Computer-Assisted Analysis of the Anderson-Hájek Ontological Controversy

We present an exemplary study in Computational Metaphysics, which is an emerging, interdisciplinary field aiming at the rigorous formalisation and deep logical assessment of rational, philosophical arguments on the computer. The particular focus here is on the ontological argument for the existence of God. While related work [9, 7] has concentrated on Anselm’s simpler original version of the ontological argument and formalized it in classical predicate logic, we here focus on modern variants of Kurt Gödel’s seminal contribution [12] requiring higher-order modal logic. In preceding experiments [1, 4, 6], we have already demonstrated that the technology we employ is well suited for the task. In fact, computers may even contribute philosophically relevant new knowledge. For example, the theorem prover Leo-II [2] detected an inconsistency in Gödel’s original script [12] of the argument, which was undetected by philosophers before. This inconsistency renders pointless Gödel’s original version of the argument. Nevertheless, as our preceding experiments also confirmed, Scott’s variant [13] from Fig. 1 is immune to this issue. Hence, in the remainder of this article the term Gödel’s ontological argument actually refers to Scott’s variant, whose logical validity has been formally verified with our technology (for higher-order modal logic KB (or stronger logics) with constant domain or varying domain