  The world-books are on permanent display in the divine intellect. This is what Leibniz means when he says that they reside in the realm of eternal verities. But one thing should be absolutely clear: Leibniz is no modal realist à la David Lewis. Although Leibniz claims that there are an infinity of possible worlds, he does not mean that infinitely many possible worlds exist in the same way as this (actual) world does, or that infinitely many worlds are running, as it were, parallel to this one, or that “actual” is an indexical expression like “here” and “now.” The existence claim commits Leibniz only to the existence of different ways the world could be and to the shelving of these world-books in the infinite and eternal library of the divine mind. As he puts it in the same letter to Arnauld, “there is no other reality in pure possibles than the reality they have in the divine understanding.” (G II 45/AG 75) But it is crucial to Leibniz's position that there be one and only one actual world, the best of all possible worlds. As we have seen, God is obligated to bring this one world into existence. And, we have also seen that, according to Leibniz, if there were no uniquely best world, then God would not have brought any world into existence. (And God could not simply play Eenee, Meenee, Mainee, Mo! with two worlds; he must, according to the Principle of Sufficient Reason, have a ground for his decision.) Further, there cannot be two worlds that are absolutely equal in terms of their degrees of perfection, for God, by virtue of his omnipotence and omniscience, must be able to determine some distinction between the worlds. And if God had actualized more than one world and they had been of different degrees of perfection, then God would have brought into existence that which is less perfect than possible (a violation of the requirements of divine benevolence). (Concerning the reasons for this world, more below.)