SATURDAY: We encountered the word "cognition!"

SATURDAY, JULY 13, 2024

It brought us a moment of pleasure:  Once in a while—it happens quite rarely—we're afforded a moment of pleasure.

As the world of "our democracy" turns, it happens less and less often. 

This past Tuesday, almost wholly by accident, we were afforded one such tiny moment. In between several medical appointments, we bumped into the word "cognition," a key word at this highly fraught time. 

We encountered the word at the end of the official Foreword to the 2001 revised edition of Nagel and Newman's classic text, Godel's Proof. The twelve-page foreword to the revised edition of the book was penned by Douglas Hofstadter, a highly renowned authority figure in the world of high academics.

Professor Hofstadter wrote the foreword to the revised edition of Nagel and Newman's 1958 book. At the end of his twelve-page essay, his institutional affiliation appeared:

Center for Research on Concepts and Cognition
Indiana University, Bloomington

Just like that, there it was! "Cognition"—one of the present day's most prominent "it words!" 

Why were we perusing Godel's Proof as we lounged about, killing time between a set of brief appointments? By pure serendipity, we'd grabbed the slender volume off the top of a pile of books as we went out the door that day.                                                                                              

We hadn't looked at the book in years. We thought it might be ripe for review.

When we began to peruse the book, we could see, by our markings, that we'd never made it past page 5 in Nagel and Newman's text. When we first struggled with the book, we had plainly devoted more attention to Professor Hofstadter's foreword. 

The burst of pleasure we experienced came from that foreword's sixth page. One page earlier, Professor Hofstadter had finally begun to address this question, and we're quoting directly: 

"What is Godel’s work about?"

We'll bite! What is Godel's (famous) work about? The professor began to seem to explain. And then, three paragraphs into his effort, we encountered this:

This wraparound was a truly unexpected turn of events, for it inevitably brought ancient paradoxes of self-reference to Godel’s mind—above all, “This statement is false.” Using this type of paradox as his guide, Godel realized that, in principle, he could write down a formula of Principia Mathematica that perversely said about itself, “This formula is unprovable by the rules of Principia Mathematica.”

Just for the record: 

By this point, the non-specialist will have no idea what Hofstadter's talking about. 

Having said that, oh good grief! We were back to that ancient "paradox"—that "paradox of self-reference."

Extremely long story short:

Back in 2001, the publisher said that Hofstadter's efforts would make this classic text "even more accessible." In fact, nothing the professor wrote in that foreword would make Godel's work accessible to the non-specialist. 

(For the record, that would be true whether the non-specialist realized it nor not.)

Having said that, dear God! There it was again, as always—that silly "ancient paradox."

“This statement is false.” Why is that short string of words supposed to qualify as some sort of "paradox?"

In theory, here's your answer. Here's what the professors will tell you:

"This statement is false!" 

If you think that statement is true, that means that the statement is false! But if you think that statement is false, that means that the statement is true!

It's like what Arsenio Hall used to say, though only in jest: Things that make you go ooohhh!

Thousands of years later, we're still supposed to be puzzled by that silly string of words. It's supposed to count as a paradox—and we're constantly told that the greatest work of logic since Aristotle was somehow built out of that mind-boggling structure.

("The mind crashes" in the face of that paradox, Professor Goldstein wrote in her 2005 book, Incompleteness: The Proof and Paradox of Kurt Godel. The book was widely praised, in blurbs and reviews, by some of the author's favorite professors and friends. For her fuller text about the crash of the mind, see below.)

Sad! This paradox is just a silly game played by a bunch of conchas. This is the way the later Wittgenstein might have approached such a silly reaction to a meaningless string of words:

Normally, when someone says that a statement is false, he's referring to an actual statement which someone has already made.

He may have seen a public speaker make a statement. He may have read a statement in a newspaper or a book. But he believes the statement is false, and now he proceeds to say so.

In this normal situation, the speaker is referring to a pre-existing statement. In his own subsequent statement, he says the original statement was false. At any rate, some original statement must exist before we can say it is false.

But alas! In the short string of words which makes Professor Goldstein's mind crash, there is no pre-existing statement! There's nothing to denounce as false!

Sad! People can also assemble such strings of words as these:

Up is down.
Day is night.
War is peace.

Stripped of any possible context, would such short word bursts cause the mind to crash? Only if the mind is remarkably weak—and so too with the short word burst presented by Professor Hofstadter.

For ourselves, we received a burst of pleasure when we encountered the passage in question in Professor Hofstadter's foreword. That said, the professor's failed attempt to make Godel easy reminds us of a major human problem:

The woods are lovely, dark and deep, but our human discernment is extremely limited. As a species, we're highly skilled at building tall buildings (and the like), but we're almost wholly unskilled at almost everything else.

Einstein couldn't make Einstein easy. Wittgenstein was almost wholly incapable of explaining his own work. And when Professor Goldstein sees "This statement is false," she says it makes the mind crash.

This is the general state of play as we humans attempt to maintain the way of life we now refer to as "our democracy."

Demagogues are all about, paid by corporate interests. So are people who are cognitively impaired (even as judged by normal standards) or are "mentally ill" in some major way.

Our intellectual leadership barely exists. Our major journalists are inclined to drift toward their time-honored pastime—Candidate Gaffe Alert.

So it goes in this most self-deluded of all possible worlds. Bring on our nation's pseudo-discussion of this year's presidential election!

Starting in the late 1960s, we've spent a good number of years examining topics of the kind lurking in that foreword. It started with the undergraduate course in Wittgenstein, then proceeded to Professor Cavell's graduate seminar on that same topic.

At the time, the later Wittgenstein was very hot, though no one was pretending that they understood his remarkably garbled work. We've continued to puzzle him out down through the several years.

On Tuesday, we encountered a key word—"cognition." It brought us pleasure to think back on all the transparent foolishness we've encountered over the years.

Should our candidates take cognition tests? How about our ranking journalists, or maybe our top professors?

For extra credit only: That ancient paradox has been kicking around for thousands of years. Professor Goldstein is a good, decent person, but here's the way she limned it in 2005:

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 true, then it is false, since that's what it says. And if it is false, well then, it is true, since, again, that is what it says. It must, then, be both true and false. The mind crashes.

"This book is a gem," the first blurb says. Could that statement make the mind crash?

All sentences must be either true or false? A person might imaginably agree with that formulation—if we're speaking about actual sentences, and if the authors of the sentences in questions intended them to be true or false.

(Some sentences are intended to be flights of fancy or purveyors of amusement. They aren't supposed to be true or false.)

At any rate, some strings of words may not exactly qualify as actual sentences. Absent further explanation, some strings of words don't seem to make any recognizable sense. 

In that circumstance, it falls to the person emitting the string of words to explain what he or she means by the emission. Or he or she can sit around, pretending to grapple with matters of logic as our discourse turns into an open joke and as "our democracy" burns.

We grabbed the slim book off the top of a pile. Midway through its jumbled foreword, it brought us a moment of pleasure.

Later, we saw that one key word. We mordantly chuckled:

Cognition!