It is necessarily true that water is H2O, but it is a contingent fact that there is any water at all. Water therefore seems ill suited to ground the necessary truth that water is H2O. One view traditionally attributed to Scotus and Henry of Ghent was that while water is contingent, the essence of water is necessary; hence, the essence of water can ground the so-called eternal truth that water is H2O. Francisco Suárez rejects this view on the grounds that it contradicts the Christian doctrine of creation, according to which everything other than God was contingently created in time. Suárez’s own view of the eternal truths has proven elusive to commentators, but I argue that Suárez ultimately endorses a version of the view he rejects: essences ground the eternal truths. But this raises several puzzles: how is Suárez’s view distinct from the views traditionally ascribed to Scotus and Henry? How does Suárez’s view escape the argument from creation, which Suárez raises against his opponents? I argue that Suárez distinguishes between his view and his opponents’ view by saying that essences have “extrinsic being,” whereas his opponents claim that essences have “intrinsic being.” The distinction between intrinsic and extrinsic being has not received much attention, but I argue that it marks an important fault line in scholastic thinking about the ontological status of non-existents. I argue that the notion of extrinsic being can be explicated in terms of ontological pluralism and grounding. The notion of extrinsic being helps differentiate Suárez’s view from his Scotistic and Henrician opponents, and it allows Suárez to respond to the creation argument he raises against his opponents. On my reading, Suárez’s solution to the problem of eternal truths turns out to be both highly original and philosophically satisfying.