What Kind of Ultrafilter is Gödel's God?

Christoph Benzmüller (Freie Universität Berlin)

Emendations of the Gödel/Scott modal ontological argument have been proposed amongst others by Anderson and Fitting. Their variants preserve the intended conclusion, the necessary existence of God, while avoiding a controversial side result of the premises of the Gödel/Scott argument(s), known as the ``modal collapse''. The modal collapse expresses that there are no contingent truths (everything is determined; one may say, there is no free will).

At first sight the variants of Anderson and Fitting appear different. However, when linking and assessing their detailed notions of positive properties with the notion of an ultrafilter from set theory, then some intriguing commonalities between both variants can be revealed. Moreover, by adopting the same idea, Anderson's and Fitting's notions of positive properties can be further compared with the one of the Gödel/Scott variant(s), which is different. This analysis provides an explanation why the modal collapse holds for the latter, but not for the former. We may thus ask: What kind of ultrafilter is actually meant by Gödel's God? One that avoids modal collapse, or one that doesn't?

All findings reported in this talk were discovered in interaction with modern theorem provering technology by adopting Benzmüller's universal (meta-)logical reasoning approach. These experiments are thus exemplifying the new area of computational metaphysics.

Last modified: Mon Feb 11 09:44:18 CET 2019