I took a full semester course on Godel's Incompleteness Theorems in college and found it rewarding. It was one of those experiences that convinced me that hand-wavy familiarity with stuff sometimes pales by contrast to a deep dive.
One of the professors also had a very old newspaper clipping taped up (it was brown then and that was quite a while ago), about several mathematicians committing suicide in the wake of those proofs. I've looked for corroboration of this and have never found it. A bit difficult to comprehend from a modern perspective, but more plausible with an appreciation of the 19th Century faith in rationalism / logical positivism that Godel helped overturn.
Not many people are aware that Godel spent much of his life secretly working on a modern update of an ontological argument for God's existence, and didn't reveal this until late in life -- https://en.wikipedia.org/wiki/G%C3%B6del%27s_ontological_pro...
As far as I know it's not like the proofs caused a wave of suicides, but mathematicians studying this topic often became mentally unstable, including Godel (who starved himself in a sanatorium) and others like Georg Cantor.
I'm curious where you studied; I also took a semester course on "logic and computability" where the main text we read was 'Godel, Escher, Bach'
We briefly talked about Godel's proofs, but they are nontrivial. Henkin's proof of completeness is hard enough[1]. I don't mean to sound dismissive, but a class where Godel, Escher, Bach is the text does not seem very rigorous. Logic is very tricky stuff. And once you get into infinities, it's not even intuitive.
This article referenced some guys jumping off buildings... maybe it was more of the journalist's interpretation, connecting the sort of thing you mentioned with the suicides in a less direct way than I recall. I have wondered if it was a real news clipping (it looked like one), or some kind of old joke.
To answer your question, I went to one of the so-called "elite" American colleges that still has a primarily classical/analytic philosophy program (as opposed to what is known as a "Continental" program). Would rather not say which one, but I was able to take some great logic courses through the philo department.
We used Godel's work directly, and if memory serves also some Goldfarb.
Though not a proof of the existence of God as worked on by Godel, but Al Platinga is known for his work for the logical discussion of the rationality or religious belief
Somewhat related excerpt: https://www.princeton.edu/~hhalvors/restricted/plantinga-Rea...
Plantinga is known for his proof of God's existence, and in fact a proof of any sentence you like, using the modal logic operators of possibility and necessity: "possibly necessarily pigs fly, therefore pigs fly". (Where "possibly" is shorthand for "in some possible world", and "necessarily" is shorthand for "in all possible worlds".) It's a valid proof if you buy the assumption, but the assumption is dubious at best.
Of course it's valid! A world-renowned philosopher like Plantinga wouldn't publish a proof that's not valid. That's like saying Dijkstra's code compiles :)
The main problem with ontological arguments (and why, even as a Christian, I don't like them) is because they seem to embed the conclusion in their first premise. E.g.: the possibility of a maximally great being seems to definitionally imply its necessity. Why? Because such a being B must have some properties P = { ? ? ? ... }. We may not be sure what's inside P, but we know, with absolute certainty, that existence is in there.
Kant would disagree. He thinks that existence is not a property. This is a rare case when I think he's right.
> E.g.: the possibility of a maximally great being seems to definitionally imply its necessity.
One of my favourite tongue-in-cheeek replies I read to these ontological arguments: Ah, but surely there is no greater being than one who could create the universe despite not existing!
> The main problem with ontological arguments (and why, even as a Christian, I don't like them) is because they seem to embed the conclusion in their first premise
But that is also true of the informal rhetorical arguments that are more common in (christian) apologetics.
The gift of formal proofs is that they make explicit and unavoidable this embedding of conclusion in premise, which is fundamental to all (epistemologically rational) apologetics
One of the professors also had a very old newspaper clipping taped up (it was brown then and that was quite a while ago), about several mathematicians committing suicide in the wake of those proofs. I've looked for corroboration of this and have never found it. A bit difficult to comprehend from a modern perspective, but more plausible with an appreciation of the 19th Century faith in rationalism / logical positivism that Godel helped overturn.
Not many people are aware that Godel spent much of his life secretly working on a modern update of an ontological argument for God's existence, and didn't reveal this until late in life -- https://en.wikipedia.org/wiki/G%C3%B6del%27s_ontological_pro...