so on. Notice how the question we ask depends on the result of the experiment? See how the label switches?
What do Tom, Laura and orthonormal have in common? They are all conscious observers.
So, if orthonormal wakes up in a room, what orthonormal knows is that at least one conscious observer exists. P(blue room | at least one conscious observer exists)=0.5
neq1′s first paragraph refers to Jordan’s scenario. neq1′s second paragraph alters the scenario to be more like the one in the OP. In the altered version, we view the situation “from the outside”. We have no way to specify any particular individual as I before the experiment begins, so our reasoning can only capture the fact that someone ended up in a room. Since we already knew that that would happen, we are still left with the prior probability of .5 that the coin came up heads.
If you repeat the experiment, does who you call I stay the same (e.g., they might not get selected at all)? If so, then that person was labeled as special a priori, and if they find themself in a room, then the probability of blue is 0.99.
But.. I’m arguing that anyone who is selected, whether it is one person or 99 people, will all think of themselves as I. When you think of frequentist properties then, you have to think about the label switching each time. That changes everything. The fact that you were selected just means that someone was selected, and that was a probability 1 event. Thus, probability of blue door is .5.
The frequentist perspective requires no special labeling. It’s an outside observation that requires no concept of I. Keeping tabs on all the results we would simply see that 99% of people would have been correct to guess they were in a blue room.
It’s hard to keep the indexicals out. You used one yourself when you wrote “99% of people would have been correct to guess they were in a blue room.” (Emphasis added.) Granted: this particular use of an indexical can be avoided by writing “99% of people put into rooms would have been correct to guess that everyone who is in a room was in a blue room.” Then there are no indexicals in the conclusions that the people reach.
However, there is still an indexical implicit in each person’s reasoning procedure. Each person reasons according to the following rule: “If I am put into a room, guess that everyone who is in a room is in a blue room.”
That, as I understand it, is neq1′s point. If indexicals are ruled out of the reasoning process, then the people in your scenario can get no further than “If someone is put into a room, then guess that everyone who is in a room is in a blue room.” With this reasoning procedure, only half the people will guess right.
I did use an indexical, you’re right, damn.
If you rule out indexicals completely how can you even begin to reason about the probability of a statement (“I am in a blue room”) that uses an indexical?
We shouldn’t rule out indexicals in your scenario, but we should understand their meaning in a non-indexical way.
In your scenario, where everyone in the pool of people exists, we can just suppose that each person has a unique identifier, such as a unique proper name. Then, for each proper name N, the person named “N” can reason according to the rule “Upon learning that N is in a room, guess that N is in a blue room.” This allows them to achieve the 0.99 success rate that indexical reasoning allows.
[ETA: Note that this means that each person N is employing a different rule. This is reasonable because N will have learned that information regarding N is especially reliable. We can imagine minds that could go through this reasoning process without ever thinking to themselves “Hey, wait a minute — I myself am N.”]
In real life, people share proper names. But we can still suppose that each person can be picked out uniquely with some set of non-indexical properties.
For example, there might be more than one person who is named “Bob”. There might be more than one person who is named “Bob” and was born on January 8th, 1982. There might even be more than one person who is named “Bob”, was born on January 8th, 1982, and has red hair. But, if we keep adding predicates, we can eventually produce a proper definite description that is satisfied by exactly one person in the pool.
This is what justifies the kind of indexical reasoning that works so well in your scenario.
What makes the scenario in the OP different is this: Some of the possible people in the “pool” are distinguished from the others only by whether they exist. The problem here is that existence is not a predicate (according to most analytic philosophers). Thus, “exists” is not among the properties that we can use to pick out a unique individual with a proper definite description. That’s what makes it problematic to carry over indexical reasoning to the scenario in the OP.
Interesting. Thanks for clarifying that.
Regardless of if “I” is a valid index in this case though, certainly “person P used the word ‘I’ and concluded ‘I am in a blue room’ ” is a valid predicate, even if person P’s use of “I” was gibberish.
We can then say that 99% of people, if they concluded that gibberish, would have gone on to conclude the gibberish, “I was, in fact, right to conclude that I was in a blue room.”
Um, no. It’s not even controversial that you’re wrong in this case.
(For purposes of intuition, let’s say there are just 100 people in the world. Do you really think that finding yourself selected is no evidence of blue?)
About what, precisely, is neq1 wrong? neq1 agreed with Jordan that the probability of blue in Jordan’s scenario was 0.99. However, as neq1 rightly points out, in Jordan’s scenario a specific individual is distinguished prior to the experiment. This doesn’t happen in neq1′s scenario.
If neq1 was saying that any person who finds themselves selected in that scenario should conclude “blue” with probability 0.99, then I’ve misunderstood his/her last sentence.
It’s a hidden label switching problem.
If Laura exists, she’ll ask P(blue door | laura exists). Laura=I
If Tom exists, he’ll ask P(blue door | Tom exists). Tom=I
If orthonormal exists, s/he will ask P(blue door | orthonormal exists). orthonormal=I
and so on. Notice how the question we ask depends on the result of the experiment? See how the label switches?
What do Tom, Laura and orthonormal have in common? They are all conscious observers.
So, if orthonormal wakes up in a room, what orthonormal knows is that at least one conscious observer exists. P(blue room | at least one conscious observer exists)=0.5
neq1′s first paragraph refers to Jordan’s scenario. neq1′s second paragraph alters the scenario to be more like the one in the OP. In the altered version, we view the situation “from the outside”. We have no way to specify any particular individual as I before the experiment begins, so our reasoning can only capture the fact that someone ended up in a room. Since we already knew that that would happen, we are still left with the prior probability of .5 that the coin came up heads.