  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.
