ABSTRACTBrandon Carter's anthropic principle reminds us that observers are most likely to find themselves in the spatiotemporal regions containing most of them. One should tend to prefer theories which make one's own observed spatiotemporal position fairly ordinary. This could much increase the estimated likelihood that our technological civilisation was not the very first in a universe which would include hugely many such civilisations. Similarly, which is the Carter‐Leslie ‘doomsday argument’, it could much increase the estimated likelihood that you and I are not in the earliest 0.01%, for instance, of all humans who will ever have lived—as we would be if the human race survived for long even at its present size, let alone if it colonised the galaxy. With the aid of thought‐experiments, the article defends this argument against many objections. Other thought‐experiments suggest, though, that the argument is weaker if the world is radically indeterministic. In this case, it perhaps indicates only that we should not be highly confident in humankind's long survival, because high confidence would be equivalent to saying that any indeterminism would be unlikely to