There are strong reasons for assuming that Thomas Aquinas conceived of God’s existence in terms of logical necessity in a broad sense. Yet this seems to stand in some tension with the fact that he excludes the possibility of a priori arguments for the existence of God. One apparently attractive way of handling this tension is to use a two-dimensional framework inspired by Saul Kripke. Against this, this article demonstrates that a Kripke-inspired framework is inapt in this context because it (...) allows for the conceivability of God’s non-existence, thereby rendering his non-existence possible in some important, and for Aquinas inacceptable, sense. Drawing on David Chalmers, the article submits that the existence of God can only be necessary if God’s non-existence is ideally inconceivable. On the basis of Aquinas’ own understanding of God, however, the article argues further that God’s non-existence in fact is inconceivable. The alleged conceivability of God’s non-existence is ultimately due to our (human) inability to grasp the nature of being, whereas creatures who grasp the nature of being are unable to conceive of God’s non-existence. This removes God’s non-existence from the realm of relevant conceivability and, therefore, from the range of possible worlds. (shrink)