A Third Route to the Doomsday Argument preprint

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. I begin by strengthening both competing models by highlighting some variations of their ancestors models, which renders them less vulnerable to some objections. I describe then a third line of solution, which incorporates insights from both Leslie and Eckhardt's models and fits more adequately with the human situation corresponding to DA. I argue then that this two-sided 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 argue in section 5 that both competing models are capable of handling an indeterministic situation. I present then in section 6 a two-sided analogy that incorporates insights from both Carter-Leslie's and Eckhardt et al.'s models. Finally, I show in section 7 that this two-sided model is capable of handling the reference class problem and leads to a novel formulation of the argument. 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)'.