Computer-Assisted Analysis of the Anderson–Hájek Ontological Controversy

C. Benzmüller, L. Weber, B. Woltzenlogel Paleo
2017 Logica Universalis  
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
more » ... 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. 1 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 This work was supported by German National Research Foundation (DFG) under grants BE 2501/9-1 and BE 2501/11-1. 1 Gödel avoids the first conjunct ϕ(x) in the definition of essence (D2), which Scott added for cosmetic reason. However, as Leo-II detected, one can prove from Gödel's definition that the empty property becomes an essence of every individual, which, together with theorem T1, axiom A5 and the defintion of necessary existence (D3) causes the inconsistency. For more details see Benzmüller and Woltzenlogel Paleo [1].
doi:10.1007/s11787-017-0160-9 fatcat:flqsjus6v5axtkj2neqwnr57si