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