Considering public moral attitudes is a hallmark of the anticipatory governance of emerging biotechnologies, such as heritable human genome editing. However, such anticipatory governance often overlooks that future morality is open to change and that future generations may perform different moral assessments on the very biotechnologies we are trying to govern in the present. In this article, we identify an ’anticipatory gap’ that has not been sufficiently addressed in the discussion on the public governance of heritable genome editing, namely, uncertainty (...) about the moral visions of future generations about the emerging applications that we are currently attempting to govern now. This paper motivates the relevance of this anticipatory gap, identifying the challenges it generates and offering various recommendations so that moral uncertainty does not lead to governance paralysis with regard to human germline genome editing. (shrink)