Paul is at it again, making me and others think about statistics, and analytic philosophy. Damn him, doesn't he know that if I wanted to think all the time I would have wasted the last decade or more trying to be an intellectual?
I've never studied the Doomdsday Argument, because I've never done serious analytic philosophy but more importantly because (after looking at the argument) I think I got a better training in statistics than all that. In other words, it seems to me that one does not need to make a philosophical critique of the argument, because it's based on an utterly invalid application of Bayesian statistics. Bayesian theory tells us that we can revise prior probabilities in light of new information. Like most probability theory it relies heavily on the idea a random sample. This paper that Paul linked to is actually much clearer than the link above. It gives the example of balls in an urn: if we don't know if there are 10 balls in the urn or 100, then our prior probability is .5 for each possibility (10 or 100). If we then pick one ball out of the urn and it turns out to be numbered 1 through 10, we can revise the probability of there being only 10 balls upward (since the chances of picking 1-10 if there are only 10 is much higher than picking 1-10 if there are 100). Fine by me. Go Mr. Bayes.
The Doomdsday argument says we can apply this reasoning to the population of the species. If you sample US - that is, the human population today - we seem to be the 1-10 balls, increasing the chances that there are only going to be 10 or so balls, ever. But we aren't a random sample of the entire history of the human species! I don't know if it's bad philosophy, but it's awful statistics. If we went to the end of time, when the human species was extinct, then sampled from all of human history and picked one of us that would tell us that there's a good chance humans didn't live very long. But we are not at the end of time, we are in time and we always will be. Sometimes we want to freeze things to look at statical samples, but we can never do that with humanity as a whole and certainly not with the future history of humanity.
Part of the problem with applying statistical theory more broadly - to thinking about human problems, politics, history, the world, etc. - is that it has no space for a sense of temporality. It is either completely static, or it moves through points in time in the most fixed and linear sense possible. Statistical reasoning is almost always very contrained by its prior assumptions of a random sample (and others). And the world we live in is filled with patterns and choices that make it only rarely a random sample. The world (and us) is marked by a temporality that will always thwart our own efforts to fix that world in place with logic.