I think the issue with the Doomsday argument is its claim that each of us is equally likely to find ourselves at any position n of the total population N. As I said here, we're not disembodied souls that are randomly placed inside any one of the human bodies which will ever live. — Michael

I had the impression you thought that criticism applied only to AJJ's version of the argument. But yes, I think that is at least the right track. Since @SophistiCat pointed out this problems similarity with other problems, like "Sleeping Beauty", I wonder if we can apply the same kind of criticism there.

In the Sleeping Beauty problem, the question can be rephrased as whether you are more likely to be an observer in a world that has more observers in total. The result of the view that this is the case (i.e. Sleeping Beauty is more likely to have been woken twice) interestingly enough runs directly counter to the result of the Doomsday argument, since the more humans will ever exist, the more possible observers "you" have to choose from.

But your criticism applies either way, since again assuming that you are more likely to be an observer in a world with more observers assumes "you" are a disembodied spirit that is the randomly assigned an observer "slot". It therefore seems that in these kinds of problems, the copernican principle does not apply.

Very nice explanation. Also didn't know about the sleeping beauty problem, very nice thought.

Thanks guys, I've learned a lot :)

I also pointed out that I think there is a problem with the doomsday argument on page one. — Echarmion

As did I.