In this week’s podcast, “The Chaitin interview I: Chaitin chats with Kurt Gödel,” Walter Bradley Center director Robert J. Marks interviewed mathematician and computer scientist Gregory Chaitin. Earlier, we noted his comments on the almost supernatural awareness that the great mathematicians had of the foundations of reality in the mathematics of our universe. Yesterday, we heard Chaitin’s recollection of how he (almost) met the eccentric genius Kurt Gödel (1906–1978). One way that Gödel stood out from many of his contemporaries was that he believed in God. He even wrote a mathematical proof of the existence of God.

This portion begins at 17:16 min. A partial transcript, Show Notes, and Additional Resources follow.

Robert J. Marks: One of the things Gödel did that wasn’t published until after his death was his ontological proof of the existence of God, based on Anselm’s argument. (Anselm is pictured in this sixteenth century engraving.)

Note: Born in Austria–Hungary, Gödel (1906–1978) could not adjust to the presumption of atheism fashionable there in his day: “Despite his brilliance, Gödel never felt that he fit in with the Vienna Circle, since his theistic beliefs clashed with the popular ideas of logical positivism, which argued that the only real knowledge is that which can be demonstrated empirically. In 1931, he published what is known as Gödel’s incompleteness theorems.” – Aimee Lamoureux, “Despite Being A Renowned Mathematician, Kurt Gödel Starved Himself Out Of Paranoia” All That’s Interesting, July 11, 2018

Gödel’s incompleteness theorems (“among the most important results in modern logic” according to the Stanford Encyclopedia of Philosophy) showed that “we cannot devise a closed set of axioms from which all the events of the external world can be deduced.” Logical positivism never really recovered from the blow Gödel dealt it. Atheism had to be established on some other ground.

Gödel’s ontological proof of God was modeled on that of Anselm (1033–1109): “St. Anselm’s ontological argument, in its most succinct form, is as follows: ‘God, by definition, is that for which no greater can be conceived. God exists in the understanding. If God exists in the understanding, we could imagine Him to be greater by existing in reality. Therefore, God must exist.’ A more elaborate version was given by Gottfried Leibniz; this is the version that Gödel studied and attempted to clarify with his ontological argument.” – Apologetics Wiki

“Gödel’s ontological proof” at Apologetics Wiki provides both the proof and a great deal of supporting and evaluative material, including biographical details.

See also: “Gödel and God: A surprising history”: A thought-provoking account of master logician Gödel’s largely unknown proof of the existence of God.

Gregory Chaitin: He was definitely a theist. There’s a wonderful story about that, that Rebecca Goldstein published in Incompleteness: The Proof and Paradox of Kurt Gödel:

The Princeton Institute for Advanced Study would occasionally have fancy dinners, basically for people who might contribute additional funding to the Institute or provide political support. And at these dinners, they would ask their stars to be present to impress the potential donors and other members of the Institute. So Gödel was at such a dinner. You had to go, it wasn’t optional. He probably wouldn’t have wanted to be there.

He was sitting next to a young astrophysicist. And the astrophysicist was very proud of some discovery he had made, an observational discovery and he spent a lot of time explaining it to Gödel. And finally he stopped, expecting Godel to express admiration for the story he told. Instead of which, Gödel replied, “I don’t believe in empirical science. I only believe in a priori truths.” That’s an answer from the Middle Ages. I priori truths are necessary truths. So maybe he didn’t believe in evolution either, I’m not sure.

Robert J. Marks: Well, he didn’t. There’s a famous quote where he said evolution is, I forget the analogy, but it was basically that a printing factory exploded and resulted in a book or something like that. So he was not a big believer in evolution either.

Note: We are told that Kurt Gödel wrote in a 1972 letter to Hao Wang: “I believe that mechanism in biology is a prejudice of our time which will be disproved. In this case, one disproof, in my opinion, will consist in a mathematical theorem to the effect that the formation within geological time of a human body by the laws of physics (or any other laws of similar nature), starting from a random distribution of the elementary particles and the field, is as unlikely as the separation by chance of the atmosphere into its components.” – Stack Exchange – Philosophy (November 27, 2019)

So, while an analogy Gödel used may be hard to pin down, the thought was definitely there.

Gregory Chaitin: He was a very interesting person. Interesting mind, very powerful.

The previous stories on this podcast with Gregory Chaitin:

Gregory Chaitin’s “almost” meeting with Kurt Gödel. This hard-to-find anecdote gives some sense of the encouraging but eccentric math genius. Chaitin recalls, based on this and other episodes, “There was a surreal quality to Gödel and to communicating with Gödel.”

and

Gregory Chaitin on the great mathematicians, East and West: Himself a “game-changer” in mathematics, Chaitin muses on what made the great thinkers stand out. Chaitin discusses the almost supernatural awareness some mathematicians have had of the foundations of our shared reality in the mathematics of the universe.

You may also wish to read: Things exist that are unknowable: A tutorial on Chaitin’s number (Robert J. Marks)

and

Five surprising facts about famous scientists we bet you never knew: How about juggling, riding a unicycle, and playing bongo? Or catching criminals or cracking safes? Or believing devoutly in God… (Robert J. Marks)

Show Notes

• 00:23 | Introducing Gregory Chaitin
• 05:00 | Chaitin’s Youth
• 06:33 | Chaitin’s journey to computer science
• 08:26 | Chaitin’s thoughts on Leonard Euler
• 12:42 | Chaitin’s near brush with Kurt Gödel
• 17:16 | The quirks of Gödel

Additional Resources

• Gregory Chaitin’s Website
• Unravelling Complexity: The Life and Work of Gregory Chaitin, edited by Shyam Wuppuluri and Francisco Antonio Doria
• Conversations with a Mathematician: Math, Art, Science and the Limits of Reason by Gregory J. Chaitin
• Meta Math!: The Quest for Omega by Gregory Chaitin
• Thinking About Gödel and Turing: Essays on Complexity by Gregory J. Chaitin
• Proving Darwin: Making Biology Mathematical by Gregory Chaitin
• “On the Length of Programs for Computing Finite Binary Sequences” by Gregory J. Chaitin, written and published when he was a teenager
• Leonard Euler, Swiss mathematician and physicist
• Kurt Gödel, Austrian-born mathematician
• Georg Cantor, German mathematician
• Dr. Robert J. Marks’ critiques of Gregory Chaitin’s ideas on Youtube
• “Active Information in Metabiology“: Winston Ewert’s, William Dembski’s, and Robert J. Marks’ paper on Chaitin’s metabiology

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