The Doomsday argument purports to show that the risk of the human species g
oing extinct soon has been systematically underestimated. This argument has
something in common with controversial forms of reasoning in other areas,
including: game theoretic problems with imperfect recall, the methodology o
f cosmology, the epistemology of indexical belief, and the debate over so-c
alled fine-tuning arguments for the design hypothesis. The common denominat
or is a certain premiss: the Self-Sampling Assumption. We present two stran
ds of argument in favor of this assumption. Through a series of thought exp
eriments we then investigate some bizarre prima facie consequences - backwa
rd causation, psychic powers, and an apparent conflict with the Principal P
rinciple.