The Doomsday argument was conceived by the astrophysicist
Brandon Carter some fifteen years ago, and it has since been
developed in a Nature article by Richard Gott [1993], and in
several papers by philosopher John Leslie and especially in his
recent monograph The End of The World (Leslie [1996]). The core
idea is this. Imagine that two big urns are put in front
of you, and you know that one of them contains ten balls and
the other a million, but you are ignorant as to which is which.
You know the balls in each urn are numbered 1, 2, 3, . N. Now you
take a ball at random from the left urn, and it is number 7.
Clearly, this is a strong indication that that urn contains only
ten balls. If originally the odds were fifty-fifty, a swift
application of Bayes' theorem gives you the posterior probability
that the left urn is the one with only ten balls.
(Pposterior (L=10) = 0.999990). But now consider the case where
instead of the urns you have two possible human races, and
instead of balls you have individuals, ranked according to birth
order. As a matter of fact, you happen to find that your rank
is about sixty billion. Now, says Carter and Leslie, we should
reason in the same way as we did with the urns. That you should
have a rank of sixty billion or so is much more likely is
only 100 billion persons will ever have lived than if there will be
many trillion persons. Therefore, by Bayes' theorem, you should
update your beliefs about mankind's prospects and realise that
an impending doomsday is much more probable than you have
hitherto thought.
I have recently written a paper on the DA which is
available at
http://www.hedweb.com/nickb/140797/doomsday.htm
For people who think they have an easy refutation, it might be worth
to take a look at Leslie's book, where many standard objections
are successfully countered.
Nicholas Bostrom