When 7 plus 5 equaled 12: Where have our logicians been?
You're asking a very good question! We've badly needed the help of logicians as our public discourse has steadily slid to its current dangerous place.
In the mid-1990s, we needed help untangling the semantic pseudo-discussion which passed, for almost two years, as the "Medicare debate" which was driving Newt Gingrich along.
Starting in March 1999, we needed help with the logic of paraphrase as mainstream journalists kept inventing strange, psychiatrically troubling misstatements by Candidate Gore. This bullshit went on for twenty straight months and sent George Bush to the White House.
Right now, at this very juncture, we could use the help of a J. L. Austin type (Sense and Sensibilia; How to Do Things With Words) concerning the logic of terms which (falsely) appear to be synonyms.
What does it mean when every misstatement is lustily turned into a lie? Among other things, it means we're trying to start tribal war, at a time when a person who seems to be mentally ill controls all the ultimate weapons.
(Beyond that, we're rejecting the wisdom of thousands of years of "crowdsourcing" among the many generation who created the verbal distinctions we now, in our lusty tribal pique, lustily throw away. But so it goes among our self-impressed kind—among us sub-rational animals.)
Where have the logicians been as this downward spiral has occurred? Could it be they've been working, not in the garden, but tragicomically deep in the weeds?
Could it be that they've been in the weeds? Because we love the passage so much, we're going to post it again today. It comes from "made man" science writer Jim Holt, explaining in The New Yorker (and also, this year, in a new book) what "the greatest logician since Aristotle" was worried about as of the 1930s:
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. 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.Less than a century ago, our greatest logician since Aristotle had been "seduced by the notion that abstractions like numbers and circles had a perfect, timeless existence independent of the human mind."
For that reason, he was involved in a great debate with other major logicians. They were fighting about how we can know that 2 plus 2 equals 4.
The world was proceeding toward its second "great war." Our logicians were thus occupied.
Should it seem strange to think that our greatest logician had been seduced by such a strange idea, was locked in such an oddball debate? We'll explore that question as our essays proceed. But for today, we add an autobiographical note:
Long ago and far away, we confronted a version of this "philosophical question" as a mere college freshman.
It was the fall of 1965. Planning to major in philosophy, we took the introductory course—Phil 3, "Problems in philosophy."
Our professor was 26 years old; he may have looked a bit younger. Meanwhile, one of the "problems" we studied was this:
How can we know that 7 plus 5 equals 12?We'll admit that this happened at Harvard. This may account for the harder arithmetic problem we were asked to review.
That said, this was our introduction to the types of "problems" which constitute the world of academic philosophy. Possibly owing to widespread ignorance, many students in the class seemed unhappy with this young professor, who, just to complete the record, seemed like the nicest guy in the world.
In the Harvard of that day, students were supposed to applaud at the end of every lecture. At the end of the semester's final lecture, students were supposed to deliver a standing ovation, as if to wonder what their worthless lives could have been like before they were lucky enough to take transformative course.
That didn't happen in this instance. As the lectures dragged along, the applause lessened from class to class. Eventually, it totally died.
Most strikingly, no one applauded even after the final lecture. We remember feeling bad for our very nice but extremely young professor. We remember thinking that we were watching this young man's career implode.
Students in that introductory class tended to think that we were pursuing fairly ridiculous "problems." Years later, we occasionally treated the problem of 7 plus 5 equaling 12 in the occasional comedy venue.
We would recall the anguish of our teaching assistant, Mr. [NAME WITHHELD], who truly seemed to be tortured by the question of 7 plus 5 adding up to 12.
Who are these "problems" problems for? we would wittily ask at such times. It all depends on the delivery, of course, but we still like that line.
Full disclosure! The career of that very pleasant, extremely young professor wasn't imploding that year. That good-natured fellow was the late Robert Nozick. Within a few years, he was the biggest thing in American philosophy, though we've never quite understood why.
Like several others, we decided we wouldn't major in philosophy after taking that course. We majored in History and Lit for one miserable year, then returned to the fold at the start of our junior year.
That spring, we took the undergraduate Wittgenstein class. The gentleman's name is mentioned in the passage from Holt which we've posted above. We'll briefly touch on the work of "the later Wittgenstein" before this week's foofaw is done.
That said, some questions remain:
Who was that problem a problem for? And why in the world was our greatest logician involved in "Platonist" thoughts about where numbers and circles reside? Why were others fighting with him about this? Does any of this make sense?
Our logicians have left us on our own. This has helped lead us to Trump.
Meanwhile, Professor Harari has said an odd thing about our warlike species. He has said this in his giant best-seller, Sapiens: A Brief History of Humankind.
Harari has said that our "intolerant," possibly "genocidal" species runs on gossip and fiction. Is it possible that our greatest logicians have just never been all that sharp?
Tomorrow: Lord Russell's anecdote
Another passing tradition: At that time, students had to wear a coat and tie to eat in the college's dining halls. One day, we encountered a freshman debating the working-class Cambridge woman who checked students in for meals.
For his jacket, he wore a windbreaker. Beneath it, he was wearing a white t-shirt. A shoelace draped around his neck constituted his "tie."
The woman wasn't letting him in. "How do you know that isn't a tie?" he was officiously asking.
That working-class Cambridge woman was a mother, a daughter, a sister, a wife. That horrible kid had a lot to learn (as do we all). But which were the courses for that?