Observer-relative chances in anthropic reasoning?

Abstract

John Leslie presents a thought experiment to show that chances are sometimes observer-relative in a paradoxical way. The pivotal assumption in his argument - a version of the weak anthropic principle - is the same as the one used to get the disturbing Doomsday argument off the ground. I show that Leslie’s thought experiment trades on the sense/reference ambiguity and is fallacious. I then describe a related case where chances are observer-relative in an interesting way. But not in a paradoxical way. The result can be generalized: At least for a very wide range of cases, the weak anthropic principle does not give rise to paradoxical observer-relative chances.