I will post this on my trombone forum to see what the atheist response will be.
There are a lot of people over there that assure me that the Bible is a work of fiction, and that is a fact. I'm not sure how they proved that fact, but I'm interested in reading their response the Gobel's Incompleteness Theorom.
From Trombone Player #1:
Interesting angle. But, even allowing the step where he claims that GIT implies the existence of something physically outside the universe (of which more below), it breaks down quite trivially where Perry Marshall then inserts a religious position into that, and claims that that is the logical thing to do. No, the logical thing to do at that point would be to recognise that one had reached a point where a consequence of incompleteness had become crucial, and then explore further axioms that one might assume in order to complete the particular gap that one had arrived at. One could use a religious position as an axiom - but what would be the point, scientifically? Axioms should be as simple as possible, and the assumption that there is a complex set of interacting and anthropomorphic forces out there acting on us (as described by most religions in their god concept) would be both way more complex and less specific than would be sensible.
It is worth remembering that the devisings of religions are always in response to a sense of incompleteness (though not the mathematical sense used by Godel) - and so GIT will naturally make people think of religious comparisons, whatever they personally may think of religiousness. But existing religions are all a throwing up of the hands that occurred in response to problems that we as a people have now long since solved... Sun gods and creation stories? We know a bit more about cosmology, geology and biology now. Maybe one day we will demonstrate that we have reached the limit of knowledge in some direction - but we don't seem to be anywhere near that limit in any direction yet!
However, to return to an earlier point as promised, there is a second big philosophical hole in this... GIT asserts that, in any sufficiently interesting system (and "interesting" has quite a low threshold here), there exist statements about that system that you cannot prove - not that things physically exist outside of that system. It says that a system cannot physically describe itself in total completeness, not that things are required to exist outside that system in order to make it look more complete. Using GIT to assert that things must exist outside of the universe is not logical.
Perhaps the biggest (and simplest) hole though, is this: If GIT really does assert that any system must have things physically outside of it, then what does it say about Perry Marshall's supposedly complete {universe + god} system? Why, that there must be something outside of that...
If you want to learn more about GIT, I recommend a highly entertaining (but brainbashing) book by Douglas Hofstadter, entitled "Godel, Escher, Bach, an Eternal Golden Braid", in which (en route to musing on the nature of consciousness) he gradually lays out the steps to a detailed lay understanding of GIT, interweaved with a lot of entertaining and thought-provoking chapters illustrating the points through whimsical examples and metaphors, named and structured after puns on J.S. Bach's works. It's a great book, but not a quick read.