On the Maximality of Positive Properties and Modal Collapse in Variants of Gödel’s Ontological Proof for the Existence of God

Abstract

Gödel’s ontological proof for the existence of God – as an inference from the level of rational, logical structure to the level of being – was strongly influenced by Leibniz’s monadology, which is based on the Ur-Monade – God – conceived as absolutely infinite. Gödel defines God as the maximum of positive properties and he characterizes this maximum (of being) with his postulates implicitly as an ultrafilter structure. Using maximality as criterion we have compared the set of positive properties in Scott’s version of Gödel’s theistic theory with modified variants of it to see whether a maximum is still achieved, or not, and what effect this has on modal collapse. The motivation for these, typically weakened, variants of Gödel’s theistic theory has been to avoid modal collapse and the limited determinism associated with it, and to show that the necessary existence of God can still be proved with less strong axioms. A weakening of the maximality criterion of the ultrafilter structure imposed by Gödel’s (and Scott’s) postulates have thus been applied to the set of positive properties in order to allow for alternative models in which modal collapse does not hold. In these alternative models, however, the maximality criterion for the basic quantity of positive properties is abandoned, so that in them God as a “maximum” is not reached. We argue that this is contrary to Gödel’s intention, and that for his conception of God, maximality and absolute infinity are non-negotiable. What Gödel had in mind, as we argue here, was a holistic – absolutely infinite – view of the world, i.e. with modal collapse, but without limited determinism.