A Modal-Ontological Argument and Leibniz's View of Possible Worlds

Abstract

We critically discuss an ontological argument that purports to prove not only that God, or a God-like being, exists, but in addition that God's existence is necessary. This requires turning to a modal logic, $S5$ in particular, in which the argument is presented. We explain why the argument fails. We then attempt a second version in which one of its premises is strengthened. That attempt also fails because of its use of the Carnap-Barcan formula in a context in which that formula is not valid. A third is presented as well using the proper name 'God' as a singular term, but it too fails for the same reason, though in a later section we show how this last argument can be validated under a re-interpretation of the quantifiers of the background logic. In our later sections, we explain what is wrong with the original first premise as a representation of what Leibniz meant by the consistency of God's existence, specifically as God's existence in a possible world. Possible worlds exist only as ideas in God's mind, and the consistency of God's existence cannot be God's existence in a possible world. Realism regarding possible worlds must be rejected. Only our world is real, the result of an ontological act of creation. We also explain in a related matter why according to Leibniz, Boethius, Aquinas and other medieval philosophers, God s omniscience does not imply fatalism.