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At MMN How an eccentric mathematician opened up the world

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Science writer Ashutosh Jogalekar has written a wonderful essay that explains how Kurt Gödel (1906–1978) defeated crass materialism:

“So what had Gödel done? Budiansky’s treatment of Gödel’s proof is light, and I would recommend the 1950s classic “Gödel’s Proof” by Ernest Nagel and James Newman for a semi-popular treatment. Even today Gödel’s seminal paper is comprehensible in its entirety only to specialists in the field. But in a nutshell, what Gödel had found using an ingenious bit of self-referential mapping between numbers and mathematical statements was that any consistent mathematical system that could support the basic axioms of arithmetic as described in Russell and Whitehead’s work would always contain statements that were unprovable. This ingenious scheme included a way of encoding mathematical statements as numbers, allowing numbers to “talk about themselves”. What was worse and even more fascinating was that the axiomatic system of arithmetic would contain statements that were true, but whose truth could not be proven using the axioms of the system – Gödel thus showed that there would always be a statement G in this system which would, like the old Liar’s Paradox, say, “G is unprovable”. If G is true it then becomes unprovable by definition, but if G is false, then it would be provable, thus contradicting itself. Thus, the system would always contain ‘truths’ that are undecidable within the framework of the system. And lest one thought that you could then just expand the system and prove those truths within that new system, Gödel infuriatingly showed that the new system would contain its own unprovable truths, and ad infinitum. This is called the First Incompleteness Theorem. – Ashutosh Jogalekar, “Kurt Gödel’s Open World” at 3quarksdaily (July 12, 2021)”

The big materialist project was then formally over. Many people did not realize that fact and, in any event, it would take a long time to mop up. We are still mopping.

News, “How eccentric mathematician Kurt Gödel opened the world” at Mind Matters News

As often happens, few people understood the significance of what had just happened. The one exception was John von Neumann.

Takehome: The First Incompleteness Theorem means that the big materialists project is essentially already over. But it takes a long time to mop up.

You may also wish to read:

Gregory Chaitin’s “almost” meeting with Kurt Gödel: This hard-to-find anecdote gives some sense of the encouraging but eccentric math genius.

5 Replies to “At MMN How an eccentric mathematician opened up the world

  1. 1
    Seversky says:

    I’m not sure what you mean by the “materialist project” or how it is somehow defeated by the Incompleteness Theorem.

  2. 2
    Belfast says:

    Good question, Sev.
    But what do you mean by “mean”?

  3. 3
    polistra says:

    It’s the other way around. Godel didn’t end materialism, he ended spiritualism in math. The Platonist project of building a fake foundation under math should have stopped after Godel showed it was fake.

    If anyone had listened, math would have retracted into real PURPOSE-DRIVEN MATERIALISM, serving MATERIAL purposes like engineering and electronics. Aristotle wins.

    Unfortunately the SPIRITUALISTS kept going, like Wlle E. Coyote off a cliff. They’re still going strong today, focusing on totally meaningless theorems and proofs and axioms. They still insist that math starts with faith.

  4. 4

    What a nonsense. Some mathematicians already refuted Godel’s theorem, but more generally, it makes no sense that the material domain would not be logically consistent.

  5. 5
    Bob O'H says:

    I’m not sure what you mean by the “materialist project” or how it is somehow defeated by the Incompleteness Theorem.

    I’m sure Denyse has an explanation, but unfortunately the margins aren’t large enough to contain it.

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