A Computationally-Discovered Simplification of the Ontological Argument

The authors investigate the ontological argument computationally. The premises and conclusion of the argument are represented in the syntax understood by the automated reasoning engine prover9. Using the logic of definite descriptions, the authors developed a valid representation of the argument that required three non-logical premises. prover9, however, discovered a simpler valid argument for God’s existence from a single non-logical premise. Reducing the argument to one non-logical premise brings the investigation of the soundness of the argument into better focus. Also, the simpler representation of the argument brings out clearly how the ontological argument constitutes an early example of a ‘diagonal argument’ and, moreover, one used to establish a positive conclusion rather than a paradox. ∗The following paper is forthcoming in the Australasian Journal of Philosophy. The authors would like to thank Branden Fitelson for introducing us to otter, prover9, and mace4, and Bill McCune for answering our questions about them. We’d also like to thank Johan van Benthem, Nathan Tawil, and Jeffrey Kegler for comments about the paper, which led us to develop additional interesting points about the prover9 proof. Paul E. Oppenheimer and Edward N. Zalta 2