[sramsay]

I seriously doubt that. Most "professional philosophers" these days are doing analytical philosophy, and it's been at least 500 years since a non-crazy person has been persuaded one way or the other about God by studying logic.

I suppose Georg Cantor might be an exception to this.

[manicbovine]

Gödel had an unpublished ontological "proof" [1] that's fairly simple to understand. It hinges on two things: 1.) accepting a logical system in which possibly necessary truths are necessary; 2.) accepting his argument that it's possible for god to exist.

But I guess you said non-crazy.

[1] https://en.wikipedia.org/wiki/G%C3%B6dels_ontological_proof

[Apocryphon]

How about Bayes's theorem for proving the existence of God? http://en.wikipedia.org/wiki/Richard_Swinburne