Third letter to today's 9-year old kids!

THURSDAY, APRIL 2, 2020

An early glimpse of a method:
After reviewing the moral and intellectual squalor of our nation's daily briefings—"in the darkness of this time"—it's hard to redirect one's sensibilities toward a loftier realm.

For that reason, we went outside and experienced sunshine and air. Let's consider how Wittgenstein entered the world of academic philosophy in 1911, at the age of 22.

Professor Goldstein described this history in her 2005 book about Godel's incompleteness theorems. The history involves a comical part of 20th century high-end "philosophy. It also gives us an early look at a certain Wittgensteinian method.

Goldstein sets the scene. For the moment, we're leaving the squalor of Donald J. Trump and the walking dead behind:
GOLDSTEIN (page 90-91): Wittgenstein came from one of the wealthiest and most culturally elite families of Vienna, "the Austrian version of the Krupps, the Carnegies, the Rothschilds, whose lavish palace on Alleegasse had hosted concerts by Brahms and Mahler"...While studying aeronautical engineering at the Technische Hochschule in Berlin, he had learned of Russell's paradox, and became interested in the foundations of mathematics.
(The quotation comes from Professor Monk.)

Wittgenstein "became interested in the foundations of mathematics," whatever that might mean. In October 1911, therefore, he presented himself, unannounced, at (Bertrand) Russell's lodgings in Cambridge.

Before the decade was done, he was one of the foremost figures in the world of English-language academic philosophy.

We'll examine "Russell's Paradox" at some point in the future. Suffice to say that it concerns "the set of all sets not members of themselves," a silly theoretical construct which, to this very day, provokes the laughter of the gods lounging about on Olympus.

Russell's Paradox will come a bit later. That said, Goldstein compares it to the ancient "liar's paradox," which she describes like this:
GOLDSTEIN (page 49-50): Paradoxes, in the technical sense, are those catastrophes of reason whereby the mind is compelled by logic itself to draw contradictory conclusions. Many are of the self-referential variety; troubles arise because some linguistic term—a description, a sentence—potentially refers to itself. The most ancient of these paradoxes is known as the "liar's paradox," its lineage going back to the ancient Greeks. It is centered on the self-referential sentence: "This very sentence is false." This sentence must be, like all sentences, either true or false. But if it is true, then it is false, since that is what it says; and if it false, well then, it is true, since, again, that is what it says. It must, therefore, be both true and false, and that is a severe problem. The mind crashes.
Should the mind of a sensible person "crash" when confronted with the liar's paradox? Should any sensible person regard the liar's paradox as "a catastrophe of reason?"

We'll have to say that the answer is no. Follow us down this byway:

"This very sentence is false!" So goes the liar's paradox. Professor Goldstein explains why it makes the mind crash. She starts with this assertion:
"This sentence must be, like all sentences, either true or false."
"Like all sentences," the liar's paradox must be true or false. On its face, that may seem to make perfect sense.

That said, the later Wittgenstein came to lodge a type of objection. Some collections of words which look like well-formed sentences are neither true nor false, he said, demonstrated or implied.

Those collections of words are incoherent. They don't make recognizable sense. They don't rise to the level of being false. They're neither true nor false.

Certain collections of words are simply incoherent. That said, these collections will often resemble other collections of words which do make perfect sense.

For that reason, they may seem to make sense. They may seem to make sense, but they actually don't in any established manner.

Consider some other collections of words which do make perfect sense. On the surface, these collections of words resemble the collection of words known as the liar's paradox:
Four collections of words:
1) The second sentence on page 98 of John Smith's book is false.
2) The very first thing you just said was false.
3) Every sentence out of your mouth last night was false.

4) This very sentence is false.
Those first three sentences can be said to share a "surface grammar" with the liar's paradox. That said, we all know how to evaluate such sentences. We look at the (pre-existing) sentence in question and decide if it's true or false.

On the surface, those first three sentences resemble the liar's paradox. That said, a major difference exists in what might be called their "depth grammar." Here's what we mean by that:

In each of those three sentences, we're told that some pre-existing sentence or statement is false. By the well-known rules of the game, we then examine that pre-existing sentence to determine whether we agree.

Everyone knows how to do this! But in the case of the liar's paradox, there is no pre-existing sentence for us to evaluate. No one has actually presented a statement. Nothing has been offered which could be true or false.

In that sense, the peculiar collection called "the liar's paradox" is fundamentally different from a wide array of very familiar statements. On the surface, the liar's paradox resembles those familiar statements, but it's fundamentally different.

The younger Wittgenstein was drawn to Cambridge by "Russell's Paradox." He bought the package Russell was selling. By the time of his later work, he had decided that vast amounts of his celebrated early work were just plain old wrong.

The later Wittgenstein decided that the early Wittgenstein was wrong. He might also be seen to have said something like this:

Much of traditional philosophy is comprised of statements which resemble perfectly reasonable statements. Because they resemble familiar statements, we may not notice that, in the depth of their logic (or "grammar"), they aren't like the familiar statements at all, and they don't make any obvious sense.

"The very sentence is false?" I have no idea why a sensible person would regard that as a "catastrophe of reason" which makes "the mind crash." It's just a bit of silly wordplay, apropos of nothing.

"Up is down" is rather odd too, but it's just a bunch of words. No one's mind should crash when they hear it said. So too with the ancient liar's paradox.

Shortly after the turn of the century, Bertrand Russell was wasting his time attempting to ponder "the set of all sets not members of themselves." He was trying to limn "the foundations of mathematics," whatever that might mean.

Russell was all tangled up in his eponymous "paradox." As a very young fellow from Vienna, Wittgenstein got sucked in.

Years later, he reconsidered. He ended up producing the book you shouldn't attempt to read.

Next: The preface and the first few pages of Philosophical Investigations. "Not a good book," he said.

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  2. "Those collections of words are incoherent."

    Yes, dear Bob, unlike the good, super-extra-meaningful ones, like "Hope!", "Change!", and "Yes We Can!"

    ReplyDelete
  3. There are two ways to interpret the remarks that Somerby is continually making, about things being muddled, incoherent, or "whatever that means" ill-defined. One is to assume that Somerby knows enough about philosophy to make such criticisms and the fault lies in whatever he is critiquing. The other is to assume that Somerby, with an undergraduate understanding of a complex field, doesn't understand and considers things to be muddled or unclear as an expression of his own lack of understanding. You could arbitrate this by going to the field itself and asking what eminent philosophers think. Often Somerby says these things about statements made by such philosophers themselves. There seems to be widespread agreement that the work by Wittgenstein that Somerby likes is the work disliked by many philosophers.

    I am inclined to think that this essay is ego-stroking, mental masturbation on Somerby's part. I don't believe he was such a whiz at philosophy that his opinions about Wittgenstein are worth reading, while Russell is a dunce and Godel is "mentally ill". Somerby is pretending to be competent in philosophy, but he knows nothing more than the notes he took in his undergrad classes, many years ago.

    This is embarrassing to him.

    ReplyDelete
    Replies
    1. The other is to assume that Somerby, with an undergraduate understanding of a complex field, doesn't understand and considers things to be muddled or unclear as an expression of his own lack of understanding.

      Oh, professor, what an excellent pun! All the more enjoyable for me because I’m sure you had no inkling that you were making it. But we don’t have to assume that the Slowest Boy in Arithmetic Class doesn’t understand mathematics or physics. He demonstrates that every time he posts on these topics.

      You could arbitrate this by going to the field itself and asking what eminent philosophers think.

      I don’t think so. I’m neither a philosopher nor an expert in Wittgenstein, and apparently Ludwig changed his mind quite a bit from his early years of Tractatus to his later years of Investigations, but he pretty much thought the investigations of eminent philosophers was mostly either nonsense (unsinnig) or senseless (sinnlos). So those eminent, dismissed philosophers probably aren’t the best place to get disinterested arbiters.

      I am inclined to think….

      In my experience, professor, this is rarely your inclination.

      I don't believe he was such a whiz at philosophy that his opinions about Wittgenstein are worth reading, while Russell is a dunce and Godel is "mentally ill".

      Wittgenstein, who was a student of Russell’s, thought that everyone should read Russell’s work on logic, but that no one should read Russell on esthetics and philosophy. So there is that.

      Godel was almost certainly mentally ill when he died.

      This is embarrassing to him [TDH].

      Now how do you know that? Or did you mean, “This is embarrassing for him”?

      In either case, how droll and ironic for you to say. Wittgenstein has some advice for you, professor, that I’ve updated to be politically correct:

      Wovon sie nicht sprechen kann, davon muss sie schweigen.

      Delete
    2. You're nasty even when you agree with me.

      Delete
    3. Google, copy, paste.

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    4. Cecelia laughs in your face when you express sympathy for Trumpandemic victims and then encourages others to do the same. But I'm the one you tell to fuck off.

      Go figure.

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    5. deadrat,
      Looks like Corby took a page out of the Somerby (and MSM's) playbook, and decided only non-Right-wingers have agency.

      Delete
    6. And here I thought I laughing at yet one more expression of scolding lecture on insensitivity, this time focused on zombies being used as a analogy in a point Somerby was making about an evolving U.S. dystopia.

      A potential offense to potentially grieving people, potentially reading this blog, who potentially would not be simpatico with Somerby’s opinion of Trump’s America.

      Now it’s turned into the set of all sets who aren’t members of themselves.

      Well, how dare you deny these families the benefit of such a poignant and relevant analogy of what is happening to our nation and to them in the most devastating way imaginable. How dare you consider them so wrapped up in their personal losses as to not champion those who voice their feelings and fears for a just and humane society, in this perilous time!

      Get a heart! And a soul too...while you’re out!...

      Delete
    7. Meh. Vulgar virtue signaling is one of several kinds of natural zombie excreta. They just can't help it, poor things. And they're immune to sarcasm.

      Delete
  4. “We'll examine "Russell's Paradox" at some point in the future. Suffice to say that it concerns "the set of all sets not members of themselves," a silly theoretical construct which, to this very day, provokes the laughter of the gods lounging about on Olympus.”

    Somerby is the silly one here. Russell was analyzing the rules of set theory as formulated by Frege and, using the permitted rules, came up with a contradiction.

    Russell wasn’t trying to be clever or obtuse, or misuse language. He was pointing out a flaw in set theory. In other words, it was set theory that led to what Somerby calls a silly theoretical concept, the one pointed out by Russell.

    It might be instructive to review the solution proposed by Russell.

    ReplyDelete
  5. Having studied a lot of mathematics, I have some sympathy for Bob's view (or what I think his view is.) Mathematics started with the real world: counting, angles, circles, etc. Mathematicians extended and generalized the field. By doing so, they arrived at many useful deductions and ideas. However, at some point, mathematics was extended beyond any conceivable relationship to the real world.

    Consider the hierarchy of infinities. There's a certain elegant consistency. But, none of these infinities exist. Does it matter whether c = aleph-1? I don't think so. Does it matter whether the Axiom of Choice is true or false? I don't think so.

    ReplyDelete
  6. Yo Bob, keep it coming!

    Leroy

    ReplyDelete
  7. Off topic...

    https://www.currentaffairs.org/2019/11/isaac-chotiner-interviews-historical-figures

    Leroy

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  9. "We'll examine 'Russell's Paradox' at some point in the future." I'll wait with bated breath. But, TDH is continuing with his self indulgence, going on and on about something that has no present relevance. It probably is all very interesting about Wittgenstein and Russell, and if someone wanted to devote the time to trying to understand what they were saying, it might enrich their mind. Is TDH aware that there are lots of other philosophers besides these two? And as far as I'm concerned, most things people say are neither true nor false; or they can be partly true and partly false. Wittgenstein has no relevance as far as I can see to the inadequacies of our pundits, or the shortcomings of reporters when questioning politicians. I've seen it written that Russell was a genius, but I don't see how anyone could judge whether that's the case based on TDH's seemingly shallow and unsupported observations. TDH is upset (god knows why) that our 'logicians' haven't stepped in to straighten out the populace about all the illogic that permeates our discourse, as if they could. But Russell is one philosopher who did just that all the time. He protested World War I for example. Russell wrote on subjects directed at the average, intelligent lay person - check out his 'Why I am not a Christian' - pretty good book.

    ReplyDelete
    Replies
    1. That's the Russell stuff Wittengenstein didn't like.

      Delete
  10. I love a lot of your work, Bob. I have for many years. I've even had students in some of my (philosophy) courses read your work, to help them understand the poverty of our public discourse, and what it looks like to achieve a critical perspective on it. But your work on the liar paradox, and on Wittgenstein's alleged neglect by the field of philosophy and what it means for public discourse more broadly, is plain Dunning-Krugerism. Please give it up and go back to what you know. Or get a PhD in philosophy.

    ReplyDelete
  11. I feel like I should qualify that last comment (4/4 at 5:07). When I was an undergrad at UCLA in the late 80s, Wittgenstein was very big (esp. Philippa Foot, David Pears, and Gavin Lawrence). Foot was especially excited about Wittgenstein, and shared your sense that the philosophical community had suffered terribly by not engaging with him more. She related that Wittgenstein had intended readers of PI to treat its questions as genuine, and to pause whenever he asked one to actually think it through themselves. After I graduated I took 2 years off before going to grad school, and one of the things I did during that time was exactly that: I read PI through, pausing whenever a question was asked to try to think it through for myself. It was enormously helpful, not just in introducing me to certain issues but primarily in contributing to my ability to think things through. So I am absolutely all aboard your plea for using Wittgenstein as a teacher in this way. But I think you under-appreciate just how widely Wittgensteinian insights and methods already are appreciated and used in philosophy, and radically under-estimate the difficulty of coming to a satisfactory resolution of issues like the liar paradox even if those insights and methods are deployed.

    I agree with you that lots of popular philosophy is BS - hell, lots of academic philosophy is BS (or, more charitably, it is of poor quality). But to blame philosophy for the poor state of public discourse seems unfair - how exactly are philosophers supposed to have improved it, beyond doing what they're already doing? And to blame neglect of Wittgenstein for philosophy's poor performance is peculiar. Yes, philosophy would be on average higher quality if more philosophers engaged with Wittgenstein in the way I did way back when. But the same is true of Hume, Berkeley, and many others.

    The Horrwichian conspiracy theory that philosophers froze out Wittgenstein because he revealed that what they're doing isn't so valuable is laughable. Wittgenstein has been read closely and fruitfully by many brilliant philosophers, who have in turn influenced many others (his wikipedia entry gives a long list). If contemporary philosophers don't look to Wittgenstein for answers to their questions, it may be partly due to neglect, but a lot of it is that they've absorbed his insights and methods and moved past him. You should really grapple with, for example, the SEP entry on the liar paradox before concluding that it's so easy to dismiss. You're really struggling at the surface level, imagining that one step of progress means it's basically all worked out, not realizing that, actually, enormous depths remain. That's why I called it Dunning-Krugerism.

    Of course, I am very open to learning that I'm wrong, that a few moves can resolve the paradox, and/or that greater attention to Wittgenstein can indeed transform philosophy to a state of radically greater clarity and understanding. I am sure my colleagues are open to that as well. But you're going to need to say a lot more to show that it's so.

    ReplyDelete
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