P. Kyle Stanford’s Exceeding our Grasp (2006) shows how the problem of unconceived alternatives presents a significant challenge to realism. Stanford argues that the history of science offers repeated instances of scientists failing to conceptualize rational alternatives to ruling scientific doctrines, implying that our present scientific theories are likely to be similarly underdetermined. This article extends Stanford’s argument and provides it with a longer history. It shows how the principle of unconceived alternatives was explicitly deployed during the medieval and early modern periods to undermine scientific realism in particular cases. These arguments typically made reference to divine omnipotence and the principle that God could have produced phenomena in numerous ways inconceivable to finite human minds. In this theological register, unconceived alternatives offered a way of minimizing potential tensions between theological doctrines and prevailing scientific theories. The article concludes with some brief reflections on the applicability of the principle of unconceived alternatives to conceptions of God.