The Doomsday argument purports to show that the risk of the human species going extinct soon has been systematically underestimated. This argument has something in common with controversial forms of reasoning in other areas, including: game theoretic problems with imperfect recall, the methodology of cosmology, the epistemology of indexical belief, and the debate over so-called fine-tuning arguments for the design hypothesis. The common denominator is a certain premiss: the Self-Sampling Assumption. We present two strands of argument in favor of this (...) assumption. Through a series of thought experiments we then investigate some bizarre prima facie consequences – backward causation, psychic powers, and an apparent conflict with the Principal Principle. (shrink)

Gott (Nature 363:315–319, 1993) considers the problem of obtaining a probabilistic prediction for the duration of a process, given the observation that the process is currently underway and began a time t ago. He uses a temporal Copernican principle according to which the observation time can be treated as a random variable with uniform probability density. A simple rule follows: with a 95% probability.

Cosmology raises novel philosophical questions regarding the use of probabilities in inference. This work aims at identifying and assessing lines of arguments and problematic principles in probabilistic reasoning in cosmology. -/- The first, second, and third papers deal with the intersection of two distinct problems: accounting for selection effects, and representing ignorance or indifference in probabilistic inferences. These two problems meet in the cosmology literature when anthropic considerations are used to predict cosmological parameters by conditionalizing the distribution of, e.g., the (...) cosmological constant on the number of observers it allows for. However, uniform probability distributions usually appealed to in such arguments are an inadequate representation of indifference, and lead to unfounded predictions. It has been argued that this inability to represent ignorance is a fundamental flaw of any inductive framework using additive measures. In the first paper, I examine how imprecise probabilities fare as an inductive framework and avoid such unwarranted inferences. In the second paper, I detail how this framework allows us to successfully avoid the conclusions of Doomsday arguments in a way no Bayesian approach that represents credal states by single credence functions could. -/- There are in the cosmology literature several kinds of arguments referring to self- locating uncertainty. In the multiverse framework, different "pocket-universes" may have different fundamental physical parameters. We don’t know if we are typical observers and if we can safely assume that the physical laws we draw from our observations hold elsewhere. The third paper examines the validity of the appeal to the "Sleeping Beauty problem" and assesses the nature and role of typicality assumptions often endorsed to handle such questions. -/- A more general issue for the use of probabilities in cosmology concerns the inadequacy of Bayesian and statistical model selection criteria in the absence of well-motivated measures for different cosmological models. The criteria for model selection commonly used tend to focus on optimizing the number of free parameters, but they can select physically implausible models. The fourth paper examines the possibility for Bayesian model selection to circumvent the lack of well-motivated priors. (shrink)

The Doomsday argument and anthropic reasoning are two puzzling examples of probabilistic confirmation. In both cases, a lack of knowledge apparently yields surprising conclusions. Since they are formulated within a Bayesian framework, they constitute a challenge to Bayesianism. Several attempts, some successful, have been made to avoid these conclusions, but some versions of these arguments cannot be dissolved within the framework of orthodox Bayesianism. I show that adopting an imprecise framework of probabilistic reasoning allows for a more adequate representation of (...) ignorance in Bayesian reasoning and explains away these puzzles. (shrink)

Physicist J. Richard Gott uses the Copernican principle that “we are not special” to make predictions about the future lifetime of the human race, based on how long the human race has been in existence so far. We show that the predictions which can be derived from Gott’s argument are less strong than one might be inclined to believe, that Gott’s argument illegitimately assumes that the human race will not last forever, that certain versions of Gott’s argument are incompatible with (...) Bayesian conditionalization, and that Gott’s argument is self-refuting. -/- *****Note: For Bradley Monton's up-to-date thoughts on Gott's argument, see his _Philosophical Quarterly_ paper co-authored with Brian Kierland, "How To Predict Future Duration from Present Age".*****. (shrink)

The physicist J. Richard Gott has given an argument which, if good, allows one to make accurate predictions for the future longevity of a process, based solely on its present age. We show that there are problems with some of the details of Gott's argument, but we defend the core thesis: in many circumstances, the greater the present age of a process, the more likely a longer future duration.

In several papers, John Norton has argued that Bayesianism cannot handle ignorance adequately due to its inability to distinguish between neutral and disconfirming evidence. He argued that this inability sows confusion in, e.g., anthropic reasoning in cosmology or the Doomsday argument, by allowing one to draw unwarranted conclusions from a lack of knowledge. Norton has suggested criteria for a candidate for representation of neutral support. Imprecise credences (families of credal probability functions) constitute a Bayesian-friendly framework that allows us to avoid (...) inadequate neutral priors and better handle ignorance. The imprecise model generally agrees with Norton's representation of ignorance but requires that his criterion of self-duality be reformulated or abandoned. (shrink)

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)