The greatest challenge to aggregative consequentialism is infinitarian paralysis: if there are infinitely many beings like us in the universe, no action can change the cardinal sum of value or disvalue and so (apparently) all actions are morally indifferent. I survey some approaches to this problem developed by Bostrom and conclude (as he does) that they are unsatisfactory. I then offer a new solution, based on a modification to Hume’s principle, and show that it succeeds where previous solutions fail in rescuing most ordinary consequentialist moral judgments. But my solution also carries significant metaphysical commitments and has potentially unwelcome implications concerning the moral status of future generations.