One's inaccuracy for a proposition is defined as the squared difference between the truth value (1 or 0) of the proposition and the credence (or subjective probability, or degree of belief) assigned to the proposition. One should have the epistemic goal of minimizing the expected inaccuracies of one's credences. We show that the method of minimizing expected inaccuracy can be used to solve certain probability problems involving information loss and self-locating beliefs (where a self-locating belief of a temporal part of (...) an individual is a belief about where or when that temporal part is located). We analyze the Sleeping Beauty problem, the duplication version of the Sleeping Beauty problem, and various related problems. (shrink)

The Carter-Leslie Doomsday argument, as standardly presented, relies on the assumption that you have knowledge of your approximate birth rank. I demonstrate that the Doomsday argument can still be given in a situation where you have no knowledge of your birth rank. This allows one to reply to Bostrom's defense of the Doomsday argument against the refutation based on the idea that your existence makes it more likely that many observers exist.

If the human race comes to an end relatively shortly, then we have been born at a fairly typical time in the history of humanity; if trillions of people eventually exist, then we have been born in the first surprisingly tiny fraction of all people. According to the 'doomsday argument' of Carter, Leslie, Gott and Nielsen, this means that the chance of a disaster which would obliterate humanity is much larger than usually thought. But treating possible observers in the same (...) way as those who actually exist avoids this conclusion: our existence is more likely in a race which is long-lived, and this cancels out the doomsday argument, so that the chance of a disaster is only what one would ordinarily estimate. (shrink)

I discuss two versions of the doomsday argument. According to ``Gott's Line'',the fact that the human race has existed for 200,000 years licences the predictionthat it will last between 5100 and 7.8 million more years. According to ``Leslie'sWedge'', the fact that I currently exist is evidence that increases the plausibilityof the hypothesis that the human race will come to an end sooner rather than later.Both arguments rest on substantive assumptions about the sampling process thatunderlies our observations. These sampling assumptions have (...) testable consequences,and so the sampling assumptions themselves must be regarded as empirical claims.The result of testing some of these consequences is that both doomsday argumentsare empirically disconfirmed. (shrink)

Making only the assumption that you are a random intelligent observer, limits for the total longevity of our species of 0.2 million to 8 million years can be derived at the 95% confidence level. Further consideration indicates that we are unlikely to colonize the Galaxy, and that we are likely to have a higher population than the median for intelligent species.

In the form in which it was originally expounded, the anthropic principle was presented as a warning to astrophysical and cosmological theorists of the risk of error in the interpretation of astronomical and cosmological information unless due account is taken of the biological restraints under which the information was acquired. However, the converse message is also valid: biological theorists also run the risk of error in the interpretation of the evolutionary record unless they take due heed of the astrophysical restraints (...) under which evolution took place. After an introductory discussion of the ordinary ('weak') anthropic principle and of its more contestable ('strong') analogue, a new application of the former to the problem of the evolution of terrestrial life is presented. It is shown that the evidence suggests that the evolutionary chain included at least one but probably not more than two links that were highly improbable (a priori) in the available time interval. (shrink)

In a recent paper in this journal, Ken Olum attempts to refute the Doomsday argument by appealing to the self-indication assumption, the idea that your very existence gives you reason to think that there are many observers. In contrast to earlier refutation attempts that use this strategy, Olum confronts and try to counter some of the objections that have been made against SIA. We argue that his defense of SIA is unsuccessful. This does not, however, mean that one has to (...) accept the Doomsday argument. A developed theory of observation selection effects shows why the Doomsday argument is inconclusive and how one can consistently reject both it and SIA. (shrink)