A Third Route to the Doomsday Argument preprint Paul Franceschi

In this paper, I present a solution to the Doomsday argument based on a third type of solution, by contrast to on the one hand, the Carter-Leslie view and on the other hand, the Eckhardt et al. analysis. The present line of thought is based on the fact that both aforementioned analyses are based on an inaccurate analogy. After discussing the imperfections of both models, I present then a two-sided model that fits more adequately with the human situation corresponding to DA and encapsulates both Carter-Leslie's and Eckhardt et al.'s models. I argue then that this new analogy also holds when one takes into account the issue of indeterminism and the reference class problem. This leads finally to a novel formulation of the argument that could well be more consensual than the original one. In this paper, I present a solution to the Doomsday argument (DA, for short) based on a third type of solution, by contrast to on the one hand, the Carter-Leslie view and on the other hand, the Eckhardt et al. analysis. In section 1, I describe the Carter-Leslie view. In section 2, I review the Eckhardt et al. line of reasoning. I point out then in section 3 an atemporal-temporal disanalogy in the Carter-Leslie analogy, which leads to the description of a strengthened variation of this latter model. In section 4, I raise some criticisms against the Eckhardt et al. analogy, thus leading to reformulate this latter analogy more accurately. I present then in section 5 a new two-sided analogy that fits more adequately with the human situation corresponding to DA and encapsulates both Carter-Leslie's and Eckhardt et al.'s models. This leads to a novel formulation of the argument that could well be more consensual than the original one. I argue in section 6 that this last two-sided analogy also holds when one takes into account the issue of indeterminism. Finally, I show in section 7 that the two-sided model is also capable of handling the reference class problem. 1. The Carter-Leslie View Let us begin by sketching briefly the Doomsday argument. The argument can be described as a reasoning leading to a Bayesian shift, from an analogy between what has been termed the two-urn case and the corresponding human situation. Consider, first, the two-urn case (slightly adapted from Bostrom 1997): 1 The solution to DA presented here is a somewhat condensed and enhanced version of the ideas expressed in Franceschi (2002), that also discusses at length the problems related to DA: God's Coin Toss, the Sleeping Beauty Problem, the Shooting-Room Paradox, the Presomptuous Philosopher. 2 Cf. Korb & Oliver (1998). 3 Cf. Bostrom (1997): '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, 4 ... etc. 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)'.