Modal Logic vs. Ontological Argument

Abstract

The contemporary versions of the ontological argument that originated from Charles Hartshorne are formalized proofs (in the metalogical sense of the word) based on unique modal theories. The simplest well-known theory of this kind arises from the b system of modal logic by adding two extra-logical axioms: (AA) “If the perfect being exists, then it necessarily exists” (Anselm’s Axiom) and (AL) “It is possible that the perfect being exists” (Leibniz’s Axiom). In the paper a similar argument is presented, however none of the systems of modal logic is relevant to it. Its only premises are the axiom (AA) and, instead of (AL), the new axiom (AN): “If the perfect being doesn’t exist, it necessarily doesn’t”. The main goal of the work is to prove that (AN) is no more controversial than (AA) and – in consequence – the whole strength of the modal ontological argument lies in the set of its extra-logical premises. In order to do that, three arguments are formulated: ontological, “cosmological” and metalogical.