MONDAY, JULY 11, 2022
Took it but seem to have failed: To us, it felt like a four-day weekend. Also, the weather in the Baltimore/Washington area was unseasonably superb.
Under the circumstances, we did what anyone else would have done over the recent July 4 weekend. We gifted ourselves with the ongoing pleasures of "The Gödel Challenge," resulting in this report.
Major figures have taken the Gödel Challenge. In its simplest form, the challenge consists in this:
At its simplest, the challenge consists in the attempt to explain Kurt Gödel's incompleteness theorem(s) in a way the general reader can understand.
As the days and weeks pass, we'll add a bit to that description of the Gödel Challenge. That said, major figures have taken the challenge. In our view, they seem to have failed.
Question! Since almost no one has ever heard of Kurt Gödel, why should such folderol matter?
Given the way the world really works, it doesn't matter at all! Given the way we might wish the world worked, it matters for this reason:
Kurt Gödel (1906-1978) has often been described as "the greatest logician since Aristotle." Given the role logic is said to play in idealized pictures of human life, you'd almost think we'd want to know what he showed or proved.
Alas! We know of no one who has been able to explain that matter in a way the general reader can hope to understand. Today, we present a roster of some major figures who have taken the Gödel Challenge—who have taken the challenge and failed:
Professor Rebecca Goldstein:
Rebecca Goldstein took the challenge in her well-received book, Incompleteness: The Proof and Paradox of Kurt Godel.
The book appeared in 2005, part of a larger series aimed at general readers. It was festooned with blurbs from leading intellectuals who testified to its lucidity.
At the time, Goldstein was a philosophy professor at Barnard. She graduated as valedictorian from Barnard in 1972, then received her doctorate in philosophy from Princeton.
Aside from her work in philosophy, Goldstein is also a well-regarded novelist. In 2014, she received a MacArthur genius grant.
Biographer Stephen Budiansky:
In 2021, Stephen Budiansky took the challenge in a similar biography aimed at general readers. His book was called Journey to the Edge of Reason: The Life of Kurt Gödel.
The book was favorably reviewed. Budiansky benefited from access to a wide array of private papers which has previously been inaccessible to Gödel scholars.
Professors Nagel and Newman:
Longer ago and farther away, Ernest Nagel and James Newman also took the challenge. Initially, they did so in an article for Scientific American.
Nagel and Newman were highly regarded scholars in their respective fields. Later, their article was expanded into a short book, Gödel's Proof.
The book appeared in 1958, becoming an instant classic. In 2001, New York University Press published a slightly revised edition of the original text, describing the book as shown:
An accessible explanation of Kurt Gödel's groundbreaking work in mathematical logic
In 1931 Kurt Gödel published his fundamental paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences—perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."
However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.
New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.
According to NYU Press, Gödel's Proof provides non-specialists with "a readable and accessible explanation of the main ideas and broad implications of Gödel's discovery." The overview notes that the new edition of the book included "a new introduction by Douglas R. Hofstadter."
"What is Gödel's work about?" Hofstadter asks at one point in that introduction. That said, Hofstadter was already very well known, and highly regarded, for having taken the challenge at an earlier point.
Professor Douglas Hofstadter:
Perhaps the best-known attempt at the Gödel Challenge came from Professor Hofstadter in his 1979 book, Gödel, Escher and Bach.
The 777-page book won the Pulitzer Prize for general non-fiction and the National Book Award for Science Hardcover. Hofstadter's explanation of Gödel's work was one of the building-bocks of the book—and Hofstadter didn't stop there.
In 2001, Hofstadter took the challenge again, writing that preface to the latest edition of the Nagel and Newman book. Again, he tried to explain what Gödel had done in a way which would be accessible to the general reader.
Others have taken the Gödel Challenge over the many long years. That said, we'll be focusing on the efforts listed above as we attempt to discern if anyone has successfully taken this challenge.
Above, you see our roster. We've cited five highly-regarded scholars and writers who have taken the Gödel Challenge. But has anyone succeeded at this daunting task?
We're inclined to say that the answer is no. As we noted in our earlier post, we'll raise a related set of questions as we continue along with our quest. Our questions will go like this:
Do Gödel's theorems even make sense? Yes, the theorems are hard to explain. But is it possible that these famous theorems don't even make good sense, judged on their own terms?
That may seem like a ridiculous thought. For reasons we'll note as we proceed, we can't necessarily say that we automatically agree.
Our reasons for doubt will follow. We think this 20th-century story is wonderfully comic. It's anthropology all the way down!
Coming next: Expanding the terms of the Gödel Challenge
Earlier in this continuing series:
TOOK THE GODEL CHALLENGE: To their credit, they took the challenge! See THE DAILY HOWLER, 7/5/22.
ERRORS: We pivot away from our tribe's mistakes in search of some comic relief! See THE DAILY HOWLER, 7/7/22.