Children of paradox: Did it make sense for Europe's great minds to imitate Wittgenstein's tics?
In her well-received 2005 book about Godel's incompleteness theorems, Rebecca Goldstein rolls her eyes, at considerable length, at the way this aping went down. (See yesterday's report.)
In fairness, Goldstein draws her material from published sources, and the conduct does seem absurd. That said, Professor Von Wright saw this phenomenon in a kinder, gentler light in his Biographical Sketch of Wittgenstein, a portrait which is part of Norman Malcolm's 1958 book, Ludwig Wittgenstein: A Memoir:
VON WRIGHT (page 19): Because of the depth and originality of his thinking, it is very difficult to understand Wittgenstein's ideas and even more difficult to incorporate them into one's own thinking. At the same time the magic of his personality and style was most inviting and persuasive. To learn from Wittgenstein without coming to adopt his forms of expression and catch-words and even to imitate his tone of voice, his mien and gestures, was almost impossible. The danger was that the thoughts should deteriorate into a jargon...Von Wright was a friend and admirer of Wittgenstein. Writing roughly five decades later, Goldstein sounded a bit like a detractor, perhaps and possibly of the type Professor Horwich would later describe.
Wittgenstein's most characteristic features were his great and pure seriousness and powerful intelligence. I have never met a man who impressed me so strongly in either respect.
Whatever! Moving along to a central concern, why has Wittgenstein's later work tended to wither on the vine? Why has his later work proven hard to be quite hard to explain and apply?
We'll add one important point to Von Wright's explanation. It isn't just "the depth and originality" of Wittgenstein's later work which has made it hard to employ and apply. It's the fact that his seminal later work, Philosophical Investigations, is in fact extremely jumbled and extremely hard to follow.
Simply put, Wittgenstein didn't "produce a good book," an unfortunate fact to which he confessed in his preface to the Investigations. In truth, the basic ideas of the book were quite poorly expressed, while his mannerism and his "mien"—"the magic of his personality and style"—were apparently quite compelling and easy to imitate.
Question! Was Mr. NAME WITHHELD, our freshman year teaching assistant, aping Wittgenstein's famous intensity when he tore his hair at a third-story window, tortured by the maddening logic of 7 plus 5 making 12?
We can't answer your question! But should all that foolishness have transpired over the question of 7 + 5? And what might that foolishness have to say about the smarts of our greatest logicians extending all the way back through the annals of time?
Is it possible that our greatest logicians have never been all that sharp in any significant sense? To us, the aping of Wittgenstein's tics does seem relevant to this question. Then too, there's the work by Professor Goldstein herself on the power of paradox and "paradoxicality."
The full title of Professor Goldstein's book is this: Incompleteness: The Proof and Paradox of Kurt Godel. Perhaps because Goldstein is also a highly-regarded novelist, she pushes the role of "paradox" hard as she seems to struggle to make her book readable for the non-specialist.
In the following passage, she's discussing one of Godel's peculiar beliefs—the belief, in Goldstein's words, "that there was a vast conspiracy, apparently in place for centuries, to suppress the truth 'and make men stupid.' "
In fairness, anyone who has read a major newspaper or watched a "cable news" show will perhaps be tempted to join Godel in this gloomy belief. Conceivably, enrollment in an introductory philosophy course could trigger similar musings.
For today, ignore all that! As she continues, Goldstein is direct enough to attribute Godel's peculiar belief to "paranoia." But so believed our greatest logician. Goldstein further reacts:
GOLDSTEIN (page 48-49): That the greatest logician since Aristotle should have followed reason so unwaveringly to such illogical conclusions has struck many people as paradoxical. But, as I hope will become ever clearer in the chapters to come, the paradoxes in Godel's personality were at least partially provoked by the world's paradoxical responses to his famous work...Paradox was everywhere as Goldstein surveyed the scene. But then she turned to "technical paradoxes," entities which lay at the heart of Godel's stupendous work:
[T]he metamathematical import of his theorems, which to Godel was their most important aspect, was disregarded. Even more paradoxically, the racier currents in the culture, hawking postmodern uncertainty and the false mythology of all absolutes, scooped his theorems up...reinterpreting them so that they precisely negated the convictions that Godel...had so passionately wanted to demonstrate.
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.""Paradoxes like the liar's play a technical role in the proof that Godel devised for his extraordinary first completeness theorem," Goldstein goes on to say. "Godel was able to take the structure of self-referential paradoxicality...and turn it into an extraordinary proof for for one of the most surprising results in the history of mathematics."
Yes, paradoxicality! According to Nexis, the word last appeared in the New York Times in July 1990—in an "On Language" column in an "On Language" column criticizing the use of such terms.
That's a mere aside. A bit later in her book, Goldstein turns to "Russell's paradox," the formulation which lured Wittgenstein back into philosophy when he was still rather young:
"Russell's paradox concerns the set of all sets that are not members of themselves," Goldstein correctly if murkily says.
When we first encountered Goldstein's book, we were surprised, perhaps amazed, by some of what we found. Citing one key example, we were amazed to find that a ranking philosophy professor could still be treating these paradoxes in the reverential way Goldstein does some 52 years after the appearance of Philosophical Investigations.
How hard has it been to integrate Wittgenstein's later work into the realms of elite logic? Apparently, it's been very hard, and this leaves us asking our basic questions:
How sharp have our ranking logicians been? How sharp are we great apes at all?
Next week: Goldstein on the liar's paradox and on "the set of all sets"