Gödel’s Ontological Proof
Gödel’s ontological proof is a formal argument by the mathematician Kurt Gödel (1906–1978) for the existence of God. The argument is in a line of development that goes back to Anselm of Canterbury (1033–1109). St. Anselm’s ontological argument, in its most succinct form, is as follows: “God, by definition, is that for which no greater can be conceived. God exists in the understanding. If God exists in the understanding, we could imagine Him to be greater by existing in reality. Therefore, God must exist.” A more elaborate version was given by Gottfried Leibniz (1646–1716); this is the version that Gödel studied and attempted to clarify with his ontological argument.
The argument uses modal logic, which deals with statements about what is necessarily true or possibly true. From the axioms that a property can only be positive if not-having-it is not positive, and that properties implied by a positive property must all also be themselves positive, it concludes that (since positive properties do not involve contradiction) for any positive property, there is possibly a being that instantiates it. It defines God as the being instantiating all positive properties. After defining what it means for a property to be “the essence” of something (the one property that necessarily implies all its other properties), it concludes that God’s instantiation of all positive properties must be the essence of God. After defining a property of “necessary existence” and taking it as an axiom that it is positive, the argument concludes that, since God must have this property, God must exist necessarily.
