THE GODEL FILE: We've been seeing ourselves from afar!

FRIDAY, SEPTEMBER 7, 2018

Bushmen meet Aristotle:
Long ago and far away, even before Kurt Godel died, we were teaching delightful fifth graders in the Baltimore City Schools.

(For our previous report, click here.)

At one point, we came upon a rather dull textbook which included a memorable anecdote. If memory serves, it was the third or fourth grade social studies text of one of the major publishers.

The textbook focused on the planet's many peoples and cultures. The memorable anecdote concerned the Bushmen of the Kalahari. They were among the shortest people in the world, the lower grade textbook said. In part for that reason, they have a standard traditional greeting:

"I saw you from afar."

Theoretically, this greeting was this group's attempt to compensate for smallness of stature. The greeted party was so large and imposing that he'd been seen from afar!

We never used that textbook, but the anecdote stuck in our heads. As it turns out, it had probably surfaced through the work of Marlin Perkins, later of TV's Wild Kingdom fame.

In 1965, Perkins and his wife, Carole Morse Perkins, had written a children's book about the Kalahari. The book was well received in a short review in the New York Times:
BERKVIST (5/9/65): This delightful little book, 50-odd pages of well-chosen words and photographs, opens a window on the world of the Bushmen, a remarkable handful of people who have somehow managed to strike a precarious bargain with nature in South Africa's vast, inhospitable Kalahari Desert.
"During their stay in the Kalahari," the reviewer went on to say, "the authors watched [the Bushmen] meet the harsh demands of desert life with good-humored dignity."

You can possibly guess the name of the Perkins book: "I Saw You From Afar!" The Times explained this traditional greeting as that textbook later did:

"The title echoes a highly complimentary form of greeting among Bushmen, most of whom are less than five feet tall and like to be told otherwise."

So the Times reviewer said—and so it went as the western world reached out to indigenous peoples. But the anecdote always stuck in our heads. At long last, we may know why:

Long ago and far away, Aristotle, the father of logic, is said to have made an basic assessment, one which became iconic:

"Man [sic] is the rational animal."

So Aristotle is commonly said to have said. Or words to that effect!

As the centuries passed, this flattering assessment came to define our species' basic self-assessment, at least within western culture. It strikes us as a near relation to "I saw you from afar."

Are we humans really "rational" in some definitive way? Aristotle, the father of logic, may have been wrong about that. And what better illustration, one might imagine, than the tragedy of Kurt Godel, who is commonly said to be our second greatest logician?

How odd! The western world's second greatest logician was severely mentally ill and given to crazy ideas! In the face of this slightly odd state of affairs, along come the popularizers, with their slavish, scripted enablers within the mainstream press corps.

The popularizers pretend to explain Godel's "incompleteness theorems." In turn, the journalists say that they've managed to make Godel's ideas and achievement just amazingly clear.

Along the way, we gullibles are told that the second greatest logician in history devoted his life to a key idea. The great logician was a Platonist, we're told. This "doctrine" is then made stunningly clear:
HOLT (page 8): Gödel entered the University of Vienna in 1924. He had intended to study physics, but he was soon seduced by the beauties of mathematics, and especially by the notion that abstractions like numbers and circles had a perfect, timeless existence independent of the human mind. This doctrine, which is called Platonism, because it descends from Plato’s theory of ideas, has always been popular among mathematicians...
Godel believed that numbers and circles have a perfect, timeless existence! At least, that's the way Jim Holt explains the "doctrine" in the title essay of his new, perhaps slightly plagiarized book, When Einstein Walked With Godel: Excursions to the Edges of Thought.

Holt derives his material, with lax attribution, from Rebecca Goldstein's 2005 book, Incompleteness: The Proof and Paradox of Kurt Godel. In that general interest book, Goldstein describes the great logician''s key belief like this:
GOLDSTEIN (page 44): Platonism is the view that the truths of mathematics are independent of any human activities...The truths of mathematics are determined, according to Platonism, by the reality of mathematics, by the nature of the real, though abstract, entities (numbers, sets, etc.) that make up that reality.
See there? According to Goldstein, our second greatest logician believed that the truths of mathematics are determined by the reality of mathematics! More specifically, the truths of mathematics are determined by the nature of the entities that make up that reality!

We humans! We've been seeing ourselves from afar for an extremely long time! At long last, along came the later Wittgenstein, making something resembling that claim about the various proclamations and assertions which constitute historical philosophy.

Wittgenstein said our allegedly greatest minds—not excluding himself, in his earlier efforts—had been seduced and led to ruin by conceptual confusion.

Back in 1969, we told Professor Cavell that we'd give him and Albritton fifty year to get this whole thing straightened out.
After that, we'd have to speak up, we said. Or words to that effect.

Stanley Cavell died in June, at age 91. Even as this loss occurs, the inanity of modern American journalism has finally overwhelmed even us.

This morning, we watched the clowning on Morning Joe as the children burned oodles of time trying to guess who wrote the op-ed column. We just can't go there any more. We're finally saying goodbye to all that, at least for the most part.

We've decided to move on to the larger story which has been lurking here. We've started with Godel this week because Holt's favorably-reviewed new book has brought the topic to mind.

"I saw you from afar," the Bushmen are said to say. We're forced to say that we hear an echo in Aristotle's famous remark.

Over here in the western world, we self-flattering human beings have hidden behind that remark. Now, we're going to bring you the never-before-told, dramatic true stories of human intellectual failure at its highest levels.

In truth, the extended tale we're going to tell is largely a comical tale. If you could ignore the endless wars and the endless killing, it would be humorous all the way down.

Along the way, we'll offer two paradigms—a pair of competing capsule accounts of our ballyhooed human race. One will come from Aristotle, one from Professor Harari:
The Aristotelian account: We humans are the rational animal.

The Harari heuristic: Our human species, Homo sapiens, is a slightly improved great ape. We drove all other human species into extinction because, through chance mutations, we developed 1) the ability to "gossip," and 2) the ability to promulgate, and believe and affirm, irrational, sweeping group "fictions."
So says Professor Harari in his widely-praised best-seller, Sapiens: A Brief History of Humankind, or words to that effect.

Along the way, we'll describe the building blocks of the Harari heuristic in more detail. For today, we'll only say this:

The idea that numbers have a perfect timeless existence is a remarkably good example of what Harari means when he describes the group "fictions" which gave our particular human species a competitive advantage. In Harari's account, this advantage came from the new ability to believe and affirm sweeping claims which don't make observable sense.

So how about it? Does the number 3 have a perfect timeless existence independent of the human mind? Do circles share that perfect existence with their good friends, the numbers?

According to Holt, that's what the second greatest logician in history believed from the time of his youth. According to Goldstein, he didn't believe in evolution, in part because Stalin said.

Numbers and circles have a perfect existence! Holt makes little attempt to explain what such a "belief" could possibly consist in or mean. But then again, so what?

At the New York Times, at the Wall Street Journal, rational animals stood in line to say how clear it all is. This has been going on forever, and it's a comical tale.

Next week: A Platonist among them!

31 comments:

  1. I love Bob, but I sure hope that he explains why it's a mistake to talk about math and numbers as having an existence independent of the human mind. That concept seems pretty easy for me to grasp, but perhaps I'm missing something.

    ReplyDelete
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  2. One question is timeless, independent of the human mind: is philosophy stupid? Richard Carrier asks.

    https://www.youtube.com/watch?v=YLvWz9GQ3PQ

    ReplyDelete
  3. Oh, you prefer music? Here's some 1950 television jazz:

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    ReplyDelete
  4. Here's how I understand the statement of Godel's incompleteness theorem. A mathematician named Peano came up with 5 simple postulates from which all the laws of arithmetic on the natural numbers can be derived. http://mathworld.wolfram.com/PeanosAxioms.html The only defined number is zero, but the successor of each number (sn) is also a number. Successor really means adding 1. So s0 is 1, ss0 is 2, sss0 is 3, etc.

    In principle one could use these rules to prove that 2 + 2 = 4 or 10*10 = 100 or any other arithmetic statement.

    But, Godel showed that these 5 axioms are not enough to prove every true statement about the natural numbers. Furthermore, even if you add more axioms, they will never be enough to prove every true statement about the natural numbers.

    ReplyDelete
    Replies
    1. I appreciate your interest in Gödel, David, and your attempts to discuss what he actually accomplished. Bob will not share your interest unfortunately.

      Delete
    2. I thought that it was Russell's work that Goedel sought to prove when he proved his Incompleteness Theorem. I think that, in general, it state that within every axiom-based mathematical system there's at least one postulate that cannot be proven within that system. No algebraic system is complete.

      Delete
    3. Ilya -- I was giving a specific application of Godel's result. It's easier for me to think about unprovable theorems number theory than about algebraic systems in general.

      Delete
    4. I don't think Godel was trying to prove Russel's Principia, which he certainly studied. Rather the work inspired him to come up with the technique to prove his incompleteness theorems.

      Not "one postulate." Postulates are assumed and not subject to proof. One statement derivable from the postulates.

      No sufficiently-complicated arithmetical system. The bar is pretty low -- include addition and multiplication.

      Delete
  5. Somerby's misanthropy seems to grow with each passing day. He is prompted by a Harari or Gödel, not to marvel at the insights of Harari or Gödel, but to indulge in his bleak speculations about the stupidity and arrogance of the human race. So, instead of an interest in Gödel's accomplishments, Somerby stresses his mental illness and his so-called crackpot Platonic notions about mathematics as yet another "proof" of the ridiculousness of human beings. And to cap it all, Somerby has now simply given up the fight and disengaged himself from the ongoing crises in our current affairs.

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  6. It's amazing to remember that Somerby was a philosophy major at Harvard. His account of Plato's views is full of juvenile snark, his rebuttal of them is utterly amateurish, and his unwillingness to examine what Gödel actually thought and said about his Platonic views and how they led him to his important contributions is lazy and uninformed.

    ReplyDelete
  7. Everyone should read "Extraordinary Popular Delusions and The Madness of Crowds" to learn about historical episodes where illogical thought led to disaster. https://www.amazon.com/Extraordinary-Popular-Delusions-Madness-Crowds/dp/1539849589/ref=sr_1_1?ie=UTF8&qid=1536339311&sr=8-1&keywords=charles+mackay+extraordinary+popular+delusions

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  8. For some reason the Bushmen of the Kalahari were a really big deal in the 60s. I remember a primetime CBS documentary about them. Those were the days, huh.

    ReplyDelete
  9. I thought the term for this is metaphysics.

    ReplyDelete
  10. "I saw you from afar" because Bushmen were uncomfortably aware that they were among the world's shortest peoples? That's what we were telling American children, way back when?

    I have a recollection from my British schooldays, also way back when. It was Latin class, and we were translating a description of a battle between some barbarians (Picts?) and some Romans (led by Agricola?)...perhaps it was Tacitus. Tacitus "quoted" the leader of the barbarians giving a speech to fire up his troops prior to the battle, in which he referred to the Romans as having come here to this battlefield at the very ends of the earth. Our teacher suggested that it was unlikely that Tacitus was truly quoting that barbarian general...after all, he said, people tend to think of where they live as the center of the world, not its outermost periphery. I remember being struck by the insight of our teacher's remark. You might prefer to call it "woke", at least if you can grasp the principles underlying that notion, beyond a mere set of slogans.

    Anyway...if first century Picts were unlikely to think of themselves as living at the ends of the earth, it seems equally implausible that bushmen thought of themselves as filling out the left tail of the global height distribution.

    ReplyDelete
  11. Bob,
    It has come to the point where you, DinC and Mao believe you are the arbiters of philosophical thoughts.
    It brings to mind Fredo Corleone: "I'm smart!, I can do things!"
    Ha!
    3 Jackasses in a tree.
    Does the fuck-up Trump show on your radar?

    ReplyDelete
  12. Somerby — and I’m going to use his last name as he seems to have abdicated the position of TDH — has descended to a distressing level of dumb. Dumber than a boxcar load of ball-peen hammers dumb. Dumb as in David in Cal dumb. Somerby has made the rookie mistake of not checking his sources. “Man is the rational animal” is often attributed to Aristotle with the translation from the Latin of animal rationale, which in turn is claimed as a translation of ζῷον λόγον ἔχον.

    The first problem is that this phrase does not appear in Aristotle. The second is that for Aristotle λόγον, logon doesn’t mean logicality or reason or rationality, which is what Somerby thinks it does. The word means speech, and in a very particular way, namely spoken language that conveys to others a sense of good and bad, just and unjust. Other animals have vocalization (φωνή, phonē), but only humans have logon, which is the basis for human society. This makes for Aristotle’s actual characterization of human beings as the political or consciously social animal (ζῷον πολιτικόν, zōon, politikon).

    <rant>
    Harari’s book is garbage. Harari, a historian, has exactly as much understanding of biology as Somerby does of physics. Harari spins us a tale of the Golden Age of Hunting and Gathering before the hellish existence of farming (in an “Agricultural Revolution”) and subsequent development of large states (in a “Cognitive Revolution”) held together by gossip about our neighbors and common fictions about our group in particular and life in general. Along the way, we killed the megafauna of every place we migrated to, and just for spite we were mean to the Neanderthals.

    None of this is implausible. But we have little to no evidence for the environment of 70K years ago or 40K years ago, so all of Harari’s speculation is what the late paleontologist Stephen Jay Gould called evolutionary Just-so stories. And like all tall tales, they’re tripped up by speculative detail. According to Harari, farming was a trap, luring humans away from a idyllic nomadic existence and chaining them to agriculture because of the extra food farming made available. Once farmers became farmers, which one was going to stand up in front of 99 of his community and say, “Farming is terrible; let’s go back to H&G. Unfortunately, once we do, we won’t have food for all of you, so let’s pick 10 people to leave behind to starve in the uncultivated fields”?

    But Harari also thinks existence in farming communities was pestilential because of the overcrowding. So why couldn’t that same speech have been made after one of the many epidemics: “Farming is terrible; let’s go back to H&G. No problem with the food supply. The latest plague killed half of us”?

    Harari can’t tell the difference between abstraction and fiction. Apparently seduced by the term “legal fiction”, he believes that corporations are fictional because they operate under the legal fiction that they’re individuals when they clearly aren’t. Sure, you can’t shake hands with a corporation, and corporations can’t marry or vote, but that doesn’t mean they’re not real. They have an operational reality that coincides with your world — they can inherit property, buy and sell goods and services, borrow and lend money, take people to court and defend suits, etc. You think the gas company is as fictional as the Epic of Gilgamesh or the first chapters of Genesis? Try not paying your bill.

    And here’s a gem:

    It’s common today to explain anything and everything as the result of climate change, but the truth is that earth’s climate never rests. (p 66)

    Straight outta Climate Change Denial 101.
    </rant>

    Lately it occurs to me
    What a long, strange trip it's been
    Keep on truckin’, Bob

    ReplyDelete
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  14. Some here would do well to read this book:

    Guns, Germs, and Steel

    Others would do well to watch this documentary about the Bushmen:

    The Gods Must Be Crazy


    And a very select few here have assumed the role of authority and expert while demonstrating neither, for those:

    Do The Right Thing Y'all take a chill

    ReplyDelete
    Replies
    1. Guns, Germs, Steel Great! Three Just-so stories for the price of one.

      And your admonishment about authority would carry more weight if you didn't think that the film The Gods Must Be Crazy was a documentary.

      Delete
    2. How the Blowhard Got His Bluster

      Diamond's book has many angry critics and may even have explanations that are unverifiable, if you can find an expert in the field to make such assertion then more power to you.

      The claim, if made, that his book or even that any unverifiable explanation holds no value strikes me as intellectual vanity. Darwin himself appreciated just so stories - Aristotle even supposed natural selection.

      Perhaps for you it is Absolute Certainty all the way down. Do I really think that the film TGMBC is a documentary?

      Delete
    3. Diamond's book has many angry critics and may even have explanations that are unverifiable, if you can find an expert in the field to make such assertion then more power to you.

      I have no idea what this run-on sentence is supposed to mean, so help me out. You concede that Diamond’s book has critics, but you don’t think I can cite experts to gainsay him? Are you saying that none of his critics are experts in his field (or fields, since the google reports that he’s a professor of geography and physiology)? Since you say it’s possible that Diamond puts forward “unverifiable” explanations, why should it be such a difficult challenge to find them or at least find an “expert” who will point them out?

      Did Darwin appreciate just-so stories? A bold claim. Can you back it up? Here’s Stephen Jay Gould from his book Leonardo’s Mountain of Clams and the Diet of Worms:

      … Darwin did not much favor the fatuous “just-so story” mode for illustrating natural selection by plausible speculation alone.

      (Emphasis mine.) But maybe Gould got it wrong.

      Aristotle didn’t “suppose” natural selection, except in the sense that he considered it and rejected it for the opposite, a goal-oriented, purpose-driven description of nature. This from Book II of his Physics, which I read in translation. This presents its own problems, but if my Greek was ever up to reading Aristotle in the original, it’s certainly not now. Feel free to correct me with your own reading.

      Just-so stories about evolution are useful for the purpose of debunking creationist claims that no possible evolutionary path can explain some characteristic or other of living things. But that’s about it, no matter what “strikes” you. Unverifiable claims are worthless. Not so for unverified but potentially verifiable claims. Those can be the starting point for scientific investigation, but that’s not what we have in the treatises of Harari and Diamond.

      As for “Absolute Certainty”, let me set that straw man on fire for you. Those are your words; don’t impute them to me. Science doesn’t deal in absolute truth, and that’s not what I require. I just want evidence. Got any?

      Finally, I have no idea what you “really think” about anything, including TGMBC. All I have is what you write. If you don’t want me to conclude that you think the film is a documentary, perhaps you should have put scare quotes around the word in your comment at 1:42A on Sep 8.

      Delete
    4. I think you mostly get it right, but perhaps you were too wrapped up in yourself to realize an obvious joke, conceivably proving the point of those with insight into your "interesting ideas", which likely was the point of the joke.

      It seems you were unable to extract any value from Diamond's work, it is a long book and regretfully you wasted your time. Maybe try returning the book for a refund? You gotta hang tough, idk

      Mr Mom I Don't Know

      Aristotle Explained Natural Selection, But Rejected It

      This Sounds Familiar, for some, their knowledge is as deep as their cut and paste abilities, which is fine, more power to them, perhaps they are engaging in regurgitation, not discourse, which is fine, but in part explains why they are not engaging.

      Absolute Certainty is generally rejected by those that are sharp-witted, that is not lost on even some of the less sharp amongst us. Does willful ignorance exist in a plane? Then again, someone's inability to go beyond extreme literalism could indicate something like "Asperger syndrome", perhaps caught from a prostitute, I hear it's been going around.

      Some say blog comments are not the same as science journals, overly committing to rationality and evidence is not always necessary or appropriate - it only takes forming a bond with another entity, especially a human, to see this, which I will grant you, means it will not be seen by some.

      Briscoe Darling - More Power to ya

      Delete
  15. I do not understand why Somerby keeps returning to Aristotle when his interest to modern philosophy is purely historical. All of the fields of knowledge Somerby discusses have progressed way beyond the early Greeks.

    It does not matter whether Aristotle called people rational or not, the Enlightenment philosophers certainly did. Then logic itself changed, making advances such as modal logic and fuzzy logic, that much better accommodate the kinds of problems that humans face in their lives.

    I see no problem with Harari speculating about early days. No one was there. Their speculations need only be consistent with the archaeological record and human biology. Harari has as much right to assert his ideas as Somerby or Stephen Jay Gould (who has also gotten some things wrong) or anyone else. It is what scientists do. They theorize.

    Somerby's writing these days reminds me of Drunk History. But he is so stuck in the same old rants. Why doesn't his thinking have any flexibility, why doesn't he open himself to new ideas, why does he have to keep saying the same things over and over. I am sure that deadrat is boring himself responding to the same mistakes. Time for Somerby to read a new book.

    ReplyDelete
    Replies
    1. Somerby returns to misquoting Aristotle because it’s a reliable trope that allows him to bash liberals, journalists, and others who don’t live up to his standards of rationality. He returns to the topic of logic because that allows him to bash the usual suspects for being illogical. I don’t mind the bashing, but the ignorance annoys me.

      You see no problem with Harari’s speculations about “early days” because “[n]o one was there.” I see a problem for precisely that reason. You say that their speculations — do you mean his speculations? — need only be consistent with the “archaeological record and human biology.” But the relevant archaeological record is almost nonexistent, and human biology may tell us what happened to our evolutionary line, but it won’t tell you squat about why it happened.

      I’m not disputing Harari’s “right” to assert his ideas. I’m saying his ideas are garbage, vapid and without evidence. No doubt Gould got some things wrong, but he was doing science, which is practically the business or correcting wrong ideas. Harari isn’t a scientist, and he’s not doing science. He’s a historian and he’s just making shit up. You may call that “theorizing” if you wish, but that’s not what scientists mean by that word.

      Don’t worry about me. History says I never get bored with the sound of my own voice.

      Delete
  16. This morning I attended a talk about investing with Robo-Advisors. The idea is that a computer buys and sells securities in your account, based on whatever general criteria you established. This seems a way to get 100% rational trading, without the risk of human foibles.

    ReplyDelete
  17. "based on whatever general criteria you established"

    GIGO.

    ReplyDelete
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