Suppose there are possible worlds in which God exists but Anselm does not. Then (I argue) there are possible worlds in which Anselm does not exist, but God cannot even entertain the thought that he does not. In such worlds Anselm does not exist, but God does not know that. This, I argue, is incompatible with (a straightforward construal of) the doctrine of God's essential omniscience. Considerations involving negative existentials also call into question a certain picture of creation, on which God chooses which particular (possible) individuals to create. They suggest that there is an element of brute contingency about which individuals exist.

Mediaeval philosophical theologians held – so far as I know without exception – that God was essentially omniscient. In what follows, I shall argue that the existence of individuals whose non-existence is compossible with God's existence raises serious difficulties for the doctrine of God's essential omniscience. If there are individuals that might not have existed even though God did, then – I shall try to show – questions arise about whether God would have been omniscient, if He had existed, but they hadn't.