The comments seemed to again stop working, so I’m not using them any longer. Sooner or later this will switch to Movable Type I guess, at which stage I can use some slightly more sophisticated commenting system. Feel free to email me with questions/comments, and note if you want something posted to the site.

From Dave Chalmers, here is a list of many variants on Sleeping Beauty.

I have another, which has some slightly odd characteristics. There is an atom in an opaque box. It has a half-life of one hour. If it decays within the next hour, an epistemic duplicate of you shall be created at that moment, and kept in a state of being an epistemic duplicate of you until the hour is up. You shall not know of the duplicate’s existence, nor, naturally, it of yours.

Let p be the proposition that the atom decays within this hour (where that last phrase is a demonstrative, not a description, so p is a de dicto, not a de se, proposition).

According to the ‘thirder’ solution to Sleeping Beauty, you should (a) now have credence 1/3 in p, (b) have credence 2/3 in p at the end of the hour, and (c) have a constantly increasing credence in p as the hour progresses. This does seem odd.

I spent the flight from Atlanta to Boston working out what happens when there are two atoms in the box, with a duplicate to be created whenever a decay occurs. During the hour, there are 10 de se propositions that you need to keep track of in order to work out the credences in propositions like p, and to figure them out you have to solve 10 simultaneous equations. That is the kind of thing that I imagine is much easier to do in business class than coach.