Abstract

The last two decades have seen a heated debate between "halfers" and "thirders": those who believe Sleeping Beauty’s credence in a coin landing heads is 1/2 and those who believe it is 1/3 – as well as quite some alternative positions. This paper attempts to settle the debate in favour of thirdism. I present a new argument for thirdism which cannot be resisted using any of the previously used halfer strategies. My argument uses an analogy in which Sleeping Beauty has a lucid dream on each day. To arrive at thirdism, she uses an unproblematic type of Bayesian conditionalisation, the principle of indifference, and the principal principle. I argue that all of these reasoning steps should be uncontroversial. Finally, I argue that all published defences of halfism are untenable.