On the Sleeping Beauty problem

Abstract

The Sleeping Beauty problem is a well-known problem in self-locating theory. The reason why it is so widely known is that it is a probability theoretic problem where there appear to be two different solutions: 1/2 and 1/3 . The main goal of this thesis was to find out how two conflicting solutions can emerge from a mathematical problem and why they both appear to be correct. An attempt at doing this has been undertaken by taking a critical look at the most important publications on the subject. The arguments in these publications have been analyzed extensively by checking whether the claims being made, follow from logical deduction or are simply presumed. This study revealed that several arguments were simply flawed, while others were based on controversial principles. These controversial principles are not mathematical theorems and should therefore be justified by the context of the problem, instead of being presumed at the outset. However, various interpretations of the Sleeping Beauty problem have resulted in divergent conclusions about which principles are applicable in the context of the Sleeping Beauty problem. These contrasting interpretations are a direct consequence of underspecification of the Sleeping Beauty problem: it is not clear what the answer to the problem represents. As soon as one determines what one wants to do with this answer, by adding more context and conditions to the Sleeping Beauty experiment, it is possible to decide which solution is applicable. For example, an analysis on the Doomsday argument, a problem analogous to the Sleeping Beauty problem, showed that the only correct solution in that context is 1/3 .