Inflationary cosmology has been widely accepted due to its successful predictions: for a “generic” initial state, inflation produces a homogeneous, flat, bubble with an appropriate spectrum of density perturbations. However, the discovery that inflation is “generically eternal,” leading to a vast multiverse of inflationary bubbles with different low-energy physics, threatens to undermine this account. There is a “predictability crisis” in eternal inflation, because extracting predictions apparently requires a well-defined measure over the multiverse. This has led to discussions of anthropic predictions (...) based on a measure over the multiverse, and an assumption that we are typical observers. I will give a pessimistic assessment of attempts to make predictions in this sense, emphasizing in particular problems that arise even if a unique measure can be found. (shrink)

John Leslie presents a thought experiment to show that chances are sometimes observer-relative in a paradoxical way. The pivotal assumption in his argument – a version of the weak anthropic principle – is the same as the one used to get the disturbing Doomsday argument off the ground. I show that Leslie's thought experiment trades on the sense/reference ambiguity and is fallacious. I then describe a related case where chances are observer-relative in an interesting way. But not in a paradoxical (...) way. The result can be generalized: At least for a very wide range of cases, the weak anthropic principle does not giverise to paradoxical observer-relative chances. This finding could be taken to give new indirect support to the doomsday argument. (shrink)

Paying strict attention to Brandon Carter's several published renditions of anthropic reasoning, we present a ``nutshell'' version of the Doomsday argument that is truer to Carter's principles than the standard balls-and-urns or otherwise ``naive Bayesian'' versions that proliferate in the literature. At modest cost in terms of complication, the argument avoids commitment to many of the half-truths that have inspired so many to rise up against other toy versions, never adopting posterior outside of the convex hull of one's prior distribution (...) over the ``true chance'' of Doom. The hyper-pessimistic position of the standard balls-and-urn presentation and the hyper-optimistic position of naive self-indicators are seen to arise from dubiously extreme prior distributions, leaving room for a more satisfying and plausible intermediate solution. (shrink)

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)