Ockham appeared to maintain that God necessarily knows all true propositions, including future contingent propositions, despite the fact that such propositions have determinate truth values. While some commentators believe that Ockham’s attempt to reconcile divine omniscience with the contingency of true future propositions amounts to little more than a simple-minded assertion of Ockham’s Christian faith, I argue that Ockham’s position is more sophisticated than this and rests on attributing to God a dual knowledge property: God not only knows every true proposition, but knows its modal properties as well. Future contingent propositions are determinately true when actualized, not timelessly, and God’s knowledge of their truth values is knowledge of when the truth value of a proposition is actually determined.

Th is paper examines St. Bonaventure’s arguments for the impossibility of a beginningless world, taking into consideration their historical background and context. His argument for the impossibility of traversing the infinite is explored at greater length, taking into account the classic objection to this argument. It is argued that Bonaventure understood the issues at hand quite well and that histraversal argument is valid. Because of the nature of an actually infinite multitude, the difference between the infinite by division and the infinite by addition collapses and a beginningless past entails a day infinitely distant from the present, as Bonaventure claims. Because such a chasm is not traversable, as virtually everyone admits, Bonaventure’s conclusion that the world must have a beginning is correct.