BREAKING: Wonderfully entertaining points!

MONDAY, NOVEMBER 12, 2018

But also, highly instructive:
You think Charles Blow is losing out because of his selfless focus on Donald J. Trump? Consider the wonderfully entertaining instruction which could be provided by further excursions into the world of academic logic!

We abandoned our pursuit of such topics at the time of the Blasey Ford hearings. Up until then, we'd been entertaining ourselves with tales of the greatness of Kurt Godel, "who has often been called the greatest logician since Aristotle."

We're quoting science writer Jim Holt, who was reviewing Rebecca Goldstein's 2005 book, Incompleteness: The Proof and Paradox of Kurt Godel. In an unintentionally entertaining passage, Holt described where academic logic resided as of the 1920s:
HOLT (2/28/05): 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. In the philosophical world of nineteen-twenties Vienna, however, it was considered distinctly old-fashioned. Among the many intellectual movements that flourished in the city’s rich café culture, one of the most prominent was the Vienna Circle, a group of thinkers united in their belief that philosophy must be cleansed of metaphysics and made over in the image of science. Under the influence of Ludwig Wittgenstein, their reluctant guru, the members of the Vienna Circle regarded mathematics as a game played with symbols, a more intricate version of chess. What made a proposition like “2 + 2 = 4” true, they held, was not that it correctly described some abstract world of numbers but that it could be derived in a logical system according to certain rules.

Gödel was introduced into the Vienna Circle by one of his professors, but he kept quiet about his Platonist views...
According to Holt, the western world's greatest logician since Aristotle had been seduced at an early age by "the notion that abstractions like numbers and circles had a perfect, timeless existence independent of the human mind."

Reader, do you have even the slightest idea what that formulation could possibly mean? Of course you don't! But Holt just kept plowing ahead with his discussion of Godel. His review was published in The New Yorker, whose editors possibly couldn't see that this formulation didn't quite seem to make recognizable sense.

The review was republished this year as the title piece in a collection of Holt's essays. This new book is called When Einstein Walked with Gödel: Excursions to the Edge of Thought.

Friend, do you believe that numbers and circles have some sort of perfect, timeless existence? Do you have even the slightest idea what such a statement might mean?

Truthfully, no, you don't, but who gives a fig about that? And as if that formulation wasn't foolish enough on its own, Holt went on to say that Godel and the like were devoted to trying to determine "what made a proposition like '2 + 2 = 4' true."

What makes 2 + 2 = 4 true? Godel had one idea, the Vienna Circle had another! This is where formal logic stood 2500 years after Aristotle got everything started.

Do you believe that numbers and circles have some sort of perfect, timeless existence? If you're devoted to the practice of deference to authority, you may be prepared to swallow the claim that this presentation actually makes some sort of discernible sense.

We'll suggest a different possibility. We'll suggest the possibility that "notions" like these make no discernible sense at all. We'll guess that this incoherence, on the allegedly highest levels of thought, represents an anthropology lesson—a lesson about the mental capacities of our floundering species.

Eventually, we'll be inclined to float that idea, drawing on the work of the later Wittgenstein. But for now, let's consider the early Wittgenstein, the one who published the deftly-titled Tractatus Logico-Philosophicus in 1921, though it was written years earlier.

Decades later, the later Wittgenstein would largely throw this early work under the bus. In the wake of his later work, he came to be regarded, at least for a time, as the latest of our great logicians.

That was then, but what came earlier? In the past month or so, we've been marveling at an early passage from Professor Kenny's 1973 text, Wittgenstein. Needless to say, the publisher (Harvard University Press) and the reviewers said that Kenny's "lucid" text made Wittgenstein's work, early and late, accessible to "the general reader."

Over the past few months, we've marveled at Kenny's early capsule account of "the central doctrine" of the Tractatus. Chasing after worthier topics in the manner of a Blow, we'll look at some of Kenny's text, starting that labor tomorrow.

According to Kenny, what was the central doctrine of the early Wittgenstein's famous book? We think this work will be entertaining, but we'd also say it's highly instructive concerning the intellectual limitations of our human race.

How did we manage to get ourselves into our current political / journalistic mess? Let's start with this:

Throughout his life, history's second greatest logician struggled with the logic of 2 + 2 = 4! Tomorrow, we'll start exploring the early Wittgenstein, as explained by Kenny.

Concerning our species as a whole, Professor Harari has recently said that we're built around the ability to "gossip" and to promulgate potent group "fictions." That's what we've been saying here for the past twenty years!

How did we get to this dangerous place? Starting tomorrow, more of the work of the greatest logicians our species has brought to the fore...

23 comments:

  1. "How did we get to this dangerous place?"

    Hmm. I don't think it's a particularly dangerous place, where we are, Bob.

    We've been fruitful, and we multiplied. We filled the earth, and we and govern it. We reign over the fish in the sea, the birds in the sky, and all the animals that scurry along the ground.

    Over 7 billion of us on this planet, and there will be 10 billion soon. We've made it, Bob.

    ReplyDelete
    Replies
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      EVEN SUGGEST HOW YOU CAN GET YOUR EX OR LOVER BACK, TESTIMONIES OF MOST
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      SCAM WHICH I WAS A VICTIM OF BEFORE, I GOT RIPPED OF THOUSANDS OF DOLLARS
      BECAUSE I WAS SO ANXIOUS TO GET MY HUSBAND BACK AFTER HE LEFT ME FOR OVER 2
      YEARS WITH MY 7 YEARS OLD SON HARRY,I HAVE APPLIED TO 5 DIFFERENT SPELL
      CASTER HERE AND ALL TO NO AVAIL THEY ALL ASK FOR SAME THING SEND YOUR NAME
      YOUR EX NAME ADDRESS AND PICTURE PHONE NUMBER ETC WHICH I DID OVER AND OVER
      AGAIN AND MOST OF THEM WERE FROM WEST AFRICA UNTIL I SAW A POST ABOUT DR
      ALEXZANDER SPELL AND I DECIDED TO GAVE HIM MY LAST TRAIL.HE ASK ME FOUR
      THINGS MY REAL NAME,MY EX AND MY EX MOTHER NAME AND SAID MY EX WILL COME
      BACK IN 48HOURS, I HAVE SPEND ON SPELL CASTING AND NOTHING HAVE WORK FOR ME
      AFTER 2 DAYS I WAS THINKING ABOUT HOW MUCH I HAVE LOST SO FAR SO I SAID LET
      ME GIVE HIM A TRY SO I CALLED HIM AGAIN AND SEND MY REAL NAME,MY EX AND MY
      EX MOTHER NAME. BECAUSE I SWEAR IT WAS MY LAST TRY SO I WAS WAITING AS HE
      TOLD ME TO WAIT TILL NEXT DAY AND I COULD NOT SLEEP THAT NIGHT BECAUSE I
      REALLY LOVE MY HUSBAND AND WANT HIM BACK SO MUCH, THAT DAY I SAW MY HUSBAND
      WAS ONLINE ON FACEBOOK AND HE SAID HI AT FIRST I WAS SHOCK BECAUSE HE
      NEVER TALK WITH ME FOR THE PAST A YEAR AND 11 MONTH NOW I DID NOT REPLY
      AGAIN HE SAID ARE YOU THERE? I QUICKLY REPLY YES AND HE SAID CAN WE SEE
      TOMORROW I SAID YES AND HE WENT OFF-LINE I WAS CONFUSED I TRY TO CHAT WITH
      HIM AGAIN BUT HE WAS NO MORE ON LINE I COULD NOT SLEEP THAT NIGHT AS I WAS
      WONDERING WHAT HE IS GOING TO SAY, BY 9.AM THE NEXT MORNING HE GAVE ME A
      MISS CALL I DECIDED NOT TO CALL BACK AS I WAS STILL ON SHOCK AGAIN HE
      CALLED AND I PICK HE SAID CAN WE SEE AFTER WORK TODAY I SAID YES SO HE END
      THE CALL. IMMEDIATELY I GOT OFF WORK HE CALL ME AND WE MEET AND NOW WE ARE
      BACK AGAIN I CALL DR ALEXZANDER THE NEXT DAY THANKING HIM FOR WHAT HE HAS
      DONE IN FACT I STILL CALL HIM AND THANK HIM AS MY LIFE WAS NOT COMPLETE
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      Delete


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  2. “Reader, do you have even the slightest idea what that formulation could possibly mean? Of course you don't! “

    So now we’re back to this.

    The answer is that, yes, some readers, this one included, do have an idea of what Gödel meant. But that doesn’t stop Somerby from plowing ahead with his, shall we say, assertion, or perhaps you could call it a condescension, a desire to ridicule Gödel’s idea and anyone who claims to understand it, because you see, can we talk, no sensible person could disagree with Bob Somerby. Dears, it just isn’t done! And since he doesn’t read or engage with his commenters, he can carry on
    with his pretense that there is no disagreement.

    The problem is that he doesn’t attempt to give the idea a fair hearing, nor, and perhaps because of this, he cannot provide any actual logical argument against it, just his know-nothing “of course no one understands it!” “Why is it a bad idea?” “Because it doesn’t make sense.” “Why doesn’t it make sense?” “Because it’s a bad idea!”

    ReplyDelete
    Replies
    1. I have no problem with TDH for not engaging with that waste of cyberspace that is his commentariat. And I don’t know whether he’s given the idea of Platonic forms a “fair hearing.” Perhaps he’s tried and just isn’t up to the task. What’s bothersome is his assumption that his own ignorance is dispositive.

      Our tribe of apes has noticed that any collection of three things has a certain relationship to any other collection of three things. The members of the first collection can be lined up with the members of the second collection in such a way that ever member of the first collection has a unique partner in the second collection and vice versa. This is called for obvious reasons a one-to-one correspondence.

      Let’s try it. Take the first collection to be three planets — Mars, Jupiter, Saturn. Take the second collection to be three apparently brain-benumbed commenters here — Mao, DAinCA, and a random Anonymous.

      Mars <-> DAinCA
      Jupiter <-> Anonymous
      Saturn <-> Mao

      Does every planet correspond to a unique commenter? Yep. Does every commenter correspond to a unique planet? Yep. We can’t do that for a collection of two. If we eliminate Mars from the first collection, DAinCA won’t have a partner. We can’t do that with a collection of four. If we add a Spell Caster to the second collection, the Spell Caster won’t have a planet with which to partner. So we have a basic “threeness” property of collections of three things. Let’s call that property 3 and label it with the numeral 3.

      Clearly this 3 is an abstraction conceived by minds. But is it a invention that wouldn’t exist without any minds to think about it? Or is it a discovery of something that exists independently of any mind? If there are no minds in the universe, is the collection {Mars, Jupiter, Saturn} still a triple? Gödel thought so. Of course that’s hard to prove, since in the instance there were no conscious minds, there would be no proofs given the absence of any provers.

      And you (or TDH) may think the question is a waste of time. But that’s a different issue.

      Delete
  3. Commenters here are being more disciplined in not responding to bought and paid for morons like David and Mao.

    You can see the results as those morons' posts get more desperate and provocative, trying anything to elicit a response.

    ReplyDelete
  4. This post is arguably less helpful than Charles Blow’s op-eds in identifying ways of peeling off Trump voters.

    ReplyDelete
  5. Bob, you are a jester.
    "I will become the defender of the bigots and racists". "Blow is so much more influential than Trump".
    Your legacy will be as an apologist for the bigots and racists.
    Enjoy yourself. It's later than you think.
    When things get messy, you can always turn to Aristotle.
    You, DinC and Mao will keep searching for ways to justify killing black children in Baltimore.


    ReplyDelete
  6. “the intellectual limitations of our human race.”

    “a lesson about the mental capacities of our floundering species.”

    Why berate an irrational being for being irrational?

    Why expect greatness when the mental capacities are limited?

    I assume, since he’s used the term before, that Somerby believes human beings need “gatekeepers” to protect them from their irrational selves. This admits the existence of at least a non-null group of more “enlightened” beings who have the capacity to serve as gatekeepers, although Somerby doesn’t seem to credit logicians or philosophers or perhaps mathematicians with that ability, since he derides them for holding stupid (irrational) ideas and engaging in time-wasting intellectual games. Who are these mysterious gatekeepers then? Can they exist, given that Somerby feels that we are by and large a failed, floundering, irrational, gossipy species and in fact not the “rational animal?” And, according to (Somerby’s view of) Harari, Homo sapiens are just being....homo sapiens.

    And since Western discourse seems to have been broken since at least the days of Plato, and Gödel and the Vienna Circle didn’t acquit themselves too well by not using their superpowers of logic to resist the Nazi Panzer divisions, perhaps American liberals or the media of the past 30 years aren’t quite so all-culpable?

    This idea that humanity needs gatekeepers...well, maybe. But the evidence shows that humanity has never had gatekeepers, or else those who were in a position to be gatekeepers abused their positions as surely as if they were members of the non-gatekeeper portion of humanity.

    (Somerby’s discussion, of course, is predicated on the notion that some sort of disaster has befallen us. He calls it a “political/journalistic mess.” Is it Trump? The fact that the Democrats lost a bunch of seats during the Obama years? That Gore lost? That certain media types criticized Gore’s three-button suits? Has humanity not faced dire moments before, say, Civil War, Nazism, etc? And, if we do face such a dire problem, how is Somerby’s list of the ills of humanity helpful? He has, to be fair, made a very short list of concrete suggestions of ways to improve the media and liberal politics (whether you agree with them or not). But I don’t see how this very broad critique of humanity or Homo sapiens is terribly illuminating in our present “crisis”.)

    ReplyDelete
  7. After Somerby was “forced” back into the political fray by the Kavanaugh stuff, his job of dampening Democrats’ enthusiasm before, during, and after the midterms has now run its course, (rather unsuccessfully), and he can now return to his lofty perch surveying humanity’s flaws like a self-styled anthropologist. And “anthropology” would be an apt description of what Somerby is doing, if only it were in the job description of anthropologists to ridicule the culture they are analyzing.

    ReplyDelete
  8. In any society that develops arithmetic, it will be the case that 2+2=4. In any society that develops geometry there will be circles with the usual characteristics. OTOH a society that develops games will not develop a game with the exact rules of chess. That difference is why circles and addition have perfect timeless existence, while chess does not.

    BTW the axiomatic development of the natural numbers and rules of arithmetic showed that they could be derived in a logical system according to certain rules. But, contra Holt it did NOT deny that "2+2=4" correctly describes some abstract world of numbers.

    ReplyDelete
    Replies
    1. "In any society that develops arithmetic, it will be the case that 2+2=4. In any society that develops geometry there will be circles with the usual characteristics."

      Hmm, that's rather unimaginative of you, David. To begin with, what we understand as 'circles' exists in the two-dimensional euclidean paradigm, which is not necessarily how "any society" would see the world.

      Similarly with addition: if you operate with, say, vectors, or sets (let alone vectors in a non-euclidean space), 2+2 could produce who knows what. Not to mention that just in a binary system (which is pretty common), 2+2=10.

      Delete
    2. Oops. Scratch that. In the binary system 1+1=10, and 2+2 doesn't even exist. But in the 4-based system 2+2=10.

      Delete
    3. Scratch that too. A 4-based system has fewer symbols for its numbers, so the answer to 2+2= has a different label than the answer in decimal. Same result though.

      Delete
    4. It depends on what the meaning of 'result' is. In a society that uses 3- or 4-based system, the statement ""2+2=4" correctly describes some abstract world of numbers" is incorrect.

      Delete
    5. Mao - deadrat is right. You're confusing the symbols with the concept. I said all societies would agree that 2+2+4, I didn't mean they'd use the same symbols. In base 4, 2+2=10. The Romans would write, II + II = IV. These two formulas have the same meaning as 2+2=4 in ordinary base 10 arithmetic.

      Delete
    6. I disagree; it's true that numbers can be converted from one system to another, but 'meaning' is in the eyes of the beholder. If I tell the average human that 2+2=10, I suspect at least 99.9% of them will tell me that I'm wrong.

      Not to mention that there's an Amazon tribe with the arithmetic of 'one', 'two', and then 'many'. Here, the western numbers can be converted to theirs, but not vice-versa...

      In general, I feel that Bob is perfectly correct that ""notions" like these make no discernible sense at all." YMMV, I suppose...

      Delete
    7. Speaking of arithmetic, DinC, remember when you recently came here to tout the bullshit Rasmussen poll saying that President Chickenshit's approval among blacks was an incredible 40%?

      Well, now let us review how blacks voted in the 2018 Midterms.

      Per Pew Research:

      Blacks voted overwhelmingly (90%) for the Democratic candidate, including comparable shares of black men (88%) and black women (92%).

      So, let's see:

      40% - 9% = 31%.

      So, what happened to your bullshit poll, Comrade? Only off by a factor of 4. Explain, bean counter.

      90%

      Delete
  9. Here is a logical construction Bob might want to
    consider: When writing about writers, and trying to
    critique the Press corp in such a fashion as to keep
    them honest, uncover prevalent fallacies, etc.
    it MIGHT have been, or might still be, a desirable
    approach to make sure both sides of the political
    divide are examinded. Indeed, should one side's
    journalistic champions become unduly powerful,
    it would be necessary to look at them with a tougher
    set of standards, to make sure that none are
    "given a pass" if you will.

    To ignore such an obvious necessity, might only
    lead to an embittered semi idiocy, that will ultimately
    make the task impossible under any circumstance.

    ReplyDelete
  10. I see what The Daily Howler is getting at. I could open an advanced medical textbook and read a sentence and have no idea what it means.

    When you're talking through someone else's mouth, that's one more degree of separation from the point you're making. It's one more layer of confusion.

    The intention to truly explain, and just simply restating an explanation of an idea, are different things.

    ReplyDelete
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    YEARS WITH MY 7 YEARS OLD SON HARRY,I HAVE APPLIED TO 5 DIFFERENT SPELL
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    YOUR EX NAME ADDRESS AND PICTURE PHONE NUMBER ETC WHICH I DID OVER AND OVER
    AGAIN AND MOST OF THEM WERE FROM WEST AFRICA UNTIL I SAW A POST ABOUT DR
    ALEXZANDER SPELL AND I DECIDED TO GAVE HIM MY LAST TRAIL.HE ASK ME FOUR
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    EX MOTHER NAME. BECAUSE I SWEAR IT WAS MY LAST TRY SO I WAS WAITING AS HE
    TOLD ME TO WAIT TILL NEXT DAY AND I COULD NOT SLEEP THAT NIGHT BECAUSE I
    REALLY LOVE MY HUSBAND AND WANT HIM BACK SO MUCH, THAT DAY I SAW MY HUSBAND
    WAS ONLINE ON FACEBOOK AND HE SAID HI AT FIRST I WAS SHOCK BECAUSE HE
    NEVER TALK WITH ME FOR THE PAST A YEAR AND 11 MONTH NOW I DID NOT REPLY
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    TOMORROW I SAID YES AND HE WENT OFF-LINE I WAS CONFUSED I TRY TO CHAT WITH
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    ReplyDelete
  12. You promise to "start exploring the early Wittgenstein, as explained by Kenny." Wouldn't it be a trifle more explanatory to "explore Wittgenstein...as explained by Wittgenstein?"

    ReplyDelete
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