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.”
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.”