Odifreddi: G?del's proof of the existence of God

Timothy Y. Chow tchow at math.princeton.edu
Tue Nov 8 18:39:24 EST 2022

Vaughan Pratt wrote:
> It was pretty clear that essentially all proofs had two essential 
> components: a definition of God, and an argument based on that 
> definition implicitly or explicitly based on proposed axioms and 
> inference rules.
> What's striking about the objections is that they almost invariably 
> attack the argument rather than the definition.
> Which is very strange, because which religions would recognize a 
> countably complete ultrafilter as being their God?

The presence of the word "God" distracts from what I consider to be the 
main achievement of Goedel's proof.

Almost everyone who encounters for the first time one of the classical 
ontological proofs of the existence of God instinctively feels that it is 
complete nonsense, even though it is hard to say explicitly exactly what 
is wrong with it.

Goedel's achievement was to show that the argument *is not complete 
nonsense*.  Of course, it does not prove that "God" exists in any 
conventional sense, but that is beside the point.  The point is that there 
exists at least one meaningful interpretation of a famous but seemingly 
absurd argument.


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