Recall the “freak-observer problem” plaguing Big World theories that we discussed in chapters 3 and 5. This is one application where falls short.
Suppose T1 and T2 are two Big World theories. According to T1, the vast majority of observers observe values of physical constants in agreement with what we observe and only a small minority of freak observers are deluded and observe the physical constants having different values. According to T2, it is the other way around: the normal observers observe physical constants having other values than what we observe, and a minority of freak observers make observations that agree with ours. We want to say that our observations favor T1 over T2. Yet this is not possible on . For according to , the reference class to which we belong consists of all and only those observers-moments who make the same observations as we make, since other observer-moments are subjectively distinguishable from ours. If T1 and T2 both imply that the universe is big enough for it to be certain (or very probable) that it contains at least some observer making the observations that we are actually making, then on our evidence would not favor T1 over T2. Here is the proof: