The Ontological Argument in PVS ∗

The Ontological Argument, an 11th Century proof of the existence of God, is a good candidate for Fun With Formal Methods as nearly everyone finds the topic interesting. We formalize the Argument in PVS and verify its correctness. The formalization raises delicate questions in formal logic and provides an opportunity to show how these are handled, soundly and efficiently, by the predicatively-subtyped higher-order logic of PVS and its mechanized support. The simplicity of the Argument, coupled to its bold conclusion, raise interesting issues on the interpretation and application of formal methods in the real world.