Mechanized Analysis of Anselm's Modal Ontological Argument

TL;DR

This paper employs a mechanized verification system to analyze Anselm's Modal Ontological Argument, revealing its triviality under modal axioms and demonstrating the utility of computational methods in philosophical reasoning.

Contribution

It applies formal verification to analyze and compare different formalizations of Anselm's argument, showing their equivalence and triviality under modal axioms.

Findings

All formalizations are essentially similar.

The argument is trivial with modal axioms.

Computational methods aid in detecting errors in modal reasoning.

Abstract

We use a mechanized verification system, PVS, to examine the argument from Anselm's Proslogion Chapter III, the so-called "Modal Ontological Argument." We consider several published formalizations for the argument and show they are all essentially similar. Furthermore, we show that the argument is trivial once the modal axioms are taken into account. This work is an illustration of computational philosophy and, in addition, shows how these methods can help detect and rectify errors in modal reasoning. This is a minor update with better typesetting and some small addenda to a paper published in the International Journal for Philosophy of Religion, vol. 89, pp. 135--152, April 2021.