John Leslie has published an argument that our own birth rank among all who have lived can be used to make inferences about all who will ever live, and hence about the expected survival time for the human race. It is found to be shorter than usually supposed. The assumptions underpinning the argument are criticized, especially the unwarranted one that the argument's sampling is equiprobable from among all who ever live. A mathematical derivation shows that Leslie's argument is correct only (...) if there exists a correlation of our birth rank to the event of doomsday. Such correlation is highly improbable. (shrink)