Suppose I think of my present conscious state as uniformly randomly chosen out of all of my conscious states. Now, suppose the following two hypotheses both start off as having equal probability:
- NoAfterlife: I will live for about 80 years.
- Afterlife: I will live for an infinite number of years.
The issue here isn't about infinity. Suppose that on the Afterlife hypothesis I get 8000 years. Then, if the two hypotheses start with equal probability, the observation that I am 40 leads me to assign something like 99% probability to the NoAfterlife hypothesis.
When I first thought about this argument, it perturbed me significantly. But now I see that it is fallacious because of the following parallel. Let's suppose (contrary to fact, like the rest of the story) that we know for sure there is no afterlife, and let's say that you and I are healthy 19-year-olds, the day before our 20th birthday, and if nothing goes wrong we will live until 80. But we've been captured and our captors have just flipped a fair coin out of our sight in order to decide which of us to kill tomorrow. They've given us no sign as to which of us is to die, but we know for sure they will kill one of us. I have two hypotheses:
- IDie: I will die at age 20.
- YouDie: I will die at age 80.
But it is absurd that in this case I should think that probably they chose me to die. So by the same token, the argument against the Afterlife hypothesis fails.
Still, what goes wrong? I think it's the assumption that one should treat one's present conscious state as uniformly distributed over a life. But this does lead to an interesting question. Once we drop this assumption, and reject the arguments for NoAfterlife and IDie, as we should, can we still be thirders in Sleeping Beauty?