It's only 7 plus 5: How sharp have our greatest logicians been over, let's say, the past hundred-plus years?
How sharp have our greatest logicians been? In her 2005 book, Incompleteness: The Proof and Paradox of Kurt Godel, Rebecca Goldstein provides a tiny hint of an unfriendly idea, perhaps without knowing she's done so.
Goldstein focuses on Kurt Godel, who she explicitly describes as "the greatest logician since Aristotle." Along the way, she lets us know that this second greatest logician in history cited Stalin as a source for his disbelief in evolution; said he didn't believe in the natural sciences; believed that numbers and circles live "a perfect, timeless existence independent of the human mind" (we're quoting Jim Holt's review of Goldstein's well-received book); and devoted time to trying to plumb the logic of 2 plus 2.
That's an impressive resume, but Godel was the greatest logician in more than two thousand years. How solid were the logicians and thinkers who ranked one step behind him?
How solid were Europe's greatest thinkers? Goldstein develops a lightly mocking portrait as she describes their reaction to Ludwig Wittgenstein, a somewhat controversial figure whose jumbled, confusing later work we'd strongly recommend.
Wittgenstein was once considered a major logician too. According to Professor Horwich's 2013 essay, that view has largely disappeared among "professional philosophers" (his term).
As of 2005, Professor Goldsetin seemed to think that Wittgenstein was still highly influential inside the academy, though she seemed to perhaps be rolling her eyes at this state of affairs. At any rate, the portrait by Goldstein to which we refer concerns Wittgenstein's standing in his native Vienna back in the late 1920s and early 1930s.
Let's recall the earlier history. In 1921, at the age of 32, Wittgenstein had published the Tractatus Logico-Philosophicus, an instant classic in which he believed that he had solved all philosophical problems. (The book had been written several years earlier.)
Wittgenstein retired from philosophy at that point—but before long, he returned. By the late 1920s, he was meeting with the group Goldstein describes as "the legendary Vienna Circle," the "most prominent" of the intellectual circles then active in Vienna.
The very young Kurt Godel was also part of this circle. Goldstein offers an amusing portrait of the way Vienna's most prominent thinkers and logicians reacted to the already-famous Wittgenstein's presence. Her portrait starts like this:
GOLDSTEIN (page 89): By far the most influential figure connected with the Vienna Circle was not even a member of it, and in fact steadfastly refused membership. This was the philosopher Ludwig Wittgenstein...Wittgenstein's almost mystical influence on the members of the Vienna Circle, the esteemed thinkers among whom the young logician [Godel] first came to think rigorously about the foundations of mathematics, must have struck a person of Godel's persuasion as highly dubious.Goldstein will side with Godel over Wittgenstein throughout, as is her perfect right.
At any rate, that reference to Wittgenstein's "almost mystical influence" constitutes the start of Goldstein's amusing portrait. Briefly, she flashes back to the earlier Wittgenstein's arrival at Cambridge in 1912, when his "tormentedly dramatic" demeanor helped produce a "cult of genius."
Wittgenstein arrived in Cambridge at age 22. Here's part of the way it went down:
GOLDSTEIN (pages 95-96): Wittgenstein's tormentedly dramatic way of pursuing his field, the cult of genius that he propagated, was also highly Viennese. He had read in his youth, and always retained a high respect for, the strange Viennese writer Otto Weininger, "a quintessentially Viennese figure" who had argued that the only was for a man to justify his life (for a woman there is no way) is by acquiring and cultivating genius. Weininger had chosen to shoot himself to death in the very house in which Beethoven, the genius he revered above all others, had died. Wittgenstein himself was suicidal for nine years (his three older brothers committed suicide, also a quintessentially Viennese act), until he came to Cambridge and was declared a genius by Russell.Eventually, Lord Russell would change his mind (or something like that) concerning Wittgenstein's genius. But even as a very young man, Wittgenstein's "tormentedly dramatic" manner had been turning heads in the academy's loftiest precincts.
Years later, the giants of the Vienna Circle fell victim to this "almost mystical influence." In these passages, Goldstein is referring to some of Europe's most highly-regarded intellectuals and logicians:
GOLDSTEIN (page 104): Schlick and Waismann were permitted to meet with Wittgenstein in person on a regular basis...Waismann was, perhaps, of all the Wittgenstein-enchanted Circle, the positivist who suffered the deepest from philosophical infatuation. He changed his views every time Wittgenstein did, and, like some of the equally impressionable Cambridge students, [he] began to mimic the philosopher's behavioral tics.He even began to mimic the tics! A few of those distinctive mannerisms will be described below. Goldstein's lightly mocking portrait continues:
GOLDSTEIN (page 105): Just as in Cambridge, Wittgenstein's effects on the logical positivists, particularly Schlick and Waismann, almost defies explanation. Schlick's wife recalled her husband leaving the house to go see Wittgenstein for the first time as if he were setting off on a religious pilgrimage. "He returned in an ecstatic state, saying little, and I felt I should not ask questions."For the record, these fellows were all "logical positivists," the most hard-headed logicians then in existence. But even though Wittgenstein tended to reject the views of those in the Vienna Circle, "they mostly responded with adoration," Goldstein writes. When he visited Vienna for a few months in 1933, A. J. Ayer sent a mocking note back to England about the foolishness of it all.
Feigl, in later life, reported, "Schlick adored him and so did Waismann, who, like others of Wittgenstein's disciples, even came to imitate his gestures and manner of speech..."
Foolish it may have been, but Goldstein quotes Rudolph Carnap concerning the way they were. Once again, we get a glimpse of Wittgenstein's "tormentedly dramatic" demeanor:
GOLDSTEIN (page 108): Even the most sober-minded of the positivists, Rudolph Carnap, admits, in his autobiographical notes to the Schilpp volume in his honor, to a measure of near-religious awe:Have we mentioned the fact that these were the reactions of some of Europe's allegedly greatest thinkers?
"When he started to formulate his view of some specific philosophical problem, we often felt the internal struggle that occurred in him at that very moment, a struggle by which he tried to penetrate from darkness to light under an intense and painful strain. When, finally, sometimes after a prolonged arduous effort, his answer came forth, his statement stood before us like a newly created work of art or a divine inspiration...The impression he made on us was as if insight came to him through a divine inspiration, so we could not help feeling that any sober rational comment or analysis of it would be a profanation."
Eventually, Goldstein returns us to Lord Russell, writing a letter to Lady Ottoline about Wittgenstein's reverence for the "cursing, howling and singing" that were the marks of high genius. Finally, Goldstein describes a few of the tics:
GOLDSTEIN (page 113): And Wittgenstein was that sort of man, acting out the high drama of genius, so that Russell, when he was still enthralled, described him to Lady Ottoline as "...perhaps the most perfect example I have ever known of genius as traditionally conceived, passionate, profound, intense, and dominating."Wittgenstein's eccentric mannerisms have been described by others. The same is true of the depression and torment with which he was tragically afflicted during the bulk of his life.
He was the sort of genius to attract disciples so fanatical they took to wearing their shirts unbuttoned at the top as he did and aping his tics and mannerisms, such as clapping their hands to their foreheads when struck a by a philosophical insight or its lack. They may have disagreed with each other on the correct interpretation of Wittgenstein, but agreed that the correct interpretation, if only it could be attained, would almost of necessity be true.
Norman Malcolm, his student and friend, described his difficult personality and his eccentric personal style in his 1958 book, Ludwig Wittgenstein: A Memoir. In the Biographical Sketch which accompanies Malcolm's memoir, Professor Von Wright says this of Wittgenstein:
"It is probably true that he lived on the border of mental illness." Stating the obvious, that was a tragic report.
Wittgenstein seems to have struggled throughout his life on the personal level. But we're speaking here of the cultish reactions he engendered among the greatest thinkers of Europe—they who aped his mannerisms and treated him like a god.
Should great logicians behave like that? Goldstein's comical portrait reads to us, at least in part, as an attempt to undermine Wittgenstein himself and his later work, in which he declared that much traditional "philosophical" work had been built on conceptual confusion.
(College freshmen had suspected as much down through the annals of time.)
That said, Goldstein's portrait of the aping of tics floats an intriguing idea. How sharp have our sharpest logicians been if they were inclined to behave in the ways Goldstein describes?
Godel, the second greatest in history, was a fount of nutty ideas. Those who ranked one level below him treated Wittgenstein like a god, and took to mimicking his tics.
Indeed, we've begun to wonder if we ourselves once observed a small part of this aping of tics. We return to our freshman year introductory class, Problems in Philosophy, in which we were asked to wonder how we could possibly know that 7 plus 5 equals 12.
How could we possibly know such a thing? Whatever the answer, our teaching assistant, Mr. BLANK, was plainly taking it hard.
He would stare out the third-story window of our classroom, tormentedly running his hands through his thick, wavy hair as he agonized over the greatness of this puzzling philosophical problem.
Had some small part of the aping of tics possibly found its way to him? We'd never heard of the tics at that time, so the question never arose.
Instead, we worried about Mr. BLANK and his rather obvious torment.
"Don't jump, Mr. BLANK," we wanted to cry. "It's only 7 plus 5!"
Tomorrow: Puzzled by paradox