THE SOUL OF THE ELITE LOGICIAN: The look and feel of professional logic!


The chains of Marley's ghost:
Where have all the logicians gone? We asked that question last week.

Our society has badly needed their help over the course of the past thirty years. But every time we waited for rescue, no logician arrived on the scene.

"Hold on!" the voices angrily cry. Academic logicians, those in the academy, don't waste their time on the trifling disputes which form the public discourse!

People die all over the world when our "public logic" fails. But our elite logicians are occupied with loftier concerns, such as the ones which emerge in a passage from Professor Hart's 2010 book, The Evolution of Logic.

We're basically quoting this passage at random. It appears at the start of Chapter 3, Expeditions: Which Sets Exist?

One more point should be made clear. We've selected Hart's book, not because we think it's lousy work, but because we assume it's technically competent, good:
HART (page 59): Frege layered functions. A first-level function assigns objects to objects: doubling is a first-level function that assigns six to three; and the concept:green is a first-level function that assigns truth to all and only the green things. The derivative of the square function is the doubling function, while that of the sine is the cosine, so differentiation is a second-order function. In another example, Frege reads "There are carrots," so its subject is the concept:carrot and its predicate is the concept:existence. Existence is thus a second-level concept whose value is truth at all and only the first-level concepts under which something falls. This allows Frege to refine Kant's criticism of the ontological argument for the existence of God. Kant said that existence is not a predicate, which is heroic, or even quixotic, grammar. Frege could say that since existence is a second-level predicate, it is at the wrong level to be a defining feature of an object like God.
There! That's a taste of what "logic" is like on the modern professional level. Involved in lofty discussions like this, the elite logician has little time for the minor errors which may decide presidential elections and with them the use of deadly force against children all over the world.

Professor Hart's book is part of a six-volume series, The Evolution of Modern Philosophy. The series is published by the Cambridge University Press, the world's oldest publishing house.

As noted, we chose Hart's book because we assume it represents a competent example of modern high logic. The publisher describes the book like this:
CAMBRIDGE UNIVERSITY PRESS: Examines the relations between logic and philosophy over the last 150 years. Logic underwent a major renaissance beginning in the nineteenth century. Cantor almost tamed the infinite, and Frege aimed to undercut Kant by reducing mathematics to logic. These achievements were threatened by the paradoxes, like Russell's. This ferment generated excellent philosophy (and mathematics) by excellent philosophers (and mathematicians) up to World War II. This book provides a selective, critical history of the collaboration between logic and philosophy during this period. After World War II, mathematical logic became a recognized subdiscipline in mathematics departments, and consequently but unfortunately philosophers have lost touch with its monuments. This book aims to make four of them (consistency and independence of the continuum hypothesis, Post's problem, and Morley's theorem) more accessible to philosophers, making available the tools necessary for modern scholars of philosophy to renew a productive dialogue between logic and philosophy.
According to that blurb, mathematical logic became a recognized subdiscipline in mathematics departments. As an unexplained consequence, philosophers lost touch with its monuments.

That said:

Especially at this time of year, we typically try to stress the distinction between Morley's theorem and Marley's ghost. The distinction tends to be lost on those who lack interest in logic as well as literature.

Is something gained from modern high logic as practiced down through all those years? We're not sure how to answer your thoughtful question.

Plainly, something is lost when a society's logicians ignore the failed logic of daily life, focusing solely on loftier topics. Then too, a question arises when we review the sweep of the upper-end work the Cambridge University Press blurb describes:

Is it possible, just perhaps ever so slenderly possible, that our greatest logicians have never been all that sharp? We can't stop ourselves from asking such questions when we read a book like Rebecca Goldstein's favorably-blurbed 2005 volume, Incompleteness: The Proof and Paradox of Kurt Godel.

As we've noted in the past, Goldstein is a highly-regarded novelist, but she's also a ranking philosophy professor. Her book was favorably blurbed by a trio of ranking figures—by Stephen Pinker, by Brian Greene, and also by Alan Lightman.

After that, the book was favorably reviewed by Jim Holt in The New Yorker.

Writing with a novelist's flair, Goldstein discusses the work of Godel, who she describes as "the greatest logician since Aristotle." She also describes Godel's interactions with Ludwig Wittgenstein, whose later work was very hot until, according to Professor Horwich, the professional world whose work he critiqued decided to turn him out.

How sharp have our greatest logicians been? We'll scan Goldstein's portraits all week.

Tomorrow: Aping Wittgenstein's tics

Also this: A footnote is appended to the part of Hart's text which we've highlighted. The footnote reads like this:
Perhaps more generally a quantifier is a second-level function whose value at an (n + 1)-ary first-level concept is an n-ary concept, unless n is zero, in which case its value is a truth value, an object. In that case, quantifiers would be second-level functions sometimes having first-level concepts as values and sometimes objects as values. When the value of a first-level concept at an object is truth, Frege says the object falls under the concept. Perhaps the concept:falls-under is a binary second-level concept whose first argument is an object and whose second is a first-level concept. In that case, second-level concepts could also have arguments of different levels.
We selected this book because Hart's fully competent. This is high order "logic" at work.


  1. "Our society has badly needed their help over the course of the past thirty years"

    Yeah, Bob, the society sure needed a lot of help of overeducated idiots. In digging ditches and cleaning toilets.

    1. And Mao nicely illustrates my point (11:14 am).

    2. I'd like to know what your point is, but sorry, there's a limit on the size of a drivel. And you're far beyond that limit.

      Try to summarize it in 100 words or less, dear.

    3. And Mao illustrates my point again, with his very limited reading ability and inability to focus on anything longer than 100 words.

    4. Reading is hard. That's why Trump doesn't do it either.

    5. Is it your point that longer drivel is the best drivel, superior to a short-summary drivel?

    6. You are the one overly concerned about length. Remember, it is the motion of the ocean, not the size of the boat that matters.

    7. I'm not concerned at all. I rarely read your BS, nor do I normally address you.

      Perhaps you've already forgotten, but it's you who'd chosen to initiate communication with me here.

    8. "I'm not concerned at all."

      Is there anyone anywhere, who could possibly believe this nonsense?

    9. Is there anyone who believes that Mao in Cal is not concerned at all? I believe it. Mao is a troll. Stop feeding him

    10. "Is there anyone anywhere, who could possibly believe this nonsense?"

      Yes, dembot, it's certainly very hard to believe that you had any point there at all, as you're making the third bullshit comment here instead of just writing a short summary and being done with it. You're just a random phrase generator, aren't you?

    11. I'll take that as a firm "No". Thanks for playing.

  2. Logicians live in the world, just as everyone else does. They are not ignoring every day life. Their professional occupation is being logicians, in mathematics or philosophy. When they go home at night, they go back to families and neighborhoods where they have the same obligations of citizenship as everyone else, no more and no less. Somerby has never excoriated a plumber for failing to solve the world's water problems. It is enough for him to fix local pipes.

    Why has Somerby never fixated on political science as the discipline that can and should fix our political problems? They too are academics and they too are experts at political discourse, plus they are manifestly interested in what goes on in government, democracy and our political systems. Why aren't they being held responsible for everything, the way logicians are? Can it be because Somerby never studied political science, so he doesn't know anything about them or what they do? Maybe it is because that field is too accessible to everyone else, insufficiently magical to occur to anyone as a solution, with its practitioners the saviors of our dilemmas?

    Maybe Somerby is just using logic as a proxy for all academic endeavor, continuing his crusade against all professors who don't deal with the real world but insist on creating abstract knowledge with no practical use?

    Clearly, this is another anti-science post. Who crusades against science so vehemently? Is it the left or the right who wants to dismantle the universities, throw out any professor who isn't doing his political job indoctrinating the masses? Is it the left or the right who considers professors know-nothings who don't do an honest day's work? Who has carried the banner of anti-intellectualism since early days in our nation? A+ to the student who shouted out "Republicans"! Now that we have the world's biggest boob as president, Somerby claims it is the fault of logicians because they won't correct the logical grammar of every statement made by our smocking idiot of a president and his cronies. Yes, that would have prevented Trump's election and saved us all!

    What an asshole Somerby is being today. Not enough ladies with large body parts to attack? Lets pick on the guys with the big brains, the ones who think logic is a worthwhile field of study, instead of joining the NFL or performing standup comedy. Lets pull down those guys and make the country safer for conservatism and its fellow-traveler, White supremacism thinly disguised as States Rights. Then Bob Somerby will feel safer because they won't let those lady performers with their big body parts take over his stage. Did I mention that Somerby is an ass?

  3. Logic did find its practical application in computer science. The kind of recursiveness illustrated by Hart's footnote is very important in that field. A computer scientist would have far less difficulty parsing that stuff than Somerby seems to have.

    You can argue whether computer science has improved or harmed our society, but it is a real phenomenon that exists and has changed our lives. For one thing, it made possible both the attacks on Hillary (via her emails), the hacking of the DNC, the Russian flooding of Facebook and other media with targeted memes affecting the election, and Trump's obsessive tweeting. None of this would be possible without logicians and the applicatiuon of their work in computer science. Seems to me, Somerby might better argue that logicians should have less impact on our culture, than that they should have more.

    1. The DNC was *not* hacked. That is the official Lie propagated in ALL the MSM. It has long been proven that the e-mails disclosed to the public by Wikileaks (which *never* names its sources) had been put onto a thumb-drive by a DNC insider (who may no longer be in a position to speak) and reached the public that way.

    2. Your assertion is contradicted by Mueller's indictments of Russian hackers. Please don't come here and spout Q-Anon conspiracy nonsense. See Corn & Issikoff's book Russian Roulette for a description of the hacking.

    3. "The DNC was *not* hacked"

      Exactly right. And of course we can name the unfortunate whistleblower: Seth Rich. It's a miracle that Julian Assange is still alive...

    4. 12:42,
      Of course I am the greatest person in the history of mankind. It's about time you gave up your love for President LardAss and acknowledged it.

  4. The #1 occupation chosen by philosophy undergrads after graduation is law school. They become lawyers. The #1 field contributing elected officials to our political system is law. Many become lawyers in order to run for office down the line and lawyers are overrepresented among presidents too.

    Maybe logicians have already influenced politics by forming the minds of those who will participate in politics. It may be too much to expect logicians to influence the general public as well. You have to want to think about this stuff -- clearly Somerby doesn't want to, so he mocks it instead. But lawyers are trained to waste brain power on all kinds of boring stuff, because that's what our politicians spend most of their time doing -- when they aren't busy fundraising.

  5. “Our society has badly needed” the help of logicians “over the course of the past thirty years.”

    But they “have never been all that sharp”, according to Somerby, who, by way of proof, randomly quotes, without attempting to explain or provide context to, a passage from a book by one of them.

    So, if they have never been all that sharp, and produce incoherent bull roar, why would we even want their help in the first place?

    The logical conclusion is that we *wouldn’t* want their help.

    So why does Somerby continue to write these pointless posts lamenting their failure to help us?

  6. While the philosophers and logicians are working at an incomprehensible level of abstraction, the psychologists are pointing out fallacies in reasoning in a way that ordinary people can understand. E.g., see

    However, IMHO it does only limited good. The great majority of people have no interest in learning how to fix the flaws in their reasoning process.

    1. Even when you "win" an argument, you don't usually convince anyone else of your belief. Persuasion isn't necessarily about logic or discussion or reasoning. Psychology also studies persuasion. If Somerby studied it, he would understand a lot more about why people voted for Trump.

    2. Well said, anon.

      Of course persuasion is not done in a vacuum. It has to resonate with one's own life experiences. And those, in turn, reflect prevailing socioeconomic conditions...

    3. Exactly.
      One doesn't just fall for bullshit about refugees being murderous, drug-running thugs. One has to want to believe bullshit about refugees being murderous, drug-running thugs.

  7. Breaking News: TDH’s Bob Somerby Agrees With Republican Operative and TV talking head Scott Jennings

    Both make the argument that the SDNY’s main concern is that the American People ought to know about Trump having extramarital sex, and not that he committed campaign finance violations.

    1. "Breaking News: TDH’s Bob Somerby Agrees With Republican Operative and TV talking head Scott Jennings"

      If that's true, then does it mean that, in your dembot 'mind', it is somehow problematic to agree with this Scott Jennings person?

      What if Scott Jennings said that the sky is blue?

    2. It’s just interesting to note that a conservative shill and a self-described progressive come up with the same twisted logic. Just a simple ‘anthropological’ observation, that’s all.

    3. There's no such thing as dembots 'observing' humans, dembot.

  8. Have any of those "great logicians" even tried to read (let alone understand) Hegel's "The Science of Logic?" Who did? Well, Lenin for one. In 1916, depressed by the collapse of the Marxist Second International into supporting all sides of the Imperialist War, he decided to resume his deep philosophical studies, and what he found surprised him. It turned out not only that the materialism/idealism contrast central to his "materialism and empirio-criticism" was badly off the mark, but (entre autres) that it was "impossible to understand the first chapters of Das Kapital without a thorough understanding of the whole of the "Science Of Logic." Thus, to this day, none of the Marxists have understood Marx."