I found the following argument here (although the paper is about a different topic):
A General Argument Against Immortality:
The method of Theory Confirmation can be applied to the question of immortality. In general, if we are immortal, there would be two classes of observations: Those made by normal people within a normal lifespan, and those made in the ‘afterlife’. For ‘quantum immortality’ the ‘afterlife’ will be taken to mean those who find themselves to be much older than a normal human lifespan. If the ‘afterlife’ is infinite, then it will have infinitely more integral measure than the normal life. Thus, the effective probability of finding oneself in a normal lifetime would be zero. If there is no ‘afterlife’ then the effective probability of that would be unity. By applying Bayesian reasoning, this implies that if one does find oneself in a normal lifetime, as we do, there must be no infinite afterlife.
Is this argument valid? To me, it seems that it is obviously false, but I may be missing the nuances of the argument. I would object that there is no random sampling here, which the author seems to assume. We are not randomly sampling the time in which we exist. If this argument is valid, we can make a general argument against the possibility of indefinite time. If time is indefinite, there is a zero probability that time is where it is currently, yet it is.
So, is this argument valid? How does it avoid my objections, especially the seeming conclusion that time cannot be indefinite?