Abstract. How important is it that we reduce the risk of human extinction? This depends sensitively on fundamental questions in moral theory. On the one hand, if humanity goes extinct prematurely, vast amounts of well-being will be lost – all the well-being that would have been contained in the future lives that are prevented, by the premature extinction event, from coming into existence. On the other hand, if humanity goes extinct prematurely, then (aside from the suffering involved in the process of extinction itself) the extinction event seems to be in one clear sense victimless – precisely because of the extinction, there
do not exist any persons who lose the well-being in question. The first thought suggests that reducing the risk of extinction is about the most important thing we could do; the second suggests it is a matter of relative indifference. I will argue for the first thought over the second, via arguing that the moral theory that would be required to justify the second, however initially intuitive, is not in the end coherent. A further question, initially apparently unrelated, is what the optimal size is for the human population at any given time; many in the public sphere are increasingly concerned about overpopulation, for reasons related to resource scarcity, climate change, economic growth or others. I will first suggest that if the arguments in the first part of my talk are correct, these make it much harder to argue that population size ought to be reduced via any of the usual routes. Second, however, I will sketch one new (and tentative) argument for population-size reduction that is a *result* of the thesis that extinction risk is overwhelmingly important.