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Gödel and God: A Surprising History

A thought-provoking account of master logician Gödel’s largely unknown proof of the existence of God

In a recent podcast, “Kurt Gödel’s Proof of the Existence of God,” Walter Bradley Center director Robert J. Marks and Dr. Selmer Bringsjord discuss mathematician Kurt Gödel’s ontological argument for the existence of God. A partial transcript follows:

01:44 | A book about Kurt Gödel

Robert J. Marks: Before we talk about the paper that you presented in Romania in 2019 titled “The Argument for God’s Existence from AI,” let’s talk about the book that you’re writing. You’re writing about Kurt Gödel (1906–1978) and his proofs. Could you tell us what your book is about? Gödel was just a monster genius in terms of mathematics.

Selmer Bringsjord: The book’s little different in that I’ve set myself the goal of covering all his great theorems. I may miss one or two that some people would say are great but…

Robert J. Marks (right): Oh, so this would include the continuum hypothesis and, probably, … he did things in cosmology too, didn’t he?

Selmer Bringsjord: “The Gödel time travel theorem” is what that chapter is called. It was his birthday present to Einstein showing him that Einstein’s Theory of General Relativity, as Einstein’s equations had it, is consistent with a form of backwards time travel. He proved that.

02:53 | Gödel’s “God Theorem”

So there is a chapter for each of the great theorems and there is a chapter on what I call the God theorem.

Robert J. Marks: And that’s what we’re going to talk about today. What’s the history of this so-called “God theorem.” Gödel never published it, did he?

Selmer Bringsjord (right): No, he didn’t. And there could be varying degrees of speculation about how speculative the hypotheses were, as to how long he worked on it, and how seriously he worked on it.

But it seems pretty much undeniable that he worked on it for a long time and put a tremendous amount of concentrated effort into it. And the first time, to my knowledge, that it left his consciousness… was when he thought he was dying and showed his notebook to Dana Scott, who was not one of his students but… he was learning from Gödel. Dana Scott copied out a proof of God’s existence. It’s now been reproduced; it’s in the literature, it’s in the AI literature in formal form. That’s, I believe, the first transmission of this discovery from Gödel to another human and perhaps any other externalization of the idea.

I mean, even if one doesn’t think that the argument ultimately succeeds, it’s still a discovery.

Robert J. Marks: You know, I actually have arguments with people about whether God exists and I think it’s fun to just show them the page of Gödel’s proof—for those not aware of the mathematics, it look like hieroglyphics. But say, “Here’s the proof Kurt Gödel did. Take a look and if you have any more questions, you can ask me about whether God exists or not.”

05:03 | Was Gödel a deist?

Robert J. Marks: Is there any evidence that Gödel was a deist? Theist? Christian? that you’re aware of?

Selmer Bringsjord: I’d like to meet the person who denies that its certain he was a theist. It’s also certain that he was, maybe, a “non-organizational Christian.” As things got worse, he wasn’t able to socialize in any environments. Just having a dinner without thinking someone was going to kill him…

Gödel’s mental problems tormented him until his death: Obsessed with the fear of being poisoned, he only ate what his wife prepared for him. When she had to stay in a hospital for a while, Gödel refused to eat, eventually starving to death in 1978.

Florian Aigner, Vienna University of Technology, “Kurt Godel studied statements which refer to themselves, and his results shook the foundations of mathematics” at Phys.org (June 24, 2014)

Selmer Bringsjord:

I mean, he died under very, very distressing psychological circumstances so… he’s not ultimately the barometer of whether someone could tolerate organized religion but… I believe you can find some stuff regarding his wife’s observations and his relationship also about his relationship with his mother who was very devout.

On a personal note, having look at, not the argument, but a lot of the life’s work, and the picture we have emerging, you would pretty much have to be an idiot to take pot shots at any such proposition as that he wasn’t really a believer, whether fully orthodox or not.

“Gödel had a happy childhood, and was called “Mr. Why” by his family, due to his numerous questions. He was baptized as a Lutheran, and remained a theist (a believer in a personal God) throughout his life.” –

Tucker McElroy (2005). A to Z of Mathematicians. Infobase Publishing. p. 118. ISBN 978-0-8160-5338-4.

Selmer Bringsjord: Across the board, his views on the mind, his views on the future, it’s really a compelling picture. But again, for people expecting… if it was John Calvin who showed up to interview him, there would be big problems for the systematic theologian. But no, he clearly was in that direction, to put it mildly.

Robert J. Marks: Well, if he wasn’t at least a deist or a theist, what motivation would he have for offering such a proof for the existence of God?

Selmer Bringsjord: Right. The only countervailing (argument) you would get is that he really liked the thinking or the thoughts or work of Leibniz rather than the topics, and that’s absurd.

07:31 | The history of Gödel’s proof (illustrated below)

Robert J. Marks: The origin of Gödel’s proof goes back to Leibniz, as you mention. Unpack some of the history of the proof.

Selmer Bringsjord: This is an unsanitized, politically incorrect history. In your armchair, consider the idea of whether or not God is possible, determine that God is possible, and then infer validly from the mere possible existence of God that God must exist.

About 1070 AD, Anselm (1033–1109), who was a very subtle thinker, comes up with this idea, an ontological argument for God’s existence…

We can prove certain negative existential claims merely by reflecting on the content of the concept. Thus, for example, we can determine that there are no square circles in the world without going out and looking under every rock to see whether there is a square circle there. We can do so merely by consulting the definition and seeing that it is self-contradictory. Thus, the very concepts imply that there exist no entities that are both square and circular.

The ontological argument, then, is unique among such arguments in that it purports to establish the real (as opposed to abstract) existence of some entity. Indeed, if the ontological arguments succeed, it is as much a contradiction to suppose that God doesn’t exist as it is to suppose that there are square circles or female bachelors. In the following sections, we will evaluate a number of different attempts to develop this astonishing strategy.

Kenneth Einar Himma, “Anselm: Ontological Argument for God’s Existence” at Stanford Encyclopedia of Philosophy

But the problem is, you have to go about two centuries before anyone does anything significant with this. That’s Aquinas (1225–1274) and Aquinas doesn’t like these ideas. So that’s like, 1260 AD.

And then you have Descartes (1596–1650), showing up in the 1640s, saying, I do need to prove that God exists because otherwise, to modernize it, we might be living in the Matrix, and I don’t want that. So what I’ll first do is prove that God exists. And, since God exists and is good and all-powerful, he’ll ensure that you’re not living in the Matrix. Therefore, you can trust your senses. So that’s 1635. And he claims he didn’t read Anselm, that this is original to him… And some people believe Descartes, some people don’t. I tend to believe him. So Descartes says the same thing as Anselm; the mere possibility of this being existing—you can see by definition that if it is possible, it must exist.

So then Gottfried Leibniz (1646–1716, left) writes his own version at the turn of the century, just after 1700.

This is where everything gets much, much more serious, at least from the standpoint of modern formal logic and even first-rate, I think, rigorous philosophy—and also AI [artificial intelligence]. Because what Leibniz says is, well, I’m a Christian. He only published one thing, Theodicy early in his life, where he is just aggressively orthodox—he talks about Jesus and so forth—so he is not happy with Descartes’ work. And when Jones, on the street, is not happy with your work, that’s one thing but when leibniz is not happy, he’s probably got a reason for being not happy.

He comes to the conclusion that Descartes just assumes that God is possible. After all, how do we know that the conception of God that we have—omnipotence, omniscience, omnipresence—if we put all these attributes together—are consistent? So he sets himself the task of demonstrating this and giving another version of the argument.

And then we jump all the way to the twentieth century and another source of political incorrectness is that there are lots of other people here. When we go to Gödel, we skip over the modern advocates of this argument. It’s harsh—I’m just going to say it—from the standpoint of someone who’s reasonably well-versed in formal logic, I think it’s a bit of a doldrums, despite some of the attention, until Gödel does his thing.

Gödel does it formally and then some folks in Germany, doing automated reasoning, verified it a few years back. They verified the version that Dana Scott copied out of the notebook. That is, what they verify is that there is no doubt; it’s machine-verified proof. So now we’re left with just the truth of the premises and how we judge them.

So that’s really the history and the subsequent chapter is about how Gödel’s own version, accurately transcribed from his notebooks, was not formally valid. So Dana Scott made some decisions in the transcription that were, well—if one is a theist—quite fortuitous. Now we have an invalid version and we have a valid version. And the valid version, post-Gödel, has been improved and repaired. Some of its supposed deficiencies have been repaired. This goes beyond what I discuss in my book and it’s not what my book is about. I’d get in trouble if I went to these more modern modifications. This is basically the history and I think the argument will never die.


Further reading:

Faith is the most fundamental of the mathematical tools: An early twentieth century clash of giants showed that even mathematics depends on some unprovable assumptions. (Daniel Andrés Díaz-Pachón)

and

God’s existence is proven by science. Arguments for God’s existence can be demonstrated by the ordinary method of scientific inference. (Michael Egnor)

Show Notes

  • 01:05 | Introducing Selmer Bringsjord, Professor — Rensselaer Polytechnic Institute (RPI)
  • 01:44 | A book about Kurt Gödel
  • 02:53 | Gödel’s “God Theorem”
  • 05:03 | Was Gödel a deist?
  • 07:31 | The history of Gödel’s proof
  • 13:46 | The reasoning behind Anselm’s ontological proof

Gödel’s Ontological Proof

Gödel's ontological proof of the existence of God
Gödel’s ontological proof of the existence of God. From Wikipedia

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Gödel and God: A Surprising History