Blurring Out Cosmic Puzzles

The Doomsday argument and anthropic arguments are illustrations of a paradox. In both cases, a lack of knowledge apparently yields surprising conclusions. Since they are formulated within a Bayesian framework, the paradox constitutes a challenge to Bayesianism. Several attempts, some successful, have been made to avoid these conclusions, but some versions of the paradox 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.