A (Simplified) Supreme Being Necessarily Exists, says the Computer: Computationally Explored Variants of Gödel's Ontological Argument
Abstract
An approach to universal (meta)logical reasoning in classical higherorder logic is employed to explore and study simplifications of Kurt Gödel's modal ontological argument. Some argument premises are modified, others are dropped, modal collapse is avoided and validity is shown already in weak modal logics K and T. Key to the gained simplifications of Gödel's original theory is the exploitation of a link to the notions of filter and ultrafilter from topology. The paper illustrates how modern knowledge representation and reasoning technology for quantified nonclassical logics can contribute new knowledge to other disciplines. The contributed material is also well suited to support teaching of nontrivial logic formalisms in classroom.
 Publication:

arXiv eprints
 Pub Date:
 January 2020
 arXiv:
 arXiv:2001.04701
 Bibcode:
 2020arXiv200104701B
 Keywords:

 Computer Science  Logic in Computer Science;
 Computer Science  Artificial Intelligence;
 Computer Science  Computation and Language;
 Mathematics  General Topology;
 Mathematics  Logic;
 03Axx;
 03B15;
 03B45;
 03B60;
 03B80;
 68T15;
 68T27;
 68T30;
 F.4.0;
 F.4.1;
 I.2.3;
 I.2.4;
 J.5;
 I.1.3
 EPrint:
 11 pages, 11 figures