The rapidly growing field of cognitive neuroscience holds the promise of explaining the operations of the mind in terms of the physical operations of the brain. Some suggest that our emerging understanding of the physical causes of human (mis)behaviour will have a transformative effect on the law. Others argue that new neuroscience will provide only new details and that existing legal doctrine can accommodate whatever new information neuroscience will provide. We argue that neuroscience will probably have a transformative effect on the law, despite the fact that existing legal doctrine can, in principle, accommodate whatever neuroscience will tell us. New neuroscience will change the law, not by undermining its current assumptions, but by transforming people's moral intuitions about free will and responsibility. This change in moral outlook will result not from the discovery of crucial new facts or clever new arguments, but from a new appreciation of old arguments, bolstered by vivid new illustrations provided by cognitive neuroscience. We foresee, and recommend, a shift away from punishment aimed at retribution in favour of a more progressive, consequentialist approach to the criminal law.