The authors investigated 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. (shrink)

In this paper, we discuss formal reconstructions of Anselm’s ontological argument. We first present a number of requirements that any successful reconstruction should meet. We then offer a detailed preparatory study of the basic concepts involved in Anselm’s argument. Next, we present our own reconstructions—one in modal logic and one in classical logic—and compare them with each other and with existing reconstructions from the reviewed literature. Finally, we try to show why and how one can gain a better understanding of (...) Anselm’s argument by using modern formal logic. In particular, we try to explain why formal reconstructions of the argument, despite its apparent simplicity, tend to become quite involved. (shrink)

The authors investigated 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. (shrink)