TOOK THE GODEL CHALLENGE: To their credit, they took the challenge!

TUESDAY, JULY 5, 2022

But did they succeed in their quest?: To their credit, against all odds, they took The Gödel Challenge.

That said, did they succeed in their attempts—in their attempts at the Gödel Challenge as we will define it? 

It seems to us that the answer is no. But to their credit, the challenge was taken. They gave the challenge a try.

In fact, quite a few people have taken the Gödel Challenge over the past fifty years. At issue is the so-called "incompleteness theorem" (or theorems) of Kurt Gödel, the logician, mathematician, and philosopher who published this theorem in 1931 at the age of 25.

As a result of this work, Gödel has often been called "the greatest logician since Aristotle." This would seem to suggest that his work was highly significant.

Gödel has often been called "the greatest logician since Aristotle!" But can anyone explain his work in a way non-specialists can understand?

In the course of the next few weeks (or months), we'll define the Gödel Challenge in a much more challenging way. We'll even ask this:

Is it possible that Gödel's work doesn't even make sense?

Such a suggestion may seem highly counterintuitive. Eventually, we'll go ahead and raise that possibility, even offering reasons for our concern. But for today, we'll settle for this opening parry:

Has anyone been able to explain Godel's work in a way non-specialists can understand?

Major players have taken the challenge, but has anyone succeeded? As we discuss this topic in the next few weeks, we'll focus on a relatively limited set of attempts.

In our next presentation in this series, we'll define the limited roster on whose efforts we'll focus. The people we'll list have all taken the challenge—but blurbs and book reviews to the side, has anyone ever succeeded at this Herculean task?

Later this week: The roster


11 comments:

  1. "Has anyone been able to explain Godel's work in a way non-specialists can understand?"

    Indeed, it can't be explained to a liberal, dear Bob, because liberal=braindead, as you know.

    Normal ordinary people, that's a different story. Not too complicated.

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  2. Good morning,
    Quick reminder that both sides know Right-wing snowflakes threw a childish temper tantrum just because black peoples votes counted in the 2020 Presidential election

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  3. "Is it possible that Gödel's work doesn't even make sense?"

    You would have to understand it to answer this question. Since Somerby cannot understand it and does not understand and even posits that no one else understands it, the answer must be no -- because if you cannot understand Godel and cannot determine whether his theorem makes sense or not, you cannot know whether it makes sense or not, and thus it both does and does not make sense as far as Somerby is concerned. So no, it is not possible that it doesn't make sense because Somerby's own question cannot be answered. Godel would probably agree with this argument.

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  4. "As a result of this work, Gödel has often been called "the greatest logician since Aristotle." This would seem to suggest that his work was highly significant."

    Godel was probably called this because of his proof of the existence of God. His work on incompleteness was of major significance in the age of computer science and AI, which came later. But it had a specific effect on those contemporary philosophers who were attempting to use logic to prove the foundation of mathematics because it showed the limitations of such an approach.

    It is unclear why Somerby thinks someone needs to understand Godel's work personally to understand why others in his field considered his work important. I can understand why fire fighters are important without knowing how to do their jobs.

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    Replies
    1. How did Godel "prove the existence of God?" And if he "proved" it, what was the "God" that he proved existed? what were this God's features, characteristics, consciousness, etc? E.g.,Does this "God" wish to be worshipped by humans?

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    2. You need to read one of the Godel books for this.

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  5. "As we discuss this topic in the next few weeks, we'll focus on a relatively limited set of attempts."

    Why? This seems like a colossal waste of time.

    We do seem to be in an age when "non-specialists" are finding many areas of knowledge inaccessible without further education. That was predicted at least 50 years ago and social scientists have been talking about a knowledge-gap, a widening gulf between those with technical expertise and those without, the difficulties finding well-paying jobs without technical training, and the importance of college to obtaining such jobs.

    There is also a backlash against such demands. One symptom is the claim that there are many career paths that don't require college and the demand that pressure on kids to go to college be reduced. (I don't see any leveling off of the advantage having a degree provides in terms of income.) Another symptom is the anti-intellectualism on the right, echoed by Somerby here. The idea that knowledge is irrelevant, that facts have no special status and that truth is whatever lie you choose to tell, The right will even call videos "deep fakes" if they show something they don't want to see. It is one thing to say that nothing can be known, but as the pandemic showed, there is a reality independent of people's disinformation and it does not change or go away simply because people want something else to be true. But I see this as a revolt against expertise based on knowledge.

    Just when the accumulation of knowledge seemed to be more than a person could absorb, the internet and search engines came along to put information at our finger tips. The only excuse now for not knowing things, is lack of curiosity and literacy skills. But there still exist complex ideas that require a foundation based in prior learning in order to understand some things, such as Godel's ideas.

    There is another odd recursion in the fact that Somerby seems to think that he, himself, a person who admittedly doesn't understand Godel's work, has appointed himself the arbiter of the attempts to explain that work in terms a layperson can understand. I doubt Somerby's motives, but why should I assume he has the requisite layperson's ability to understand anything?

    Somerby is 76. He may have dementia that prevents him from understanding anything, no matter how clearly it is explained. In that case, it isn't the explanations that are at fault. How do we know that isn't true? I think Somerby's first step must be to select a representative layperson, but how will he decide what knowledge that person should have? Isn't there some circularity to that task, a mini-version of the follow-on task of understanding Godel?

    So, this is a big fool's errand. Somerby may be finding this amusing, but it is a joke made at the expense of other people, which makes it kind of mean-spirited, especially for someone who shoud have the instincts of an educator (that has always been doubtful in Somerby's case). More and more it appears that Somerby's pleasure here is to watch people chase each other down rabbit holes. Not nice.

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  6. Somerby’s fixation with Gödel is bizarre.

    He cannot resolve this question for himself as to whether Gödel’s theorems make sense. He will never be able to resolve it, so he merely suggests without ever offering or being able to offer any convincing arguments. He is content to spin his wheels forever.

    Look for the usual mocking of Gödel’s Platonism or his “mental illness” late in life, all irrelevancies.

    And it’s unclear what relevance this has to the media or American discourse, or, to take something from his previous post, the false notion that Democrats are too extreme.

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